The 4-source photometric stereo technique for three-dimensional surfaces in the presence of highlights and shadows We present an algorithm for separating the local gradient information and Lambertian colour by using 4-source colour photometric stereo in the presence of highlights and shadows. We assume that the surface reflectance can be approximated by the sum of a Lambertian and a specular component. The conventional photometric method is generalised for colour images. Shadows and highlights in the input images are detected using either spectral or directional cues and excluded from the recovery process, thus giving more reliable estimates of local surface parameters. The motivation for this paper is the problem of illumination-invariant 1 characterisation of three-dimensional surfaces with unknown reflectivity, which, however, can be assumed to be well approximated by a Lambertian component plus a specular component.. Characterisation of 3-dimensional surfaces from 2-dimensional images is not an easy task.. The 2-dimensional images depend on variation in both surface reflectance and surface relief. While the reflectance properties are intrinsic to a surface, the surface relief produces a pattern of shadings that depends strongly on the direction of the illumination. The appearance of a 3D surface changes drastically with illumination. It is often useful to recover some surface parameters that are independent of the illumination direction, for example, local surface orientation and reflectance.. The photometric stereo (PS) technique [20] uses several images of the same surface taken from the same viewpoint but under illuminations with different directions. Thus the changes of the intensities in the images depend only on the local surface orientation, which can be recovered by combining the information from all images. Let us consider a surface patch. When imaged under a particular illumination, it produces a camera intensity value which depends on the properties of the illumination configuration, the surface reflectance and the surface orientation, according to some photometric equation (hence the term "photometric stereo"). Having several images of the same surface patch gives us a system of such equations which can be solved for surface orientation and possibly some reflectance parameters. For Lambertian surfaces it is enough to have 3 images to recover both local surface normal and albedo. Various developments of the method were offered in later years, utilising different reflectance models and assumptions about the surface (see Section 2 for more details). One of these methods ( [3] ) suggests using 4. images to detect specularities. Under the assumption of nearly Lambertian behaviour outside the specularity region, one can exclude a highlighted pixel from consideration, and recover the local surface gradient from the remaining three pixels.. We propose a generalisation of an existing greyscale photometric stereo (GPS) technique for use with colour images. We proceed to show how the method mentioned above is susceptible to errors in the presence of shadows. We make use of spectral information as an additional cue for detecting highlights. For the case when the spectral information is not sufficient for the detection of highlights, an alternative method, based on comparing a recovered normal with the corresponding specular direction, is presented. As a result, we propose a combined method for recovering local gradient and colour for 3-dimensional nonLambertian surfaces from colour images, capable of coping with shadows and highlights.. This paper is structured as follows. In Section 2 we discuss previous work and relate our approach with the bulk of surface reconstruction problems tackled by other researchers.. In Section 3 we state our assumptions and establish terms and notation. In Section 4. we describe the linear photometric stereo method for grey-scale images, and generalise it to colour images. In Section 5 we discuss the effect shadows and highlights have on the outcome of the linear algorithm. Section 6 is devoted to highlight and shadow detection, and ways of dealing with them are suggested. Section 7 presents the results of experiments with synthetic and real data. Conclusions are drawn in Section 8. Shadows and highlights in the input images pose a problem for surface reconstruction.. We propose a modification of a well-known photometric stereo algorithm, which uses 4 images to detected highlights and shadows in the input images, and, excluding them from the recovery process, allows one to obtain more reliable estimates of surface parameters.. Using pixel-wise estimates of colour, we are able to detect highlights locally. Then the Figure 9 : Rendered surfaces, recovered with and without correction shadows can be detected as disturbances of linearity on the input quadruples of pixels.. In the greyscale case, when there are no spectral cues for highlight detection, we resolve to comparing the recovered normals with shadowlines and specular directions. Comparing the recovered normals with the shadowlines can be considered as a variation of the thresholding process. However as it uses both the local surface albedo and the illumination strength in the process of recovery, it does not rely on a global shadow thresholding value.. The performance of the proposed algorithm may be improved if one uses some postprocessing technique to reduce "pepper noise" which appears when we apply thresholding on various stages of the algorithm. The method fails in the greyscale case for pixels which are shadowed in more than one images and are affected by secondary illumination. To deal with misclassifications of this kind, one may detect multiple shadows in a quadruple, using an already derived local shadowing threshold. The photometric stereo method has been around for 20 years now, and it has received an extensive theoretical and experimental treatment. It was conceived by Woodham [19] [20] who first used it to recover local surface orientation. The method was based on the use of the so called reflectance maps in the form of look-up tables. These tables were obtained by means of a calibrating sphere made of the same material as that of the imaged surface, which allowed one to map obtained sets of intensities directly to surface normals.. Since then the idea was extended to recover not only surface orientation but also some reflectance parameters for a number of reflectance models. In what follows we discuss the existing PS techniques for both greyscale and colour images.

O O B I O O O O O O O O B O B O O O O O O O O O O O O O O O O O B I O O O O B O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O B O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O B O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O B O O O O O O O O O O O O O O O O O B I O O O O O O O B O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


Partitions of graphs into small and large sets Let G be a graph on n vertices. We call a subset A of the vertex setMoreover, we denote by ϕ k (G) the minimum integer t such that there is a partition of V (G) into t k-small sets, and by Ω k (G) the minimum integer t such that there is a partition of V (G) into t k-large sets. In this paper, we will show tight connections between k-small sets, respectively k-large sets, and the k-independence number, the clique number and the chromatic number of a graph. We shall develop greedy algorithms to compute in linear time both ϕ k (G) and Ω k (G) and prove various sharp inequalities concerning these parameters, which we will use to obtain refinements of the Caro-Wei Theorem, the Turán Theorem and the Hansen-Zheng Theorem among other things.

