Error estimates for least squares finite element methods Abstract-A least squares finite element scheme for a boundary value problem associated with a second-order partial differential equation is considered. Previous work on this subject is generalized and improved by considering a larger class of equations, by working in the natural context, without additional smoothness conditions, and by deriving error estimates, not only in the H'-norm and the Hd+norm, but also in the &-norm. Some of these estimates are sharpened by using finite element spaces with the grid decomposition property. The error estimates are supported by numerical results which extend previous numerical work. Least squares finite element methods for boundary value problems associated with partial differential equations have become more and more popular lately, mainly because they are not subject to the Brezzi-Babuska conditions, but also because these methods have a series of other advantages over classical finite element methods, such as freedom in choosing the finite element spaces, easy implementation and programming, application to a wide range of problems, and the fact that the resulting discrete system can be solved by a variety of algebraic methods, being symmetric and positive definite. An extensive coverage of these methods can be found in [l] . Also, a good outline of the advances made so far in developing these methods can be found in [2] and the references therein. A large number of studies that numerically demonstrate the efficiency of the least squares finite element methods seem to be ahead of the development of the mathematical context and the error analysis attached to these experiments.. Nevertheless, the mathematical foundation is a key step to the full success of these methods, as it indicates the extent of efficiency and the directions to be taken for further development.. In the present article, we consider the problem -div(AVu) + QU = f, in R, ( where R c R" (n = 2 or 3), R is a connected bounded convex polygonal domain with a Lipschitz boundary 00, PD U rN = df& the measure of PD is strictly positive, and Y is the outward unit vector directed normal to the boundary. Also, A : (L2(s2))n --) (L2(s2))n is a linear operator, and q = q(z) is a function defined for x E 6.. If A is the identity operator, the analysis of a least squares finite element method applied to this problem has been made in [3] , and extended in [4] for the case where A is an operator and q = 0. Also, a number of basic error estimates have been obtained in [5] and [6] for the case where A is a symmetric n x n matrix and AVu represents the multiplication of A by the vector Vu. In all these articles, the method is based on first writing problem (l.l)- (1.3) as a boundary value problem associated with a first-order system of partial differential equations, and then reformulating the problem as the minimization of a least squares functional associated with the first-order system, over an appropriate space. In [3] and [4] , this space is a subspace of H1(0) x (H1(s2))", while in [5] it is a subspace Of H'(a) X H&v(n).. We shall follow the same procedure for problem (l.l)-(1.3), by first writing it as the following equivalent problem:. AVu-+=O, in R, (1.4) then formulating it as the minimization of a least squares functional. The goal of this article is to make the same type of analysis as made in [3] and [4] , but over a subspace of H'(0) x H&v(n), since this is the natural context that arises from the very formulation of the least squares problem, without additional smoothness assumptions (see also [7] and [8] ). At the same time, while working on H'(n) X ffdiv(fl),. we extend the results in [3] by considering the case where A is a linear operator (not necessarily the identity operator), and extend the results in [4] by considering cases where q is bounded, q # 0. We also extend and improve the results in [5] , by proving additional error estimates for u and 4 in the L2-norms (some of which assume the grid decomposition property of the finite element spaces [3] ), and by considering the case where A is an operator (not necessarily a symmetric matrix).. We now introduce a series of notations. Denote by (. , .)o, (. ,.)I, and (.,. )div the inner products on the spaces L2(fl), H'(a), and Notice that for w E Vs and Q E SO, the Stokes theorem gives of a solution, and deriving other basic results. In Section 3, we apply a finite element method to the least squares formulation and derive basic error estimates for the couple (u,+) in the norm of HI(Q) x Hdiv(s2). In addition, we derive L2-error estimates separately for U, and finally, assuming the grid decomposition property, we derive L2-error estimates of the same order for 4.. Section 4 presents a number of computational results that support the estimates obtained in Section 3, and complement the results provided in [3-51. The error analysis of a least squares finite element method for solving second-order problems has been made for certain elliptic cases. The analysis extends and improves previous work made in , and refers to partial differential equations with homogeneous boundary conditions. The numerical results presented here support the theoretical conclusions, and extend previous numerical work. Similar numerical experiments yield the same conclusions for problems with nonhomogeneous boundary conditions, suggesting the fact that this analysis could be extended to nonhomogeneous problems of this type. Also, the results presented here suggest that condition (2.5) is too restrictive, and the analysis could be valid in a larger context. These issues will be the object of future work.

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


A NOTE ON THE LOCALLY LINEAR EMBEDDING ALGORITHM The paper presents mathematical underpinnings of the locally linear embedding technique for data dimensionality reduction. It is shown that a cogent framework for describing the method is that of optimisation on a Grassmann manifold. The solution delivered by the algorithm is characterised as a constrained minimiser for a problem in which the cost function and all the constraints are defined on such a manifold. The role of the internal gauge symmetry in solving the underlying optimisation problem is illuminated. High-dimensional data can often be converted to low-dimensional data with little or no fundamental loss of information. A simple and widely used method for dimensionality reduction is principal component analysis (PCA). The method represents data points by their respective orthogonal projections on a subspace of low dimension spanned by the directions (also called components, features, factors or sources) of greatest variance in the data set. The locally linear embedding (LLE) 12 and ISOMAP 16 algorithms are two recently proposed nonlinear generalisations of PCA. Originally developed for visualisation purposes, these two methods project (embed) high-dimensional data into a two-or low-dimensional subspace by extracting meaningful components in a non-linear fashion. For a brief but informative overview of a class of dimensionality reduction methods that includes PCA, LLE and ISOMAP, see Ref. 14. This paper focuses on the all-important LLE scheme, the utility of which can hardly be overestimated. Alongside earlier applications in visualisation 4, 12, 13 and classification, 17 the scheme has most recently found use to such tasks as 3D-object pose estimation, 20 face membership authentication, 11 multipose face synthesis, 18 facial animation, 10 image denoising, 15 hyperspectral image processing, 8 digital watermarking, 6 feature extraction, 7 gait recognition, 9 and manifold learning 19 -to name a few. In most applications, LLE is invoked as a ready-to-use dimensionality reduction tool. In contrast, this article touches upon some theoretical issues regarding the foundational basis of the algorithm.. The paper gives a detailed account of the mathematical underpinnings of LLE. It is shown that LLE solves a constrained optimisation problem that is usefully viewed as a problem posed on a certain non-Euclidean space, namely, a Grassmann manifold. Such a manifold is the collection of all linear subspaces of fixed dimension in some ambient linear space. Optimisation on manifolds related to the orthogonal group such as Stiefel and Grassmann manifolds frequently appear in the context of neural networks, signal processing, pattern recognition, and computer vision. The benefit of the Grassmann manifold-based formulation of LLE's optimisation problem is in allowing one to see more clearly an internal symmetry, or gauge freedom, related to the arbitrariness of the choice of coordinates in which to naturally state the problem. This paper demonstrates that once recognised, the gauge freedom can be used advantageously to isolate a solution of the optimisation problem. The present exposition of LLE can be seen as an expansion of the presentations given in Refs. 2 and 13.. The paper is arranged as follows. The next section sketches the main ideas behind the working of LLE. The following section presents auxiliary material needed to formulate LLE's optimisation problem. The subsequent section describes the structure of the optimisation problem and a path to its solution. It is here that the main contribution of this note resides, this being an illumination of the role played by the gauge degrees of freedom in isolating the solution. Following concluding remarks, two appendices provide some matrix calculations, which -with a view to self-reliance -are performed in a detailed, explicit manner. The optimisation problem solved by the LLE algorithm has been presented as one posed on a Grassmann manifold. The advantage of this formulation is at least twofold. First, it helps reveal the internal degrees of freedom present in the natural, coordinate-specific formulation of the problem that initially involves a Euclidean space and upon refinement operates with a Stiefel manifold. Second, with the gauge freedom properly recognised, it facilitates an adequate choice of a coordinate system for reducing the equation for a critical point of the Lagrange function, in terms of which the problem is expressed, to an easily solvable eigenvalue problem.

