Multilevel preconditioning of rotated bilinear non-conforming FEM problems Preconditioners based on various multilevel extensions of two-level finite element methods (FEM) lead to iterative methods which often have an optimal order computational complexity with respect to the number of degrees of freedom of the system. Such methods were first presented in [6, 7] , and are based on (recursive) two-level splittings of the finite element space. The key role in the derivation of optimal convergence rate estimates plays the constant γ in the so-called CauchyBunyakowski-Schwarz (CBS) inequality, associated with the angle between the two subspaces of the splitting. More precisely, the value of the upper bound for γ ∈ (0, 1) is a part of the construction of various multilevel extensions of the related two-level methods.In this paper algebraic two-level and multilevel preconditioning algorithms for second order elliptic boundary value problems are constructed, where the discretization is done using Rannacher-Turek non-conforming rotated bilinear finite elements on quadrilaterals. An important point to make is that in this case the finite element spaces corresponding to two successive levels of mesh refinement are not nested in general. To handle this, a proper two-level basis is required to enable us to fit the general framework for the construction of two-level preconditioners for conforming finite elements and to generalize the method to the multilevel case.The proposed variants of hierarchical two-level basis are first introduced in a rather general setting. Then, the involved parameters are studied and optimized. The major contribution of the paper is the derived estimates of the constant γ in the strengthened CBS inequality which is shown to allow the efficient multilevel extension of the related two-level preconditioners. Representative numerical tests well illustrate the optimal complexity of the resulting iterative solver. In this paper we consider the elliptic boundary value problem Lu ≡ −∇ · (a(x)∇u(x)) = f (x) in Ω, u = 0 on Γ D , (a(x)∇u(x)) · n = 0 on Γ N ,. where Ω is a convex polygonal domain in R 2 , f (x) is a given function in L 2 (Ω), the coefficient matrix a(x) is symmetric positive definite and uniformly bounded in Ω, n is the outward unit vector normal to the boundary Γ = ∂Ω, and Γ =Γ D ∪Γ N . We assume that the elements of the diffusion coefficient matrix a(x) are a piece-wise smooth functions onΩ. The weak formulation of the above problem reads as follows: given f ∈ L 2 (Ω) . We assume that the domain Ω is discretized by the partition T h which is obtained by a proper refinement of a given coarser partition T H . We assume also that T H is aligned with the discontinuities of the coefficient a(x) so that over each element E ∈ T H the coefficients of a(x) are smooth functions. The variational problem (2) is then discretized using the finite element method, i.e., the continuous space V is replaced by a finite dimensional subspace V h . Then the finite element formulation is: find u h ∈ V h , satisfying. a(e)∇u h · ∇v h dx.. Here a(e) is a piece-wise constant symmetric positive definite matrix, defined by the integral averaged values of a(x) over each element from the coarser triangulation T H . We note that in this way strong coefficient jumps across the boundaries between adjacent finite elements from T H are allowed. The resulting discrete problem to be solved is then a linear system of equations. with A h and F h being the corresponding global stiffness matrix and global right hand side, and h being the discretization (meshsize) parameter for the underlying partition T h of Ω. The aim of this paper is to investigate multilevel preconditioners of optimal complexity for solving the system (4). The general setting and some well-known results for the case of conforming finite elements are summarized in the rest of this section. The next sections are devoted to the study of twolevel and multilevel preconditioners for the case of non-conforming Rannacher-Turek finite elements. A unified hierarchical splitting of the FEM spaces is developed, followed by uniform estimates of the related CBS constants. The numerical results that are presented towards the end of the paper are completed by some concluding remarks. This study is strongly motivated by the expanding interest in non-conforming finite elements, which are very helpful for solving problems, where the standard conforming elements suffer from so-called locking effects. The success of the non-conforming finite elements can be often explained e.g. by the fact that they produce algebraic systems that are equivalent to the Schur complement system for the Lagrange multipliers arising from the mixed finite element method for Raviart-Thomas elements (see [1] ). In this paper, we presented a general setting of hierarchical splittings of the Rannacher-Turek non-conforming FEM spaces. New estimates for the constant in the strengthened CBS inequality are derived for the considered model problem.. At this stage of the study we underline the following issues.. • The DA algorithm allows for a direct extension of the γ estimate to the multi-level case if the condition (ii) holds. However, the latter is not a trivial problem even for the considered anisotropic model problem. In the general case, we are not able to say anything about the existence of a DA splitting satisfying condition (ii) so far.. • For the FR algorithm, the theoretically derived estimates of the CBS constant γ are not directly applicable to the multilevel case. However, the recursively computed γ-s show a very promising behaviour which could be advantageous from a practical point of view.. • The numerical tests fully confirm the theoretical estimates. Moreover, they indicate some selfstabilization of the FR algorithm and the nonlinear AMLI which is especially important for the case of stronger anisotropy.

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 O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 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 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 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


Real-time visuomotor update of an active binocular head Abstract In order for a binocular head to perform optimal 3D tracking, it should be able to verge its cameras actively, while maintaining geometric calibration. In this work we introduce a calibration update procedure, which allows a robotic head to simultaneously fixate, track, and reconstruct a moving object in real-time. The update method is based on a mapping from motorbased to image-based estimates of the camera orientations, estimated in an offline stage. Following this, a fast online procedure is presented to update the calibration of an active binocular camera pair. The proposed approach is ideal for active vision applications because no image-processing is needed at runtime for the scope of calibrating the system or for maintaining the calibration parameters during camera vergence. We show that this homography-based technique allows an active binocular robot to fixate and track an object, whilst performing 3D reconstruction concurrently in real-time. The estimation of scene-structure from a binocular image pair is an important task in robot vision. Once the epipolar geometry between the two cameras is known, image-features can be matched more easily, and depth information can be recovered (Hartley and Zisserman, 2004) . For an active binocular robot head, which continuously fixates a moving target, a real-time method for updating the relationship between the cameras is required. Such an online method would allow independent or coupled camera vergence rotations while maintaining geometric calibration. This will enable the robot to perform 3D reconstruction while actively examining different parts of the scene, or while tracking a moving object (Grosso and Tistarelli, 1995; Barreto et al, 2010; Hansard and Horaud, 2008) . Furthermore, this online calibration update must be computationally efficient if it is to be used alongside other complex algorithms such as object tracking and 3D reconstruction.. Popeye is an active binocular robot (POP Consortium, 2008) , which reproduces the sensory configuration of the human head (Fig. 1) . The orientation of the robot head (pan/tilt) is controlled by motors, as is the direction of the eyes (version/vergence). The robot can therefore direct its attention towards a visual stimulus in its surroundings using combined stereo and tracking techniques (Bellotto and Hu, 2010) . The advantage of an active vision system is that information about the environment can be gathered more efficiently, by appropriately re-orienting the