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Simulation of a Flapping Flexible Filament in a Flowing Soap Film by the Immersed Boundary Method This paper reports the computer simulation of a flapping flexible filament in a flowing soap film using the immersed boundary method. Our mathematical formulation includes filament mass and elasticity, gravity, air resistance, and the two wires that bound the flowing soap film. The incompressible viscous Navier-Stokes equations, which are used to describe the motion of the soap film and filament in our formulation, are discretized on a fixed uniform Eulerian lattice while the filament equations are discretized on a moving Lagrangian array of points which do not necessarily coincide with the fixed Eulerian mesh points of the fluid computation. The interaction between the filament and the soap film is handled by a smoothed approximation to the Dirac delta function. This delta function approximation is used not only to interpolate the fluid velocity and to apply force to the fluid (as is commonly done in immersed boundary computations), but also to handle the mass of the filament, which is represented in our calculation as delta function layer of fluid mass density supported along the immersed filament. Because of this nonuniform density, we need to use a multigrid method for solving the discretized fluid equations. This replaces the FFT-based method that is commonly used in the uniform-density case. Our main results are as follows. (i) The sustained flapping of the filament only occurs when filament mass is included in the formulation of the model; within a certain range of mass, the more the mass of the filament, the bigger the amplitude of the flapping. (ii) When the length of filament is short enough (below some critical length), the filament always approaches its straight (rest) state, in which the filament points downstream; but when the length is larger, the system is bistable, which means that it can settle into either state (rest state or sustained flapping) depending on the initial conditions. This numerical result we observed in computer simulation is the same as that of the laboratory experiment even though the Reynolds number 1 Current address: Department of Computer Science, University of California at Santa Barbara, Santa Barbara, CA 93106. E-mail: zhuld@cs.ucsb.edu. Many problems in biofluid dynamics involve interactions between deformable elastic bodies and incompressible viscous fluids, for instance the swimming motions of eel, sperm, and flagella. As a model of hydrodynamic interaction of deformable bodies with surrounding fluid flows, Zhang et al. [1] studied experimentally the dynamics of flexible filaments in a flowing soap film (see Fig. 1 for the experimental setup): separating at a nozzle attached to the bottom of a soapy-water reservoir, two thin nylon wires extend at a angle, then run parallel downward, and finally converge to a receiving container below. With the stopcock being turned on, which controls the rate of flow through the nozzle, under the actions of gravity and air resistance, a thin flowing soap film is formed on the two wires and reaches its terminal velocity quickly. A flexible filament (thread) is introduced at the middle line of the two wires, with the top end anchored by using a thin tube perpendicular to the soap film below the position where the film reaches its terminal velocity. Such a system (a filament in a thin film) is a two-dimensional version of the flag-in-wind problem. In the past several decades, people commonly believed that the flapping of a flag in the wind arises by a linear instability mechanism. However, recent experiments performed at the Courant Institute's wetlab by Zhang et al. [1] have shown that the flexible filament in the flowing soap film is actually bistable. In addition to that, the system itself (a free boundary problem) is very interesting: we have a one-dimensional immersed moving boundary with one end tethered in a two-dimensional laminar flow, and the boundary has mass and applies elastic forces (stretching, compression, and bending) to the film and moves at the local film velocity. Vortices are shed from the free end of the filament, get carried away by the flow, and are diffused by the film viscosity. A vortex street is formed downstream.. Currently Shelley et al. [2] is working on the instability analysis of this system; Fast and Henshaw [3] are working on the simulation by the overset grid method. Here we report our numerical simulation of such a system by the immersed boundary method.. The immersed boundary method has turned out to be a practical and efficient way to simulate fluid-structure interaction in the incompressible case. It has been applied successfully to a wide range of problems, particularly, in computational biofluid mechanics: blood flow in the human heart [4] [5] [6] [7] [8] [9] [10] [11] , the design of prosthetic cardiac valves [12] , aquatic animal locomotion [13] [14] [15] , wave propagation in the cochlea [16, 17] , platelet aggregation during blood clotting [14, 18] , flow of suspensions [19, 20] , valveless pumping [21] , flow in a collapsible tube [22] , flow and transport in a renal arteriole [23] , cell and tissue deformation under shear flow [24] [25] [26] . At present there exist several versions of the immersed boundary method. The version we use here is different from most existing versions [5, 7, 9, 11, 27, 28] in two aspects. (i) The discretization of the Navier-Stokes equations is different; the fractionalstep-projection scheme is applied and the skew-symmetric scheme is used for the nonlinear term instead of upwind differencing. (ii) The numerical method to solve the resultant system of linear algebraic equations is different: a multigrid method is applied to solve the system of linear algebraic equations with nonconstant coefficients (therefore the FFT method is no longer applicable), which result from discretizing Navier-Stokes equations with variable density as a consequence of the mass of the filament. The first example (unpublished) of such a computation can be found in [29] ; here we report on another such example.. Our mathematical formulation includes filament mass and elasticity, gravity, air resistance, and the two wires that bound the flowing soap film. The incompressible viscous Navier-Stokes equations, which are used in our formulation to depict the motion of the whole system (soap film + filament), are discretized on a fixed uniform Eulerian lattice while the filament equations are discretized on a moving Lagrangian array of points which do not necessarily coincide with the fixed Eulerian mesh points of the fluid computation. The interaction between the filament and the fluid (the soap film) is handled by a smoothed approximation to the Dirac delta function. This delta function approximation is used not only to interpolate the fluid velocity and to apply force to the fluid (as is commonly done in immersed boundary computations), but also to handle the mass of the filament, which is represented in our calculation as delta function layer of fluid mass density supported along the immersed filament. Because of this nonuniform density, we need to use a multigrid method for solving the discretized fluid equations. This replaces the FFT-based method that is commonly used in the uniform-density case.. Our main results are as follows. (i) The sustained flapping of the filament only occurs when filament mass is included in the formulation of the model: within a certain range of mass, the more the mass of the filament, the bigger the amplitude of the flapping. (ii) When the length of filament is short enough (below some critical length), the filament always approaches its straight (rest) state, in which the filament points downstream; but when the length is larger, the system is bistable, which means that it can settle into either state (rest state or sustained flapping) depending on the initial conditions. This numerical result we observed in computer simulation is the same as that of the laboratory experiment even though the Reynolds number of the computations is lower than that of the laboratory experiment by two orders of magnitude.. Our numerical method used here can be generalized to the three-dimensional case to study numerically problems involving interactions of fluids and immersed boundaries which are not neutrally buoyant, as is usually the case in aerodynamic problems such as flag-in-wind, insect flight, and so forth.

O O O O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O


Detection of anomalous bids in procurement auctions Procurement auctions may be affected by abnormally low bids, whose acceptance may have negative consequences on the auctioneer. A method, based on the average submitted bid, is considered to detect such anomalous bids and aid the auctioneer in the possible rejection decision. Analytical expressions or simulation results are provided for the detection probability and for the false alarm probability. The performances heavily depend on the number of tenderers and on the dispersion of bid values. Both performance indices improve as the number of tenderers grows and generally degrade as the dispersion grows. The presence of multiple anomalous bids leads to a significant worsening of the performance, while courtesy bids raise both the false alarm probability and the detection probability. The use of the average-bid criterion, though officially endorsed in national legislations, is therefore recommended as a strongly precautionary criterion, i.e. when the need to avoid anomalous bids is considered much more relevant than the costs associated to deeper investigation of anomalous bids or to the erroneous rejection of regular bids.

