Variational studies and replica symmetry breaking in the generalization problem of the binary perceptron

We analyze the average performance of a general class of learning algorithms for the nondeterministic polynomial time complete problem of rule extraction by a binary perceptron. The examples are generated by a rule implemented by a teacher network of similar architecture. A variational approach is used in trying to identify the potential energy that leads to the largest generalization in the thermodynamic limit. We restrict our search to algorithms that always satisfy the binary constraints. A replica symmetric ansatz leads to a learning algorithm which presents a phase transition in violation of an information theoretical bound. Stability analysis shows that this is due to a failure of the replica symmetric ansatz and the first step of replica symmetry breaking (RSB) is studied. The variational method does not determine a unique potential but it allows construction of a class with a unique minimum within each first order valley. Members of this class improve on the performance of Gibbs algorithm but fail to reach the Bayesian limit in the low generalization phase. They even fail to reach the performance of the best binary, an optimal clipping of the barycenter of version space. We find a trade-off between a good low performance and early onset of perfect generalization. Although the RSB may be locally stable we discuss the possibility that it fails to be the correct saddle point globally. ©2000 The American Physical Society.

Pulsar binary systems in a nonsymmetric theory of gravitation II. Dipole radiation

This paper deals with the emission of gravitational radiation in the context of a previously studied metric nonsymmetric theory of gravitation. The part coming from the symmetric part of the metric coincides with the mass quadrupole moment result of general relativity. The one associated to the antisymmetric part of the metric involves the dipole moment of the fermionic charge of the system. The results are applied to binary star systems and the decrease of the period of the elliptical motion is calculated.

First stars XI. Chemical composition of the extremely metal-poor dwarfs in the binary CS 22876-032

Context. Unevolved metal-poor stars constitute a fossil record of the early Galaxy, and can provide invaluable information on the properties of the first generations of stars. Binary systems also provide direct information on the stellar masses of their member stars. Aims. The purpose of this investigation is a detailed abundance study of the double-lined spectroscopic binary CS 22876-032, which comprises the two most metal-poor dwarfs known. Methods. We used high-resolution, high-S/N ratio spectra from the UVES spectrograph at the ESO VLT telescope. Long-term radial-velocity measurements and broad-band photometry allowed us to determine improved orbital elements and stellar parameters for both components. We used OSMARCS 1D models and the TURBOSPECTRUM spectral synthesis code to determine the abundances of Li, O, Na, Mg, Al, Si, Ca, Sc, Ti, Cr, Mn, Fe, Co and Ni. We also used the (COBOLD)-B-5 model atmosphere code to compute the 3D abundance corrections, notably for Li and O. Results. We find a metallicity of [Fe/H] similar to -3.6 for both stars, using 1D models with 3D corrections of similar to -0.1 dex from averaged 3D models. We determine the oxygen abundance from the near-UV OH bands; the 3D corrections are large, -1 and -1.5 dex for the secondary and primary respectively, and yield [O/Fe] similar to 0.8, close to the high-quality results obtained from the [OI] 630 nm line in metal-poor giants. Other [alpha/Fe] ratios are consistent with those measured in other dwarfs and giants with similar [Fe/H], although Ca and Si are somewhat low ([X/Fe] less than or similar to 0). Other element ratios follow those of other halo stars. The Li abundance of the primary star is consistent with the Spite plateau, but the secondary shows a lower abundance; 3D corrections are small. Conclusions. The Li abundance in the primary star supports the extension of the Spite Plateau value at the lowest metallicities, without any decrease. The low abundance in the secondary star could be explained by endogenic Li depletion, due to its cooler temperature. If this is not the case, another, yet unknown mechanism may be causing increased scatter in A( Li) at the lowest metallicities.

A binary engine fuelling HD 87643's complex circumstellar environment Determined using AMBER/VLTI imaging

Context. The star HD 87643, exhibiting the ""B[e] phenomenon"", has one of the most extreme infrared excesses for this object class. It harbours a large amount of both hot and cold dust, and is surrounded by an extended reflection nebula. Aims. One of our major goals was to investigate the presence of a companion in HD87643. In addition, the presence of close dusty material was tested through a combination of multi-wavelength high spatial resolution observations. Methods. We observed HD 87643 with high spatial resolution techniques, using the near-IR AMBER/VLTI interferometer with baselines ranging from 60 m to 130 m and the mid-IR MIDI/VLTI interferometer with baselines ranging from 25 m to 65 m. These observations are complemented by NACO/VLT adaptive-optics-corrected images in the K and L-bands, and ESO-2.2m optical Wide-Field Imager large-scale images in the B, V and R-bands. Results. We report the direct detection of a companion to HD 87643 by means of image synthesis using the AMBER/VLTI instrument. The presence of the companion is confirmed by the MIDI and NACO data, although with a lower confidence. The companion is separated by similar to 34 mas with a roughly north-south orientation. The period must be large (several tens of years) and hence the orbital parameters are not determined yet. Binarity with high eccentricity might be the key to interpreting the extreme characteristics of this system, namely a dusty circumstellar envelope around the primary, a compact dust nebulosity around the binary system and a complex extended nebula suggesting past violent ejections.