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


Online Estimation of Architectural Vulnerability Factor for Soft Errors Abstract Soft errors (or single event upsets or transient errors) caused by alpha particles from packaging materials or high energy particle strikes from cosmic rays can flip bits in storage cells or cause logic elements to generate the wrong result. Such errors have become a major challenge to processor design. Previous research shows that soft error rate (SER) per chip is growing substantially, mainly due to the fast growth of the number of transistors on the chip [3, 11, 15] .. If a particle strike causes a bit to flip or a piece of logic to generate the wrong result, we refer to it as a raw soft error event. Fortunately, not all raw soft errors cause the processor to fail. In a given cycle, only a fraction of the bits in a processor storage structure and some of the logic structures will affect the final program output. A raw error event that does not affect these critical bits or logic structures has no adverse effect on the program outcome and is said to be masked. For example, a soft error in the branch prediction unit or in an idle functional unit will not cause the program to fail. Research has shown that there is a large masking effect at the architecture level [1, 4, 10, 18, 20] .. Mukherjee et al. [10] introduced the term architectural vulnerability factor (AVF) to quantify the architectural masking of raw soft errors in a processor structure. The AVF of a structure is effectively the probability that a visible error (failure) will occur, given a raw error event in the structure [10] . The AVF can be calculated as the percentage of time the structure contains Architecturally Correct Execution (ACE) bits (i.e., the bits that affect the final program output). Thus, for a storage cell, the AVF is the percentage of cycles that this cell contains ACE bits. For a logic structure, the AVF is the percentage of cycles that it processes ACE bits or instructions.. For a large class of systems and workloads, including those studied here, the AVF of a structure directly determines its mean time to failure (MTTF) [5] -the smaller the AVF, the larger the MTTF and vice versa. It is therefore important to accurately estimate the AVF in the design stage to meet the reliability goal of the system. Many soft er-ror protection schemes have significant space, performance, and/or energy overheads; e.g., ECC, redundant units, etc. Designing a processor without accurate knowledge of the AVF risks over-or under-design. An AVF-oblivious design must consider the worst case, and so could incur unnecessary overhead. Conversely, a design that under-estimates the AVF would not meet the desired reliability goal.. Recently, there has been significant work motivating the need to estimate AVF at runtime as well. Studies have shown significant variation in the AVF value across different applications and within different phases of the same application [6, 17] . Thus, depending on the workload, the processor may be more or less vulnerable at different times. This observation creates new opportunities to reduce the soft error protection overhead while meeting the MTTF goal. If we are able to estimate AVF in real-time accurately, we can adjust the protection scheme based on the current AVF value. We can have more protection during highly vulnerable periods and less protection during less vulnerable periods, minimizing performance and/or energy overhead. For example, Soundararajan et al. [16] propose to use the AVF input to control instruction throttling and selective redundancy schemes. In this case, a real-time online AVF estimation is a must since a slow offline method will not be able to give timely input to the control logic.. There is some previous work that provides online AVF estimation; however, it is either dependent on extensive offline workload analysis [17] or targeted to a single structure [16] (see Section 2) . In general, estimating AVF online is a challenging task since the complex computation used in offline analysis is not feasible in real-time. The AVF for many structures depends on many factors that are hard to measure and observe. For example, the AVF of the floating point unit depends not only on its utilization, but also on variables such as the percentage of dead values and speculative instructions. For storage structures, AVF estimation is even more difficult. It may be intuitive to think that the number of reads/writes to a storage structure may be correlated with the AVF of this structure. However, it is easy to construct two read/write sequences that have the same number of reads and writes, but very different AVF values.. In this paper, we describe a general online method to estimate AVF for a variety of structures (including logic and storage structures) without need for extensive offline workload analysis. Our approach is motivated by offline (complex) AVF estimation approaches. Specifically, a common method for offline estimation is to inject an error in a lowlevel simulator and determine whether it results in program failure. Many such injections are performed, and the AVF is calculated as the fraction of such injections that lead to failure. Our online estimation method effectively seeks to perform error injection while the program is running in production mode and uses the program execution to determine whether the error will result in failure. Of course, we cannot actually inject an error into a production run. We therefore introduce some additional error bits through the processor pipeline that can emulate the generation and propagation of an error.. To estimate the AVF of a structure, we emulate the injection of an error in the structure by setting its error bit to 1. An instruction touching this structure then propagates the injected error to its destination and so on. In this way, an error is propagated by the executing program. Our algorithm waits a fixed number of cycles to determine if the error could (potentially) result in program failure. Multiple such injections are done and as with offline error injection, the fraction that are determined to potentially result in failure provide an estimate of the AVF of the structure.. Our method depends on two key parameters to get an accurate estimate of AVF: (1) how many times to inject an error, and (2) after injecting an error, how long to wait to see if the error will cause a program failure. Setting these parameters too high can result in an estimation procedure that lasts too long and does not adequately track the AVF changes in the program. Setting them too low can result in incorrect estimates. We use analytical and experimental methods to determine these two parameters.. To evaluate our method, we implement it in a simulator and perform experiments to estimate the AVF for both logic and storage structures (integer ALU, FPU, instruction queue, and register file) for 100 to 200 intervals in each of eleven SPEC benchmarks. In order to validate our results, we compare against SoftArch, which is a more detailed (but complex) offline AVF estimation method (see Section 2). Our results show that our method generates very similar results to SoftArch. The absolute difference in AVF estimated by the two methods rarely exceeds 0.08 across all application intervals and structures studied. The mean absolute difference is less than 0.05 for any given application and structure. Further, we also compare an intuitive and simple AVF estimation method that uses the utilization of logic structures as a proxy for their AVF (an analogous extension of such a method for storage structures is not clear). We show that compared to our method, this simple method shows significant inaccuracies relative to SoftArch, providing evidence for the need for the hardware support required by our method. Overall, our results show that our novel method for online estimation of AVF is both accurate and robust in a variety of situations. In this paper, we have proposed and studied a novel technique to estimate architectural vulnerability factors for soft errors in real-time. We have described the AVF estimation algorithm and the simple hardware modifications to the processor for effectively estimating the AVF. Our method is general and applies to both logic and storage structures in a microprocessor. We tested our method with a widely used simulator from industry, for four processor structures running SPEC benchmarks. The results show that our method provides acceptably accurate run-time AVF estimates under a wide variety of scenarios, compared to a detailed (and complex) offline AVF estimation tool. Below, by absolute error of an estimation method for a given application interval that contains 1 million cycles, we refer to the absolute difference between the AVFs reported by that method and by SoftArch. By relative error of an estimation method, we refer to |Estimated AV F − Sof tArchAV F | Sof tArch AV F * 100. Also, we often refer to the SoftArch AVF as the real AVF.. The charts on the left side of Figure 3 give three statistics for the absolute errors. For each bar, the lowest (shaded) stack gives the mean absolute error (referred to as Mean) for the corresponding estimation method and application (averaged across the different 1M cycle estimation intervals for that application). The full height of the bar is the maximum absolute error, ignoring the top four errors to exclude unrepresentative outliers (referred to as Max). The middle stack is the standard deviation of the absolute error (referred to as Standard Deviation).. Since AVF values can range only from 0 to 1, it is most meaningful to compare the absolute errors. Small absolute errors may be acceptable even if the relative error is large; e.g., an estimate of AVF=0.12 for a real AVF of 0.1 reflects a 20% relative error; however, it is unclear if this difference of 0.02 absolute error is practically significant. Nevertheless, the charts on the right side of Figure 3 provide the relative errors for reference.. For a more detailed look, we take two applications as examples and plot AVF values for them for each 1M cycle estimation interval for each structure in Figure 4 . For each application, we show the AVF value calculated by SoftArch and the AVF value estimated by our method. For both the FPU and FXU, we also show the AVF calculated by the utilization-based method.. We make the following observations from the figures. There have been several studies on estimating the AVF [10, 6, 19, 17, 16] . However, most studies estimate AVF using offline analysis with complex simulators [10, 6, 19] . This offline estimation is a complex pro-cess, requiring many resources to track values and instructions as they travel through a processor. Normally only a limited number of instructions can be analyzed in a reasonable amount of time. These methods are therefore not suitable for online real-time AVF estimation.. There has been some work on estimating the AVF in real time [16, 17] . Walcott et al. [17] apply statistical analysis using a detailed simulator to analyze the AVF behavior. Then they use regression to explore the relationship between AVF and various micro-architecture level variables such as structure occupancy, number of instructions executed, etc. After running the regression offline for certain workloads, the correlation coefficients between AVF and each micro-architecture variable are established. Since the micro-architecture variables are observable, the AVF value can be estimated through them. This method can potentially be implemented to estimate the AVF online; however, it requires heavy offline simulation and calibration for different workloads. It is not clear that the parameters calibrated for one set of workloads will give accurate estimation for another set.. Soundararajan et al. [16] propose a method to estimate AVF for the reorder buffer (ROB) in the processor. This method determines the AVF by estimating the occupancy of the instruction queue. The occupancy of the instruction queue is in turn estimated by counting the number of instructions that are dispatched or retired. This method can be implemented online, but is limited to a single structure. For example, it is hard to extend the same method to estimate the AVF for the register file.. There have been at least two major works that use bits similar to our error bits, but for different purposes. First, Weaver et al. [20] proposed the π bit to address false detected errors. Every instruction and register entry is associated with a single π bit. When an error is detected (e.g., via parity), the affected instruction's π bit is set by the instruction queue and the instruction is allowed to progress down the pipeline. When the affected instruction reaches the commit point, if it is determined to contribute to correct program outcome, a machine check error is raised; otherwise the set π bit is ignored. Second, the poison bit [12] and the analogous NaT bit of the Itanium architecture [14] are used to track deferred speculative exceptions. Our use of the error bits is different -we use them to estimate the AVF due to soft errors. Nevertheless, the hardware support required for all of these techniques is likely to be similar.. Finally, we use the offline estimation technique of SoftArch to provide the reference AVF used to validate our online estimator [6] . SoftArch uses simple probability theory to model the error generation and propagation process in a processor. It keeps track of the error probability of the different values in the processor. Integrated with a program timing simulator, SoftArch also identifies which values could affect program outcome and when that might happen. Using the error probability and the timing information, SoftArch is able to determine the MTTF and the AVF value for a workload. Our method differs from SoftArch in that we estimate the AVF online in hardware while the program is running. Instead of using complex probability calculations and detailed error tracking that are suited for offline analysis, we use a simple mechanism that can be efficiently realized in hardware. Whereas SoftArch (probabilistically) tracks every raw error that could be generated in the processor, our method takes an online statistical fault injection based approach to estimate the AVF in real-time.