cameras. Hence visual information is combined with motor control, in a feedback loop, which enables the robot to react to a dynamic environment (Bajcsy, 1988) . The results described in section 3.4 show that the new method of homography-generation is sufficiently accurate for practical use. For example, the method can be used to predict the coordinates of image-features, after controlled rotations of the cameras. The method is also useful for binocular vision, in which the fundamental matrix is updated as described in section 1.2. Furthermore, the new method is also fast, because the mapping (b) The active head has detected a face and begins to track its movement whilst reconstructing matched points in this region of interest.. (c) As the target moves closer to the camera, the vergence angle between the cameras is updated to continually maintain fixation. from motor settings to image transformations is only estimated once. No additional point-correspondences are needed at run-time, and so computationally expensive feature-extraction and matching is avoided. The methods described here have enabled active tracking and image-stabilization to be performed in real-time by the Popeye robot.. Future work will consider more complicated models for the mapping φ ≈ f (θ, η) which relates the motor and homography angles (3). It is expected that the method can be extended, in this way, to systems that have poor alignment between the optical and rotational centres. Finally, the idea of estimating the relationship between control-based and image-based parameters could be applied to other visual processes, such as active zoom. The results obtained after computing the RMS transfer error for our motor-image method, over all six data sets, 2 was 2.09 pixels (in the 1024 × 768 images). The maximum and standard deviation of the transfer errors were 6.68 and 1.16 pixels, respectively. The purely image-based method achieved an RMS transfer error of 1.03, and a maximum and standard deviation of 3.28 and 0.58 pixels respectively. The plots in Fig. 9 show a breakdown of the errors across the two cameras, nine angles and three experimental trials.. Note that image-based results are representative of an ideal case, in which sufficient stable points and perfect correspondences are available to the algorithm. In practice, an automatic interest point detector and correspondence algorithm will have to cope with low textured scenes, and imperfect matches. The results from Fig. 9 show that in an ideal case, the purely image-based method will produce lower pixel errors. However, a collection of independently fitted homographies has many more parameters than our synthesis model, so indeed they should produce a better fit. Let N c and N r denote the number of monocular cameras and monocular camera rotations respectively. Then, the number of estimated parameters for the image-based method is 8 × N r × N c , estimated online (H has 8 degrees of freedom). For the motor-image method, the number of parameters is (1 + 8) × N c , estimated offline (1 dof from φ, and 8 from the U matrix). U has at most eight degrees of freedom, as it is obtained from the 3 × 3 matrix H , which is defined up to an overall scale. More importantly, it is clearly seen that the number of parameters estimated by our method does not depend on the number of camera rotations, N r . For example in our experiments, the number 2 The statistics were computed after excluding the 'perfect' values at θ = 0.. Left Camera Note that H 0 = I , by definition, and so there is no error at θ = 0. The image-based method (green) represents the best case scenario where there are sufficient stable points, prefect correspondences, and necessary scene structure to avoid degenerate cases. Our motor-image approach (black) shows performance in practice and does not require point correspondences, scene texture or a particular structure.. of estimated parameters totalled 8 × 8 × 2 = 128 for the image based method, and (1 + 8) × 2 = 18 for the motor-camera method.. It is additionally important to point out that for our motor-image based technique, the scene-structure or texture is of no particular importance; each image-point could represent any scene-point on the corresponding ray (as indicated in Fig. 2) . Hence the motor-image based results generalize immediately to any scene.. In contrast, purely image-based methods do depend on the scene texture and structure to compute feature correspondences and to avoid degenerate cases. In the case where F is re-estimated online, at least n ≥ 7 point correspondences are needed after each camera rohal-00768615, version 2 -22 Dec 2012 tation, subject to the points being in general 3D position. This means that the points must not lie on (or near) a plane or other 'degenerate' surface, (Hartley and Zisserman, 2004) . The image based method to which we compare involves the re-estimation of homographies to update F . In order to compute each H , at least four (no three collinear) point correspondences per camera rotation are required. Since the motor-image method does not depend on computing H from feature point correspondences, it is not susceptible to the degeneracies described above, making it invariant to scene texture and structure. A complete theoretical error analysis of the epipolar geometry (Csurka et al, 1997; Brandt, 2008) is beyond the scope of this work.. In these experiments we have shown that our method accounts for small misalignments in the optical and rotational camera centres. The development of a similar approach which accounts for the purposeful misalignment of camera rotation and optical centres (Hayman and Murray, 2003) is left for future work. In order to preserve the calibration of the stereo system after camera vergence, one could continually recalibrate the system. This would, however, be very difficult to perform in real-time. A more efficient method would be to calibrate the system once, and then to update this calibration as the cameras move. This technique was used in (Björkman and Eklundh, 2002) , where the epipolar geometry was updated by extracting information from feature correspondences in the current images. This required an iterative approach to estimate the stereo-head geometric parameters, which is computationally expensive. Furthermore, such an approach ignores kinematic information that can be used to improve the real-time performance of the system. The problem was also tackled in (Hart et al, 2002) who developed an epipolar-kinematic model in which motor data is used to compute an updated representation of the epipolar geometry. The kinematics of the system are obtained by rotating the cameras and observing the relationship between the images of two views before and after the rotation. After this calibration procedure, the essential matrix (Hartley and Zisserman, 2004) can be updated, provided that the current settings of the camera motors are known. This approach allows computation of the essential matrix in real-time. Related methods can be used to coordinate an active camera with a static camera (Horaud et al, 2006) .. The Popeye robot belongs to a class of active binocular robot heads with very accurate motors (Shih et al, 1998; Aryananda and Weber, 2004; Beira et al, 2006; Miwa et al, 2002) . Moreover, the design of the eye pan mechanical structures allows each camera position to be precisely adjusted to achieve close agreement between the optical and rotational centres of the cameras. This permits a direct approach to epipolar-update, as described in section 2. The accuracy and negligible backlash of the DC brushed motors ensures the repeatability of the new method, as demonstrated in section 3.. The present work is closely related to certain autocalibration procedures (Hartley, 1997; Ruf and Horaud, 1999; Knight and Reid, 2006) , in which constrained movements are used to estimate the camera parameters. The aim of the present work is somewhat different; we estimate a direct mapping from motor-settings to image-transformations, without explicitly estimating the calibration parameters.. The paper is organized as follows. The problem definition and main contributions of this work are stated in sections 1.2 and 1.3. Sections 2.1, 2.2 and 2.4 describe the estimation, analysis and synthesis of homographies, respectively. The new method is based on the statistical model (3), which allows for uncertainty in the homography estimates, as defined in section 2.3. Section 3 describes the results of experiments using Popeye. The conclusions of the work are stated in section 4. The update-procedure will now be presented, in order of execution. Most importantly, section 2.3 introduces a model and solution for the angle mapping (3).

