Consistency of regularized spectral clustering

Clustering is a widely used technique in machine learning, however, relatively little research in consistency of clustering algorithms has been done so far. In this paper we investigate the consistency of the regularized spectral clustering algorithm, which has been proposed recently. It provides a natural out-of-sample extension for spectral clustering. The presence of the regularization term makes our situation different from that in previous work. Our approach is mainly an elaborate analysis of a functional named the clustering objective. Moreover, we establish a convergence rate. The rate depends on the approximation property and the capacity of the reproducing kernel Hilbert space measured by covering numbers. Some new methods are exploited for the analysis since the underlying setting is much more complicated than usual. Some new methods are exploited for the analysis since the underlying setting is much more complicated than usual.     

Dynamical localization of two electrons in triple-quantum-dot shuttles

The dynamical localization phenomena in two-electron quantum-dot shuttles driven by an ac field have been investigated and analyzed by the Floquet theory. The dynamical localization occurs near the anti-crossings in Floquet eigenenergy spectrum. The oscillation of the quantum-dot shuttles may increase the possibility of the dynamical localization. Especially, even if the two electrons are initialized in two neighbor dots, they can be localized there for appropriate intensity of the driven field. The studies may help the understanding of dynamical localization in electron shuttles and expand the application potential of nanoelectromechanical devices.     

Target extraction from blurred trace infrared images with a superstring galaxy template algorithm

Accurate and efficient targets extraction from blurred trace infrared images has very important meaning for latent trace evidence collection in crime scene. Based on the superstring theory, a superstring galaxy template extraction algorithm for infrared trace target is presented. First, all of the pixels are divided into three classes: target pixels, background pixels and blurred pixels. Next, the superstring template characteristics for every pixel in a blurred infrared image are calculated as the features of each pixel. Finally, a galaxy covering algorithm is proposed, target pixels and background pixels are used for training the galaxy covering domain of every galaxy classifiers, and these classifiers will divide each blurred pixel into two classes: a target pixel or a background pixel. Experimental results indicate that the superstring galaxy template algorithm can improve the target extraction rate and reduce the extraction error rate.     

Characterizing localization properties of two spinless electrons in a one-dimensional Harper model with concurrence

By mapping the Fock space of many local fermionic modes isomorphically onto a many-qubit space and using the measure of concurrence, this paper studies numerically the mode entanglement of two spinless electrons with on-site interaction U moving in the one-dimensional Harper model. Generally speaking, for electrons in extended regimes （potential parameter λ 〈 2）, the spectrum-averaged concurrence N（C） first decreases slowly as A increases until its local minimum, then increases with λ until its peak at λ = 2, while for electrons in localized regimes （λ 〉 2）, N（C） decreases drastically as λ increases. The functions of N（C） versus λ are different for electrons in extended and localized regimes. The maximum of N（C） occurs at the point λ= 2, which is the critical value in the one-dimensional singleparticle Harper model. From these studies it can distinguish extended, localized and critical regimes for the two-particle system. It is also found for the same λ that the interaction U always induce the decreases of concurrence, i.e., the concurrence can reflect the localization effect due to the interaction. All these provide us a new quantity to understand the localization properties of eigenstates of two interacting particles.     

The Integrated Density of States for Some Random Operators with Nonsign Definite Potentials

We study the integrated density of states of random Anderson-type additive and multiplicative perturbations of deterministic background operators for which the single-site potential does not have a fixed sign. Our main result states that, under a suitable assumption on the regularity of the random variables, the integrated density of states of such random operators is locally Hölder continuous at energies below the bottom of the essential spectrum of the background operator for any nonzero disorder, and at energies in the unperturbed spectral gaps, provided the randomness is sufficiently small. The result is based on a proof of a Wegner estimate with the correct volume dependence. The proof relies upon the L^p-theory of the spectral shift function for p?1 (Comm. Math. Phys.218 (2001), 113-130), and the vector field methods of Klopp (Comm. Math. Phys.167 (1995), 553-569). We discuss the application of this result to Schrödinger operators with random magnetic fields and to band-edge localization.     

Dynamical Localization II with an Application to the Almost Mathieu Operator

Several recent works have established dynamical localization for Schrödinger operators, starting from control on the localization length of their eigenfunctions, in terms of their centers of localization. We provide an alternative way to obtain dynamical localization, without resorting to such a strong condition on the exponential decay of the eigenfunctions. Furthermore, we illustrate our purpose with the almost Mathieu operator, H _{, ,} =–+ cos(2(+x)), 15 and with good Diophantine properties. More precisely, for almost all , for all q>0, and for all functions ²( ) of compact support, we show that The proof applies equally well to discrete and continuous random Hamiltonians. In all cases, it uses as input a repulsion principle of singular boxes, supplied in the random case by the multi-scale analysis.     

Reactivity of solids

A review of studies of reactivities of solids is presented, concentrating on localization and autolocalization phenomena. Some examples of feed-back and structure of the reaction zone are given. Plenary lecture