Parsimonious additive models We present a new method for function estimation and variable selection, specifically designed for additive models fitted by cubic splines. Our method involves regularizing additive models using the l 1 -norm, which generalizes Tibshirani's lasso to the nonparametric setting. As in the linear case, it shrinks coefficients, some of them reducing exactly to zero. It gives parsimonious models, select significant variables, and reveal nonlinearities in the effects of predictors. Two strategies for finding the parsimonious additive model solutions are proposed. Both algorithms are based on a fixed point algorithm, combined with a singular value decomposition that considerably reduces computation. The empirical behavior of parsimonious additive models is compared to the adaptive backfitting BRUTO algorithm. The results allow us to characterise the domains in which our approach is effective: it performs better than BRUTO when model estimation is challenging. These results extend and agree with those already obtained in linear regression. An implementation of this method is illustrated using real data from the Cophar 1 ANRS 102 trial. Parsimonious additive models are applied to predict the indinavir plasma concentration Preprint submitted to Elsevier Science in HIV patients. Results suggest that our method is a promising technique for the research and application areas. Nonparametric regression methods encompass a large class of flexible models which provide a means of investigating how a response variable Y depends on one or more predictor variables X 1 , ..., X p , without assuming a specific shape for the relationship. However, as dimension p increases, these techniques suffer from the curse of dimensionality; moreover the ability to visually inspect estimated relationships is often lost when p > 2.. An elegant solution to these problems is provided by additive models, popularized by Hastie and Tibshirani [24] . An additive model is defined by. where the error ε is independent of the predictor variables X j , E(ε) = 0 and var(ε) = σ 2 . f j are univariate smooth functions, defined such that E X j (f j ) = 0 in order to ensure unicity, and α 0 is a constant.. The additive structure does not assume a rigid form for the dependence of Y on X 1 , ..., X p so nonparametric flexibility is preserved. Also, the additive model retains an important interpretive feature of the linear model: we can represent the functions f j to analyze the effects of the predictors on the response. Moreover, it overcomes problems of high-dimensionality: since the response variable is modeled as the sum of univariate functions of predictor variables, the number of observations required to get variance-stable estimates grows only linearly in p. The price to pay for such interesting properties is the possible misspecification of the model.. As in any statistical learning task, model selection is an important issue in the estimation of additive models. The problem of determining the model structure that best fits the data can be decomposed in two subproblems: complexity tuning and variable selection. In nonparametric regression there is a fundamental trade-off between the bias and variance of the estimate, which is typically governed by a regularization or smoothing parameter. Complexity tuning addresses the question "what is the right amount of smoothing" [24, 25] .. Variable selection consists in selecting input variables that are most predictive of a given outcome. Appropriate variable selection aims at improving prediction performance, enhancing understanding of the underlying concept that generated the data and reducing training time [22] .. Subset selection strategies have been applied to additive models. These proposals exploit the fact that additive regression generalizes linear regression.. Thus, we find hypothesis tests [13, 11, 23, 42, 17] , techniques based on a prediction error estimator [10, 7, 33] , as well as Bayesian approaches [35, 34] .. A different approach to variable selection consists of regularizing additive models using the l 1 -norm. We present a new method for variable selection and complexity tuning specifically designed for additive models fitted by cubic splines. We use a three-part objective function that includes goodness-of-fit and a double penalty: on the l 1 -norm of linear components of cubic splines coefficients and on the (generalized) l 1 -norm of nonlinear components of cubic spline coefficients. Because of their nature, these penalties shrink linear and nonlinear compounds, some of them reducing exactly to zero. Hence they give parsimonious models, select significant variables, and reveal nonlinearities in the effects of predictors.. Two strategies for finding the parsimonious additive model solutions are pro-posed. In both, curve fitting is based on a fixed-point algorithm solving the penalized optimization problem, combined with a singular value decomposition that considerably reduces computation. The empirical behavior of parsimonious additive models is compared to the adaptive backfitting BRUTO algorithm for additive models [24] . The results allow us to deduce conditions of application for each method. Our method performs better than BRUTO when model estimation is challenging. These results extend and agree with those already obtained in linear regression.. This new approach is applied to predict indinavir (an antiretroviral from the protease inhibitor class) plasma concentration in HIV patients, from the Cophar 1 ANRS 102 trial.. This article is organized as follows. In section 2 we review penalization techniques. Additive models fitted by cubic splines are introduced in section 3.. We present our approach in section 4. In section 5 we discuss estimation of the regularization parameters. Simulation studies are described in section 6. A real data example is given in section 7. Finally, section 8 contains concluding remarks and perspectives. Additive and generalized additive models provide a flexible alternative to the standard linear and generalized linear models, preserving the ability to summarize relationships in an intuitive way. These models are thus applied in several domains including economics [35, 4] , engineering [41] and public health [2, 14] . Most of these applications deal with few predictor variables. Additive models are seldom applied to variable selection problems, owing to the limitations of current methods.. In this paper we have