Large deviation principles for the Ewens-Pitman sampling model

Let $M_{l,n}$ be the number of blocks with frequency $l$ in the exchangeable random partition induced by a sample of size $n$ from the Ewens-Pitman sampling model. We show that, as $n$ tends to infinity, $n^{-1}M_{l,n}$ satisfies a large deviation principle and we characterize the corresponding rate function. A conditional counterpart of this large deviation principle is also presented. Specifically, given an initial sample of size $n$ from the Ewens-Pitman sampling model, we consider an additional sample of size $m$. For any fixed $n$ and as $m$ tends to infinity, we establish a large deviation principle for the conditional number of blocks with frequency $l$ in the enlarged sample, given the initial sample. Interestingly, the conditional and unconditional large deviation principles coincide, namely there is no long lasting impact of the given initial sample. Potential applications of our results are discussed in the context of Bayesian nonparametric inference for discovery probabilities.Comment: 30 pages, 2 figure

Robust Preparation of GHZ and W States of Three Distant Atoms

Schemes to generate Greenberger-Horne-Zeilinger(GHZ) and W states of three distant atoms are proposed in this paper. The schemes use the effects of quantum statistics of indistinguishable photons emitted by the atoms inside optical cavities. The advantages of the schemes are their robustness against detection inefficiency and asynchronous emission of the photons. Moreover, in Lamb-Dicke limit, the schemes do not require simultaneous click of the detectors, this makes the schemes more realizable in experiments.Comment: 5 pages, 1 fiure. Phys. Rev. A 75, 044301 (2007

Lattice Boltzmann Approach to High-Speed Compressible Flows

We present an improved lattice Boltzmann model for high-speed compressible flows. The model is composed of a discrete-velocity model by Kataoka and Tsutahara [Phys. Rev. E \textbf{69}, 056702 (2004)] and an appropriate finite-difference scheme combined with an additional dissipation term. With the dissipation term parameters in the model can be flexibly chosen so that the von Neumann stability condition is satisfied. The influence of the various model parameters on the numerical stability is analyzed and some reference values of parameter are suggested. The new scheme works for both subsonic and supersonic flows with a Mach number up to 30 (or higher), which is validated by well-known benchmark tests. Simulations on Riemann problems with very high ratios ($1000:1$) of pressure and density also show good accuracy and stability. Successful recovering of regular and double Mach shock reflections shows the potential application of the lattice Boltzmann model to fluid systems where non-equilibrium processes are intrinsic. The new scheme for stability can be easily extended to other lattice Boltzmann models.Comment: Figs.11 and 12 in JPEG format. Int. J. Mod. Phys. C (to appear

A Shadowing Lemma Approach to Global Error Analysis for Initial Value ODEs

This is the published version, also available here: http://dx.doi.org/10.1137/0915058.The authors show that for dynamical systems that possess a type of piecewise hyperbolicity in which there is no decrease in the number of stable modes, the global error in a numerical approximation may be obtained as a reasonable magnification of the local error. In particular, under certain conditions the authors prove the existence of a trajectory on an infinite time interval of the given ordinary differential equation uniformly close to a given numerically computed orbit of the same differential equation by allowing for different initial conditions. For finite time intervals a general result is proved for obtaining a posteriori bounds on the global error based on computable quantities and on finding and bounding the norm of a right inverse of a particular matrix. Two methods for finding and bounding/estimating the norm of a right inverse are considered. One method is based upon the choice of the pseudo or generalized inverse. The other method is based upon solving multipoint boundary value problems (BVPs) with the choice of boundary conditions motivated by the piecewise hyperbolicity concept. Numerical results are presented for the logistic equation, the forced pendulum equation, and the space discretized Chafee–Infante equation

