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ANOMALOUS DIFFUSION - THE thinning PROPERTY OF FRACTIONAL BROWNIAN MOTION

ACTA PHYSICA POLONICA B 2012年第5期43卷 1157-1167页

作者： Sikora, Grzegorz Wroclaw Univ Technol Hugo Steinhaus Ctr PL-50370 Wroclaw Poland Wroclaw Univ Technol Inst Math & Comp Sci PL-50370 Wroclaw Poland

We show that thinning of increments of the fractional Brownian motion with Hurst exponent H not equal 1/2 breaks its H-self-similarity property. As a result, we obtain a new Gaussian process with stationary increments which is not the fractional Brownian motion for any H. Moreover, in the subdiffusion case (H < 1/2), the new process statistically resembles the classical Brownian motion (H = 1/2). To this end, we study analytically the second moment of such processes. Finally, Monte Carlo simulations show that the H estimator obtained by mean square displacement is close to the Brownian motion case with H = 1/2. These results show that stationary data describing anomalous diffusion phenomenon can lead to different statistical conclusions for different resolution of measurement. Therefore, one should be very careful in statistical inference, especially in strong subdiffusion regimes (H approximate to 0).

关键词： DIFFUSION thinning algorithms FRACTIONAL calculus BROWNIAN motion processes EXPONENTS (Algebra) MONTE Carlo method STATISTICS MEAN square algorithms

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Evaluation by three-point-bend and ball-on-ring tests of thinning process on silicon die strength

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MICROELECTRONICS RELIABILITY 2012年第9-10期52卷 2278-2282页

作者： Barnat, Samed Fremont, Helene Gracia, Alexandrine Cadalen, Eric Univ Bordeaux 1 Lab IMS CNRS ENSEIRBUMR 5218 F-33405 Talence France NXP Semicond F-14000 Caen France IPDiA F-14000 Caen France

With the onset of ultra-compact packages, systems in package may include stacked dies and mechanical sensors. Thus the thinning of silicon becomes necessary. The risk of failure, especially die crack, is often a major concern in the reliability of electronic packages. Therefore chip strength assessment becomes necessary for reliability prediction. In this paper, three-point-bend test and ball-on-ring test are compared to evaluate the risk of fracture of a silicon die as a function of its thickness, and of surface quality induced by the thinning process. Five thinning processes and six thicknesses (from 300 mu M down to 80 mu m) are statistically evaluated. (C) 2012 Elsevier Ltd. All rights reserved.

关键词： BENDING (Metalwork) thinning algorithms STRENGTH of materials ELECTRONIC packaging FAILURE analysis (Engineering) SURFACES (Technology)

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Reflectarray thinning using sub-wavelength coupled-resonant elements

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ELECTRONICS LETTERS 2012年第7期48卷 359-U86页

作者： Ethier, J. Chaharmir, M. R. Shaker, J. Commun Res Ctr Ottawa ON K2H 8S2 Canada

Anovel design technique is presented whereby a reflectarray comprising sub-wavelength coupled-resonant elements can be array thinned without significant reduction in gain at the centre frequency. A thinned reflectarra... 详细信息

关键词： Reflectarray antennas Wavelengths thinning algorithms Lattice theory Polarization (Electricity)

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Estimating the volume of tephra deposits: A new simple strategy

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GEOLOGY 2012年第5期40卷 415-418页

作者： Bonadonna, C. Costa, A. Univ Geneva CH-1205 Geneva Switzerland Univ Reading Reading RG6 6AH Berks England Ist Nazl Geofis & Vulcanol I-80125 Naples Italy

Volume determination of tephra deposits is necessary for the assessment of the dynamics and hazards of explosive volcanoes. Several methods have been proposed during the past 40 years that include the analysis of crystal concentration of large pumices, integrations of various thinning relationships, and the inversion of field observations using analytical and computational models. Regardless of their strong dependence on tephra-deposit exposure and distribution of isomass/isopach contours, empirical integrations of deposit thinning trends still represent the most widely adopted strategy due to their practical and fast application. The most recent methods involve the best fitting of thinning data using various exponential segments or a power-law curve on semilog plots of thickness (or mass/area) versus square root of isopach area. The exponential method is mainly sensitive to the number and the choice of straight segments, whereas the power-law method can better reproduce the natural thinning of tephra deposits but is strongly sensitive to the proximal or distal extreme of integration. We analyze a large data set of tephra deposits and propose a new empirical method for the determination of tephra-deposit volumes that is based on the integration of the Weibull function. The new method shows a better agreement with observed data, reconciling the debate on the use of the exponential versus power-law method. In fact, the Weibull best fitting only depends on three free parameters, can well reproduce the gradual thinning of tephra deposits, and does not depend on the choice of arbitrary segments or of arbitrary extremes of integration.

关键词： PUMICE EMPIRICAL research VOLCANIC eruptions WEIBULL distribution thinning algorithms

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Recognition of Atomically-Resolved STM Images of Graphite

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JOURNAL OF COMPUTATIONAL AND THEORETICAL NANOSCIENCE 2010年第2期7卷 404-407页

作者： Wang, Maofa Zou, Xiaoping Cheng, Jin Zhu, Guang Su, Yi Yang, Gangqiang Lue, Xueming Beijing Informat Sci & Technol Univ Res Ctr Sensor Technol Beijing Key Lab Sensor Beijing 100101 Peoples R China Minist Educ Key Lab Modern Measurement & Control Technol Beijing 100101 Peoples R China

It is important and interesting thing to recognize the atomic structure of graphite by processing graphite STM images, which is useful to automatically give the hexagonal topology structure during in-situ STM scanning of graphite. In this paper, we report some digital image processing algorithm applications on the recognition of atomic structure of graphite. At last, we also write the software with c(++) codes, which applying the digital image processing algorithms. And from the result of processing a typical STM image of graphite, we can clearly see graphite hexagon structure.