The young, tight, and low-mass binary TWA22AB: a new calibrator for evolutionary models? Orbit, spectral types, and temperature

Context. Tight binaries discovered in young, nearby associations are ideal targets for providing dynamical mass measurements to test the physics of evolutionary models at young ages and very low masses. Aims. We report the binarity of TWA22 for the first time. We aim at monitoring the orbit of this young and tight system to determine its total dynamical mass using an accurate distance determination. We also intend to characterize the physical properties (luminosity, effective temperature, and surface gravity) of each component based on near-infrared photometric and spectroscopic observations. Methods. We used the adaptive-optics assisted imager NACO to resolve the components, to monitor the complete orbit and to obtain the relative near-infrared photometry of TWA22 AB. The adaptive-optics assisted integral field spectrometer SINFONI was also used to obtain medium-resolution (R(lambda) = 1500-2000) spectra in JHK bands. Comparison with empirical and synthetic librairies were necessary for deriving the spectral type, the effective temperature, and the surface gravity for each component of the system. Results. Based on an accurate trigonometric distance (17.5 +/- 0.2 pc) determination, we infer a total dynamical mass of 220 +/- 21 M(Jup) for the system. From the complete set of spectra, we find an effective temperature T(eff) = 2900(-200)(+200) K for TWA22A and T(eff) = 2900(-100)(+200) for TWA22 B and surface gravities between 4.0 and 5.5 dex. From our photometry and an M6 +/- 1 spectral type for both components, we find luminosities of log(L/L(circle dot)) = -2.11 +/- 0.13 dex and log(L/L(circle dot)) = -2.30 +/- 0.16 dex for TWA22 A and B, respectively. By comparing these parameters with evolutionary models, we question the age and the multiplicity of this system. We also discuss a possible underestimation of the mass predicted by evolutionary models for young stars close to the substellar boundary.

A VLT/FLAMES survey for massive binaries in Westerlund 1 III. The WC9d binary W239 and implications for massive stellar evolution

Context. There is growing evidence that a treatment of binarity amongst OB stars is essential for a full theory of stellar evolution. However the binary properties of massive stars - frequency, mass ratio & orbital separation - are still poorly constrained. Aims. In order to address this shortcoming we have undertaken a multiepoch spectroscopic study of the stellar population of the young massive cluster Westerlund 1. In this paper we present an investigation into the nature of the dusty Wolf-Rayet star and candidate binary W239. Methods. To accomplish this we have utilised our spectroscopic data in conjunction with multi-year optical and near-IR photometric observations in order to search for binary signatures. Comparison of these data to synthetic non-LTE model atmosphere spectra were used to derive the fundamental properties of the WC9 primary. Results. We found W239 to have an orbital period of only similar to 5.05 days, making it one of the most compact WC binaries yet identified. Analysis of the long term near-IR lightcurve reveals a significant flare between 2004-6. We interpret this as evidence for a third massive stellar component in the system in a long period (> 6 yr), eccentric orbit, with dust production occuring at periastron leading to the flare. The presence of a near-IR excess characteristic of hot (similar to 1300 K) dust at every epoch is consistent with the expectation that the subset of persistent dust forming WC stars are short (< 1 yr) period binaries, although confirmation will require further observations. Non-LTE model atmosphere analysis of the spectrum reveals the physical properties of the WC9 component to be fully consistent with other Galactic examples. Conclusions. The simultaneous presence of both short period Wolf-Rayet binaries and cool hypergiants within Wd 1 provides compelling evidence for a bifurcation in the post-Main Sequence evolution of massive stars due to binarity. Short period O+OB binaries will evolve directly to the Wolf-Rayet phase, either due to an episode of binary mediated mass loss - likely via case A mass transfer or a contact configuration - or via chemically homogenous evolution. Conversely, long period binaries and single stars will instead undergo a red loop across the HR diagram via a cool hypergiant phase. Future analysis of the full spectroscopic dataset for Wd 1 will constrain the proportion of massive stars experiencing each pathway; hence quantifying the importance of binarity in massive stellar evolution up to and beyond supernova and the resultant production of relativistic remnants.