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A space and time efficient algorithm for SimRank computation Abstract SimRank has become an important similarity measure to rank web documents based on a graph model on hyperlinks. The existing approaches for conducting SimRank computation adopt an iteration paradigm. The most efficient deterministic technique yields O n 3 worst-case time per iteration with the space requirement O n 2 , where n is the number of nodes (web documents). In this paper, we propose novel optimization techniques such that each iteration takes O (min {n · m, n r }) time and O (n + m) space, where m is the number of edges in a web-graph model and r ≤ log 2 7. In addition, we extend the similarity transition matrix to prevent random surfers getting stuck, and devise a pruning technique to eliminate impractical similarities for each iteration. Moreover, we also develop a reordering technique combined with an over-relaxation method, not only speeding up the convergence rate of the existing techniques, but achieving I/O efficiency as well. We conduct The work was supported by ARC Grants DP0987557 and DP0881035 and Google Research Award. We also appreciate the general support from NICTA. extensive experiments on both synthetic and real data sets to demonstrate the efficiency and effectiveness of our iteration techniques. In recent years, the complex hyperlink-based similarity search has attracted considerable attention in the field of Information Retrieval. One of the promising measures is the SimRank similarity with ubiquitous applications to search engine ranking, document corpora clustering, collaborative filtering for recommender systems, etc. SimRank is a recursive refinement of co-citation measure that computes similarity by common neighbours alone [12] . The intuitive model for SimRank measure is based on random walk over a web-graph like Google PageRank [20] . The SimRank similarity between two web pages is defined recursively as the average similarity between their neighbours, along with the base case that one page is maximally similar to itself. Unlike many other domain-specific measures that require humanbuilt hierarchies, SimRank can be used in any domain in combination with traditional textual similarity to produce an overall similarity measure [9, 10] .. Motivations For achieving high efficiency of SimRank computation, it is desirable to develop optimization techniques that improve the time and space complexity of the similarity algorithm. The state-of-the-art approaches for SimRank optimization can be outlined into the following two categories: (a) deterministic techniques [1, 3, 16, 17, 26] that estimate the exact SimRank solution s (·, ·) (i.e., a fixed point) by utilizing an iterated similarity function. (b) stochastic techniques [9, 10] that approximate similarities by the expected value s (a, b ) = E (c τ (a,b ) ), where τ (a,b ) is a random variable denoting the first hitting time for nodes a and b , and c ∈ (0, 1) is a decay factor. Several deterministic strategies have been studied as the iterative algorithms often produce better accuracy than stochastic counterparts for similarity estimation. The straightforward SimRank iterative paradigm is time-consuming, yielding O Kn 4 worst-case time and O n 2 space [12] . Recent work on structural/attribute-similaritybased graph clustering [27] has also raised the need for developing efficient methods for similarity computation. Nonetheless, unlike content-based similarities, it is considerably more challenging to design a deterministic and efficient algorithm that allows significant savings in time and space for SimRank computation.. To the best of our knowledge, to the present there are three most efficient techniques [11, 14, 17 ] for deterministic SimRank computation. Lizorkin et al. [16, 17] deployed a partial sums function reducing the computational time from O Kn 4 to O Kn 3 in the worst case. Li et al. [14] developed an approximation algorithm for estimating similarities on static and dynamic information networks. He et al. [11] proposed a parallel algorithm based on graphics processing units (GPU) for similarity computation.. Contributions In this extended paper of the conference version [25] , we present the additional optimization techniques to further improve the efficiency of SimRank deterministic computation by orders of magnitude. We outline the main contributions made in this paper as follows:. -We extend the SimRank transition matrix in [25] to avoid locking random surfer into an enclosed subsection of the entire graph by overlaying a teleportation matrix. -We represent similarity equations in a matrix form and employ a sparse storage scheme for SimRank transition matrix, which lays a foundation for optimizing computational time from O n 3 to O (min {n · m, n r }) in the worst case, where r ≤ log 2 7 with the space requirement from O n 2 to O (m + n). -We devise a pruning technique for the similarity matrix to eliminate impractical almost zero similarity values by setting a threshold, keeping the sparseness of similarity matrix for each iteration. -We develop a heuristic optimal permutation technique for minimizing SimRank transition matrix bandwidth for digraphs, improving the I/O efficiency of SimRank iteration. -We show a successive over-relaxation method for SimRank computation to significantly speed up the convergence rate of the existing technique. -We validate the performance of our algorithm with an extensive experimental study on both synthetic and real-life data sets, demonstrating that it outperforms the state-of-the-art algorithms by orders of magnitude.. Organizations The rest of the paper is organized as follows. In the next section, the problem definition for SimRank is formally introduced. In Section 3, a solution framework for SimRank optimization techniques is established. In Section 4, three optimization techniques for SimRank computation are suggested; the time and space complexity of the proposed algorithm is analyzed. In Section 5, the experimental results are reported on the efficiency of our methods over synthetic and real-life data sets. The related work appears in Sections 6 and 7 concludes the paper. This paper investigated the optimization issues for SimRank computation. We first extended the SimRank transition matrix in our conference paper [25] , and formalized the SimRank equation in matrix notations. A compressed storage scheme for sparse graphs is adopted for reducing the space requirement from O n 2 to O (n + m), whereas a fast matrix multiplication for dense graph is used for improving the time complex from O n 2 · d to O (min {n · m, n r }), where r ≤ log 2 7. Then, for achieving the I/O efficiency of our algorithm, we developed a permuted SimRank iteration in combination of the extended Reversed Cuthill-McKee algorithm. We also devised a pruning technique for the similarity matrix to get rid of the impractical almost zero similarity values, keeping the sparseness of similarity matrix for each iteration. Finally, we have shown a successive over-relaxation method for computing SimRank to significantly speed up the convergence rate of the existing technique. Our experimental evaluations on synthetic and real-life data sets demonstrate that our algorithms have high performances in time and space, and can converge much faster than the existing approaches. The issue of measuring object-to-object similarity has attracted a lot of attention. Existing work on similarity search techniques can be distinguished into two broad categories: text-based and link-based [9, 10, 12, 19, 21] .. The link-based similarity computation can be modeled by a web-graph, with vertices corresponding to web pages and edges to the hyperlinks between pages. In terms of a graph structure, the methods of bibliographic coupling [22] and cocitation [23] have been applied to cluster scientific papers according to topic. In both schemes, similarities between two nodes are measured only from their immediate neighbors. As a generalization of similarity functions to exploit the information in multi-step neighborhoods, HITS [18] , PageRank [19] , SimRank [12] and SimFusion [24] algorithms were suggested by adapting link-based ranking schemes.. Jeh first introduced a similarity measure called SimRank [12] aiming at "two pages are similar if they are referenced by similar pages". The underlying intuition behind the SimRank approach somewhat resembles the one for SimFusion "integrating relationships from multiple heterogeneous data sources". In [12] , SimRank is known to be efficient since it recursively refines the co-citation measure and forms a homogenous language-independent data set.. Optimization algorithms for SimRank computation have been explored in [1, 3, 10, 16] . Results show that the use of fingerprint trees and random permutations with extended Jaccard coefficient can approximately compute SimRank scores under a scalable Monte Carlo framework. The algorithms in [10] use probability theory to calculate the expected-f meeting time τ (u, v) and estimate s (u, v) by E c τ (u,v) . The solution is rather stochastic. In comparison, our algorithm can get a deterministic solution by using numerical techniques for computing SimRank.. There has also been a host of work for computing SimRank deterministically, the most efficient optimization techniques presented in [16, 17] introduced a partial sum function to reduce the number of access operations to the SimRank function and speed up similarity scores calculation by s k (u, * ) values clustering. The algorithm in [16, 17] has improved SimRank computational complexity from O Kn. where d is the average node degree, n is the number of nodes. In comparison, our method has achieved the same time complexity O (Kn · m) for sparse graphs, where m is the number of edges. When the graph is rather dense, the time complexity in [16, 17] is O Kn 3 , whereas our technique only requires O (n r ) operations, where r ≤ log 2 7, taking advantage of fast matrix multiplications. In addition, our algorithm also accelerates the convergence rate of [16, 17] .. Li et al. [14] proposed a novel approximate SimRank computation algorithm for static and dynamic information networks. Their approximation algorithm is based on the non-iterative framework, taking O n 2 α 4 time and O n 2 space, where α is the rank of graph adjacency matrix. However, the optimization technique of Kronecker product in their approach is prohibitively costly in computational time. Additionally, for a sparse graph, the SVD decomposition cannot keep the sparsity of the graph adjacency matrix. Therefore, in practice their method is not preferable.. As for SimRank parallel algorithms, Yu et al. [26] devised an AUG-SimRank algorithm over undirected graphs on distributed memory multi-processors. They combined the PLAPACK solvers with their partition techniques to parallelize the SimRank algorithm. He et al. [11] also proposed a graphics processing units (GPU) based parallel framework for similarity computation.. Li et al. [13] developed a BlockSimRank algorithm that partitions the web graph into several blocks to efficiently compute similarity of each node-pair in the graph. Their approach takes O(n 4 3 ) time, which is based on the random walk model. Zhao et al. [28] proposed a new structural similarity measure called P-Rank (Penetrating Rank) that says "two entities are similar if (a) they are referenced by similar entities; and (b) they reference similar entities." This similarity takes into account of both in-and out-link relationships of entity pairs and penetrates the structural similarity computation beyond neighborhood of vertices to the entire information network. Antonellis et al. [1] extended the weighted and evidence-based SimRank yielding better query rewrites for sponsored search; however, their framework lacks a solid theoretical background and the edge weight in the transition probability is an empirical distribution.. Meanwhile, Xi et al. [24] introduced SimFusion algorithm to represent heterogeneous data objects. The Unif ied Relationship Matrix (URM) approach is employed to support for various intra-nodes relations and information spaces. SimFusion iterative reinforcement similarity score takes the form:. where L urm is a single step probability transformation matrix in a Markov Chain that combines all the relationships among nodes, S urm is a Unif ied Similarity Matrix (USM) that represents similarity values between node pairs. The computational complexity for SimFusion is O n 3 whilst our approach takes the time O (min {n · m, n r }), where r ≤ log 2 7. The storage for SimFusion requires O n 2 , whereas we use CSR representation for reducing the space requirement to O (n + m) for sparse graphs. Moreover, our algorithm is I/O efficient, minimizing the bandwidth during the precomputation and has the faster convergence rate. Finally, some of the iterative matrix-analytic methods used in this work are surveyed in [2] .