关键词： Graphite STM Digital Image Processing thinning algorithms Mathematical Morphology

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Meshfree thinning of 3D point clouds

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FOUNDATIONS OF COMPUTATIONAL MATHEMATICS 2008年第4期8卷 409-425页

作者： Dyn, Nira Iske, Armin Wendland, Holger Univ Hamburg Dept Math D-20146 Hamburg Germany Tel Aviv Univ Dept Math IL-69978 Tel Aviv Israel Univ Sussex Dept Math Brighton BN1 9RH E Sussex England

An efficient data reduction scheme for the simplification of a surface given by a large set X of 3D point-samples is proposed. The data reduction relies on a recursive point removal algorithm, termed thinning, which outputs a data hierarchy of point-samples for multiresolution surface approximation. The thinning algorithm works with a point removal criterion, which measures the significances of the points in their local neighbourhoods, and which removes a least significant point at each step. For any point x in the current point set Y subset of X, its significance reflects the approximation quality of a local surface reconstructed from neighbouring points in Y. The local surface reconstruction is done over an estimated tangent plane at x by using radial basis functions. The approximation quality of the surface reconstruction around x is measured by using its maximal deviation from the given point-samples X in a local neighbourhood of x. The resulting thinning algorithm is meshfree, i.e., its performance is solely based upon the geometry of the input 3D surface point-samples, and so it does not require any further topological information, such as point connectivities. Computational details of the thinning algorithm and the required data structures for efficient implementation are explained and its complexity is discussed. Two examples are presented for illustration.

关键词： surface simplification thinning algorithms meshfree methods approximation by radial basis functions 3D point cloud

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A 3D fully parallel surface-thinning algorithm

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THEORETICAL COMPUTER SCIENCE 2008年第1-2期406卷 119-135页

作者： Palagyi, Kalman Univ Szeged Dept Image Proc & Comp Graph H-6720 Szeged Hungary

The thinning is an iterative layer by layer erosion until only the "skeletons" of the objects are left. This paper presents a thinning algorithm for extracting medial surfaces from 3D binary pictures. The strategy which is used is called fully parallel, which means that the same parallel operator is applied at each iteration. An efficient implementation of the proposed algorithm on conventional sequential computers is given and the topological correctness for (26, 6) binary pictures is proved. (c) 2008 Elsevier B.V. All rights reserved.

关键词： Discrete geometry Digital topology Skeleton thinning algorithms Topology preservation

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Progressive scattered data filtering

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JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 2003年第2期158卷 297-316页

作者： Iske, A Tech Univ Munich Zentrum Math D-85747 Garching Germany

Given a finite point set Z subset of R-d, the covering radius of a nonempty subset X subset of Z is the minimum distance r(X,Z) such that every point in Z is at a distance of at most r(X,Z) from some point in X. This paper concerns the construction of a sequence of subsets of decreasing sizes, such that their covering radii are small. To this end, a method for progressive data reduction, referred to as scattered data filtering, is proposed. The resulting scheme is a composition of greedy thinning, a recursive point removal strategy, and exchange, a postprocessing local optimization procedure. The paper proves adaptive a priori lower bounds on the minimal covering radii, which allows us to control for any current subset the deviation of its covering radius from the optimal value at run time. Important computational aspects of greedy thinning and exchange are discussed. The good performance of the proposed filtering scheme is finally shown by numerical examples. (C) 2003 Elsevier B.V. All rights reserved.

关键词： thinning algorithms progressive scattered data reduction scattered data modelling k-center-problem data clustering

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Approximation to Boolean functions by neural networks with applications to thinning algorithms

Approximation to Boolean functions by neural networks with a...

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17th IEEE Instrumentation and Measurement Technology Conference

作者： Xiong, SS Zhou, ZY Zhong, LM Zhang, WD Tsinghua Univ Dept Precis Instruments & Mechanol Beijing 100084 Peoples R China

ISBN: (纸本)0780358902

In this paper, a theorem on approximation to Boolean functions by neural networks and its proof are proposed. A Boolean function, f:{0,1}(n) --> {0,1}, is proved to be approximated by a three layer neural network with 2(n) hidden nodes. With the theorem, a thinning algorithm using the neural network technique is concluded. A hard processor implementing the thinning algorithm is designed to raise the thinning efficiency, which can meet the practical needs better This makes the algorithm suitable for real-time image processing.

关键词： Boolean functions neural nets functional analysis mathematics computing signal processing approximation theory Boolean functions neural networks thinning algorithms three layer neural network hidden nodes thinning efficiency real-time image processing engineering applications

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Shape understanding system: Understanding the thin object

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Computers & Graphics 2002年第6期26卷 951-970页

作者： Z. Les The University of Melbourne PO Box 654 3142 Toorak Melbourne Vic. Australia

This paper presents the method of understanding objects that can be considered as thin objects. The proposed method of understanding thin objects is part of the shape understanding method developed by the author. The main novelty of the presented method is that the process of understanding thin objects is related to the visual concept represented as a symbolic name of the possible class of shapes. The possible classes of shape, viewed as hierarchical structures, are incorporated into the shape model. At each stage of the reasoning process that led to assigning of an examined object to one of the possible classes, novel processing methods are used. These methods are very efficient because they deal with a very specific class of shapes. In this paper, the 2-D objects that are classified as thin objects are regarded as geometrical objects without any reference to the real world objects. However, the shape under standing method is designed to understand an object at many levels of interpretation, such as the topological level, the linguistic level and the real world reference level. This approach influences the way in which the system of shape understanding is designed. The system consists of different types of experts that perform different processing and reasoning tasks.

关键词： Shape understanding thinning algorithms Thin class

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