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


A canonical model for interactive unawareness Heifetz, Meier and Schipper (2006) introduced unawareness structures. These are generalized state-space models that allow for non-trivial unawareness among several individuals and strong properties of knowledge. We show that a canonical unawareness structure arises naturally if states consist of maximally consistent sets of formulas in an appropriate axiom system. As a corollary, we obtain a strong soundness and completeness theorem for this axiom system with respect to the class of unawareness structures. Unawareness refers to lack of conception rather than to lack of information. In standard models of incomplete information, decision makers share the conception of the interactive decision problem but may have asymmetric information. While models of asymmetric information are common in game theory and economics, the modelling of unawareness in interactive decision making proves to be a tricky task. Modica and Rustichini (1994) and Dekel, Lipman and Rustichini (1998) showed that standard state-space models of asymmetric information preclude non-trivial forms of unawareness.. Heifetz, Meier and Schipper (2006a) introduced a generalized state-space model that allows for non-trivial unawareness among several individuals and strong properties of knowledge. Such an unawareness structure involves a lattice of state-spaces, ordered according to their expressive power. If individual i considers as possible states in a space with low expressive power, this means that she is unaware of aspects of reality not expressible in that space. If in these states another individual j considers as possible only states in an even lower space of the lattice, it means that i thinks that j is unaware of some aspects of reality of which i is aware. This is how mutual beliefs about unawareness are captured in the model.. In this paper we substantiate this construction with logical building blocks. Such an investigation of foundations is indeed necessary. Any structure for modeling asymmetric cognition -even if it has the desired properties -begs the question whether the model itself should not be an object for further uncertainties of the individuals. One way to show that a model is comprehensive is to describe in minute detail the beliefs and mutual beliefs of all individuals in each state. If each relevant combination of such beliefs are described in some state of the model, then we are convinced that the phenomena we aim at modeling is captured by our construction.. For the case of knowledge and mutual knowledge, such a detailed substantiation of the beliefs in the standard partition model has been carried out by constructing the canonical model of all maximally-consistent sets of formulas in the S5 system of epistemic logic (Aumann, 1999) . This is the standard propositional logic (with negations, conjunctions and disjunctions of formulas), augmented with a knowledge modality for each individual: For each formula ϕ and each individual i, there is also a formula k i ϕ ("individual i knows ϕ"). The axioms of the system then specify (on top of the standard logical tautologies) that what an individual knows is true, and that the individual knows what she knows and what she ignores. The canonical construction in which the states are the maximally-consistent sets of formulas in this logical system turns to have a natural partition structure, and the knowledge of events in this partition model reflects exactly the knowledge of formulas in the states. That's how the canonical model is substantiated by the internal structure of its own states.. In this paper we aim at an analogous foundation for the case of unawareness. Two main differences arise.. First, the axiom system has to be amended: An individual knows that she doesn't know some fact only if she is aware of that fact. Our axiom system manifests this feature. It is a multi-person extension of a (variant) of the axiom system proposed by Modica and Rustichini (1999) .. Second, in the lattice of spaces of an unawareness structure, only the states in the upper-most space are full descriptions of all aspects of reality relevant to the interaction among the individuals. States in lower spaces are subjective portraits of situations, in the mind of individuals who are unaware of some of these relevant dimensions. Therefore, to construct these subjective descriptions, one has to use a sub-language, with a proper subset of the primitive propositions of the logical syntax.. With these modifications done, we are able to accomplish our mission: The collections of maximally-consistent sets of formulas (across all sub-languages) constitute an unawareness structure (Theorem 1), in which knowledge of events reflects exactly the knowledge of formulas in states (Theorem 2).. This result entails an important corollary. Logicians are often interested whether an axiom system is sound and complete with respect to a given family of models. Soundness means that every theorem derivable from the axioms obtains in all states of all these models. Completeness means the reverse implication: Every formula that obtains in all states of all the models in the family is provable from the axioms of the system. Our results imply that the axiom system we devised is sound and complete with respect to the family of unawareness structures (Theorem 3). 1 The caveat here is that each space in the lattice of an unawareness structure is associated with a sub-language (determined by a subset of the primitive propositions), and that higher spaces in the lattice are associated with richer sub-languages. In a state which is a subjective description of reality in the mind of an individual who is unaware of a primitive proposition ϕ, neither ϕ nor ¬ϕ obtain. If one were to insist on a truth value for ϕ in such a state, it would have to be "mu" -a third value, distinct than "true" and "false". In this sense, our logic is 3-valued.. In a parallel work, Halpern and Rêgo (2005) propose another sound and complete axiomatization for our unawareness structures. It is a multi-person version of an axiomatization formulated in Halpern (2001) for the single-person case, an axiomatization which he showed to be equivalent to that of Modica and Rustichini (1999) . 2