O O O O O O O B O O B O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O B O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O B O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O B O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


Dynamic Background Subtraction Based on Local Dependency Histogram Abstract Moving objects detection and segmentation from a video sequence is one of the essential tasks in object tracking and video surveillance. A common approach for this task is background subtraction, which first builds an adaptive statistical background model, and then pixels that are unlikely to be generated by this model are labeled as foreground. Despite a large number of background subtraction methods have been proposed in the literature over the past few decades, the task remains challenging when the scenes to be modeled contain dynamic backgrounds such as waving tree, spouting fountain, illumination changes, camera jitters, etc. A robust background subtraction method should work well in these scenes since they are common phenomena in real world. It is always desirable to achieve very high accuracy in the detection of moving objects. The performance of background subtraction depends mainly on the background modeling technique used.. Early approaches operated on the premise that the color of a pixel over time in a static scene could be modeled by a single Gaussian distribution. Wren et al. [15] modeled the color of each pixel with a single three-dimensional Gaussian. Its mean and variance were learned from pixel observations in previous frames. Once the pixel-wise background model was built, the likelihood of each incident pixel generated by this model could be computed. Based on the likelihood, the pixel was labeled as background or foreground. However, a single-Gaussian model is unsuited to most outdoor situations since repetitive object motion, shadows or reflectance often cause multiple pixel colors to belong to the background at each pixel. To overcome the limitations of single-Gaussian model, the mixture of Gaussians (MOG) approach was used to model the complex, non-static scenes [12] . An incident pixel was compared to every Gaussian distribution in the pixel's model and, if a match (defined by a fixed threshold) was found, the mean and variance of the matched Gaussian distribution was updated, otherwise a new Gaussian distribution with the mean equal to the current pixel color and some initial variance was introduced into the mixture. Each pixel was labeled depending on whether the matched distribution represented the background process. Many authors have proposed improvements and extensions to this algorithm. In Ref. [3] , new update algorithms for learning mixture models were presented. In Ref. [18] , not only the parameters but also the number of components of the mixture was adapted for each pixel.. The Gaussian-based methods have an assumption that the pixel color values over time could be modeled by one or multiple Gaussian distributions, however, this assumption does not always hold in the real world. To deal with the limitations of parametric methods, a nonparametric approach to background modeling was proposed in [1] . The method utilized a general nonparametric kernel density estimation technique for building a statistical representation of the scene. The probability density function for pixel intensity was estimated directly from the observation data without any assumptions about the underling distributions. In [5] , a quantization/clustering technique to construct a nonparametric background model was presented. The background was encoded on a pixel by pixel basis and samples at each pixel were clustered into the set of codewords. A similar approach in [16] was proposed, which combined color and texture features by a multi-layer model.. In [4, 9] , each pixel was modeled with a Kalman filter. The method can adapt to changes in illumination, but performs poorly in complex dynamic scenes. This approach was used in the automatic traffic monitoring application presented in [6] . In [8] , the dynamic background was modeled by an autoregressive moving average (ARMA) model. A robust Kalman filter algorithm was used to iteratively estimate the intrinsic appearance of the dynamic scenes.. Hidden Markov Models (HMMs) have also been used to model pixel intensity [10, 13] . In these approaches, the pixel intensity variations were represented as discrete states corresponding to scene modes. In [10] , the approach was used in a traffic monitoring application where the pixel states represented the road, vehicles and shadows. In [13] , HMM states corresponded to global intensity modes each modeled with a single Gaussian distribution. The model was capable of handling sudden illumination changes.. Although the methods mentioned above demonstrated their success cases, their performance will notably deteriorate in the presence of dynamic backgrounds such as waving tree, spouting fountain, illumination changes, camera jitters, etc. There are two causes for this. First, these methods model the background model of a pixel exploiting only its intensity information and ignoring the useful dependencies existing in intensities of neighboring pixels. In dynamic scenes, although some pixels significantly changes over time , they should be considered as background. However, the background models of these methods can not effectively model such changes since they exploit the pixel's intensity information lonely. Second, these methods use a fixed threshold to define whether a pixel matches to its model, which also will result in the notable performance deterioration of these methods since the extents of dynamic changes of different pixels are distinctly different. Using a fixed threshold can not model such difference and it will result in the performance deterioration of these methods.. In order to effectively model the dynamic scenes, in this paper, we present a dynamic background subtraction method that has three contributions. First, we present a novel local dependency descriptor, called Local Dependency Histogram (LDH), which is computed over the region centered on a pixel. The LDH effectively extracts the spatial dependency statistics of the center pixel, which contain substantial evidence for labeling the pixel in dynamic scenes. Second, based on the proposed LDH descriptor, we present a novel dynamic background subtraction method, in which each pixel is modeled as a group of weighted LDHs. Labeling the pixel as foreground or background is done by comparing the new LDH computed in current frame against its model LDHs. The model LDHs are adaptively updated by the new LDH. Finally, unlike traditional approaches which define whether a pixel matches to its model using a fixed threshold, an adaptive thresholding technique is also proposed. The proximity value computed using histograms intersection between the LDH and its model LDH over time is modeled by a Gaussian distribution. The match is defined as the proximity value within 2.5 standard deviations of the Gaussian distribution. The Gaussian distribution is adaptively updated using the proximity value.. The rest of the paper is organized as follows: Section 2 describes the proposed local dependency histogram (LDH). The proposed approach to dynamic background subtraction based on LDH is presented in Section 3. The qualitative and quantitative experimental results and analysis are shown in Section 4, followed by some conclusions in Section 5. In this paper, we present a dynamic background subtraction method that has three contributions. First, we present a novel local dependency descriptor, called Local Dependency Histogram (LDH), which is computed over the region centered on a pixel. The LDH effectively extracts the spatial dependency statistics of the center pixel which contain substantial evidence for labeling the pixel in dynamic scenes. Second, based on the proposed LDH descriptor, we present a novel dynamic background subtraction method, in which each pixel is modeled as a group of weighted LDHs. Labeling the pixel as foreground or background is done by comparing the new LDH computed in current frame against its model LDHs. The model LDHs are adaptively updated by the new LDH. Finally, unlike traditional approaches which define whether a pixel matches to its model using a fixed threshold, an adaptive thresholding technique is also proposed. The proximity value computed using histograms intersection between the LDH and its model LDH over time is modeled by a Gaussian distribution. The match is defined as the proximity value within 2.5 standard deviations of the Gaussian distribution. The Gaussian distribution is adaptively updated using the proximity value. Experimental results on a variety of dynamic scenes validate that the proposed method significantly outperforms the widely used Mixture of Gaussian (MOG).

B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


Process algebra for performance evaluation This paper surveys the theoretical developments in the ÿeld of stochastic process algebras, process algebras where action occurrences may be subject to a delay that is determined by a random variable. A huge class of resource-sharing systems -like large-scale computers, clientserver architectures, networks -can accurately be described using such stochastic speciÿcation formalisms. The main emphasis of this paper is the treatment of operational semantics, notions of equivalence, and (sound and complete) axiomatisations of these equivalences for di erent types of Markovian process algebras, where delays are governed by exponential distributions. Starting from a simple actionless algebra for describing time-homogeneous continuous-time Markov chains, we consider the integration of actions and random delays both as a single entity (like in known Markovian process algebras like TIPP, PEPA and EMPA) and as separate entities (like in the timed process algebras timed CSP and TCCS). In total we consider four related calculi and investigate their relationship to existing Markovian process algebras. We also brie y indicate how one can proÿt from the separation of time and actions when incorporating more general, non-Markovian distributions. Performance evaluation means to describe, to analyse, and to optimise the dynamic, time-dependent behaviour of systems. However, it is rather common for a system to be fully designed and functionally tested before any attempt is made to determine its performance characteristics. Redesign of both, hardware and software, is costly and may cause late system delivery. Therefore, performance evaluation has to be integrated into the design process from the very beginning [46, 31] (cf. Fig. 1 ). The saw-tooth curve schematically shows the system development process when temporal aspects are considered at a too late stage. Early integration of both functional and temporal behaviour in a uniÿed methodology allows to diminish these setbacks and improves the design productivity.. The need for integrated modelling techniques was already recognised in the 1970s. The most successful examples are stochastic Petri nets [2] , stochastic graph models [91] and stochastic automata networks [85] . Nevertheless, performance evaluation of complex transportation and processing systems remained an art mastered only by a small group of specialists. Now, process algebras with their unique features o er means which promise a major progress for systematic modelling of complex systems. Therefore, some 10 years ago a small group of researchers started to deal intensively with stochastic extensions of process algebras. In this paper we survey the state-of-the art in the theoretical achievements for these stochastic process algebras, argue the beneÿts for performance evaluation (including reliability aspects) and indicate the future challenges.