proposed an extension of the lasso technique to additive models. In general, simulation results extend and agree with those previously obtained for linear regression [5, 37] . However, in a nonlinear context, results are less categorical. On the one hand, the situation itself is more complex, but on the other hand, many factors act on the difficulty of the problem. We evaluate the performance of our method by comparing it to BRUTO, an adaptive method for estimating an additive model using smoothing splines that combines the backfitting algorithm with the model selection algorithm, allowing a continuous regimen of fits for each term [24] . The model selection is based on an approximation to the GCV criterion, which is used at each step of the backfitting procedure. Once the selection process stops, the model is backfit using the chosen amount of smoothing. Simulations concerning BRUTO were carried out using the mda package of R 2.1.1.. Parsimonious additive models are computed by the two proposed algorithms:. PAM1 and PAM2. Model selection for parsimonious additive models is carried out using CV criterias, which are evaluated over a 8 × 8 grid of (µ, λ). values regularly spaced on a logarithmic scale. Leave-one-out CV (for linear smoothers) is used by PAM2 and 5-fold CV is used by PAM1, which involves much more calculations. The performance of CV is compared to the optimal performance, achieved by choosing the model that minimizes the test error (the crystal ball model, using Breiman's terminology [5] ), and calculated over the same grid of values. Simulations concerning parsimonious additive models were carried out using Matlab 6.5.. Results obtained by the constant model (CM), estimated by the mean response, are also provided as a reference.

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


An Approach to Extracting Trunk from an Image Rendering realistic trees is quite important for simulating 3D natural scene. Separating trunk from its background is the first step toward the 3D model construction of the tree. In this paper, a three-phase algorithm is developed to extract the trunk structure of the tree and hence segment the trunk from the image. Some experiments were conducted and results confirmed the feasibility of proposed algorithm. Creating a realistic virtual environment is the dream of many people working in computer science. Since tree is a very common object in natural environment, its 3D model creation is necessary for simulating 3D natural scene. In fact, tree rendering is a research topic in computer graphics and some approaches have been developed to render and create realistic trees [1] - [4] . In computer graphics, trees are often created by some algorithmic rules plus some random variations. Although the generated trees are quite realistic presently, they are sometimes not what we want. For instance, if we want to create a 3D virtual scene of our surrounding environment, then the created tree should have a similar 3D trunk structure and global leaf appearance to the true one, not generated artificially. We should create the 3D tree model from the real tree. One method to achieve this goal may be accomplished by taking several views of the tree and exploiting the techniques of structure from motion to construct a 3D tree model similar to the real one. Specifically, we can first extract the trunk from the image and establish its 2D trunk structure. Subsequently, we can utilize trunk correspondences in different views to extend the 2D trunk structure to 3D trunk model. The leaves can be generated using graphical methods and pruned according to the tree in the images. The created 3D tree model is definitely not identical to the true one but is similar to it at least and for some applications this is enough. From this viewpoint, trunk extraction plays a rather important role for a similar 3D tree model construction. In fact, trunk extraction is also useful for other applications such as image retrieval and scene analysis. Therefore, in this paper, we develop an algorithm to extract trunk from an image. We first segment the image using the well-known EM algorithm [5] and then model the extraction of trunk structure as an optimization problem. An energy function is formulated according to the color, position, and orientation of the segmented regions. We propose an approach to minimize this energy function and thus extract the trunk structure of the tree. In the following, we will describe the detailed procedures of how to extract the trunk structure from the segmented regions. representing them. Hence, our basic idea is to trace the trunk by exploiting the skeletons of the segmented regions. However, the trunk of a tree is generally segmented into several regions, thus an efficient algorithm must be provided to connect these extracted skeletons. We partition the skeleton image into a number of small blocks called trunk elements as shown in Fig. 1 . These small blocks are the basic elements for extracting trunk structure. To facilitate the extraction of trunk structure, we attach several useful properties to each trunk element. These properties are summarized in Table 1 . We formulate the problem of extracting trunk structure as an optimization problem and define an energy function according to the color, position, and direction of the trunk elements. This energy function is the function of the connecting configuration of these trunk elements and can be minimized via connecting possible trunk elements. When the energy function is minimized, the trunk elements belonging to the true trunk regions are well-connected. The trunk structure can then be obtained by tracing these connected trunk elements from the root. These connected trunk elements are named trunk flow (see Fig. 1 ) in this paper. Because there are many non-trunk regions in the image, their skeletons will interfere with the connection of true trunk elements. Therefore, to correctly extract the trunk structure, these non-trunk regions should be removed in advance. In this research, we employ a systematic method to remove the non-trunk regions. Several rules are designed to test the color, orientation and position of the segmented regions and only the survived regions are processed in the subsequent procedures. However, this systematic method cannot fully filter out all the non-trunk regions. To reduce the interference of these survived non-trunk regions, we develop a three-phase algorithm to extract the trunk flow.

