Dually discrete spaces

A neighbourhood assignment in a space X is a family O = {O-x: x is an element of X} of open subsets of X such that X is an element of O-x for any x is an element of X. A set Y subset of X is a kernel of O if O(Y) = U{O-x: x is an element of Y} = X. We obtain some new results concerning dually discrete spaces, being those spaces for which every neighbourhood assignment has a discrete kernel. This is a strictly larger class than the class of D-spaces of [E.K. van Douwen, W.F. Pfeffer, Some properties of the Sorgenfrey line and related spaces, Pacific J. Math. 81 (2) (1979) 371-377]. (c) 2008 Elsevier B.V. All rights reserved.

消除采集脚印的处理方法研究

Seismic technique is in the leading position for discovering oil and gas trap and searching for reserves throughout the course of oil and gas exploration. It needs high quality of seismic processed data, not only required exact spatial position, but also the true information of amplitude and AVO attribute and velocity. Acquisition footprint has an impact on highly precision and best quality of imaging and analysis of AVO attribute and velocity. Acquisition footprint is a new conception of describing seismic noise in 3-D exploration. It is not easy to understand the acquisition footprint. This paper begins with forward modeling seismic data from the simple sound wave model, then processes it and discusses the cause for producing the acquisition footprint. It agreed that the recording geometry is the main cause which leads to the distribution asymmetry of coverage and offset and azimuth in different grid cells. It summarizes the characters and description methods and analysis acquisition footprint’s influence on data geology interpretation and the analysis of seismic attribute and velocity. The data reconstruct based on Fourier transform is the main method at present for non uniform data interpolation and extrapolate, but this method always is an inverse problem with bad condition. Tikhonov regularization strategy which includes a priori information on class of solution in search can reduce the computation difficulty duo to discrete kernel condition disadvantage and scarcity of the number of observations. The method is quiet statistical, which does not require the selection of regularization parameter; and hence it has appropriate inversion coefficient. The result of programming and tentat-ive calculation verifies the acquisition footprint can be removed through prestack data reconstruct. This paper applies migration to the processing method of removing the acquisition footprint. The fundamental principle and algorithms are surveyed, seismic traces are weighted according to the area which occupied by seismic trace in different source-receiver distances. Adopting grid method in stead of accounting the area of Voroni map can reduce difficulty of calculation the weight. The result of processing the model data and actual seismic demonstrate, incorporating a weighting scheme based on the relative area that is associated with each input trace with respect to its neighbors acts to minimize the artifacts caused by irregular acquisition geometry.

Using a Discrete Hidden Markov Model Kernel for lip-based biometric identification

In this paper, a novel and effective lip-based biometric identification approach with the Discrete Hidden Markov Model Kernel (DHMMK) is developed. Lips are described by shape features (both geometrical and sequential) on two different grid layouts: rectangular and polar. These features are then specifically modeled by a DHMMK, and learnt by a support vector machine classifier. Our experiments are carried out in a ten-fold cross validation fashion on three different datasets, GPDS-ULPGC Face Dataset, PIE Face Dataset and RaFD Face Dataset. Results show that our approach has achieved an average classification accuracy of 99.8%, 97.13%, and 98.10%, using only two training images per class, on these three datasets, respectively. Our comparative studies further show that the DHMMK achieved a 53% improvement against the baseline HMM approach. The comparative ROC curves also confirm the efficacy of the proposed lip contour based biometrics learned by DHMMK. We also show that the performance of linear and RBF SVM is comparable under the frame work of DHMMK.

An edge-based matching kernel through discrete-time quantum walks

In this paper, we propose a new edge-based matching kernel for graphs by using discrete-time quantum walks. To this end, we commence by transforming a graph into a directed line graph. The reasons of using the line graph structure are twofold. First, for a graph, its directed line graph is a dual representation and each vertex of the line graph represents a corresponding edge in the original graph. Second, we show that the discrete-time quantum walk can be seen as a walk on the line graph and the state space of the walk is the vertex set of the line graph, i.e., the state space of the walk is the edges of the original graph. As a result, the directed line graph provides an elegant way of developing new edge-based matching kernel based on discrete-time quantum walks. For a pair of graphs, we compute the h-layer depth-based representation for each vertex of their directed line graphs by computing entropic signatures (computed from discrete-time quantum walks on the line graphs) on the family of K-layer expansion subgraphs rooted at the vertex, i.e., we compute the depth-based representations for edges of the original graphs through their directed line graphs. Based on the new representations, we define an edge-based matching method for the pair of graphs by aligning the h-layer depth-based representations computed through the directed line graphs. The new edge-based matching kernel is thus computed by counting the number of matched vertices identified by the matching method on the directed line graphs. Experiments on standard graph datasets demonstrate the effectiveness of our new kernel.

