Exponential Stability of Interval Dynamical Systems with Quadratic Nonlinearity

This article proposes an approach for investigating the exponential stability of a nonlinear interval dynamical system with the nonlinearity of a quadratic type on the basis of the Lyapunov’s direct method. It also constructs an inner estimate of the attraction domain to the origin for the system under consideration.     

Macroscopic model for multispecies ion-exchange kinetics

A model for multispecies ion-exchange kinetics based on the Nernst-Planck equation is suggested. It is analyzed in comparison with the “locally-determinate” model described by Hwang and Helfferich [1]. The model makes possible simple computation. The conditions for the occurrence of unusual kinetic curves with a maximum are clarified. The proposed model is developed for different types of kinetic problems and verified by the experimental investigation of a kinetics in ternary systems.     

Cardioinotropic Effects in Subchronic Intoxication of Rats with Lead and/or Cadmium Oxide Nanoparticles

Subchronic intoxication was induced in outbred male rats by repeated intraperitoneal injections with lead oxide (PbO) and/or cadmium oxide (CdO) nanoparticles (NPs) 3 times a week during 6 weeks for the purpose of examining its effects on the contractile characteristics of isolated right ventricle trabeculae and papillary muscles in isometric and afterload contractions. Isolated and combined intoxication with these NPs was observed to reduce the mechanical work produced by both types of myocardial preparation. Using the in vitro motility assay, we showed that the sliding velocity of regulated thin filaments drops under both isolated and combined intoxication with CdO–NP and PbO–NP. These results correlate with a shift in the expression of myosin heavy chain (MHC) isoforms towards slowly cycling β–MHC. The type of CdO–NP + PbO–NP combined cardiotoxicity depends on the effect of the toxic impact, the extent of this effect, the ratio of toxicant doses, and the degree of stretching of cardiomyocytes and muscle type studied. Some indices of combined Pb–NP and CdO–NP cardiotoxicity and general toxicity (genotoxicity included) became fully or partly normalized if intoxication developed against background administration of a bioprotective complex.     

The use of severe plastic deformation techniques in grain refinement

Severe plastic deformation (SPD) has emerged as a promising method to produce ultrafine-grained materials with attractive properties. Today, SPD techniques are rapidly developing and are on the verge of moving from lab-scale research into commercial production. This paper discusses new trends in the development of SPD techniques suchas high-pressure torsion and equal-channel angle pressing, as well as new alternative techniques for introducing SPD. The paper also contains a comparative analysis of SPD techniques in terms of their relative capabilities for grain refinement, enhancement of properties, and potential to economically produce ultrafine-grained metals and alloys. For more information, contact Terry C. Lowe, Science and Technology Base Programs, Los Alamos National Laboratory, Los Alamos, NM 87545; (505) 667-7824; fax (505) 665-3199; e-mail tlowe@lanl.gov.     

Controllability of mechanical systems near a degeneration subset of nonholonomic constraints

An asymptotic behavior of a controlled mechanical system in general position with linear non-holonomic constraints is considered in a neighborhood of a submanifold on which rank of the constraint system is reduced by one. It is shown that, if control is a finite generalized force, then the reachability region of an arbitrary fixed initial point cannot contain a neighborhood of this submanifold. On the other hand, in the case of a controlled kinematic system determined by the same constraints, the reachability region of any regular point does contain such a neighborhood. An example of a system with constraint degeneration, which consists of a beam and two skates, is presented.     

The structure of nanocomposite 1D cationic conductor crystal@SWNT

Nanocomposites consisting of one-dimensional (1D) crystals of the cationic conductors CuI, CuBr and AgBr inside single-walled carbon nanotubes, mainly (n, 0), were obtained using the capillary technique. 1D crystal structure models were proposed based on the high resolution transmission electron microscopy performed on a FEI Titan 80-300 at 80 kV with aberration correction. According to the models and image simulations there are two modifications of 1D crystal: hexagonal close-packed bromine (iodine) anion sublattice (growth direction <001>) and 1D crystal cubic structure (growth direction <112>) compressed transversely to the nanotube (D(m) ～1.33 nm) axis. Tentatively this kind of 1D crystal can be considered as monoclinic. One modification of the anion sublattice reversibly transforms into the other inside the nanotube, probably initiated by electron beam heating. As demonstrated by micrographs, copper or silver cations can occupy octahedral positions or are statistically distributed across two tetrahedral positions. A 1DAgBr@SWNT (18, 0; 19, 0) pseudoperiodic 'lattice distortion' is revealed resulting from convolution of the nanotube wall function image with 1D cubic crystal function image.     

An efficient learning procedure for deep Boltzmann machines

We present a new learning algorithm for Boltzmann machines that contain many layers of hidden variables. Data-dependent statistics are estimated using a variational approximation that tends to focus on a single mode, and data-independent statistics are estimated using persistent Markov chains. The use of two quite different techniques for estimating the two types of statistic that enter into the gradient of the log likelihood makes it practical to learn Boltzmann machines with multiple hidden layers and millions of parameters. The learning can be made more efficient by using a layer-by-layer pretraining phase that initializes the weights sensibly. The pretraining also allows the variational inference to be initialized sensibly with a single bottom-up pass. We present results on the MNIST and NORB data sets showing that deep Boltzmann machines learn very good generative models of handwritten digits and 3D objects. We also show that the features discovered by deep Boltzmann machines are a very effective way to initialize the hidden layers of feedforward neural nets, which are then discriminatively fine-tuned.