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Accurate recovery-based upper error bounds for the extended finite element framework This paper introduces a recovery-type error estimator yielding upper bounds of the error in energy norm for linear elastic fracture mechanics problems solved using the extended finite element method (XFEM). The paper can be considered as an extension and enhancement of a previous work in which the upper bounds of the error were developed in a FEM framework. The upper bound property requires the recovered solution to be equilibrated and continuous. The proposed technique consists of using a recovery technique, especially adapted to the XFEM framework that yields equilibrium at a local level (patch by patch). Then a postprocess based on the partition of unity concept is used to obtain continuity. The result is a very accurate but only nearly-statically admissible recovered stress field, with small equilibrium defaults introduced by the postprocess. Sharp upper bounds are obtained using a new methodology accounting for the equilibrium defaults, as demonstrated by the numerical tests. The eXtended Finite Element Method (XFEM) is currently a well established very efficient numerical technique for modelling inclusions and cracks [1, 39] . With respect to the standard Finite Element Method (FEM), XFEM has the advantage of making the finite element mesh independent of the crack geometry. Thus, the mesh does not need to be modified during the crack propagation process. The XFEM uses the partition of unity concept [2] to add new interpolation functions that enrich the mathematical representation of the solution in the vicinity of the crack.. The first developments in this method [1, 39] were soon followed by a considerable amount of publications as described in [3] . Thanks to all these developments and to the latter contributions in this field (see for example [4] [5] [6] [7] [8] [9] [10] [11] ) the XFEM is now considered to be a robust and highly accurate tool to analyze Linear Elastic Fracture Mechanics (LEFM) problems.. As in the FEM, the results obtained using the XFEM are affected by the discretization error associated with the finite size of the elements. In fact, this technique tends to be used with coarse discretizations. Thus, it is necessary to quantitatively assess their quality and, consequently, error estimation techniques are also required in the XFEM context. This paper presents a theoretical upper bounded estimator for the error in energy norm and a strategy to evaluate its computable version for LEFM problems solved using XFEM. The technique here proposed is an enhancement of a previous technique developed for FEM [31] and an adaptation to XFEM approximations.. The proposed procedure consists of two phases: a) evaluation of a nearly statically admissible recovered stress field that provides a very accurate estimation of the error in energy norm; and b) correction of the error estimation to account for the equilibrium defects of the nearly statically admissible field, which guarantees that the error obtained is an upper bound of the exact error.. The recovery technique providing the nearly statically admissible stress field is based on the SPR technique and the use of a splitting Fig. 15 . Mode I. Evolution of E SPR-CX and E UBex . Fig. 16 . Mode I. Evolution of the absolute value of the correction terms.. technique that decomposes the stress field into a singular part and a smooth part. The proposed procedure uses a recovery technique which ensures that, at each patch, σ i ⁎ is statically admissible, matching body loads and boundary tractions. Finally, a PUM based technique is used to obtain a continuous recovered field σ ⁎ , which, on the other hand, introduces lacks of equilibrium in the recovered solution.. A new technique for the evaluation of the correction terms associated with the lack of equilibrium has also been presented. The technique requires the problem to be solved using a sequence of refined meshes. The numerical experiments show the high accuracy of the proposed technique. The need for a mesh sequence and the lack of accuracy in the last mesh suggest developing new procedures for the estimation of the error in the displacement field, without using any mesh sequence. This is left for future research.. The numerical results show that the estimation of the discretization E SPR-CX is very accurate, with effectivities within the range (0.95−1.01). Despite of the fact that E SPR-CX is not an upper bound of the exact error, the numerical results indicate that this value could be considered as a low-cost computed version of the theoretical upper bound where the effect of all the correction terms due to equilibrium defects has been neglected.