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Bursty content sharing mechanism for energy-limited mobile devices The strategy to send data in high speed bursts has been observed to be useful for energy-efficient communication of wireless applications. In this paper we investigate how to apply this approach to peer-to-peer (P2P) content sharing. Our main focus is on battery savings that can be achieved by properly shaping the traffic at the application level. Our primary target is BitTorrent based content sharing on mobile phones connected with 3G cellular networks. However, the results also apply to WLAN communication as well as to other energy-limited devices in addition to mobile phones. We propose a novel BitTorrent extension and evaluate it via flow-level simulations. In comparison to standard BitTorrent, the energy-limited peers can achieve 50% energy savings without significantly affecting the download speeds of regular peers. The gap between the performance of mobile devices and desktop computers is becoming narrower. Improved processing and networking capabilities of mobile phones have opened up the possibility of their use in peer-to-peer networks. Our previous research on P2P applications for mobile phones, such as Symella [1] and SymTorrent [2] , shows that today's mobile phones can effectively join and contribute to distributed content sharing networks.. However, the major issue that prevents mobile peer-to-peer content sharing from becoming ubiquitous is battery consumption. The energy measurement results with the SymTorrent BitTorrent client on Symbian based mobile phones show that SymTorrent uses about the same amount of power as a voice call [3] , meaning that a modern mobile phone can be used for two to five hours for peer-to-peer content sharing before its battery is completely depleted. This is clearly far from the optimal operation time.. The energy consumed by a mobile phone is the result of several factors. Communication via wireless radio, such as transferring data over the cellular network or wireless LAN, is power hungry and clearly dominates the energy consumed by data processing [4] . Therefore, we would need new solutions that, instead of speed, optimize the energy consumption of the wireless communication in P2P content sharing scenarios.. The essence of this research is the efficient use of the wireless interface. As observed in [5] , in the context of mobile web access, data should be transferred at the maximum throughput when the wireless link is active. Then the wireless interface should remain off until the next download. We would thus like to reach an alternating sequence of states, where the wireless link either communicates with its maximum speed or is idle in the sleep state. The mechanisms that can be used to reach this target behavior in a distributed P2P system are the key objectives of our research.. We use BitTorrent as the base of our research since it is widely used and already supported by a wide range of platforms. Although it has been the target of extensive research, there is very little prior work on mobile BitTorrent and its energy consumption. Our goal is to propose a new protocol extension, BurstTorrent, which allows content transfer for mobile peers in a way that consumes less energy than the standard BitTorrent protocol. Furthermore, our target is that the new protocol would require only minor modifications to the existing clients.. The rest of the paper is structured as follows. In Section 2 we discuss the energy consumption in wireless P2P networks in detail. Section 3 presents how the battery saving ideas can be applied to BitTorrent based content transfer. Section 4 presents the proposed BurstTorrent protocol in detail. In Section 5 we discuss the flow-level simulations we have used to analyze the behavior of BurstTorrent, and compare it with the standard BitTorrent. In Section 6 we discuss our findings and in Section 7 reflect how our work is related to prior research. Finally, in Section 8 we summarize and conclude our work with future research directions. In this paper we have shown that significant energy conservation can be achieved by transferring data in high speed bursts. BurstTorrent clearly outperforms standard BitTorrent in almost all cases in terms of the energy consumption of mobile peers, while the download time of regular peers is not affected significantly. This implies that other file transfer protocol could also benefit from using the concepts presented in this paper. Future work could include evaluating BurstTorrent with different wireless technologies, such as wireless LAN, further analyzing the effects causing the increase of regular peers' download time, and implementing the protocol on a mobile platform to perform measurements in a live network. The results show that the BurstTorrent approach has a lot of potential in heterogeneous content sharing networks which consist of both energy-limited and regular peers. However, there are at least two difficulties to consider. First, although BurstTorrent is able to operate with current BitTorrent peers, they are not fully compatible. To support the energy-efficient operation both regular and energy-limited peers need to implement the new protocol. Thus, we cannot rely on existing BitTorrent users. Furthermore, we cannot necessarily assume that desktop clients will start using BurstTorrent since even if it does not affect their download times, they do not benefit from using the protocol either.. Moreover, the content that mobile devices would like to download could be different from the content available in desktop clients. The same music files probably work in all devices but handheld devices would require, for instance, different lowresolution video files.. However, a mobile community alone might be sufficient, the devices on chargers acting as regular peers. This would need further evaluations, based on the time an average user leaves their phone on the charger.. In cases dominated by energy-limited devices, long download times limit the applicability of BurstTorrent. It might be useful in cases where download time is not an issue like downloading noncritical software updates or synchronizing media files overnight. Extending BurstTorrent to handle data transfer also between energy-limited devices would require further research. It would require the ability to accept incoming connections on the devices (not possible in most mobile network), and might not improve download times to the desirable extent, since transfers can only be scheduled for active periods. Negotiating several parallel transfers for the same time would be possible only in rare cases.. The area where optimization could be applied to the protocol is the peer and piece selection strategy. The currently applied method results in close to optimal energy consumption if energylimited peers were serving regular peers, but in free riding mode and with higher energy-limited peer ratios, the gap between the optimal and the achieved results becomes larger. Therefore, different, more sophisticated peer selection algorithms could be defined to achieve more energy-efficient operation. Since the task of selecting the right peers can be derived from the classic setcover problem, using the available approximation solutions can also be applied here.. The evaluations used energy values obtained using 3G networks, but the protocol can be operated over other wireless networking technologies as well, most importantly Wireless LAN. The most important difference in the case of WLAN is that the power per transfer speed rate cannot be described by a binary on/off function, since lower transfers speeds requires less power as well. However, the energy per bit ratio is still lower at higher transfer speeds, thus BurstTorrent is more energy-efficient than BitTorrent unless the latter can download data at the highest speed. While there are numerous studies about BitTorrent and peer-topeer content sharing, there is very little research on the energy aspects of content sharing.. Reference [3] investigates the battery consumption of a standard BitTorrent client on mobile phones. Reference [10] studies cooperative content downloading where pieces downloaded from the Internet are shared via proximity connections over short-range radio. Fritsche [11] investigates the possibility of using BitTorrent in sensor networks and observes that the communication is the dominant energy consumer with 63% of total energy.. Blackburn [12] has a very different angle to energy consumption in content sharing. While our work is focusing on the energy consumption of the active downloading phase, his target is the stand-by energy consumption of the seeding servers participating in the BitTorrent networks. His goal is to reduce the total energy consumption and environmental load of computers participating in content sharing networks.. Venugopal et al. [13] presents a time-slotted P2P protocol, in which the slots where the peer is sleeping are determined based on the node id. Other peers that have access to the peer id thus have a chance to know when the peer is going to be in active state. In contrast with our protocol, this mechanism does not focus on content sharing. Furthermore, they use regular sized time slots that are independent of the application or of the peers while our sleep intervals are based on negotiations with other peers.. The research presented in [5] is not P2P related, but discusses an approach similar to ours to achieve energy-efficient mobile web access. The paper states that the minimum possible energy spent for a web page download is obtained by assuming that the transfer from the access point to the mobile host is performed in a single phase. Specifically, the wireless interface is turned on, all data are transferred at the maximum throughput allowed by the wireless link, and then the wireless interface remains off until the next download. This is similar to the way our protocol handles mobile peers and switches between active and idle periods.