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


Algebraic Properties for Selector Functions The nondeterministic advice complexity of the P-selective sets is known to be exactly linear.Regarding the deterministic advice complexity of the P-selective sets-i.e., the amount of KarpLipton advice needed for polynomial-time machines to recognize them in general-the best current upper bound is quadratic [Ko83] and the best current lower bound is linear [HT96] .We prove that every associatively P-selective set is commutatively, associatively P-selective. Using this, we establish an algebraic sufficient condition for the P-selective sets to have a linear upper bound (which thus would match the existing lower bound) on their deterministic advice complexity: If all P-selective sets are associatively P-selective then the deterministic advice complexity of the P-selective sets is linear. The weakest previously known sufficient condition was P = NP.We also establish related results for algebraic properties of, and advice complexity of, the nondeterministically selective sets. Selman [Sel79, Sel81, Sel82a, Sel82b] defined the P-selective sets about twenty years ago. In addition to being of interest in their own right, they have recently had some surprising applications. For example, selectivity is a powerful tool in the study of search versus decision problems [HNOS96a] , and nondeterministic generalizations of selectivity are the key tools used to show that even NP machines cannot uniquely refine satisfying assignments unless the polynomial hierarchy collapses [HNOS96b] , that even weaker refinements are also precluded unless the polynomial hierarchy collapses [Ogi96, NRRS98] , and that many cardinality types of nondeterministic function classes cannot collapse unless the polynomial hierarchy collapses [HOW02] . We call such a function f a P-selector function for B.. That is, a set B is P-selective if there is a polynomial-time function f that given any two strings always chooses one of them, and f does this in such a way that if exactly one of the strings is in B then the P-selector function chooses that string. f (x, y) is often described, very informally, as choosing one of x or y that is more likely to be in the set, though a more accurate description would be that f chooses one of x or y that is logically no less likely then the other to be in the set.. The P-selective sets have been extensively studied, and much about them is well understood (see the recent book [HT03] about selectivity theory). Though some P-selective sets are very complexhighly undecidable-the P-selective sets nonetheless have a broad range of structural simplicity properties. Most crucially in terms of the study in this paper, Ko [Ko83] showed that they have low nonuniform complexity (P-sel ⊆ P/O(n 2 )). A few among the many other simplicity results known to hold are: Ko and Schöning [KS85] showed that all P-selective sets in NP are in the second level of the low hierarchy of Schöning [Sch83] , and Allender and Hemachandra [AH92] showed that the Ko-Schöning result is the strongest lowness result for P-sel that holds with respect to all oracles; a long line of work starting with Selman [Sel79] and Toda [Tod91] (see also [Siv99] and the citations therein) has shown that no P-selective set can be NP-hard under ≤ p m or various other reductions unless P = NP; Naik and Selman [NS99] have shown that no P-selective set can be truth-table-hard for NP unless certain (intuitively unlikely) containments hold in the relationship between adaptive and nonadaptive queries to NP; and as a consequence of the work of Ko [Ko83] and Cai [Cai01] no P-selective set can be truth-table-hard for NP (or even Turing-hard for NP) unless the polynomial hierarchy collapses to S 2 , where S 2 is the symmetric alternation class of Canetti [Can96] and Russell and Sundaram [RS98] . Note that S 2 ⊆ ZPP NP ⊆ NP NP [Cai01] , where ZPP as usual denotes expected polynomial time, so this is a very dramatic collapse.. In this paper, we show that sets having P-or NP-selector functions with nice algebraic properties have simplicity properties far beyond those known for general P-selective or NP-selective sets. More generally, we study the class of languages one obtains from P-and NP-selector functions having certain algebraic properties, and the possibility of obtaining such algebraically nice P-or NP-selector functions.. In particular, Section 4 shows that any P-selective (NP-selective) set having an associative Pselector (NP-selector) function also has a commutative, associative P-selector (NP-selector) function. Section 5 shows that sets having an associative P-selector can be accepted by deterministic advice interpreters using only a linear amount of advice. In contrast, the best upper bound on the deterministic advice complexity of the P-selective sets is the quadratic bound obtained by Ko [Ko83] .. Our result provides a new sufficient condition-all P-selective sets are associatively P-selectivefor all P-selective sets having linear deterministic advice; the weakest previously known sufficient condition was the quite demanding assumption that P = NP.. Section 6 shows that associatively NP-selective sets with weak census functions cannot be coNPimmune. Section 7 establishes a structural sufficient condition for all P-selective sets being associatively, commutatively P-selective, and proves that if all NPMV-selective sets have associative NPMV-selector functions then the polynomial hierarchy collapses.