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Incorporating partial matches within multiobjective pharmacophore identification This paper describes the extension of our earlier multiobjective method for generating plausible pharmacophore hypotheses to incorporate partial matches. Diverse sets of molecules rarely adopt exactly the same binding mode, and so allowing the identification of partial matches allows our program to be applied to larger and more diverse datasets.The method explores the conformational space of a series of ligands simultaneously with their alignments using a multiobjective genetic algorithm. The principles of Pareto ranking are used to evolve a diverse set of pharmacophore hypotheses that are optimised on conformational energy of the ligands, the goodness of the overlay and the volume of the overlay. A partial match is defined as a pharmacophoric feature that is present in at least two, but not all, of the ligands in the set. The number of ligands that map to a given pharmacophore point is taken into account when evaluating an overlay. The method is applied to a number of test cases extracted from the Protein Data Bank where the true overlay is known. † Current address: A pharmacophore describes the spatial arrangement of chemical features required for a small molecule to bind to a receptor. Pharmacophore identification methods are usually applied to a series of molecules known to bind to a receptor, when the three-dimensional structure of the receptor is unknown. The first generation of pharmacophore identification programs have been around for more than a decade [1] [2] [3] [4] . However, recently some of the limitations of these early methods have been highlighted [5, 6] and several new approaches are now beginning to appear that address some of these limitations [7] [8] [9] [10] .. Pharmacophore identification involves identifying common pharamcophoric features within the molecules, that is, atoms or functional groups that can interact with a receptor in a similar way, and then aligning the bioactive conformations of the molecules such that their corresponding features are overlaid. The bioactive conformations of the molecules are not usually known and so some form of conformational analysis is usually carried out. For many datasets, there are numerous plausible ways of overlaying the molecules, due to the presence of multiple features within the molecules and due to the multiple accessible conformers that may exist for each molecule. In such cases, it is important that the chemist is presented with a range of alternative hypotheses that can be validated further, for example, by database searching or by the synthesis of new compounds.. The quality of a pharmacophore hypothesis is usually judged on a number of criteria. For example, the GASP program [2] evaluates a pharmacophore on the number of pharmacophoric points it consists of, the quality of the mapping of each molecule onto the pharmacophore (which includes consideration of site points together with their associated heavy atoms), the common volume of the overlaid molecules and their conformational energy. GASP is based on a traditional optimisation technique in which the multiple criteria are combined into a single weighted-sum fitness function.. Specifically, the fitness function in GASP combines three components that take account of the feature alignment, the volume overlap and the conformational energy. This approach reduces the problem to a single-objective optimisation problem that can be handled by a single-objective optimisation method, such as the genetic algorithm (GA) in The paper has described the extension of our earlier work [9] to incorporate partial matches within a multiobjective optimisation approach to pharmacophore identification.. Pharmacophore methods are particularly useful if they can be applied to datasets of structurally diverse molecules, where they may be able to suggest overlays that are not obvious to the chemist. However, diverse sets of molecules rarely adopt exactly the same binding mode. Hence, programs that make the assumption of a common binding mode are not able to handle diverse datasets effectively. Allowing the identification of partial matches removes the restriction that every molecule must match every pharamcophore point, which allows the program to be applied to larger and more diverse datasets.. The datasets investigated here were extracted from the PDB so that the true solution is known and hence the program can be validated. However, pharmacophore identification is typically used when structural information on the binding site is unavailable and in the absence of such data, it is unlikely that a single solution could be predicted The partial match methodology has been applied to two sets of ligands extracted from the PDB [18] . The ligands were extracted from their respective complexes and energy minimised using the Tripos 5.2 force field with Gasteiger-Marsili charges assigned. The MOGA was then used to identify plausible pharmacophores. In the following experiments, all five-and six-membered rings were identified as possible hydrophobic features. Unless otherwise stated, the runs were performed on a 2.8 GHz Linux PC using the parameters shown in Table 2 . The number of operations and the number of mapping columns in the chromosome varied between experiments and are specified in the details of each experiment. Table 2 . MOGA parameters. We have extended the multiobjective genetic algorithm (MOGA) described previously [9] to allow the pharmacophore hypotheses identified to include partial matches. A partial match is defined as a pharmacophoric feature that is present in at least two, but not all, of the ligands in the set. The algorithm is described in detail below, with particular emphasis given to the new methodology.. The ligands are input to the program as energy minimised conformations. The first step is to identify the pharmacophoric features within each ligand. Donor and acceptor features are defined as in GASP, however, the definition of a hydrophobe has been extended to include aliphatic rings and user-defined groups, in addition to the aromatic rings defined previously. Each hydrophobic ring is represented by a virtual point created at the centre of the ring and a normal to the ring. A user-defined hydrophobe, such as a t-butyl group, is specified as a list of atoms and a virtual point is created at the centroid of the atoms. Donors and acceptors are represented by virtual points that correspond to the hypothetical positions of acceptors or donors in the receptor binding site. Thus, a virtual point is created at 2.9Å from the heavy atom attached to each hydrogen-bond donor proton and at 2.9Å from the heavy atom associated with each acceptor lone pair.

