1,377 research outputs found

    Diskrete Spin-Geometrie für Flächen

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    This thesis proposes a discrete framework for spin geometry of surfaces. Specifically, we discretize the basic notions in spin geometry, such as the spin structure, spin connection and Dirac operator. In this framework, two types of Dirac operators are closely related as in smooth case. Moreover, they both induce the discrete conformal immersion with prescribed mean curvature half-density.In dieser Arbeit wird ein diskreter Zugang zur Spin-Geometrie vorgestellt. Insbesondere diskretisieren wir die grundlegende Begriffe, wie zum Beispiel die Spin-Struktur, den Spin-Zusammenhang und den Dirac Operator. In diesem Rahmen sind zwei Varianten fĂĽr den Dirac Operator eng verwandt wie in der glatten Theorie. DarĂĽber hinaus induzieren beide die diskret-konforme Immersion mit vorgeschriebener Halbdichte der mittleren KrĂĽmmung

    CSD: Discriminance with Conic Section for Improving Reverse k Nearest Neighbors Queries

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    The reverse kk nearest neighbor (RkkNN) query finds all points that have the query point as one of their kk nearest neighbors (kkNN), where the kkNN query finds the kk closest points to its query point. Based on the characteristics of conic section, we propose a discriminance, named CSD (Conic Section Discriminance), to determine points whether belong to the RkkNN set without issuing any queries with non-constant computational complexity. By using CSD, we also implement an efficient RkkNN algorithm CSD-RkkNN with a computational complexity at O(k1.5⋅log k)O(k^{1.5}\cdot log\,k). The comparative experiments are conducted between CSD-RkkNN and other two state-of-the-art RkNN algorithms, SLICE and VR-RkkNN. The experimental results indicate that the efficiency of CSD-RkkNN is significantly higher than its competitors

    Functional Single Index Model and Jensen Effect

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    In natural ecosystems, environmental conditions are highly variable over time and space. There is much empirical evidence to show that environmental variability has significant effects on individuals and populations. The nonlinear response is modeled in this thesis in a functional single index model (FSIM), or its generalized version. In this thesis, we will investigate whether the impact is positive or negative. We will develop a nested nonlinear optimization algorithm with local quadratic approximation to estimate the second derivative of the curve in a FSIM. We will show convergence rates and consistency of the estimators. Even though our estimators perform very well theoretically, practical implementations require selections of initial value and bandwidth. Sometimes, our procedures are not able to select them properly, and will negatively impact estimation accuracy. Instead of estimating the curvature, we will estimate the Jensen Effect, or the sign of the Jensen's inequality, which only involves the link function, directly. Inspired by the SiZer method, we will skip the cross-validation step, but evaluate the Jensen Effect over a range of smoothing parameters. We will calculate a t-test statistics based on the Jensen Effect estimates, and perform a hypothesis test with critical values simulating from a Gaussian process. To analyze situations with variance heteroscedasticity in ecology data, we will consider logarithm of response variables, which lead to an exponential single index model. We will investigate the Jensen Effect, and propose a hypothesis test to see the impact of environmental factor. Then we will extend the methodology to generalized single index model for binary response, such as individual survival, or Poisson response, such as number of offspring

    Controlling Entanglement Dynamics by Choosing Appropriate Ratio between Cavity-Fiber Coupling and Atom-Cavity Coupling

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    The entanglement characteristics including the so-called sudden death effect between two identical two-level atoms trapped in two separate cavities connected by an optical fiber are studied. The results show that the time evolution of entanglement is sensitive not only to the degree of entanglement of the initial state but also to the ratio between cavity-fiber coupling () and atom-cavity coupling (). This means that the entanglement dynamics can be controlled by choosing specific v and g.Comment: 14pages, 3figures, conferenc

    Harnessing social media data to explore urban tourist patterns and the implications for retail location modelling

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    The tourism landscape in urban destinations has been spatially expanded in recent years due to the increasing prevalence of sharing economy accommodation and other tourism trends. Tourists now mix with locals to form increasingly intricate population geographies within urban neighbourhoods, bringing new demand into areas which are beyond the conventional tourist locations. How these dispersed tourist demands impact local communities has become an emerging issue in both urban and tourism studies. However, progress has been hampered by the lack of fine granular travel data which can be used for understanding urban tourist patterns at the small-area level. Paying special attention to tourist grocery demand in urban destinations, the thesis takes London as the example to present the various sources of LBSN datasets that can be used as valuable supplements to conventional surveys and statistics to produce novel tourist population estimates and new tourist grocery demand layers at the small area level. First, the work examines the potential of Weibo check-in data in London for offering greater insights into the spatial travel patterns of urban tourists from China. Then, AirDNA and Twitter datasets are used in conjunction with tourism surveys and statistics in London to model the small area tourist population maps of different tourist types and generate tourist demand estimates. Finally, Foursquare datasets are utilised to inform tourist grocery travel behaviour and help to calibrate the retail location model. The tourist travel patterns extracted from various LBSN data, at both individual and collective levels, offer tremendous value to assist the construction and calibration of spatial modelling techniques. In this case, the emphasis is on improving retail location spatial Interaction Models (SIMs) within grocery retailing. These models have seen much recent work to add non-residential demand, but demand from urban tourism has yet to be included. The additional tourist demand layer generated in this thesis is incorporated into a new custom-built SIM to assess the impacts of urban tourism on the local grocery sector and support current store operations and trading potential evaluations of future investments
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