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Integrating user preferences with particle swarms for multi-objective optimization This paper proposes a method to use reference points as preferences to guide a particle swarm algorithm to search towards preferred regions of the Pareto front. A decision maker can provide several reference points, specify the extent of the spread of solutions on the Pareto front as desired, or include any bias between the objectives as preferences within a single execution. We incorporate the reference point method into two multi-objective particle swarm algorithms, the non-dominated sorting PSO, and the maximinPSO. This paper first demonstrates the usefulness of the proposed reference point based particle swarm algorithms, then compare the two algorithms using a hyper-volume metric. Both particle swarm algorithms are able to converge to the preferred regions of the Pareto front using several feasible or infeasible reference points. The use of evolutionary algorithms in the field of multiobjective optimization has been a very popular area of research in the last decade [5] . Recently there has been an increasing interest to incorporate user-preference mechanisms seen in the Multi-Criteria Decision Making (MCDM) [11] literature into these Evolutionary Multi-objective Optimization (EMO) algorithms [2, 7, 8, 9, 22] . In this paper we Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. To copy otherwise, to republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. GECCO'08, July 12-16, 2008 , Atlanta, Georgia, USA. Copyright 2008 ACM 978-1-60558-130-9/08/07…$5.00.. describe an attempt to integrate a preference method using reference points with Particle Swarm Optimization (PSO) algorithms. These PSO algorithms can be used effectively to direct the search to preferred regions of the Pareto front. We will demonstrate how to integrate the reference point method into two multi-objective PSO algorithms, the nondominated sorting PSO (NSPSO) [16] and maximinPSO [17] , and provide a comparison of their performance.. User-preference methods as described in the MCDM literature come in two forms. 1) A priori methods, where a Decision Maker (DM) gives preferences first then the algorithm finds solutions considering those preferences; 2) A posteriori methods, where after an algorithm provides all possible solutions the DM selects the interesting ones [19] . The reference point method is an a priori approach, where first the DM provides reference points in the objective-space and the search algorithm will concentrate around those points to find solutions. The advantage is that most computing effort can be spent on the preferred areas, instead of the entire search-space. This is especially important as the number of objectives increases.. PSOs have been very successful as EMO algorithms [21] . This paper shows that using reference points as preferences, a PSO can be guided towards desired regions of the searchspace. We also propose a comparison mechanism for user preference based EMO algorithms using the hyper-volume metric. This mechanism is illustrated in the comparison of the reference point based NSPSO and maximinPSO algorithms.. The paper is organized as follows. Section 2 briefly describes the background material for the study including the formal definitions of multi-objective optimization, particleswarms and the reference point method. Section 3 presents related work carried out in the field. Section 4 presents our algorithms. The experiments used to evaluate the algorithms will be provided in section 5. Finally, in section 6, we present our conclusions and avenues for future research. In this study we have shown that a reference point based guidance can be successfully integrated into two PSO algorithms. The DM can specify varying spread as desired near multiple reference points. Bias on certain objectives can be also achieved. Our experiments showed that the proposed multi-objective PSO algorithms incorporating preferences are able to guide the search to several preferred areas of a Pareto front for both two and three-objective problems in a single run. The HV values demonstrated to be a useful metric for comparing user-preference based EMO algorithms.. The reference point is just one preference method that can be integrated into multi-objective PSO algorithms. We plan to extend this research by integrating other approaches like the light beam search. We also would like to investigate other suitable metrics, which can be used for comparing user-preference based EMO algorithms. User-preference methods are used extensively in the classical optimization methods in MCDM literature [11] . A survey by Miettinen [19] shows many different a priori and a posteriori methods for nonlinear multi-objective optimization problems. However, most existing EMO algorithms are a posteriori methods, since they perform a search first before presenting a set of final solutions to the DM. This section presents some of the early EMO algorithms incorporating a priori methods.. Deb [4] proposed a goal programming approach with Genetic Algorithms (GA) as a mechanism to find solutions to multi-objective problems. A modified NSGA algorithm was used to find a set of points closest to the supplied goal, which is a set of aspiration values for each objective. This approach did not care if the solutions were not found on the Pareto front. This is because; if the goal was in the feasible region then the algorithm is directed to that solution point. If the goal was in the infeasible region then the solution points closest to the goal was obtained.. Branke et al. [2] proposed the Guided Multi-Objective Evolutionary Algorithm (G-MOEA), where the definition of dominance was modified using the preferences given by the DM. Here the DM can provide accepted tradeoff values for each objective in a two-objective optimization problem. The tradeoff values for each objective gives a notion of preference between the two objectives. This provides guidance to the algorithm.. Thiele et al. [22] proposed an interactive EMO based on preferences. First, a rough idea of the Pareto front is presented to the DM, who then specifies some reference points as desired. The algorithm will then concentrate the search around these reference points. This method is a two-step approach since the algorithm must first find an approximate Pareto front and then incorporate the reference points.. Most recently Deb et al. [9] presented an EMO incorporating the reference point method into NSGA-II. This work was then extended to incorporate the reference direction method [7] . In a later study [8] the light beam search method [13] was integrated into NSGA-II. These studies showed that user-preference methods can be successfully integrated into GA. However, a performance metric for these user-preference based EMO algorithms was yet to be proposed. This paper extends the research in [9] by introducing reference point based PSOs. We use the HV metric as a comparison mechanism for user-preference based EMO algorithms. We will first present the background material used in this research, then give some examples of similar work in the field. We used two-objective problems from the ZDT test problem suite [23] and three-objective problems from the DTLZ test problem suite [10] . We will first demonstrate that the PSO variants can be guided using reference points and achieve various spread and bias of objectives on the Pareto front. Then we will compare the maximinPSO and NSPSO using the HV metric with varying population sizes.. The following two-objective problems were used: ZDT1 (convex Pareto optimal front), ZDT2 (concave Pareto optimal front), ZDT3 (disjoint convex Pareto optimal front) all having 30 decision variables each. DTLZ6 (concave Pareto optimal region) and DTLZ7 (disjointed Pareto optimal regions) were used as the three-objective problems. There were 12 and 22 decision variables for DTLZ6 and DTLZ7 respectively. For every decision variable xi ∈ [0.0, 1.0] in all the test problems. We set the maximum number of iterations to 500 for the two-objective problems and 750 for the three-objective problems. feasible region, while the other two reference points are in the feasible region. Figure 4 illustrates the result for maximinPSO at the end of 110 iterations. Figure 5 shows different values of δ depicting the spread of solutions near the reference point (0.2, 0.5), for the maximinPSO. For results in Figure 4 the spread was set to δ = 0.001. NSPSO depicted a similar behaviour for the solution points and spread on the Pareto front as the maximinPSO for the same reference points.