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


Data extraction from the web using wild card queries This paper presents an overview of our work for searching and retrieving facts and relationships within natural language text sources. In this work, an extraction task over a text collection is expressed as a query that combines text fragments with wild cards, and the query result is a set of facts in the form of unary, binary and general n-ary tuples. Despite being both simple and declarative, the framework can be applied to a wide range of extraction tasks. This paper presents an overview of the work and its various components. We also report some of our experiments and an evaluation of the proposed querying framework in extracting relevant information to a task. The World Wide Web contains a vast amount of information and is a rich source for data extraction, but manually extracting data from the Web is a tedious and time consuming process, especially when a large amount of data matches the extraction criteria. Example extraction tasks include compiling a list of Canadian writers, finding a list of medications for a disease, etc. Unless such lists have already been compiled and made available on the Web, one has to query a search engine, examine the pages returned, and extract a handful of instances from each page (if there is any at all).. The problem is further complicated by the flexibility of natural languages. Consider the example of extracting Canadian writers; many bona fide writers are not referred to as writers. Instead, they are often coined as authors, novelists, journalists, etc. If only the phrase "Canadian writers" is used in the query, many qualified instances will not be extracted, thus the extraction quality is compromised. Many previous data extraction systems either focus on a more specific task by imposing tight restrictions on the type of data that can be extracted (e.g. finding course offerings and job postings) or are only applicable to documents that follow a specific formatting (e.g. wrappers). For example, the KnowItAll [6] system can extract hyponyms of a user-specified class. The online prototype of the system is further extended to support a few more specific binary relations (e.g. X "ceo of " Y). A challenge facing many data extraction systems in general is that the extraction task often is not easy to define or a definition may not be accurate, leading to low precision and recall. Limiting the extraction task to a few predefined classes is one way to reduce the complexity of the problem.. This paper presents an overview of a framework that allows an extraction task to be encoded as a simple query. A query in this framework is a natural language sentence or phrase with some wild cards, and the result of a query is a ranked list of matching tuples. For instance, given the query "% is a car manufacturer", the output is expected to be a ranked list of car manufacturers, preferably the real car manufacturers ranked the highest. This query only uses one wild card, here denoted with %. In general, a query can use more than one % wild card, and the result of the query in this case is a table with one column for each occurrence of the wild card.. One of our contributions is a declarative querying framework for data extraction. Integration of wild cards in our queries can generally reduce the number of queries that must be issued, hence simplifying the extraction task. Another contribution is the idea of query expansion through a set of declarative rewriting rules between paraphrases. Since a given user query may not retrieve an adequate number of facts, rewriting rules are generally expected to improve the coverage of the queries and the quality of the results. Finally, as our last contribution, we report an experimental evaluation of our work in the setting of the Web.. The rest of the paper is organized as follows. Section 2 describes both the syntax and the semantics of wild cards, as well as the queries in our framework. An overview of our query evaluation in the context of the Web is given in Section 3. An experimental evaluation of the work is presented in Section 4 and the related work is reviewed in Section 5. We end the paper with conclusions and future work in Section 6. See the extended version of this paper [11] for more details on our query expansion, ranking algorithms and a more extensive evaluation of the work. We presented a framework for querying and large-scale data extraction from natural language text, and evaluated the effectiveness of our framework within a few data extraction tasks on the Web. We analyzed our rankings of the results in terms of the stability and the locality of the scoring functions and conducted experiments comparing their effectiveness in terms of precision and recall. Our querying interface is intuitive for writing queries and scalable to large number of rewritings and with more wild cards.. Our work opens a few interesting directions for future work. First, it would be interesting to study other wild cards, querying schemes and formalisms that are simple for writing queries and at the same time have a well-defined syntax and semantics for query evaluations and optimizations. We consider our wild card queries as a first step toward more formal querying of natural language text. Second area for possible future work is data storage and indexing. Despite the extensive work on indexing free text, there is not much work on indexing natural language text in particular. Given that natural language text can be parsed, there is much room for research on building indexes that are aware of sentence structures and queries. Third, a more formal query syntax and semantics opens the door for more study on mapping queries to evaluation plans and access path selection and optimization. These are important issues when querying large