A Heuristic Neural Network Structure Relying on Fuzzy Logic for Images Scoring

Traditional deep learning methods are sub-optimal in classifying ambiguity features, which often arise in noisy and hard to predict categories, especially, to distinguish semantic scoring. Semantic scoring, depending on semantic logic to implement evaluation, inevitably contains fuzzy description and misses some concepts, for example, the ambiguous relationship between normal and probably normal always presents unclear boundaries (normal − more likely normal - probably normal). Thus, human error is common when annotating images. Differing from existing methods that focus on modifying kernel structure of neural networks, this study proposes a dominant fuzzy fully connected layer (FFCL) for Breast Imaging Reporting and Data System (BI-RADS) scoring and validates the universality of this proposed structure. This proposed model aims to develop complementary properties of scoring for semantic paradigms, while constructing fuzzy rules based on analyzing human thought patterns, and to particularly reduce the influence of semantic conglutination. Specifically, this semantic-sensitive defuzzier layer projects features occupied by relative categories into semantic space, and a fuzzy decoder modifies probabilities of the last output layer referring to the global trend. Moreover, the ambiguous semantic space between two relative categories shrinks during the learning phases, as the positive and negative growth trends of one category appearing among its relatives were considered. We first used the Euclidean Distance (ED) to zoom in the distance between the real scores and the predicted scores, and then employed two sample t test method to evidence the advantage of the FFCL architecture. Extensive experimental results performed on the CBIS-DDSM dataset show that our FFCL structure can achieve superior performances for both triple and multiclass classification in BI-RADS scoring, outperforming the state-of-the-art methods

Generation of energetic He atom beams by a pulsed positive corona discharge

Time-of-flight measurements were made of neutral helium atom beams extracted from a repetitive, pulsed, positive-point corona discharge. Two strong neutral peaks, one fast and one slow, were observed, accompanied by a prompt photon peak and a fast ion peak. All peaks were correlated with the pulsing of the discharge. The two types of atoms appear to be formed by different mechanisms at different stages of the corona discharge. The fast atoms had energies of 190 eV and were formed at the onset of the pulsing, approximately 0.7 µs before the maximum of the photon peak. The slow peak, composed of electronically metastable He atoms, originated 30–50 µs after the photon pulse, and possessed a nearly thermal velocity distribution. The velocity distribution was typical of an undisturbed supersonic expansion with a stagnation temperature of 131 K and a speed ratio of 3.6. Peak intensities and velocities were measured as a function of source voltage, stagnation pressure, and skimmer voltage

Investigation of passive flow control techniques to enhance the stall characteristics of a microlight aircraft

This report investigates the enhancement of aerodynamic stall characteristics of a Skyranger microlight aircraft by the use of passive flow control techniques, namely vortex generators and turbulators. Each flow control device is designed and scaled to application conditions. Force balance measurements and surface oil flow visualisation are carried out on a half-model of the microlight to further investigate the nature of the flow on the aircraft with and without the flow control devices. The results indicate a clear advantage to the use of turbulators compared with vortex generators. Turbulators increased the maximum lift coefficient by 2.8%, delayed the onset of stall by increasing the critical angle by 17.6% and reduced the drag penalty at both lower (pre-stall) and higher angles of attack by 8% compared to vortex generators. With vortex generators applied, the results indicated a delayed stall with an increase in the critical angle by 2% and a reduced drag penalty at higher angles of attack

Elementary building blocks of graphene-nanoribbon-based electronic devices

Graphene nanoribbon junction based electronic devices are proposed in this letter. Nonequilibrium Green's function calculations show that nanoribbon junctions tailored from single layer graphene with different edge shapes and widths can act as metal/semiconductor junctions and quantum dots can be implemented. In virtue of the possibilities of patterning monolayer graphene down to atomic precision, these structures, quite different from the previously reported two-dimensional bulk graphene or carbon nanotube devices, are expected to be used as the building blocks of the future nanoelectronics. © 2007 American Institute of Physics.published_or_final_versio

Graphite Nanoeraser

We present here a method for cleaning intermediate-size (5~50nm) contamination from highly oriented pyrolytic graphite. Electron beam deposition causes a continuous increase of carbonaceous material on graphene and graphite surfaces, which is difficult to remove by conventional techniques. Direct mechanical wiping using a graphite nanoeraser is observed to drastically reduce the amount of contamination. After the mechanical removal of contamination, the graphite surfaces were able to self-retract after shearing, indicating that van der Waals contact bonding is restored. Since contact bonding provides an indication of a level of cleanliness normally only attainable in a high-quality clean-room, we discuss potential applications in preparation of ultraclean surfaces.Comment: 10 pages, two figure