A quantum Jensen-Shannon graph kernel using discrete-time quantum walks

In this paper, we develop a new graph kernel by using the quantum Jensen-Shannon divergence and the discrete-time quantum walk. To this end, we commence by performing a discrete-time quantum walk to compute a density matrix over each graph being compared. For a pair of graphs, we compare the mixed quantum states represented by their density matrices using the quantum Jensen-Shannon divergence. With the density matrices for a pair of graphs to hand, the quantum graph kernel between the pair of graphs is defined by exponentiating the negative quantum Jensen-Shannon divergence between the graph density matrices. We evaluate the performance of our kernel on several standard graph datasets, and demonstrate the effectiveness of the new kernel.

The undirected feedback vertex set problem has a Poly(k) Kernel

Resolving a noted open problem, we show that the Undirected Feedback Vertex Set problem, parameterized by the size of the solution set of vertices, is in the parameterized complexity class Poly(k), that is, polynomial-time pre-processing is sufficient to reduce an initial problem instance (G, k) to a decision-equivalent simplified instance (G', k') where k' � k, and the number of vertices of G' is bounded by a polynomial function of k. Our main result shows an O(k11) kernelization bound.

Visualization of predictive distributions for discrete spatial-temporal log Cox processes approximated with MCMC

An important aspect of decision support systems involves applying sophisticated and flexible statistical models to real datasets and communicating these results to decision makers in interpretable ways. An important class of problem is the modelling of incidence such as fire, disease etc. Models of incidence known as point processes or Cox processes are particularly challenging as they are ‘doubly stochastic’ i.e. obtaining the probability mass function of incidents requires two integrals to be evaluated. Existing approaches to the problem either use simple models that obtain predictions using plug-in point estimates and do not distinguish between Cox processes and density estimation but do use sophisticated 3D visualization for interpretation. Alternatively other work employs sophisticated non-parametric Bayesian Cox process models, but do not use visualization to render interpretable complex spatial temporal forecasts. The contribution here is to fill this gap by inferring predictive distributions of Gaussian-log Cox processes and rendering them using state of the art 3D visualization techniques. This requires performing inference on an approximation of the model on a discretized grid of large scale and adapting an existing spatial-diurnal kernel to the log Gaussian Cox process context.

Sistema konkurrenteak simulatzeko kernel bat: multiprozesadore sistemak

Jarraian, hainbat hilabetetan zehar garatutako proiektuaren deskribapena biltzen duen memoria dugu eskuragarri. Proiektu hau, sistema konkurrenteen simulazioan zentratzen da eta horretarako, mota honetako sistemen arloan hain erabiliak diren Petri Sareak lantzeaz gain, simulatzaile bat programatzeko informazio nahikoa ere barneratzen ditu. Gertaera diskretuko simulatzaile estatistiko batean oinarrituko da proiektuaren garapena, helburua izanik Petri Sareen bidez formalizatzen diren sistemak simulatzeko softwarea osatzea. Proiektuaren helburua da objektuetara zuzendutako hizkuntzaren bidez, Java hizkuntzaren bidez alegia, simulatzailearen programazioa erraztea eta ingurune honen baliabideak erabiltzea, bereziki XML teknologiari lotutakoak. Proiektu hau, bi zati nagusitan banatzen dela esan daiteke. Lehenengo zatiari dagokionez, konputazio munduan simulazioa aurkeztu eta honi buruzko behar adina informazio emango da. Hau, oso erabilgarria izango da programatuko den simulatzailearen nondik norakoak ulertu eta klase desberdinen inplementazioa egin ahal izateko. Horrez gain, zorizko aldagaiak eta hauen simulazioa ere islatzen dira, simulazio prozesu hori ahalik eta era errealean gauzatzeko helburuarekin. Ondoren, Petri Sareak aurkeztuko dira, hauen ezaugarri eta sailkapen desberdinak goraipatuz. Gainera, Petri Sareak definitzeko XML lengoaia erabiliko denez, mota honetako dokumentu eta eskemak aztertuko dira, hauek, garatuko den aplikazioaren oinarri izango direlarik. Bestalde, aplikazioaren muin izango diren klaseen diseinu eta inplementazioak bildu dira azken aurreko kapituluan. Alde batetik, erabili den DOM egituraren inguruko informazioa islatzen da eta bestetik, XML-tik habiatuz lortuko diren PetriNet instantziak maneiatzeko ezinbestekoak diren Java klaseen kodeak erakusten dira. Amaitzeko, egileak ateratako ondorioez gain, proiektuaren garapen prozesuan erabili den bibliografiaren berri ere ematen da.

Exact Nonparametric Two-Sample Homogeneity Tests for Possibly Discrete Distributions.

In this paper, we study several tests for the equality of two unknown distributions. Two are based on empirical distribution functions, three others on nonparametric probability density estimates, and the last ones on differences between sample moments. We suggest controlling the size of such tests (under nonparametric assumptions) by using permutational versions of the tests jointly with the method of Monte Carlo tests properly adjusted to deal with discrete distributions. We also propose a combined test procedure, whose level is again perfectly controlled through the Monte Carlo test technique and has better power properties than the individual tests that are combined. Finally, in a simulation experiment, we show that the technique suggested provides perfect control of test size and that the new tests proposed can yield sizeable power improvements.