repositories and/or posing complex queries. Another area for further study is on extracting n-ary relations for n > 3; the problem in general is difficult since the columns of target rows can be scattered in multiple sentences. Yet one more area is on mapping natural language questions to more formal queries that can be efficiently evaluated. There is a large body of work on question answering. Many systems use a combination of NLP techniques (deep or shallow), learning algorithms and hand-crafted rules to classify the questions and to establish relationships between terms of a question and a possible answer sentence (e.g. [8, 5] ). Despite some overlap, there are fundamental differences between our work and the work on question answering. Our work is not a replacement for QA systems that can often handle complex questions; it is rather a natural way of expressing short questions or extraction targets. It is possible to integrate our work within a question answering system if natural language questions can be mapped to DeWild queries.. Large-scale data extraction from the Web has been the subject of various recent work [1] . In particular, Brin [4] suggests an algorithm which takes a small number of examples of a class as a seed set and extracts more examples of the same class. His algorithm learns a set of extraction patterns for each page (or pages with the same URL prefix) that contains some of the examples and use those patterns to extract more tuples from the same page(s). This algorithm does a good job when data is structured in a tabular format but is not expected to work on free text. This is because it is generally unlikely to find more than one example (of the seed set) in a text document such that their surrounding texts are the same.. KnowItAll [6] takes the description of a concept or class (e.g. cities) as input and extracts instances (e.g. Paris, New York, . . . ) of the class. The system maintains a set of rules which can be instantiated with an input class to produce keywords that must be used to extract the instances of the class. KnowItAll uses co-occurrence statistics, specifically mutual information, to assess the relatedness of each instance. Our approach differs from KnowItAll in several important aspects: First, the query-based interface and the support of wild cards make DeWild more adaptive to different extraction tasks. Second, unlike KnowItAll where a concise description of a class must be given, a DeWild query may specify only the context in which the instances may appear, and this is useful when a concise class description is not available (this problem is somewhat addressed in TextRunner [2] ). Last but not least, our approach of porting link-based ranking algorithms for assessing extraction results from text is novel and performs better than the one used in KnowItAll.. Other related work includes the work on query expansion [3] and the work on Web query languages and wrappers (see [7] for a survey of this area before 1998). Finally, Google's fill-in-the-blank is related to our wild cards but is different. Google returns a ranked list of pages for a fill-in-the-blank search but the ranking is different (and the detail is not published). An evaluation of Google's fill-in-the-blank compared to DeWild can be found in the extended version of this paper [11] .

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Asymptotic analysis of pollution filtration through thin random fissures between two porous media We describe the asymptotic behavior of a filtration problem from a contaminated porous medium to a non-contaminated porous medium through thin vertical fissures of fixed height h > 0, of random thinness of order ε and which are ε-periodically distributed. We compute the limit velocity of the flow and the limit flux of pollutant at the interfaces between the two porous media and the intermediate one. We consider a porous medium which is contaminated by some pollutant and which communicates with another porous and non-contaminated medium through vertical fissures of height h > 0, of random thinness of order ε > 0, and which are periodically disposed. Each of these porous media is given a ε-periodic structure. Instead of considering a Stokes problem in each of these porous media, we assume that the velocity of the fluid is governed by a Darcy law with periodic permeability matrix.. The purpose of this work is to determine the influence of the fissures on the transport of the contaminant into the non-contaminated medium, computing the global flux of pollutant which penetrates in this non-contaminated medium and the asymptotic velocity of the fluid which flows through the fissures.. Let Ω be a bounded, smooth and open subset of R 3 , with boundary Γ, such that. = Ω ∩ {x 3 < −h} = ∅. . Let (Π, Υ, P ) be some probability space and (T (t)) t∈R be a group of transformations on (Π, Υ), that is satisfying    T (0) = Id Π , T (t 1 + t 2 ) = T (t 1 ) • T (t 2 ) ∀t 1 , t 2 ∈ R,. where Id Π is the identity map on Π and the set {(t, ω) ∈ R × Π | T (t) ω ∈ A} is dt × dP measurable, for every A ∈ Υ. We suppose that T is ergodic (or metrically transitive), which means that every A ∈ Υ such that T (t) A = A, for every t ∈ R, has a probability P (A) equal to 0 or 1. We introduce some random processes q and r defined on R × Π and satisfying the following conditions:. 1. q (t, ω) is a stationary random process, that is, for every positive integer n, every points t 1 , · · · , t n , every t in R, and every B ∈ B (R), one has P ({ω | q (t + t 1 , ω) , · · · , q (t + t n , ω) ∈ B}) = P ({ω | q (t 1 , T (t) ω) , · · · , q (t n , T (t) ω) ∈ B}) , where B (R) is the Borel σ-algebra on R. Since T preserves the measure P , the above equality implies that the joint distribution of {q (t 1 ) , · · · , q (t n )} is the same as the joint distribution of {q (t 1 + t) , · · · , q (t n + t)}, for every t in R.