O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 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 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 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 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 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 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 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 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 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 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


Object-based tag propagation for semi-automatic annotation of images Over the last few years, social network systems have greatly increased users' involvement in online content creation and annotation. Since such systems usually need to deal with a large amount of multimedia data, it becomes desirable to realize an interactive service that minimizes tedious and timeconsuming manual annotation. In this paper, we propose an interactive online platform that is capable of performing semi-automatic image annotation and tag recommendation for an extensive online database. First, when the user marks a specific object in an image, the system performs an object duplicate detection and returns the search results with images containing similar objects. Then, the annotation of the object can be performed in two ways: (1) In the tag recommendation process, the system recommends tags associated with the object in images of the search results, among which, the user can accept some tags for the object in the given image. (2) In the tag propagation process, when the user enters his/her tag for the object, it is propagated to images in the search results. Different techniques to speed-up the process of indexing and retrieval are presented in this paper and their effectiveness demonstrated through a set of experiments considering various classes of objects. In recent years, social networks, digital photography and web-based personal image collections have gained popularity. A social network service typically focuses on building online communities of people who share interests and activities, or are interested in exploring the interests and activities of others. At the same time, they have become a popular way to share and to disseminate information, creating new challenges for access, search and retrieval. For example, users upload their personal photos and share them through online communities, asking other people to comment or rate them. This trend has resulted in a continuously growing volume of publicly available photos on multimedia sharing websites like Flickr 1 , or social networks like FaceBook 2 . For instance, Flickr contains over 3.6 billion photos [2] , and every month more than 2 billion photos are uploaded to FaceBook [1] .. In these environments, photos are usually accompanied with metadata, such as comments, ratings, information about the uploader and their social network. Moreover, a recent trend is also to "tag" them. Tags are short textual annotations used to describe photos in order to provide meaningful information about them.. The most popular tags in photo sharing sites such as Flickr are usually related to the location where the photo was taken (e.g., San Francisco or France), the objects/persons appearing in the photo (e.g., baby, car or house), or the event/time when the photo was taken (e.g., wedding or summer) [3, 17] .. Annotations and their association with images provide a powerful cue for their grouping and indexing. This cue is also essential for image retrieval systems to work in practice. The current state-of-the-art in content-based image retrieval systems has not yet delivered widely accepted solutions, except for some very narrow application domains, mainly because of the semantic gap problem, i.e., it is hard to extract semantically meaningful information using just low-level features [19] . In social networks, the success of Flickr and FaceBook proves that users are willing to provide this semantic context ("subjective" users' impressions) through manual annotations [17] , which can help to bridge the semantic gap, and therefore improve the results of visual content search engines. Different users who annotate the same photo can provide different annotations, which is one more advantage of these systems.. However, tagging a lot of photos by hand is a time-consuming task. Users typically tag a small number of shared photos only, leaving most of them with incomplete metadata. This lack of metadata seriously impairs search, as photos without proper annotations are typically much harder to find. Therefore, robust and efficient algorithms for automatic or semi-automatic tagging (or tag propagation) are desirable to help people organize and browse large collections of personal photos in an efficient way.. The main novelty of the paper comes from the application which realizes an interactive service that minimizes the users' tedious and time-consuming manual annotation process, and the evaluation of the object duplicate detection part of the system. We propose an interactive online platform which is capable of performing semi-automatic image annotation and tag recommendation for an extensive online database of images containing various object classes. Since the most salient regions in images usually correspond to specific objects, we consider object-based tagging within the system. First, when the user marks a specific object in an image, the system performs an object duplicate detection and returns the search results with images containing similar objects. Then, the annotation of the object can be performed in two ways, i.e., tag recommendation and tag propagation. In the tag recommendation mode, the system recommends tags for the object within the query image. The corresponding tags of all matched objects within the retrieved images are shown to the user who can then select appropriate tags among them. In the tag propagation mode, when the user enters his/her tag for the object, it is propagated to other images containing similar objects.. The remaining sections of this paper are organized as follows. We introduce related work in Section 2. Section 3 describes our approach for the interactive online platform and discusses the two modes, tag recommendation and tag propagation. Experiments and results are discussed in Section 4. Finally, Section 5 concludes the paper with a summary and some perspectives for future work. Social networks are gaining popularity for sharing interests and information. Especially photo sharing and tagging is becoming increasingly popular. Among others, tags of people, locations, and objects provide efficient information for grouping or retrieving images. Since the manual annotation of these tags is quite time consuming automatic tag propagation based on visual similarity offers a very interesting solution.. In this work we have developed an efficient system for semi-automatic object tagging in images. After marking desired object in an image, the system performs object duplicate detection in the whole database and returns the search results with images containing similar objects. Then, the annotation can be performed through a tag recommendation process, in which the system recommends tags associated with the object in the images of the search results, or through tag propagation process, when the user enters his/her tag for the object and it is propagated to the images in the search results.. The performance of the system has been assessed by evaluating the performance of the object duplicated detection step, since both tag recommendation and propagation rely on its outcome. It has been shown that the detection works reliably for salient objects such as trademarks, books, newspapers, and gadgets.. Our semi-automatic tag propagation system has the potential to be improved in many ways. As a future study, we will extend it to support other classes of objects and consider evaluation of the system in the view point of the database size and latency in the system because it is important for the system to be interactive. Since our interactive system supports interaction between users, future work can also focus on modeling users' trust in such a manner that only tags from trusted users are finally propagated. In order to determine the optimal threshold for the object duplicate detection, the F-measures across the different thresholds has been computed. Figure 7 shows the threshold versus F-measure curve. The optimal threshold of 50 is chosen for the maximum F-measure of 0.49 and shown in all related figures by green markers. The final F-measure averaged over the whole dataset is 0.48. The tag recommendation will be more supported than the tag propagation because the propagation is more sensitive to the performance of the object duplicate detection.. In order to compare the different classes with each other, the F-measure is computed for each of the object classes as shown in Figure 8 . Trademarks perform best, thanks to the large number of salient regions. In the case of text or cover pages of newspapers, books or gadgets, the proposed tag propagation scenario performs worse because the objects do not have enough discriminative features. Shiny or rotated objects, such as cars, shoes or buildings, are hard to detect due to the changing reflections and varying viewpoint. The proposed system is related to different research fields including visual content analysis, social networking and tagging. The goal of this section is to review the most relevant works on human tagging and various approaches for tag recommendation.. Tagging images is a very time consuming