Hidden vorticity in binary Bose-Einstein condensates

We consider a binary Bose-Einstein condensate (BEC) described by a system of two-dimensional (2D) Gross-Pitaevskii equations with the harmonic-oscillator trapping potential. The intraspecies interactions are attractive, while the interaction between the species may have either sign. The same model applies to the copropagation of bimodal beams in photonic-crystal fibers. We consider a family of trapped hidden-vorticity (HV) modes in the form of bound states of two components with opposite vorticities S(1,2) = +/- 1, the total angular momentum being zero. A challenging problem is the stability of the HV modes. By means of a linear-stability analysis and direct simulations, stability domains are identified in a relevant parameter plane. In direct simulations, stable HV modes feature robustness against large perturbations, while unstable ones split into fragments whose number is identical to the azimuthal index of the fastest growing perturbation eigenmode. Conditions allowing for the creation of the HV modes in the experiment are discussed too. For comparison, a similar but simpler problem is studied in an analytical form, viz., the modulational instability of an HV state in a one-dimensional (1D) system with periodic boundary conditions (this system models a counterflow in a binary BEC mixture loaded into a toroidal trap or a bimodal optical beam coupled into a cylindrical shell). We demonstrate that the stabilization of the 1D HV modes is impossible, which stresses the significance of the stabilization of the HV modes in the 2D setting.

Localized modes of binary mixtures of Bose-Einstein condensates in nonlinear optical lattices

The properties of the localized states of a two-component Bose-Einstein condensate confined in a nonlinear periodic potential (nonlinear optical lattice) are investigated. We discuss the existence of different types of solitons and study their stability by means of analytical and numerical approaches. The symmetry properties of the localized states with respect to nonlinear optical lattices are also investigated. We show that nonlinear optical lattices allow the existence of bright soliton modes with equal symmetry in both components and bright localized modes of mixed symmetry type, as well as dark-bright bound states and bright modes on periodic backgrounds. In spite of the quasi-one-dimensional nature of the problem, the fundamental symmetric localized modes undergo a delocalizing transition when the strength of the nonlinear optical lattice is varied. This transition is associated with the existence of an unstable solution, which exhibits a shrinking (decaying) behavior for slightly overcritical (undercritical) variations in the number of atoms.

Phase diagram of a model for a binary mixture of nematic molecules on a Bethe lattice

We investigate the phase diagram of a discrete version of the Maier-Saupe model with the inclusion of additional degrees of freedom to mimic a distribution of rodlike and disklike molecules. Solutions of this problem on a Bethe lattice come from the analysis of the fixed points of a set of nonlinear recursion relations. Besides the fixed points associated with isotropic and uniaxial nematic structures, there is also a fixed point associated with a biaxial nematic structure. Due to the existence of large overlaps of the stability regions, we resorted to a scheme to calculate the free energy of these structures deep in the interior of a large Cayley tree. Both thermodynamic and dynamic-stability analyses rule out the presence of a biaxial phase, in qualitative agreement with previous mean-field results.

Temperature-driven collapse of a coherent binary mixture of condensates

We present a temperature- dependent Hartree- Fock- Bogoliubov- Popov theory to analyze the properties of the equilibrium states of an homogeneous mixture of bosonic atoms in two different hyperfine states and in the presence of an internal Josephson coupling. In our calculation we show that the bistable structure of the equilibrium states at zero temperature changes when we increase the temperature of the system. We investigate two mechanisms of the disappearance of bistability. In one, near the collapse of one of the equilibrium states, the acoustical branch becomes unstable and the gap of the optical branch goes to zero. In the other, there is no divergent behavior of the system and bistability disappears at a temperature in which the two equilibrium states merge at a zero- population fraction imbalance. When we further increase the temperature, this state remains as a unique equilibrium configuration.

Understanding the ""Antikick"" in the Merger of Binary Black Holes

The generation of a large recoil velocity from the inspiral and merger of binary black holes represents one of the most exciting results of numerical-relativity calculations. While many aspects of this process have been investigated and explained, the ""antikick,"" namely, the sudden deceleration after the merger, has not yet found a simple explanation. We show that the antikick can be understood in terms of the radiation from a deformed black hole where the anisotropic curvature distribution on the horizon correlates with the direction and intensity of the recoil. Our analysis is focused on Robinson-Trautman spacetimes and allows us to measure both the energies and momenta radiated in a gauge-invariant manner. At the same time, this simpler setup provides the qualitative and quantitative features of merging black holes, opening the way to a deeper understanding of the nonlinear dynamics of black-hole spacetimes.