O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O B I O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O B I O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


Nonparametric Analysis of the Order-Statistic Model in Software Reliability Abstract-In the literature on statistical inference in software reliability, the assumptions of parametric models and random sampling of bugs have been pervasive. We argue that both assumptions are problematic, the first because of robustness concerns and the second due to logical and practical difficulties. These considerations motivate the approach taken in this paper. We propose a nonparametric software reliability model based on the order-statistic paradigm. The objective of the work is to estimate, from data on discovery times observed within a type I censoring framework, both the underlying distribution F from which discovery times are generated and N, the unknown number of bugs in the software. The estimates are used to predict the next time to failure. The approach makes use of Bayesian nonparametric inference methods, in particular, the beta-Stacy process. The proposed methodology is illustrated on both real and simulated data. S OFTWARE reliability models have received a lot of attention in recent decades, as software systems have become more pervasive and vital to the operation of many important aspects of modern life. These models attempt to describe the process of bug discovery in software, typically in the prerelease stage of software development, when the software is tested to ensure that it meets its specification and to remove errors. Among their important purposes is predicting the total number of errors that will be discovered in the code and optimizing the software development process, for example, deciding on optimal testing strategies and when to release software for use.. The data usually take the form of times between bug discoveries or counts of discovered bugs at known times. The structure of the data, and so a reasonable model for them, is very dependent on the type of software, the use to which the software is put, and the circumstances under which the data were collected. Because of this, a plethora of parametric models, based on many different modeling approaches and ideas about the structure of the data, have arisen that work well for certain data but lack robustness.. In this paper, we investigate one common class of software reliability model-the order-statistic model-and, in doing so, attempt to address the problem of achieving a better flexibility in the modeling approach. We also point out a deficiency in the sampling scheme that most software reliability models assume and offer a more reasonable alternative. We consider a nonparametric approach on the basis that this provides the desired robustness in modeling. Bayesian inference is developed that infers the posterior distribution of the discovery time distributions and the number of bugs and is illustrated on real and simulated data. Once this is done, we show how the estimates may be used to predict next time to failure. As well as describing methodology for this class of models, we believe that it is an interesting extension of Bayesian nonparametric approaches.. Order-statistic models assume that there are an unknown number of bugs N in the software. Bugs are labeled i ¼ 1; . . . ; N and their discovery times are independent, specified by distribution functions G 1 ; G 2 ; . . . ; G n . The observed sequence of discovery times are the order statistics of the G i . The earliest order-statistic model for software reliability is the Jelinski-Moranda model [1] , which assumes that the G i are independent and identically distributed exponential random variables, although the authors did not categorize the model as of that type. The order-statistic model approach was first defined for use in software reliability in [2] , although the idea was implicit in the earlier work of [3] . Here, the G i were exponential (making the work of [1] a special case) but not necessarily identically distributed, equivalent to assuming that each bug failed as an independent Poisson process. There had been some work on order-statistic models in general reliability theory beforehand; see [4] . A more general order-statistic model, that moved beyond the exponential assumption was proposed in [5] .. A feature of all these papers is that a parametric form for the G i is assumed. Our work attempts to generalize to a nonparametric form for the G i . However, in order to make inference practical, we work with a special case, where the G i are identical; we explain why in Section 2. The work of [6] is the closest that we have found to our approach, where the general order-statistic model is treated nonparametrically.. When N is assumed known, inference for an orderstatistic model is typically straightforward. When N is unknown, as is the case with software testing data, the inference is a type of "how many kinds are there" problem, well-known in the literature on estimating numbers of distinct species. It is pointed out in [7] that, in some cases, the data contain little information about N; thus, inference can be more difficult. In this regard, a Bayesian approach has the advantage that it can make use of any prior knowledge about N to aid the inference. In [8] , a Bayesian approach was described for an example of an exponential order-statistic model. For the general order-statistic model, inference procedures are described in [9] and [5] , while [10] is an example of Bayesian inference.. There have been previous applications of Bayesian nonparametric methods in software reliability, but they have been restricted to a hierarchical semiparametric approach, where a parametric model for the discovery times is assumed, and a nonparametric model is assigned for the prior on a model parameter; see [11] and [12] . The approach is also related to work in warranty analysis, where the failure of systems under warranty is analyzed; see [13] .. The paper is organized as follows: In Section 2, we define the order-statistic model and demonstrate the problems that can arise for inference when a parametric form of the model is assumed. In Section 3, we define the nonparametric form of the order-statistic model and describe a Bayesian inference procedure for the distribution function from which the discovery time distribution is defined and N, the number of bugs. Section 4 discusses how to present the inference and how to apply it to prediction. Section 5 gives examples using simulated and real data. In Section 6, we close with some concluding remarks. In this paper, we have presented a Bayesian nonparametric approach to the treatment of bug discovery time data. We have argued that the assumption of a parametric model leaves the investigator vulnerable to the consequences of model misspecification. For