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


The operational meaning of min- and max-entropy We show that the conditional min-entropy Hmin(A|B) of a bipartite state ρAB is directly related to the maximum achievable overlap with a maximally entangled state if only local actions on the B-part of ρAB are allowed. In the special case where A is classical, this overlap corresponds to the probability of guessing A given B. In a similar vein, we connect the conditional max-entropy Hmax(A|B) to the maximum fidelity of ρAB with a product state that is completely mixed on A. In the case where A is classical, this corresponds to the security of A when used as a secret key in the presence of an adversary holding B. Because min-and max-entropies are known to characterize information-processing tasks such as randomness extraction and state merging, our results establish a direct connection between these tasks and basic operational problems. For example, they imply that the (logarithm of the) probability of guessing A given B is a lower bound on the number of uniform secret bits that can be extracted from A relative to an adversary holding B. A central goal of information theory is the (quantitative) analysis of processes involving the acquisition, transmission, and storage of information. For example, given a (noisy) communication channel, one may ask at which rate data can be transmitted reliably (this is the channel capacity). Or, given a source emitting signals, one may be interested in the amount of space needed to store the information in such a way that the signal can be recovered later (this is the compression rate). In the following, we call such quantities operational because they are defined by an actual information-processing task.. Traditionally, most operational quantities are defined asymptotically under the assumption that a certain process is repeated many times independently. 1 Consider for example the problem of data compression. For a random variable X and for ε ≥ 0, let ℓ ε compr (X) be the minimum length (measured in terms of bits) of an encoding enc(X) such that X can be recovered from enc(X) except with an error probability of at most ε. The compression rate of a source emitting a sequence of mutually independent pieces of data X 1 , . . . , X n , each distributed according to P X , is then defined by r compr (P X ) := lim. It is maybe one of the most remarkable features of information theory that a huge variety of operational quantities can be expressed in terms of a few simple entropy measures. In fact, in the asymptotic case where a process is repeated many times independently, the (almost) only relevant entropy measure is the Shannon entropy (or its quantum-mechanical generalization, the von Neumann entropy). For example, the compression rate (1) of a source emitting data distributed according to P X is equal to the Shannon entropy S of a random vari- 1 The independence assumption is sometimes replaced by the less restrictive requirement that the process is Markovian.. able X with distribution P X , i.e., r compr (P X ) = S(X) .. This equality is also known as the source-coding theorem [1] .. Another well-known example is the channel capacity. According to the noisy-channel coding theorem [1] , the maximum rate at which information can be transmitted over a noisy communication channel is equal to a difference between two Shannon entropies (see (13) In information theory, entropies are generally interpreted as measures of uncertainty. One method to make this interpretation more precise is to establish relations between entropy measures and operational quantities, that is, quantities that characterize actual information-theoretic tasks.. Here we consider a general scenario consisting of a (possibly quantum-mechanical) system A as well as an observer with (quantum or classical) side information B. The uncertainty of the observer about the state of system A then depends on the distribution of these states as well as the correlation between A and B.. There are two extreme situations, namely when A is completely undetermined and when A is determined. Taking into account the side information B, these two situations are described as follows.. 1. The state of A is fully correlated with (parts of) B. Note that in the first case, the requirement is merely that A is correlated with parts of B. This is because the sideinformation B may consist of additional information that is unrelated to A. For any given state ρ AB , we may characterize the uncertainty of A given B by the distance to these extreme situations.. If we take as a distance measure the overlap (i.e., the square of the fidelity), we retrieve the definitions of q corr (A|B) and q decpl (A|B) (see (20) and (22), respectively). Our main results imply that these correspond to H min (A|B) and H max (A|B), respectively. We thus conclude that H min (A|B) quantifies the closeness to a situation where A is determined by B, and, likewise, H max (A|B) corresponds to the closeness to a situation where A is independent of B (see second column of Table I ).. Given a bipartite state ρ AB , we may also ask for the number of maximally entangled or completely independent qubits one can extract from A. Very roughly speaking, this is the idea underlying the definitions of ℓ ε merg (A|B) and ℓ ε decpl (A|B), respectively (see Section I B for more details, in particular the interpretation of negative quantities). Remarkably, these quantities are (approximately) given by the smooth entropies H Table I ). 15 Despite these similarities between the (previously known) operational interpretations summarized in the last column of Table I and those given in the second column (the ones derived here), there are at least two fundamental differences. The first is that the new interpretations are exact and, in particular, valid without a smoothness parameter. In contrast, all previously established interpretations only hold up to additive terms of the order log 1 ε , where ε is a smoothness parameter (whose meaning is that of an error or failure probability). A second difference is that there does not seem to exist an obvious asymptotic counterpart for our identities. In particular, there are no analogous operational interpretations of the von Neumann entropy.. The results of this paper suggest that studying operationally defined quantities may be a viable approach to identifying relevant single-shot information measures in a multipartite setting. Of particular interest is the conditional mutual information, which has only recently been given an asymptotic interpretation [17] . and for an appropriate choice of the smoothness parameter ε ′ .

O O O O O O B 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 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 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 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 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 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