process and tagging objects within images even more. Therefore, it is necessary to understand and increase the motivation of users to annotate images. Ames and Naaman [5] have explored different factors that motivate people to tag photos in mobile and online environments. One way is to decrease the complexity of the tagging process through tag recommendation which derives a set of possible tags from which the user can select suitable ones. Another way is to provide incentives for the user in form of entertainment or rewards. The most famous examples are the ESP Game and Peekaboom, developed for collecting information about image content. The ESP Game [21] randomly matches two players who are not allowed to communicate with each other. They are shown the same image and asked to enter a textual label that describes it. The aim is to enter the same word as your partner in the shortest possible time. Peekaboom [22] takes the ESP Game to the next level. Unlike the ESP Game, it's asymmetrical. To start, one player is shown an image and the other sees an empty black space. The first user is given a word related to the image, and the aim is to communicate that word to the other player by revealing portions of the image. Peekaboom improves on the data collected by the ESP Game and for each object in the image determines precise location information. Unlike these games, LabelMe is a web-based tool that allows easy image annotation and sharing of such annotations [16] . Using this tool, a large variety of annotations are collected spanning many object categories (cars, people, buildings, animals, tools, etc.).. However, manually tagging a large number of photos is still a tedious and time-consuming task. Thus automatic image annotation has received a lot of attention recently. Automatic image annotation is a challenging task which has not been solved in a satisfactory fashion for real-world applications. Most of the solutions are developed for a specific application and usually consider only one tag type, e.g., faces, locations, or events.. Berg et al. [8] propose an approach to label people, i.e. assign names to faces within newspapers (images with captions). They cluster face images visually in appropriate discriminant coordinates and apply natural language processing techniques to the caption to check whether the person whose name appears in a caption is depicted in the associated image or not. Picasa 3 also provides a service for name tagging which automatically finds similar faces in a photo collection.. Annotating images with geographical information such as landmarks and locations is a topic which has recently gained increasing attention. Ahern et al. [4] have developed a mobile application called ZoneTag 4 which enables the upload of context-aware photos from mobile phones equipped with a camera to Flickr. In addition to automatically supplying the location metadata for each photo (provided by a GPS device or mobile phone), ZoneTag supports context-based tag suggestions in which tags are provided from different sources including past tags from the user, the user's social network, and external geo-referenced data sources like Yahoo! Local, and Upcoming.org. Through the combination of textual information with vision based methods efficient systems for tag recommendation and propagation can be developed. Kucuktunc et al. [10] incorporate visual and textual cues of semantically relevant photos to recommend tags and to improve the quality of the suggested tags. First, the system requires the user to add a few initial tags for each uploaded photo. These initial tags are used to retrieve related photos which contain other tags besides the initial ones. Then the set of candidate tags collected from a pool of images is weighted according to the similarity of the target photo to the retrieved photo. Similarity is based on visual features including color histograms and SIFT features. Finally, a scoring function is applied to the list of candidate tags and the tags with the highest scores are used to automatically expand the tags of the target photo. This approach has its limitations, since users typically do not provide initial tags for each uploaded photo, but rather tag only a small number of shared photos.. Another application that combines textual and visual techniques has been proposed by Quack et al. [15] . They developed a system that crawls photo collections on the internet to identify clusters of images referring to a common object (physical items on fixed locations), and events (special social occasions taking place at certain times). The clusters are created based on the pair-wise visual similarities between the images, and the metadata of the clustered photos is used to derive a label for the clusters. Finally, Wikipedia 5 articles are attached to the images and the validity of these associations is checked. Gammeter et al. [9] extends this idea towards object-based auto-annotation of holiday photos in a large database that includes landmark buildings, statues, scenes, pieces of art, with help of external resources such as Wikipedia. In both papers, [9] and [15] , GPS coordinates are used to pre-cluster objects which limit classes of objects to landmarks and buildings. Another limitation is that GPS coordinates may not be always available. In contrast, our work considers extensive online database of various object classes, such as landmark buildings, cars, cover or text pages of newspapers, shoes, trademarks and different gadgets like mobile phones, cameras, watches.. Lindstaedt et al. [11] developed tagr a tag recommendation system for pictures which depict fruits and vegetables. They combine three types of information: visual content, text and user context. At first, they group annotated images into classes using global color and texture features. The user defined annotations are then linked with the images. The resulting set of tags for visually similar images is then extended with synonyms derived from WordNet. When the user uploads an untagged image, it is assigned to one of the classes and corresponding tags are recommended to the user. In addition, this system analyzes tags which the user assigns to the images and returns the profiles of users with similar tagging preferences. This method has been proven to be effective to recommend tags for a set of selected fruits and vegetables, but it cannot be applied to other classes of objects, which limits its applicability. Other approaches for automatic image annotation consider only the context. Sigurbjörnsson and van Zwol [17] developed a system which recommends a set of tags based on collective knowledge extracted from Flickr. Given a photo with user-defined tags, a new list of candidate tags is derived for each of the userdefined tags, based on tag co-occurrence. The lists of candidate tags are aggregated, tags are ranked, and a new set of recommended tags is provided to the user.. The tag propagation and tag recommendation are nowadays very important in environment such as social network, since they provide efficient information for grouping or retrieving images. The system proposed in this paper provides these functionalities in an interactive way. The novelty is that image annotation is performed at the object level by making use of content based processing. It does not consider context, such as text or GPS coordinates, which may limit its applicability. This approach is suitable for all kinds of objects, such as trademarks, books, newspapers, and not just buildings or landmarks. In this section the performance of the proposed tag propagation and tag recommendation methods are evaluated and analyzed in two application scenarios. The considered dataset is described in Section 4.1. In Section 4.2 the evaluation is presented, and finally the results are discussed for both scenarios in Section 4.3.

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


Algorithms and data structures for massively parallel generic adaptive finite element codes Today's largest supercomputers have 100,000s of processor cores and offer the potential to solve partial differential equations discretized by billions of unknowns. However, the complexity of scaling to such large machines and problem sizes has so far prevented the emergence of generic software libraries that support such computations, although these would lower the threshold of entry and enable many more applications to benefit from large-scale computing.We are concerned with providing this functionality for mesh-adaptive finite element computations. We assume the existence of an "oracle" that implements the generation and modification of an adaptive mesh distributed across many processors, and that responds to queries about its structure. Based on querying the oracle, we develop scalable algorithms and data structures for generic finite element methods. Specifically, we consider the parallel distribution of mesh data, global enumeration of degrees of freedom, constraints, and postprocessing. Our algorithms remove the bottlenecks that typically limit large-scale adaptive finite element analyses.We demonstrate scalability of complete finite element workflows on up to 16,384 processors. An implementation of the proposed algorithms, based on the open source software p4est as mesh oracle, is provided under an open source license through the widely used deal.II finite element software library. Computer clusters with tens of thousands and more processor cores are becoming more and more common and are going to form the backbone of most scientific computing for the currently foreseeable future. At the same time, the number of codes that efficiently utilize these machines is relatively limited, due