the same reasons that the empirical distribution function or the Kaplan-Meier estimator might be preferred to a parametric alternative, one might well prefer a nonparametric analysis in assessing the reliability of a piece of software. The model is a nonparametric form of the order-statistic model. The inferential approach presented here has the natural robustness of a nonparametric analysis and has, as well, the ability to incorporate, through the modeling of prior information, pertinent intuition or expert knowledge that might be available in the application of interest. The approach we have taken has consciously eschewed the "random sampling" assumption that is typical of traditional treatments of the estimation problem under study. Our developments assume, instead, that the software being tested is subjected to such testing over a fixed and predetermined interval of time. Under this type I censoring scheme, the number of bugs found is a random variable, and the inference developed is based on the random discovery times between the (random) number of bugs found. The approach presented in Sections 3 through 5 requires that the tester specify a prior distribution for N and a distribution function that is the mean of the prior for F , and we have suggested how these can be defined. The computation of the posterior distribution and presentation of results can be complicated, but we have successfully demonstrated its feasibility in the examples presented herein.. The strengths of this approach are the more realistic sampling scheme and a more robust fitting procedure. The disadvantages are a complicated computation process, and the problem of evaluating convergence of the many separate Markov chains in the simulation procedure. Other criticisms are the assumption that the distributions generating the order statistics are identical and that we have not modeled a priori dependence between F and N.. The former criticism is more difficult to address than the latter. If one allowed each bug to have a possibly different F , then there would be one datum available to learn about each. The success of the inference relies on being able to treat all the observations as coming from one distribution F . Any model that relaxed the identical distribution assumption and wanted to make use of the method described here would have to allow the data to be treated in this way. We also point out that our modeling of F allows it to be multimodal and, thus, describe a mixture of subpopulations of bugs.. Modeling dependence between N and F is more straightforward; for example, one could allow the expected value of the mean of F to depend on N. An obvious extension of the work is a fully Bayesian approach, where inference is also conducted on the parameters of the prior mean of F . The problem is that it is difficult to write the likelihood in terms of these parameters. Another extension is to fit count data rather than discovery times, by using data augmentation to sample times from a sample of F conditional on the counts.. The developments in this paper provide a useful stepping stone for facilitating further research on nonparametric software reliability. As with any Bayesian analysis, we should mention the need to tailor the analysis to the intended application. A sensitivity analysis within any given application, so as to determine the extent to which the analysis is affected by the prior model, is important (see chapter 6 of [22] ). One can present a Bayesian analysis with greater conviction when the inference is fairly stable over a class of "reasonable" prior distributions than when it is quite sensitive to the prior selected within such a class.. Let there be a Dirichlet process prior for F with measure ðsÞ. Our data consist of noncensored observations at t 1 ; . . . ; t k and N À k right-censored observations at T Ã . In [21] , it is shown that the posterior distribution for F can be written in the form F ðtÞ ¼ 1 À expðÀZðtÞÞ, where ZðtÞ is a beta-Stacy process. As is described in Section 3, ZðtÞ can be written as the sum of independent increments W 1 ; . . . ; W k at the observed discovery times t 1 ; . . . ; t k and a continuous component Z c ðtÞ. In this appendix, we describe how to sample from Z c ðt i Þ À Z c ðt iÀ1 Þ, for i ¼ 1; . . . ; k, the change in the continuous component between successive discovery times. The description is also valid for sampling from Z c ðT Ã Þ À Z c ðt k Þ. The beta-Stacy process has independent increments, and so these increases in the continuous process are independent.. Define ðsÞ to be such that ðsÞ ¼ R 1 s dðuÞ. In this case, we have defined ðsÞ ¼ Be Às , from which dðsÞ ¼ Be Às ds. From [21] , in our case, the continuous part of the posterior process Z c ðtÞ has Levy measure. In process P j¼1 j , where, for small , the number of jumps is Poisson with mean. ÀzðsÞ ðsÞIðz > ; t iÀ1 < s < t i Þ 1 À e Àz dz ds ð12Þ and the jumps j are independent and come from a density. A sample from Z c ðt 1 Þ is obtained by this definition if we let t 0 ¼ 0. The approximation converges to Z c ðt i Þ À Z c ðt iÀ1 Þ as ! 0; practically, we can take to be small. In [23] , the error in this approximation as a function of is discussed, which is of the order EðÞ < ðt iÀ1 ; t i Þ. In this paper, following some exploration, we found that there was no difference in results for any < 10 À5 ; thus, we set, conservatively, ¼ 10 À7 . In order to sample the compound Poisson process P j¼1 j , we first sample , then sample from the Poisson with mean , and then independently sample 1 ; . . . ; from gðzÞ. Summing the j obtains the approximate sample from Z c ðt i Þ À Z c ðt iÀ1 Þ. This is independently repeated for i ¼ 1; . . . ; k and also for Z c ðT Ã Þ À Z c ðt k Þ. For the latter case, (11), (12) , and (13) are still valid with t iÀ1 replaced by t k , t i replaced by T Ã and N À i þ 1 (in (11) and (13)) replaced by. In [23] , it is shown how to draw a sample from and from gðzÞ. For our specific case, one would do the following (which follows exactly the Appendix of that paper): We use some data simulated from the Jelinski-Moranda model to illustrate how chain length is determined. Fig. 8a shows sampled values of (see Appendix A for its definition) for the sampling of Z c ðt 28 Þ À Z c ðt 27 Þ, which show no relationship between MCMC chain length and the sampled values. In Fig. 8b , the value of Z c ðt 6 Þ À Z c ðt 5 Þ is plotted against the number of iterations in the MCMC chain between samples of j . Cases where ¼ 0 and hence no j are sampled are omitted. Again no relationship is seen between the computed values and the chain length. Given these plots, we adopt a chain of length 20,000 for and 10,000 iterations between samples of j . This proved sufficient for the NTDS data. For the simulated Weibull data described in Section 5, the same analysis led to a chain of length 100,000 for and 10,000 for j .