Fast continuous collision detection and handling for desktop virtual prototyping Abstract This paper presents an overview of our recent work on continuous collision detection methods and constraints handling for rigid polyhedral objects. We demonstrate that continuous collision detection algorithms are practical in interactive dynamics simulation of complex polyhedral rigid bodies and show how continuous collision detection and efficient constraint-based dynamics algorithms allow us to perform various virtual prototyping tasks intuitively, precisely and robustly on commodity desktop computers. Especially, we present two applications of our system to actual industrial cases. We note that both tasks are performed with a simple 2D mouse on a high-end computer. Computer-aided design and manufacturing has been a very active research field for many years, which has contributed to the development of major product lifecycle management software.. One important aspect of product lifecycle management is virtual prototyping, which aims at designing manufactured products through digital mock-ups, in order to suppress the need for expensive real mock-ups.. Because the analysis and simulation of a product through a digital mock-up must provide insight on the product before it is manufactured, virtual prototyping requires the ability to simulate the physical properties of the objects being designed.. This paper focuses on a fundamental requirement of virtual prototyping: the ability to detect and handle collisions between virtual objects. Typical applications of collision detection and handling in virtual prototyping include path-planning, tolerance verification and assembly/disassembly tasks conception.. Most well-known collision detection methods are discrete: they sample the objects' trajectories at discrete times and report interpenetrations only (recent surveys include [11, 13] ). As a result, they can miss collisions when the objects move rapidly or are small. Moreover, even when an interpenetration has been detected, it is often difficult to reposition the objects in a contacting position (i.e. with no interpenetration). One reason being that computing the penetration depth for general objects is a difficult problem, which does not take the objects' motion into account. Relying on the penetration depth to reposition the objects might thus lead to the well-known pop-through effect, where an object enters an obstacle on one side and goes out of it on the other side, as can be seen in Fig. 1 .. Even backtracking methods, which attempt to compute the first time of collision by recursively subdividing the time interval after an interpenetration has been detected, can fail when the object is not connected. Assume that the current time interval is [t n , t n+1 ], and assume an interpenetration has been detected at time t n+1 . Essentially, one time of first contact t e is estimated in this interval (for example, by taking the midpoint of the time interval). Objects' positions are then computed at this instant and an interpenetration detection is performed again. Depending on whether the objects interpenetrate or not, the algorithm decides that the first time of collision is in [t n , t e ] or [t e , t n+1 ], respectively, and loops on this new interval. The process stops when the amount of interpenetration is smaller than a predetermined threshold.. The computational cost of backtracking can be high when objects are complex or when they have interpenetrated deeply. Besides, since backtracking is only performed when an interpenetration has been detected, non-connected objects, or even non-convex objects, can enter a configuration from which they could not get out (e.g. two torii that would become interlocked).. Consequently, discrete collision detection methods cannot guarantee the existence of complete interpenetration-free paths, and can lead to inconsistent, unrealistic or even unreachable states in the virtual scene. This may be a problem for simulation and analysis of digital mock-ups when provable information is required. Especially, some ad hoc strategies sometimes have to be defined when using a discrete collision detection method in a virtual prototyping context in order to attempt to guarantee interpenetration-free paths. One of them consists in not moving the object when the next position involves a penetration. While this may be sufficient when few obstacles only surround the moving object, this may lead to an impossibility of manipulating the object when the environment is cluttered. Moreover, this method guarantees interpenetration-free positions only, as collisions can still be missed. Other strategies include using force fields and haptic interfaces to guarantee that the manipulated object remains far from the environment.. In the following, we present an overview of our recent work on continuous collision detection methods and constraints handling for rigid polyhedral objects. We demonstrate that continuous collision detection algorithms are possible in interactive dynamics simulation of rigid bodies and show how continuous collision detection and constraint-based dynamics algorithms allow us to perform various virtual prototyping tasks intuitively, precisely and robustly on commodity desktop computers. Especially, we present two applications of our system to actual industrial cases. We note that both tasks are performed with a simple 2D mouse. This paper has presented an overview of our recent work on continuous collision detection and constraint handling methods for polyhedral rigid bodies. We have discussed various shortcomings of discrete collision detection methods, especially in the context of virtual prototyping, and have described a continuous collision detection method based upon arbitrary in-between motions. We have shown how this method can be coupled to constraint-based dynamics algorithms. Our tests show that the simulator based upon the algorithms reported in this paper can be used for interactive dynamics simulations of complex polyhedral rigid bodies. Moreover, we have presented the applicability of our algorithms to actual industrial cases provided by Renault, which seem to demonstrate that continuous collision detection algorithms combined with efficient constraint-based dynamics algorithms can be a powerful tool for virtual prototyping tasks.. Future work include in-depth tests of our simulator. The CONTACT Toolkit library is currently being tested at Renault, PSAPeugeotCitroe¨n and Airbus-EADS. This should help to evaluate more precisely the validity and the scalability of the algorithms reported in this paper.. Also, some manufacturing tasks require a haptic feedback (training applications for example). We would like to study the benefits of continuous collision detection algorithms in this context. The algorithms reported here have been integrated to form a portable C++ library, CONTACT Toolkit, which has been successfully tested in Windows and Unix environments. The resulting simulator is able to perform interactive simulations on polyhedral objects which contain up to a few hundreds of thousands of triangles on a 2 GHz Pentium PC with 256 MB of memory and an NVIDIAGeForce4 MX graphics card.. Here, we present two applications of our system to actual industrial databases provided by Renault. We note that, for many virtual prototyping tasks, it is preferable to perform first-order (quasi-static) simulations, where the objects have no acceleration, as the absence of inertia generally facilitates the manipulation of the objects. This is done by zeroing the objects' velocities at each time step and using collision response constraints only [22] .. The first application involves positioning a car door (11,000 triangles) into the corresponding car skeleton (130,000 triangles). Figure 3 shows a typical positioning sequence. Our tests demonstrate that a user can easily position the door with a few mouse motions. The interaction is greatly facilitated by the constraint-based algorithms. The continuous collision algorithms allow the user to precisely position the door, as contacts are detected with the exact objects' geometry, without ever letting them interpenetrate.. The second application consists in removing a window motor from a car door (about 20,000 triangles in the scene). Figure 4 shows a typical interaction sequence. The contact points occurring during the interaction are materialised by small light-coloured spheres. Fig. 3 Interactive positioning of a car door (11,000 triangles) on a car skeleton (130,000 triangles). Continuous collision detection algorithms and constraint-based dynamics algorithms allow the car door to be placed precisely and interactively, without any interpenetration ever. 3D models courtesy of Renault Fig. 4 Determining the existence of a path to remove the window motor from the car door. The continuous collision detection algorithms guarantee the existence of an interpenetration-free path to remove the motor while interactively and intuitively manipulating the motor thanks to efficient constraint-based dynamics algorithms. 3D models courtesy of Renault Again, this application demonstrates the quality of the interaction provided by continuous collision detection algorithms and constraint-based dynamics algorithms. The window motor is very easily removed from the car door with a few mouse motions.. We note that, in both cases, the interactive simulator guarantees complete interpenetration-free paths, and that both tasks are performed with a simple mouse on a high-end PC.. Our tests also show that a user does not notice the fact that an arbitrary in-between motion is employed to replace the actual objects' motions between successive frames.

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


Truthful Fair Division We address the problem of fair division, or cake cutting, with the goal of finding truthful mechanisms. In the case of a general measure space ("cake") and non-atomic, additive individual preference measures -or utilities -we show that there exists a truthful "mechanism" which ensures that each of the k players gets at least 1/k of the cake. This mechanism also minimizes risk for truthful players. Furthermore, in the case where there exist at least two different measures we present a different truthful mechanism which ensures that each of the players gets more than 1/k of the cake.We then turn our attention to partitions of indivisible goods with bounded utilities and a large number of goods. Here we provide similar mechanisms, but with slightly weaker guarantees. These guarantees converge to those obtained in the non-atomic case as the number of goods goes to infinity. The basic setting of fair partition problems includes a "cake" -some divisible resource -and a number of players, each with different preferences with regards to the different "pieces" of the cake. The task is to divide the cake among the players in a way that would be "fair" according to some fairness notion. This applies to numerous situations, from divorce trials to nuclear arms reduction, see e.g. [1] .. This problem has been studied extensively both in the non-atomic case and in the case of indivisible goods. In this paper we take a fresh look at fair division, by approaching it from the mechanism design point of view, and in particular in search of truthful partition mechanisms. The problem of fair division, or cake cutting, is a central and classical problem in economics. A fair partition is one where each of k players receives at least 1/k of the cake, each according to her own measure (this is also known as a proportional partition). Fair partition into two parts has long been known to be possible using a "cut-and-choose" procedure: a cake is guaranteed to be fairly divided in two if one player cuts it and the other picks a piece.. Fair partition to more than two players requires non-trivial mathematics. The founding work in this field was done by Steinhaus, Knaster and Banach in the forties (e.g. [7] , [12] , [13] ). They and others (e.g. [10] ) proved existence theorems for fair division on general measure spaces and non-atomic measures, where "fairness" was again, in general, taken to mean that each of k players receives at least 1/k of the cake, each according to her own measure. These proofs are not constructive, but nevertheless were useful in generalizing "cut-and-choose" to more than two players.. Another natural approach is "moving knife algorithms", first described by Dubins and Spanier [4] . These are not algorithms in the modern Turing Machine sense of the word (as "cut-and-choose" and its generalizations aren't), but still provide a "practical" way to cut actual cakes, if nothing else, by the same fairness criterion mentioned above.. A stronger concept of fairness is that of "envy-free" partitions ( [6] , [14] ). In an envy free partition there is no player who would trade her allocation with one given to another player. Such partitions have been studied extensively (e.g., see [1] ).. Partitioning indivisible goods is a more recently studied variant, which places the problem in a standard algorithmic setup. However, it is easy to see that fairness or envy-freeness could not be achieved in every setup as the example of one good demonstrates. Still, the results of Lipton et al. [8] show that almost envy free partitions exist. These are partitions where no player envies another player by more than the value of a single good.. Classical cake cutting mechanisms such as "cut-and-choose" usually require the players to choose a piece of a subset of the cake or make a cut in it, according to their preferences. Alternatively, the mechanism queries the player about her valuation of a particular piece of the cake. We take an approach which is more prevalent in the modern mechanism design world: each player declares their preference (i.e., their entire measure on the cake) to some "third party", which then proceeds to divide the cake according to a predetermined algorithm.. While circulating a draft of this paper, it was brought to our attention that similar questions are discusses in a recent working paper by Chen et al. [3] . They restrict themselves to a particular class of measures: "the case where the agents hold piecewise uniform valuation functions, that is, each agent is interested in a collection of subintervals of [0, 1] with the same marginal value for each fractional piece in each subinterval." In this setting, they show a truthful, deterministic, polynomial-time, fair and envy-free mechanism. For the more general setting which we study they independently derive our mechanism 2.1.