in large part to two reasons: (i) existing legacy codes are difficult to parallelize to these massive numbers of processors since data structures have to be conceived entirely differently; (ii) algorithm and data structure design is not trivial when the goal is to exploit machines of this size in a scalable way.. In the past, continuum mechanics codes-for example based on the finite element method-have been among the largest consumers of supercomputing resources. The desire to run such codes on "massively" parallel machines dates back to at least the early 1990s [Mathur et al. 1993; Devine et al. 1993; Tezduyar et al. 1994] , although the notion of what constitutes a large machine has evolved since then. On the other hand, codes that scale to the largest available machines were then, and are now, almost exclusively purpose-built for individual applications. For example, the codes SPECFEM3D [Carrington et al. 2008] , CitcomS [Tan et al. 2008] , and Rhea [Burstedde et al. 2008a ] have been written for particular geophysical applications and are not based on general-purpose finite element libraries. The reason, of course, is that none of the libraries widely used in academic and applied finite element simulations-such as PLTMG [Bank 1998 ], DiffPack [Bruaset and Langtangen 1997; Langtangen 2003 ], libMesh [Kirk et al. 2006] , Getfem++ [Renard and Pommier 2006] , OOFEM [Patzák and Bittnar 2001] , FEniCS/DOLFIN [Logg 2007; Logg and Wells 2010] , or deal.II up to version 6.x [Bangerth et al. 2007; Bangerth and Kanschat 2011] -support massively parallel computations that will run on thousands of processors and routinely solve problems with hundreds of millions or billions of cells and several billion unknowns.. This notwithstanding, there clearly is a demand for general-purpose finite element libraries supporting such computations through a relatively simple, generic interface. In this article, we will outline the algorithms that we have implemented in version 7.0 of the open source library deal.II, offering the ability to solve finite element problems on fully adaptive meshes of the sizes mentioned previously to a wider community. While deal.II provides a reference implementation of both the mentioned algorithms as well as of tutorial programs that showcase their use in actual applications, our goal is to be generic and our methods would certainly apply to other finite element libraries as well. In particular, we will not require specific aspects of the type of finite element, nor will the algorithms be restricted to quadrilaterals (2d) and hexahedra (3d) that are used exclusively in deal.II.. When using thousands of processors 1 in parallel, two basic tenets need to be followed in algorithm and data structure design: (i) no sizable amount of data can be replicated across all processors, and (ii) all-to-all communications between processors have to be avoided in favor of point-to-point communication where at all possible. These two points will inform to a large part what can and cannot work as we scale finite element computations to larger and larger processor counts. For example, even if it would make many operations simpler, no processor will be able to hold all of the possibly billions of cells contained in the global mesh in its local memory, or even be able to compute a threshold for which cells exceed a certain error indicator and should therefore be refined.. In this article, we will not be concerned with the question of how to efficiently generate and partition hierarchically refined meshes on large numbers of processors, which presents a major challenge on its own. Rather, we will assign this task to an "oracle" that allows deal.II to obtain information on the distributed nature of the mesh through a well-defined set of queries. These include for example whether a certain cell exists on the current processor, or whether it is a "ghost" cell that is owned by another processor. Using queries to the oracle, each processor can then rebuild the rich data structures necessary for finite element computations for the "locally owned" part of the global mesh and perform the necessary computations on them. In our implementation, we use the p4est algorithms for 2d and 3d parallel mesh topology [Burstedde et al. 2011b] as the oracle; however, it is entirely conceivable to connect to different oracle implementations-for example, packages that support the ITAPS iMesh interface [Ollivier-Gooch et al. 2010 ]-provided they adhere to the query structure detailed in this article, and can respond to certain mesh modification directives discussed below.. We will detail the requirements deal.II has of the mesh oracle, a description of the way p4est works, and the algorithm that builds the processor-local meshes in Section 2. In Section 3, we will discuss dealing with the degrees of freedom defined on a distributed mesh. Section 4 will then be concerned with setting up, assembling and solving the linear systems that result from the application of the finite element method; Section 5 discusses the parallel computation of thresholds for a-posteriori error indicators and postprocessing of the solution. In reality, today's supercomputers do not consist of a set of equal, interconnected single-processor machines; rather, they have multicore chips and may have general-purpose graphics processing units (GPUs). Section 6 reviews our designs in light of these considerations on processor architecture and argues that, at least given the current state of parallel linear algebra and solver software, using a "flat" MPI space consisting of single-threaded processes is still the most practical choice. We provide numerical results that support the scalability of all proposed algorithms in Section 7 and conclude in Section 8. In this article, we present a set of algorithms and data structures that enable us to parallelize all computations associated with adaptive finite element methods. The design of our methods is based on a complete distribution of all data structures and avoiding global communication wherever possible in favor of scatter/gather and pointto-point operations. However, the key to making this work in practice is not only to distribute storage but also to think about the details of finite element applicationssuch as constraints on degrees of freedom or sparsity patterns-and in particular what kind of information each processor needs. The question of what processors need to know about what happens on ghost cells turns out to be crucial to the correctness of resulting programs.. The numerical results presented in Section 7 demonstrate that we can achieve optimal scalability for those components of the two finite element applications that are within the scope of this article. In particular, we could show that all operations scale linearly with the overall problem size (with fixed number of processors) and with the number of processors (with fixed problem size, at least for large enough problems). While we have only shown results for up to 16,384 processors, these scaling results indicate that the methods presented here are likely to scale significantly further once the required technology for the solution of even larger problems becomes available in linear solver packages.. Given the complexity and size of typical finite element libraries, it must necessarily be a significant concern to convert such codes to support massively parallel computations. In Section 2, we lay out one avenue to perform such a conversion. There, we show how an existing finite element library can be extended to support fully distributed meshes by using an external scalable adaptive-mesh provider which we refer to as an "oracle". This oracle has to answer a small number of relatively simple questions, and to encapsulate mesh modification directives for refinement and coarsening, 2:1 mesh balance, and re-partitioning. In our case, the interface between the deal.II library and the oracle p4est has only around 600 lines of code (lines of C++ code with a semicolon on it), and the entire extension of deal.II to support distributed parallel computations required us to write only approximately 10,000 lines of code (some 2,000 of which have a semicolon, the majority of the rest being comments and class or member documentation). The external p4est implementation contains about 25,000 lines of code. These numbers have to be compared with the overall size of the deal.II library of currently approximately 540,000 lines and its average growth per month of 4,000 lines. A major benefit of this approach is that it allows us to re-use almost all of the existing code that has been validated for years.. Generally, we believe that our implementation of the methods introduced here can be used with relative ease by applications developers. For example, the step-40 tutorial program used in Section 7.1 has only around 150 lines of code, which can be compared to the 125 lines in its sequential predecessor step-6 upon which it is based. As a consequence, we believe that our work not only shows the efficiency of our approach with respect to scaling to very large problems, but also the possibility of implementing these methods efficiently with respect to code complexity. We also hope that this article may serve as a guideline to realize dynamic mesh parallelization within other numerical software packages, and thus can help making true scalability available to an even broader range of scientists.. The results of our work are available under an open source license starting with release 7.0 of the deal.II library, as well as through two extensively documented tutorial programs-step-32 and step-40-that explain the use of these techniques and their implementation.