O O O O O O O O B O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


On the complexity of dominating set problems related to the minimum all-ones problem The minimum all-ones problem and the connected odd dominating set problem were shown to be NP-complete in different papers for general graphs, while they are solvable in linear time (or trivial) for trees, unicyclic graphs, and series-parallel graphs. The complexity of both problems when restricted to bipartite graphs was raised as an open question. Here we solve both problems. For this purpose, we introduce the related decision problem of the existence of an odd dominating set without isolated vertices, and study its complexity. Our main result shows that this new problem is NP-complete, even when restricted to bipartite graphs. We use this result to deduce that the minimum all-ones problem and the connected odd dominating set problem are also NP-complete for bipartite graphs. We show that all three problems are solvable in linear time for graphs with bounded treewidth. We also show that the new problem remains NP-complete when restricted to other graph classes, e.g., planar graphs, graphs with girth at least five, and graphs with a small maximum degree, in particular 3-regular graphs. In order to solve the complexity questions for M ODS and CODS restricted to bipartite graphs, we introduced and studied the complexity of a new variant ¬0ODS. Our main results showed that all three problems are NP-complete when restricted to bipartite graphs. For graphs with bounded treewidth, however, all three problems were shown to be solvable in linear time, by using monadic second order logic. We also studied ¬0ODS restricted to other graph classes. By using a collection of different gadgets, we could show that ¬0ODS remains NP-complete for a number of graph classes, including planar graphs, graphs with girth at least 5, and graphs in which the maximum degree is bounded by a small constant, in particular also 3-regular graphs. By the nature of the reductions we cannot apply these results to prove complexity results for M ODS or CODS when restricted to planar graphs, graphs with girth at least 5, or graphs with small maximum degree. This implies many open problems with respect to the complexity of M ODS and CODS.

O O O O O O O O O O O B I O O B I O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O