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


A relevance model based filter for improving ad quality Recently there has been a surge in research that predicts retrieval relevance using historical click-through data [5] . While a larger number of clicks between a query and a document provides a stronger "confidence" of relevance, most models in the literature that learn from clicks are error-prone as they do not take into account any confidence estimates. Sponsored Search models are especially prone to this error as they are typically trained on search engine logs in order to predict click-through-rate (CTR). The estimated CTR ultimately determines the rank at which an ad is shown and also impacts the price (cost-per-click) for the advertiser. In this paper, we improve a model that applies collaborative filtering on click data by training a filter that has been trained to predict pure relevance. Applying the filter to ads that have seen few clicks on live traffic results in improved CTR and click-yield (CY). Additionally, in offline experiments we find that using features based on the organic results improves the relevance based filter's performance. Sponsored Search is the problem of finding candidate ads and ranking them for a search engine query. Advertisers submit creatives and bid on keywords or search queries. Ads are ranked by a combination of their estimated click-throughrate (CTR) and bid. When an ad is clicked on by a user the advertiser is charged by the search engine for the click. In the generalized second price auction used by most search engines, the cost of the click is a function of the bid and relevance of the ad below the clicked ad [4] . Models to estimate CTR are typically learned from click logs (eg., [5] ). Clicks can be interpreted as a weak indicator of relevance, and models that learn from clicks are noisy due to issues of click fraud, accidental or exploratory clicks, and positionbias. Removing bad or irrelevant ads is particularly important in sponsored search problem because poor ads not only lead to a bad user experience, but also create a bad advertiser experience because a bad advertisement with a high bid can affect the cost paid by an advertiser whose ad is shown above this bad ad in the second price auction. In this work we have proposed a relevance model based filter to remove poor ads. We have shown in both offline (human assessment) and online (live-traffic CTR) scenarios that the model improves a collaborative filtering based system that was learned on noisy click log data.

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


Using a composite grid approach in a complex coastal domain to estimate estuarine residence time We investigate the processes that influence residence time in a partially mixed estuary using a threedimensional circulation model. The complex geometry of the study region is not optimal for a structured grid model and so we developed a new method of grid connectivity. This involves a novel approach that allows an unlimited number of individual grids to be combined in an efficient manner to produce a composite grid. We then implemented this new method into the numerical Regional Ocean Modeling System (ROMS) and developed a composite grid of the Hudson River estuary region to investigate the residence time of a passive tracer. Results show that the residence time is a strong function of the time of release (spring vs. neap tide), the along-channel location, and the initial vertical placement. During neap tides there is a maximum in residence time near the bottom of the estuary at the mid-salt intrusion length. During spring tides the residence time is primarily a function of alongchannel location and does not exhibit a strong vertical variability. This model study of residence time illustrates the utility of the grid connectivity method for circulation and dispersion studies in regions of complex geometry.Published by Elsevier Ltd. Residence time can be defined as a measure of retention within defined boundaries (Zimmerman, 1976) . It is an estimate of time required for a particular substance to escape a region, and the residence time is extremely useful to determine water contamination and nutrient levels, distributions of organisms, and their spatio-temporal variations in bays and estuaries (Aikman and Lanerolle, 2004) . Estimates also provide a measure of the timescale of physical exchange that can be compared with timescales of other processes, whether they are physical, chemical, or biological. In association with residence time is the concept of age, defined as the mean time elapsed since the particle under consideration entered into a region (Liu et al., 2008) .. Estimation of residence time is difficult to quantify. Observational efforts are often hampered due to the limiting capability to measure introduced tracers into the system because they become spread out over a large region and the concentrations become too dilute to measure accurately. Previous numerical investigations have focused on several approaches. One approach is to release particles in a system (Wolanski, 2007) and measure the time for the particles to exit. Other approaches utilize the two distinctive concepts of age and residence time (Monson et al., 2002; Gourge et al., 2007) . The age is defined as the time elapsed since the particle under consideration left a certain region (or entered a region) (Deleersnijder et al., 2001; Liu et al., 2008) . The residence time is the complement of age, and is the time taken for the material to reach the outlet (Bolin and Rhode, 1973; Takeoka 1984; Yuan et al., 2007) . The residence time is determined based on a remnant function to define the amount of material remaining in the water body and is computed as the time integral of the model-predicted concentration distribution over the model domain, divided by the initial amount of material in the water body. Other more advanced methods use an adjoint advectiondiffusion method (Delhez et al. 2004; Zhang et al., 2010) . In this study we choose to follow the method as described in Yuan et al., 2007 following Takeoka (1984 to compute the residence time as the integrated concentration from individual point source releases divided by the initial amount.. The residence time in an estuary is controlled mainly by the strength of the estuarine circulation and tidal dispersion processes. Interestingly, these processes tend to vary inversely with each other. As tidal amplitude increases, the mixing increases, and the strength of the estuarine exchange flow decreases (Geyer and Cannon, 1982; Geyer et al., 2000) , thus potentially increasing the residence time. Conversely, stronger tidal velocities cause greater horizontal dispersion which can decrease residence time (Zimmerman, 1986) . So depending on the relative strength of these processes, estuarine exchange may increase or decrease with changes in tidal amplitude. We have demonstrated the methodology to create a multi-grid framework that allows an unlimited number of grids to be seamlessly connected to yield a composed grid structure. Time integration of grid points near the mesh interface is performed using data fields from the adjacent mesh. We successfully applied the composite grid method to first an idealized application to demonstrate the complete accuracy of the method, and then to a realistic estuarine setting to estimate residence time of a neutrally buoyant passive tracer. This application indicates that the springneap cycle and vertical location of the tracer release has a large and complex influence on residence time. During neap tides there is a mid-estuary near-bottom maximum in residence time created due to a combination of the estuarine circulation and the tidal advection in proximity to the estuary mouth. During spring tides the water column is well mixed and the residence time was more associated with the along-channel location of the release and did not exhibit strong vertical variability. The composite grid approach would be useful in a variety of applications in coastal and estuarine environments with complex morphologies.