Thermo-solvatochromism in binary mixtures of water and ionic liquids: on the relative importance of solvophobic interactions

The thermo-solvatochromism of 2,6-dibromo-4-[(E)-2-(1-methylpyridinium-4-yl)ethenyl] phenolate, MePMBr(2), has been studied in mixtures of water, W, with ionic liquids, ILs, in the temperature range of 10 to 60 degrees C, where feasible. The objectives of the study were to test the applicability of a recently introduced solvation model, and to assess the relative importance of solute-solvent solvophobic interactions. The ILs were 1-allyl-3-alkylimidazolium chlorides, where the alkyl groups are methyl, 1-butyl, and 1-hexyl, respectively. The equilibrium constants for the interaction of W and the ILs were calculated from density data; they were found to be linearly dependent on N(C), the number of carbon atoms of the alkyl group; van't Hoff equation (log K versus 1/T) applied satisfactorily. Plots of the empirical solvent polarities, E(T) (MePMBr(2)) in kcal mol(-1), versus the mole fraction of water in the binary mixture, chi(w), showed non-linear, i.e., non-ideal behavior. The dependence of E(T) (MePMBr(2)) on chi(w), has been conveniently quantified in terms of solvation by W, IL, and the ""complex"" solvent IL-W. The non-ideal behavior is due to preferential solvation by the IL and, more efficiently, by IL-W. The deviation from linearity increases as a function of increasing N(C) of the IL, and is stronger than that observed for solvation of MePMBr(2) by aqueous 1-propanol, a solvent whose lipophilicity is 12.8 to 52.1 times larger than those of the ILs investigated. The dependence on N(C) is attributed to solute-solvent solvophobic interactions, whose relative contribution to solvation are presumably greater than that in mixtures of water and 1-propanol.

Magnetization studies of binary and ternary Co-rich phases of the Co-Si-B system

CoB, CO(2)B, CoSi, Co(2)Si and CO(5)Si(2)B phases can be formed during heat-treatment of amorphous co-Si-B soft magnetic materials. Thus, it is important to determine their magnetic behavior as a function of applied field and temperature. In this study, polycrystalline single-phase samples of the above phases were produced via arc melting and heat-treatment under argon. The single-phase nature of the samples was confirmed via X-ray diffraction experiments. AC and DC magnetization measurements showed that Co(2)Si and CO(5)Si(2)B phases are paramagnetic. Minor amounts of either Co(2)Si or CoSi(2) in the CoSi-phase sample suggested a paramagnetic behavior of the CoSi-phase, however, it should be diamagnetic as shown in the literature. The diamagnetic behavior of the CoB phase was also confirmed. The paramagnetic behavior of CO(5)Si(2)B is for the first time reported. The magnetization results of the phase CO(2)B have a ferromagnetic signature already verified on previous NMR studies. A detailed set of magnetization measurements of this phase showed a change of the easy magnetization axis starting at 70K, with a temperature interval of about 13K at a very small field of 1 mT. As the strength of the field is increased the temperature interval is enlarged. The strength of field at which the magnetization saturates increases almost linearly as the temperature is increased above 70K. The room temperature total magnetostriction of the CO(2)B phase was determined to be 8 ppm at a field of 1T. (C) 2010 Elsevier B.V. All rights reserved.

Approximate algorithms for credal networks with binary variables

This paper presents a family of algorithms for approximate inference in credal networks (that is, models based on directed acyclic graphs and set-valued probabilities) that contain only binary variables. Such networks can represent incomplete or vague beliefs, lack of data, and disagreements among experts; they can also encode models based on belief functions and possibilistic measures. All algorithms for approximate inference in this paper rely on exact inferences in credal networks based on polytrees with binary variables, as these inferences have polynomial complexity. We are inspired by approximate algorithms for Bayesian networks; thus the Loopy 2U algorithm resembles Loopy Belief Propagation, while the Iterated Partial Evaluation and Structured Variational 2U algorithms are, respectively, based on Localized Partial Evaluation and variational techniques. (C) 2007 Elsevier Inc. All rights reserved.

AUTOMATIC CORONARY WALL SEGMENTATION IN INTRAVASCULAR ULTRASOUND IMAGES USING BINARY MORPHOLOGICAL RECONSTRUCTION

Intravascular ultrasound (IVUS) image segmentation can provide more detailed vessel and plaque information, resulting in better diagnostics, evaluation and therapy planning. A novel automatic segmentation proposal is described herein; the method relies on a binary morphological object reconstruction to segment the coronary wall in IVUS images. First, a preprocessing followed by a feature extraction block are performed, allowing for the desired information to be extracted. Afterward, binary versions of the desired objects are reconstructed, and their contours are extracted to segment the image. The effectiveness is demonstrated by segmenting 1300 images, in which the outcomes had a strong correlation to their corresponding gold standard. Moreover, the results were also corroborated statistically by having as high as 92.72% and 91.9% of true positive area fraction for the lumen and media adventitia border, respectively. In addition, this approach can be adapted easily and applied to other related modalities, such as intravascular optical coherence tomography and intravascular magnetic resonance imaging. (E-mail: matheuscardosomg@hotmail.com) (C) 2011 World Federation for Ultrasound in Medicine & Biology.