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


Improving retrievability of patents with cluster-based pseudo-relevance feedback documents selection High findability of documents within a certain cut-off rank is considered an important factor in recall-oriented application domains such as patent or legal document retrieval. Findability is hindered by two aspects, namely the inherent bias favoring some types of documents over others introduced by the retrieval model, and the failure to correctly capture and interpret the context of conventionally rather short queries. In this paper, we analyze the bias impact of different retrieval models and query expansion strategies. We furthermore propose a novel query expansion strategy based on document clustering to identify dominant relevant documents. This helps to overcome limitations of conventional query expansion strategies that suffer strongly from the noise introduced by imperfect initial query results for pseudo-relevance feedback documents selection. Experiments with different collections of patent documents suggest that clustering based document selection for pseudorelevance feedback is an effective approach for increasing the findability of individual documents and decreasing the bias of a retrieval system. Conventionally, retrieval systems are evaluated based on Average Precision, Q-measure, Normalized Discounted Cumulative Gain, and other metrics [12] . However, these metrics do not evaluate, what we can find and cannot find globally throughout the whole collection. In spite of low retrievability, systems can still achieve good precision performance 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. [1], which is a perfectly just target in precision-oriented application domains, where the focus is on providing a small set of perfectly matching results. In this paper, we argue that in recall oriented domains like legal or patent retrieval settings, it is very important to considered retrievability of each and every document, that is, whether each document can potentially be found for a query that it is relevant for. Document retrievability [1] is a measurement used in Information Retrieval (IR) for determining, in how far all documents in a collection can actually be found given a specific retrieval system. In other words, retrievability is used to analyze the bias of retrieval systems. To measure retrievability, a large set of potential queries (e.g. all combinations of all important keywords up to a pre-specified query length) are passed to a retrieval system, and the number of documents that can and that cannot be retrieved is evaluated. The resulting figure provides an estimate on the amount of bias introduced by a certain retrieval system, indicating its suitability for recall-oriented applications.. In this paper, we use Query Expansion (QE) as an approach for increasing the retrievability of individual documents in recall oriented settings. The main motivation behind our work is to analyze the strength of different QE approaches, such as to what extent they can make individual documents more findable. However, first experiments revealed, that state of art QE approaches showed worse retrievability performance. This is because in QE it is assumed, that the set of top-ranked documents used for PseudoRelevance Feedback (PRF) is relevant, and learning from these Pseudo-Relevance documents can improve the ranking [10] . However, due to system bias, top-ranked documents may contain noise [10] , which can ultimately result in the query representation drifting away from the original query.. Targeting this limitation and for improving the retrievability of individual documents, in this paper, we propose an improved clustering based resampling method for PRF selection. The main idea is to use document clustering based on local frequent terms to find dominant documents for PRF. In this paper, we evaluated the effectiveness of different retrieval systems using retrievability measurement with a focus on recall oriented application domains. Our results yield that state of the art QE methods provide a large inequality in the retrievability of documents, as compared to those systems which do not expand queries. This is due to their ineffective assumption that top rank documents for PRF are always relevant and learning from these relevance feedback documents for expanding queries can increase the effectiveness of retrieval systems. For overcoming this limitation, in this paper we utilize clustering approach for better document selection for PRF. On our extensive retrievability experiments with using large collection of queries, our clustering approach for PRF, provides less bias than all other systems on different rank factors. For our experiments, we use a collection of freely available patents from the US patent and trademark office, downloaded from (http://www.uspto.gov/). We collected all patents that are listed under United State Patent Classification (USPC) classes 422 and 423 . There are a total of 54, 353 documents in our collection, with an average document size of 3, 317.41 words (without stop words removing). Seven state-of-the art IR models and QE methods along with our proposed clustering technique are used for evaluating the retrievability inequality. These are TFIDF, OKAPI retrieval function (BM25), Exact match model, Language Modeling with term smoothing (LM) [13] , KullbackLeibler divergence (KLD) [2] , Term Selection value (QE-TS) [11] , PRF document selection using clustering (Lee et al.) [10] , and our clustering approach using local frequent terms (Cluster-LFT). For all QE models, we select the top 35 documents for PRF and 50 terms for query expansion. In our clustering approach, for accepting or rejecting clusters under intra-cluster similarity hypothesis, we set the values of parameters min_local_terms and min_term_supp as 5 and 60%, respectively.

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


From Planning to Searching for the Shortest Plan: An Optimal Transition If we want to find the shortest plan, then usually, we try plans of length 1, 2, . . . , until we find the first length for which such a plan exists. When the planning problem is difficult and the shortest plan is of a reasonable length, this linear search can take a long time; to speed up the process, it has been proposed to use binary search instead. Binary search for the value of a certain parameter x is optimal when for each tested value x, we need the same amount of computation time; in planning, the computation time increases with the size of the plan and, as a result, binary search is no longer optimal. We describe an optimal way of combining planning algorithms into a search for the shortest plan -optimal in the sense of worst-case complexity. We also describe an algorithm which is asymptotically optimal in the sense of average complexity. Since Kautz and Selman's paper [9] on satisfiability based planning there has been several papers [10, 15, 4, 5, 16, 13, 14, 11] on planning through finding models of a logical theory. Most of these papers focus on finding a plan of a given length; see also [17, 7, 2, 6, 12] . If we want to find the shortest plan, then usually, we try plans of length 1, 2, . . . , until we find the first length for which such a plan exists. When the planning problem is difficult and the shortest plan is of a reasonable length, this linear search can take a long time; to speed up the process, it has been often mentioned -as in [13] , that binary search should be used instead.. Binary search for the value of a certain parameter p is optimal when for each tested value p, we need the same amount of computation time (see, e.g., [3] ). In planning, the computation time drastically increases with the size of the plan. As a result, as we will see, binary search is no longer optimal. In this paper, we describe an optimal way of combining planning algorithms into a search for the shortest plan -optimal in the sense of worst-case complexity. We also describe an algorithm which is asymptotically optimal in the sense of average complexity.