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 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 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 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 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 O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 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 O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


Modelling long-memory volatilities with leverage effect: A-LMSV versus FIEGARCH In this paper, we propose a new stochastic volatility model, called A-LMSV, to cope simultaneously with the leverage effect and long-memory. We derive its statistical properties and compare them with the properties of the FIEGARCH model. We show that the dependence of the autocorrelations of squares on the parameters measuring the asymmetry and the persistence is different in both models. The kurtosis and autocorrelations of squares do not depend on the asymmetry in the A-LMSV model while they increase with the asymmetry in the FIEGARCH model. Furthermore, the autocorrelations of squares increase with the persistence in the A-LMSV model and decrease in the FIEGARCH model. On the other hand, the autocorrelations of absolute returns increase with the magnitude of the asymmetry in the FIEGARCH model while they can increase or decrease depending on the sign of the asymmetry in the L-MSV model. Finally, the cross-correlations between squares and original observations are, in general, larger in the FIEGARCH model than in the A-LMSV model. The results are illustrated by fitting both models to represent the dynamic evolution of volatilities of daily returns of the S&P500 and DAX indexes. October 2006 AbstractIn this paper, we propose a new stochastic volatility model, called A-LMSV, to cope simultaneously with the leverage effect and long-memory. We derive its statistical properties and compare them with the properties of the FIEGARCH model. We show that the dependence of the autocorrelations of squares on the parameters measuring the asymmetry and the persistence is different in both models. The kurtosis and autocorrelations of squares do not depend on the asymmetry in the A-LMSV model while they increase with the asymmetry in the FIEGARCH model. Furthermore, the autocorrelations of squares increase with the persistence in the A-LMSV model and decrease in the FIEGARCH model. On the other hand, the autocorrelations of absolute returns increase with the magnitude of the asymmetry in the FIEGARCH model while they can increase or decrease depending on the sign of the asymmetry in the L-MSV model. Finally, the cross-correlations between squares and original observations are, in general, larger in the FIEGARCH model than in the A-LMSV model. The results are illustrated by fitting both models to represent the dynamic evolution of volatilities of daily returns of the S&P500 and DAX indexes. One of the main empirical characteristics of financial returns is the dynamic evolution of their volatilities. There are two important properties that characterized this evolution. First of all, power transformations of absolute returns have significant autocorrelations which decay towards zero slower than in a short memory process. Many authors have argued that this pattern of the sample autocorrelations suggests that the volatilities of financial returns can be represented by long-memory processes; see Ding et al. (1993) and Lobato and Savin (1998) among many others. The second property that characterizes volatilities is their asymmetric response to positive and negative returns. This property, known as leverage effect, was first described by Black (1976) .. There are two main families of econometric models proposed to represent the dynamic evolution of volatilities. The ARCH-type models are mainly characterized by specifying the volatility as a function of powers of past absolute returns and, consequently, the volatility can be observed one-step ahead. On the other hand, Stochastic Volatility (SV) models specify the volatility as a latent variable that is not directly observable. There have been several proposals of ARCH-type models that represent simultaneously leverage effect and long-memory. For example, Hwang (2001) proposed to extend the long-memory FIGARCH model of Baillie et al. (1996) to represent the leverage effect. However, some authors have pointed out some drawbacks of this model. For instance, Davidson (2004) has recently shown that the FIGARCH model has the unpleasant property that the persistence of shocks to volatility decreases as the long-memory parameter increases. Zafaroni (2004) has also showed that the FIGARCH model cannot generated autocorrelations of squares with long memory. Finally, Ruiz and Pérez (2003) showed that the model proposed by Hwang (2001) has identification problems. Consequently, in this paper, we focus on the Fractionally Integrated EGARCH (FIEGARCH) model proposed by Bollerslev and which extends the asymmetric EGARCH model of Nelson (1991) to long memory. The statistical properties of the FIEGARCH model have been derived following the arguments given by He et al. (2002) for the short-memory EGARCH model. In particular, we give explicit analytical expressions of the kurtosis and autocorrelations of squares and absolute observations. Furthermore, we also derived the cross-correlations between |y t+k | c and y t for c = 1 and 2.. Alternatively, in the context of SV models, Harvey (1998) and Breidt et al. (1998) have independently proposed Long-Memory Stochastic Volatility (LMSV) models in which the underlying log-volatility is modelled as an ARFIMA process. On the other hand, Harvey and Shephard (1996) propose to model the leverage effect of the short memory SV model by introducing correlation between the noises of the level and volatility equations 1 . In this paper, it is our aim to go one step further and present an extension of the LMSV model to cope with the leverage effect, that we denote A-LMSV. We derive the statistical properties of the new model and compare them with the properties of the FIEGARCH model. We show that both models explain in a different way the kurtosis and correlations of absolute and squared returns. The kurtosis and autocorrelations of squares of the A-LMSV models are not affected by the presence of the leverage effect. However, in the FIEGARCH model, both moments increase with the asymmetry. Furthermore, we show that the autocorrelations of squares increase with the persistence in A-LMSV models and decrease in FIEGARCH models. On the other hand, in the A-LMSV models, the autocorrelations of absolute observations increase with respect to the autocorrelations of the symmetric model when the correlation between the volatility and the level of returns is positive. However, if, as it is usual in financial returns, this correlation is negative, the autocorrelations decrease as the magnitude of the correlation increases. With respect to the FIEGARCH model, the autocorrelations of absolute returns always increase with the magnitude of the asymmetry regardless of its sign. Finally, the asymmetric response of volatility to positive and negative returns is reflected in the cross-correlations between |y t+k | c and y t for c = 1 and 2. We show that the patterns of these cross-correlations in the two models considered in this paper is rather similar.. The rest of the paper is organized as follows. The description of the statistical properties of the A-LMSV model is done in section 2. We focus on the kurtosis, autocorrelations of absolute and squared observations and crosscorrelations between |y t+k | c and y t where c = 1 and 2. In Section 3, we describe the properties of the FIEGARCH model and compare them with the properties of the A-LMSV model. Section 4 contains an empirical illustration by fitting both models to daily financial returns of the S&P500 and the DAX indexes. Section 5 concludes the paper. In this paper, we propose an extension of the LMSV to represent the asymmetric response of volatility to positive and negative returns. We compare the statistical properties of the new model with the FIEGARCH model. As a by-product, we derive expressions of the autocorrelations of squares and absolute returns as well as cross-correlations between these transformations of returns and the original returns when they are generated by the FIEGARCH model.. We show that the A-LMSV model reproduces better the empirical features of financial data: volatility persistence, excess kurtosis, autocorrelations of absolute and squared returns and cross-correlations between returns and future squared returns. In fact, the FIEGARCH model needs simultaneously high values of d and φ, close to the level of nonstationary, and small values of δ in order to capture at the same time persistence and small first order autocorrelation. On the other hand, this last requirement interferes with generating large kurtosis. The Gaussian FIEGARCH model is only able to reproduce high kurtosis if δ is not close to zero. Therefore, it seems to exist, for this model, a trade off among different moments. Contrarily, the A-LMSV model is able to reproduce these three features of financial data for larger combinations of the parameters.. In an empirical application to daily S&P500 and DAX returns, we show that when both models are fitted to real data, the conclusions in terms of the stationarity of the volatility are similar. When one of the models imply stationarity, the other does and the other way round. If the estimated parameters of both models satisfy the stationarity conditions, then the kurtosis and autocorrelations of order one of absolute and squared returns implied by the A-LMSV model are closer to the estimated sample moments of the real data than the ones implied by the FIEGARCH model. However, in our empirical application to the DAX returns none of the implied autocorrelations explain completely the slow decay of the autocorrelations towards zero. Consequently, and given that, as we have seen in this paper, dealing with the statistical properties of the A-LMSV model is easier than when considering the properties of the FIEGARCH model, we think that the former is a model to be considered when modelling the dynamic evolution of the volatility of series with long-memory and asymmetric response to positive and negative returns.

