Error Bounds for Semi-Galerkin Approximations of Nonhomogeneous Incompressible Fluids

We consider spectral semi-Galerkin approximations for the strong solutions of the nonhomogeneous Navier–Stokes equations. We derive an optimal uniform in time error bound in the H¹ norm for approximations of the velocity. We also derive an error estimate for approximations of the density in some spaces L^r. P. Braz e Silva was supported for this work by FAPESP/Brazil, #02/13270-1 and is currently supported in part by CAPES/MECD-DGU Brazil/Spain, #117/06. M. Rojas-Medar is partially supported by CAPES/MECD-DGU Brazil/Spain, #117/06 and project BFM2003-06446-CO-01, Spain.     

Autonomous learning by simple dynamical systems with a discrete-time formulation

We present a discrete-time formulation for the autonomous learning conjecture. The main feature of this formulation is the possibility to apply the autonomous learning scheme to systems in which the errors with respect to target functions are not well-defined for all times. This restriction for the evaluation of functionality is a typical feature in systems that need a finite time interval to process a unit piece of information. We illustrate its application on an artificial neural network with feed-forward architecture for classification and a phase oscillator system with synchronization properties. The main characteristics of the discrete-time formulation are shown by constructing these systems with predefined functions.     

Dynamics of the entanglement between two oscillators in the same environment

We provide a complete characterization of the evolution of entanglement between two resonant oscillators coupled to a common environment. We identify three phases with different qualitative long time behavior. There is a phase where entanglement undergoes a sudden death. Another phase (sudden death and revival) is characterized by an infinite sequence of events of sudden death and revival of entanglement. In the third phase (no sudden death) there is no sudden death of entanglement, which persists for a long time. The phase diagram is described and analytic expressions for the boundary between phases are obtained. These results are applicable to a large variety of non-Markovian environments. The case of nonresonant oscillators is also numerically investigated.     

Beam propagation factor based on the Rényi entropy

A beam width measure based on Rényi entropy was introduced by Luis [Opt. Lett31, 3644 (2006)]. That one-dimensional analysis was limited to beam profiles with rectangular symmetry. In this Letter, we derive a general Rényi beam width measure that accounts for the diffraction properties of beams with profiles of arbitrary symmetry. We also show that the square of this measure has a quadratic dependence as a function of the propagation coordinate, so that it can be applied to propagation through arbitrary ABCD paraxial systems. The Rényi beam propagation factor, here introduced, is discussed in examples where the M(2) factor seems to have a limited effectiveness in describing the beam spreading.     

Self-correcting networks: function, robustness, and motif distributions in biological signal processing

Statistical properties of large ensembles of networks, all designed to have the same functions of signal processing, but robust against different kinds of perturbations, are analyzed. We find that robustness against noise and random local damage plays a dominant role in determining motif distributions of networks and may underlie their classification into network superfamilies.     

Distortion in optical pulse equalization through phase modulation and dispersive transmission

By combining phase modulation and dispersive transmission we propose an adjustable optical device to compress a time-varying input signal for producing ultrashort light pulses of high optical power. The relationship between the required properties of the input signal and the device parameters to get well-conformed sharp pulses with large energy concentration was established. High-order aberrations effects of the electro-optical modulator acting as the time lens of the employed setup are also considered. We found a mathematical analogy between the output signal of the analyzed device and the signal which would be obtained by using an equivalent first-order dispersive line. Some numerical simulations are shown which illustrate the feasibility of the method.     

No Phase Transition for Gaussian Fields with Bounded Spins

Let a<b, and H be the (formal) Hamiltonian defined on Ω by

Selective and efficient estimation of parameters for quantum process tomography

We present a new method for quantum process tomography enabling the efficient estimation, with fixed precision, of any of the parameters characterizing a quantum channel. The estimation strategy depends upon the set of matrix elements one selects to estimate. Furthermore, we describe a way to efficiently gather all the information required to efficiently estimate any average survival probability of the channel (i.e., to measure any diagonal element of its chi matrix).     

Interaction Study between ESIPT Fluorescent Lipophile-Based Benzazoles and BSA

In this study, the interactions of ESIPT fluorescent lipophile-based benzazoles with bovine serum albumin (BSA) were studied and their binding affinity was evaluated. In phosphate-buffered saline (PBS) solution these compounds produce absorption maxima in the UV region and a main fluorescence emission with a large Stokes shift in the blue–green regions due to a proton transfer process in the excited state. The interactions of the benzazoles with BSA were studied using UV-Vis absorption and steady-state fluorescence spectroscopy. The observed spectral quenching of BSA indicates that these compounds could bind to BSA through a strong binding affinity afforded by a static quenching mechanism (K_q~10¹² L·mol⁻¹·s⁻¹). The docking simulations indicate that compounds 13 and 16 bind closely to Trp134 in domain I, adopting similar binding poses and interactions. On the other hand, compounds 12, 14, 15, and 17 were bound between domains I and III and did not directly interact with Trp134.