The Diffusion Kernel Filter

A particle filter method is presented for the discrete-time filtering problem with nonlinear ItA ` stochastic ordinary differential equations (SODE) with additive noise supposed to be analytically integrable as a function of the underlying vector-Wiener process and time. The Diffusion Kernel Filter is arrived at by a parametrization of small noise-driven state fluctuations within branches of prediction and a local use of this parametrization in the Bootstrap Filter. The method applies for small noise and short prediction steps. With explicit numerical integrators, the operations count in the Diffusion Kernel Filter is shown to be smaller than in the Bootstrap Filter whenever the initial state for the prediction step has sufficiently few moments. The established parametrization is a dual-formula for the analysis of sensitivity to gaussian-initial perturbations and the analysis of sensitivity to noise-perturbations, in deterministic models, showing in particular how the stability of a deterministic dynamics is modeled by noise on short times and how the diffusion matrix of an SODE should be modeled (i.e. defined) for a gaussian-initial deterministic problem to be cast into an SODE problem. From it, a novel definition of prediction may be proposed that coincides with the deterministic path within the branch of prediction whose information entropy at the end of the prediction step is closest to the average information entropy over all branches. Tests are made with the Lorenz-63 equations, showing good results both for the filter and the definition of prediction.

Diseño e implementación del kernel de xDEVS, versión distribuida

Para entender nuestro proyecto, debemos comprender DEVS. Dentro de los formalismos más populares de representación de sistemas de eventos discretos se encuentra DES. En la década de los 70, el matemático Bernard Zeigler propuso un formalismo general para la representación de dichos sistemas. Este formalismo denominado DEVS (Discrete EVent System Specification) es el formalismo más general para el tratamiento de DES. DEVS permite representar todos aquellos sistemas cuyo comportamiento pueda describirse mediante una secuencia de eventos discretos. Estos eventos se caracterizan por un tiempo base en el que solo un número de eventos finitos puede ocurrir. DEVS Modelado y Simulación tiene múltiples implementaciones en varios lenguajes de programación como por ejemplo en Java, C# o C++. Pero surge la necesidad de implementar una plataforma distribuida estable para proporcionar la mecánica de interoperabilidad e integrar modelos DEVS diversificados. En este proyecto, se nos dará como código base el core de xDEVS en java, aplicado de forma secuencial y paralelizada. Nuestro trabajo será implementar el core de manera distribuida de tal forma que se pueda dividir un sistema DEVS en diversas máquinas. Para esto hemos utilizado sockets de java para hacer la transmisión de datos lo más eficiente posible. En un principio deberemos especificar el número de máquinas que se conectarán al servidor. Una vez estas se hayan conectado se les enviará el trabajo específico que deberán simular. Cabe destacar que hay dos formas de dividir un sistema DEVS las cuales están implementadas en nuestro proyecto. La primera es dividirlo en módulos atómicos los cuales son subsistemas indivisibles en un sistema DEVS. Y la segunda es dividir las funciones de todos los subsistemas en grupos y repartirlos entre las máquinas. En resumen el funcionamiento de nuestro sistema distribuido será comenzar ejecutando el trabajo asignado al primer cliente, una vez finalizado actualizará la información del servidor y este mandara la orden al siguiente y así sucesivamente.

Quantum kernels for unattributed graphs using discrete-time quantum walks

In this paper, we develop a new family of graph kernels where the graph structure is probed by means of a discrete-time quantum walk. Given a pair of graphs, we let a quantum walk evolve on each graph and compute a density matrix with each walk. With the density matrices for the pair of graphs to hand, the kernel between the graphs is defined as the negative exponential of the quantum Jensen–Shannon divergence between their density matrices. In order to cope with large graph structures, we propose to construct a sparser version of the original graphs using the simplification method introduced in Qiu and Hancock (2007). To this end, we compute the minimum spanning tree over the commute time matrix of a graph. This spanning tree representation minimizes the number of edges of the original graph while preserving most of its structural information. The kernel between two graphs is then computed on their respective minimum spanning trees. We evaluate the performance of the proposed kernels on several standard graph datasets and we demonstrate their effectiveness and efficiency.

Smoothing a Discrete Hazard Function for the Number of Patients Colonized with Methicillin-Resistance Staphylococcus Aureus in an Intensive Care Unit

A new method for estimating the time to colonization of Methicillin-resistant Staphylococcus Aureus (MRSA) patients is developed in this paper. The time to colonization of MRSA is modelled using a Bayesian smoothing approach for the hazard function. There are two prior models discussed in this paper: the first difference prior and the second difference prior. The second difference prior model gives smoother estimates of the hazard functions and, when applied to data from an intensive care unit (ICU), clearly shows increasing hazard up to day 13, then a decreasing hazard. The results clearly demonstrate that the hazard is not constant and provide a useful quantification of the effect of length of stay on the risk of MRSA colonization which provides useful insight.