O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 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 O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 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 O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 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 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 O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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


Can Internalism and Externalism be Reconciled in a Biological Epistemology of Language? Abstract This paper is an attempt at exploring the possibility of reconciling the two interpretations of biolinguistics which have been recently projected by Koster (Biolinguistics 3(1):61-92, 2009). The two interpretations-trivial and nontrivial-can be roughly construed as non-internalist and internalist conceptions of biolinguistics respectively. The internalist approach boils down to a conception of language where language as a mental grammar in the form of I-language grows and functions like a biological organ. On the other hand, under such a construal consistent with Koster's (Biolinguistics 3(1):61-92, 2009), the non-internalist version does not necessarily have to be externalist in nature; rather it is a matter of mutual reinforcement of biology and culture under the rubric of a co-evolutionary dynamics. Here it will be argued that the apparent dichotomy between these two conceptions of biolinguistics can perhaps be resolved if we have a richer synthesis that accounts for both internalism and non-internalism. Recently Koster (2009) has argued in favor of a conception of language within which language can be seen as a cultural phenomenon having a socio-cultural reality but ultimately grounded in human biology. Under such an interpretation Koster's (2009) version of biolinguistics is 'trivial' in nature. On the other hand, the internalist conception of language where language is viewed as a mental grammar in the form of I-language that grows and functions like a biological organ has been rejected by Koster (2009) . This has been called the 'non-trivial' version of biolinguistics in that such a concept of language is narrowly construed to fit the characterization of language faculty as some 'core capacity' which is constituted by recursion. The entire issue has repercussions and implications centered around the debate on the dichotomy between internalism and externalism recently revived by Lohndal and Narita (2009) , who advocate the methodology of internalism as championed by Chomsky (1986 Chomsky ( , 1995 Chomsky ( , 2000 . Overall, it seems that the dichotomy is something that can never be resolved at all. As Koster (2009) traces the history of the debate, it becomes clear that the idea of language as being external to the individual was advocated by linguists of the first half of 20th century and even goes back to Von Humboldt. With Chomskyan revolution in linguistics starting in the 1950s, the concept of internalism came up and began to be firmly rooted in scientific theories of language that were developing. And the current situation is such that the internalist vs. externalist debate goes on in the guise of autonomy vs. non-autonomy or modularity vs. distribularity or even biology vs. culture from diverse perspectives and at different scales in fields ranging from theoretical linguistics, sociolinguistics, anthropology, psycholinguistics, psychology, cognitive neuroscience, evolutionary biology, artificial intelligence to perhaps molecular genetics. The aim is not to resolve all these dichotomies in one go; rather it will be argued that all these dichotomies exhibit some central tendencies and patterns which can be addressed best if they are couched in terms amenable to a better understanding of the path toward a resolution. The nature of the stalemate is such that specifically within the discipline of linguistics, both internalist theories like generative grammar and externalist theories like functional grammar (Givón 1995 (Givón , 2002 (Givón , 2005 Dik 1997a, b; Hengeveld 2005) or systemic functional grammar (Halliday 1973 (Halliday , 1985 co-exist. The field of sociolinguistics is also externalist in nature.. The purpose of this paper is to have a refreshingly new look at the entire issue in order to reformulate the debate in a manner that may show a path toward resolving the stalemate. It will be hypothesized that intrinsic nature of language shows complementarity between internalist state and externalist state in that it shifts, undulates (it will be explicated in later sections) between two modes of existence in an elastic manner. It is as if knowledge of language is like an elastic sheet shifting and undulating continuously between two forms of existence. In other words, this means that language functions both as an internalized form of mental grammar in individual brains and as an externalized socio-cultural object existing at an intersubjective plane of reality by shifting between these two poles of reality. Hence a truly unified biolinguistic approach toward language should aim at accounting for such a complementarity. Even if such a synthesis is unlikely to be fully fleshed out at this stage, an outline of such a proposal specifying the skeletal rudiments will be drawn up here with some tentative and speculative links to lines of research in cognitive psychology, evolutionary biology and theoretical linguistics. Overall, internalism broadly construed is never at odds with non-internalism or externalism-both are in fact two faces of the same phenomenon. Complementary switch-over between them is perhaps the kind of interactionsim that Carr (1990) has intended to mean. The complementarity between I'-forms of knowledge and E-forms of knowledge raises more questions than it answers. Why does it occur the way it does? Is it because of the way language has evolved and develops or due to some other factors? We do not really know. Some speculative answers have already been provided in earlier sections, but these are sketchy enough. Still it is believed that linguistic ontology and its epistemology are more closely coupled than we may imagine them to be. Questions about the nature of language inform questions regarding the form of knowledge language yields to. Such questions are not just philosophical; they constitute the core of the biological basis of language. Therefore, the hope is that ultimately a unified biolinguistic view of language can be formulated on the principles outlined here with all the ingredients fully incorporated and fully fleshed out.

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


VDMOSFET model parameter extraction based on electrical and optical measurements Abstract Lateral device parameters for VDMOSFET (Vertical Double Diffused Metal Oxide Semiconductor Field Effect Transistor) with hexagonal cells are extracted using an original method based on electrical and optical measurements. Using microscopic observation of the ship of the device and C–V characterization, the lateral device structure parameters could be extracted. Values of the extracted parameters are in good agreement with the values given by the manufacturer. The advantage of this method is the high precision of results for a low cost. Perhaps the most important point of this method is that it can replace the other techniques usually employed, wherein devices are destroyed to obtain the cross section of the structure. The proposed technique can be very useful for analyzing any complex geometrical structure of VDMOS transistors (hexagonal, triangular, square etc…). The n-channel MOSFETs are the most popular for use in power switching circuits and applications. Various salame@ieee.org 186 C.-T. SALAME et al.. configurations [1] [2] [3] . VDMOSFET with hexagonal cells (HEXFET) has a complex geometrical structure. The size of these components is specially adapted by the manufacturers in response to the needs of the power [4] [5] [6] [7] . Technical progress of microelectronic integration involve also an evolution towards the miniaturization which requires new structural modifications to answer the sub-micronics parasitic effects [8-111. Lateral parameters of these devices are needed for software simulation models for the components structure. In order to describe our methodology, electrical measurements of the capacitance voltage relationship at a high frequency and optical measurements are performed.. The VDMOSFET structure and the measurements techniques are discussed in part 2. Part 3 deals with the extraction methodology based on the capacitance-voltage characterization and the microscopic observation.

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