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


An Empirical Evaluation of XQuery Processors This paper presents an extensive and detailed experimental evaluation of XQuery processors. The study consists of running five publicly available XQuery benchmarks -the Michigan benchmark (MBench), XBench, XMach-1, XMark and X007 -on six XQuery processors, three stand-alone (file-based) XQuery processors (Galax, Qizx/Open, Saxon-B) and three XML/XQuery database systems (BerkeleyDB/ XML, MonetDB/XQuery, X-Hive/DB). Next to assessing and comparing the functionality, performance and scalability for the various systems, the major focus of this work is to report in detail about the experiences made while performing such an exhaustive study, to discuss all the problems that we encountered and how we solved them, and hence to hopefully provide some guidelines (or even a recipe) for performing reproducible large-scale experimental research and system evaluation. Experimental evaluation and comparison of (new) techniques, algorithms and/or complete systems is a vital means to assess the practical impact and benefit of research results, especially in applied domains such as data management systems. While many publications present experimental results, the extent of the presentation -or even the experiments themselves -are often very limited due to space, time and/or other resource constraints. The major focus of most research publications is on the (so-called) scientific contributions.. In this study, we shift the focus. Performing the actual experimental evaluation becomes the primary subject. Presenting the experimental setup in detail, we do not hesitate to reveal all the "nasty details" and "minor problems" that give us headaches and cause sleep-less nights. The major contribution is hence a detailed cookbook about how to conduct an experimental comparison and assessment of data management systems. However, though focusing on the actual experimentation techniques, we also present the "hard 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. facts": the detailed performance results we gathered.. The remainder of this paper is organized as follows. We start with presenting our experimentation environment in Section 2. Section 3 lists the benchmarks that we are using and discusses adaptations of the benchmarks, their queries and documents that are necessary to perform our experiments. In Section 4, we introduce the six XQuery systems we use, and explain in detail how we compile, install, configure and use them. Section 5 reveals how we run our experiments, validate results and timings, and collect the performance data that is presented in detail in Section 6. We draw final conclusions in Section 7. First of all, we can conclude that our exercise demonstrates the feasability of such an extensive and detailed experiment -though is requires quite some work, time, and resources. We describe our experimental setup in detail and explain, how we tackle various problems to reach our ambitious goal. We hope, we provide all information that is necessary and sufficent to reproduce our results.. As expected, the actual performance results do not crown a single winner. However, some general trends can be observed. In a realistic database scenario, i.e., with the documents pre-loaded in the database, the database engines perform considerably better (up to two orders of magnitude) than the file-based stand-alone systems. Even if we add the initial document loading times, they are often still faster, but hardly ever slower. In pure document loading performance (query Q0), MonetDB/XQuery, Saxon-B and Qizx/Open lead the race neck-to-neck; X-Hive/DB and BerkeleyDB/XML follow within a factor 2-3; Galax runs about factor 10 behind the leaders. While all systems have their strengths and weaknesses, MonetDB/XQuery seems to be ahead of the pack in most cases, usually followed (in that order) by BerkeleyDB/XML, X-Hive/DB, Qizx/Open, Saxon-B, and finally Galax. Join recognition and processing (still) seems to be the biggest challenge to be solved.. For the future, we plan to extend the scenario in various dimensions, e.g., including more systems (e.g., eXist [1]) and benchmarks (e.g., XPathMark [9] , MemBeR [2] ), considering other compilers and optimization flags, using different hardware and operating systems, etc.. The goal is not to find the single best setup, but rather to show that all these often neglected factors can influence experimental results considerably. Hence, all reports of experimental results should reveal all these information explicitly in order to (1) provide all information to make the results reproducible, and (2) to put them in the right perspective. Finally, we hope that our experiences with XCheck will help to improve and extend this convenient experimentation tool.

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


Parameterized Complexity of Cardinality Constrained Optimization Problems We study the parameterized complexity of cardinality constrained optimization problems, i.e., optimization problems that require their solutions to contain specified numbers of elements to optimize solution values. For this purpose, we consider around twenty such optimization problems, as well as their parametric duals, that deal with various fundamental relations among vertices and edges in graphs. We have almost completely settled their parameterized complexity by giving either FPT algorithms or W[1]-hardness proofs. Furthermore, we obtain faster exact algorithms for several cardinality constrained optimization problems by transforming them into problems of finding maximum (minimum) weight triangles in weighted graphs. We have demonstrated through a large number of graph problems that parameterized complexity analysis is a useful, fruitful and also natural framework for studying cardinality constrained optimization problems. This framework not only complements the classical complexity theory, but may also provide us with new insight into such problems.. As expected, we have seen that many fixed-cardinality optimization problems remain hard under the framework of parameterized complexity. Nevertheless, it is rather surprising that many different graph problems are closely related through their fixed-cardinality optimization problems, and such connections are revealed only through parametric reductions among these problems. Close connections are also evidenced by the central role of k-Clique on regular graphs in our W[1]-hardness proofs, and the simplicity of most of our parametric reductions.. In terms of fixed-parameter tractability, we have used various techniques to obtain FPT algorithms. This is certainly encouraging as fixed-cardinality optimization problems are usually very difficult to solve. On the other hand, we need new tools to deal with fixed-cardinality optimization problems more effectively. In this direction, we note that the newly developed random separation method of Cai, Chan and Chan [7] is quite useful and its power seems yet to be fully explored. Furthermore, Cai and Leung [8] have recently developed an extension method to solve Maximum k-Vertex Cover on planar graphs. Their basis idea is to extend iteratively a maximum i-vertex cover to a maximum (i + 1)-vertex cover, but bound the search space to a small graph. It will be also quite interesting to see how the colour coding method of Alon, Yuester and Zwick [3] , and the iterative compression method of Reed, Smith and Vetta [23] can be applied to solve fixed-cardinality optimization problems.. We have illustrated through several W[1]-hard fixed-cardinality graph problems that we can reduce the main cost of their exact algorithms from O(n k ) to around O(n 0.8k ) by transforming them into problems of finding appropriate triangles in auxiliary graphs.. It will be interesting to come up with some sufficient conditions or necessary conditions for problems that can be solved by this approach. Of course, it is also interesting to determine whether it is possible to find a maximum weight triangle in O(n ω ) time.. For the future directions, we can certainly investigate the parameterized complexity of other cardinality constrained optimization problems. In particular, problems for digraphs seem to be very good candidates. Another important and interesting direction is to study connections between fixed-parameter tractability and various approximation schemes for cardinality constrained optimization problems. My recent work [5] has indeed revealed some close connections, and I believe that there are deep connections yet to be discovered.. As for the two open problems Minimum k-Edge Subgraph and Maximum k-Edge Multicomponent Cut in Table 1 , we note that MinES(k) is closely related to the problem of finding a subset of vertices that induces a subgraph with exactly k edges, and remind the reader that MaxEMC(k) is connected to the well studied multiway cut problem. I conjecture that MinES(k) is FPT but I am uncertain about MaxEMC(k).. It seems that if we confine ourselves to the P versus NPc question, we actually conceal, rather than reveal, the intricate complexity of cardinality constrained optimization problems. Through the lens of parameterized complexity, we see a colourful world of the complexity of cardinality constrained optimization problems. In my view, parameterized complexity analysis is a natural and integrated part in the study of cardinality constrained optimization problems, and I am looking forward to seeing more exciting results.

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 B I 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 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 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 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 B I 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