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


On the complexity of the resolvent representation of some prime differential ideals We prove upper bounds on the order and degree of the polynomials involved in a resolvent representation of the prime differential ideal associated with a polynomial differential system for a particular class of ordinary first order algebraic-differential equations arising in control theory. We also exhibit a probabilistic algorithm which computes this resolvent representation within time polynomial in the natural syntactic parameters and the degree of a certain algebraic variety related to the input system. In addition, we give a probabilistic polynomial-time algorithm for the computation of the differential Hilbert function of the ideal. The notion of a resolvent representation of a prime differential ideal in a ring of differential polynomials was introduced by Ritt (see [28, 27] ) as a tool towards an algebraic elimination theory in the realm of differential equations, although it can be traced back to the work of Kronecker (see [24] ). Roughly speaking, a resolvent representation of a prime differential ideal provides a parametrization of the generic zeros of the ideal by the general zeros of a single irreducible differential polynomial. This construction can be interpreted in several contexts, including the primitive element for field extensions, the cyclic vector for linear first order differential systems, and the shape lemma in algebraic and analytic geometry.. In order to illustrate the notion of resolvent representation, let us consider the following simple differential algebraic system (Σ) consisting of four equations in the four unknowns , where α, β ∈ Q, the variable Y is regarded as a parameter and the system is considered over the ground differential field Q(t) equipped with the usual derivation t = 1. Set γ := X 1 + tX 2 . Then, all the variables appearing in (Σ) can be written, using the equations of the system and their derivatives, as rational functions in Q(t, Y,Ẏ )(γ,γ):. In addition, γ verifies the differential equation. which is called the the minimal equation for γ. The set consisting of the irreducible polynomial giving this minimal equation and those providing the rational identities above is called a resolvent representation of the system (Σ) and γ its associated primitive element (for more examples of resolvent representations see [5] ). The present paper deals with the computation of resolvent representations of prime differential ideals associated with certain differential systems coming from control theory (see for instance [6] , [7] ):. . . .. where f 1 , . . . , f n ∈ k[X, U ] and g 1 , . . . g r ∈ k[X, U,U ] are polynomials in the variables X := {X 1 , . . . , X n } and U := {U 1 , . . . , U m } with coefficients in a zero-characteristic differential field k and total degrees bounded by an integer d, and Y := {Y 1 , . . . , Y r } is another set of variables. The variables X, U are the unknowns of the system, while the variables Y are regarded as parameters. Given a differential equation system as above, we consider the prime differential ideal ∆ generated by the polynomials f i −Ẋ i , i = 1, . . . , n, and g j − Y j , j = 1, . . . , r, in the differential polynomial ring k{Y, X, U }.. We prove the existence of a resolvent representation for the ideal ∆ consisting of polynomials which involve derivatives of order at most 2n + 2r and whose degrees are bounded by the degree of the algebraic variety V defined by the input polynomials and their derivatives up to order 2n + 2r − 1 (see Theorem 36 below) . The Bezout inequality implies that deg(V) can always be bounded by d 2(n+r) 2 .. In addition, if k = Q(t), we construct a bounded error probability algorithm which computes a resolvent representation of ∆. If the input polynomials are given by a straightline program of length L over Q (see Subsection 2.2 for the definition of this data structure), the complexity of this algorithm is linear in L and polynomial in n, m, r, d and deg(V) (see Theorem 48 below). We remark that the upper bound for deg(V) due to the Bezout inequality leads to a single exponential worst-case complexity bound for our algorithm. The error probability of the algorithm is controlled by means of the Zippel-Schwartz zero test and degree upper bounds for the polynomials giving the genericity conditions under which our algorithm works.. As a byproduct, we present a probabilistic algorithm for the computation of the differential Hilbert function of the ideal ∆ within complexity polynomial in n, m, r, d and linear in L (see Theorem 26) , extending the results in [26] to positive-dimensional situations.. Our overall strategy consists in translating a differential (non-noetherian) problem into an algebraic (noetherian) one. In this sense, some finiteness results on characteristic sets of differential ideals appearing in [29] and [30] play a fundamental role. In a first step, we compute a differential transcendence basis of the differential field extension induced by our system in order to turn to a zero-dimensional differential situation, which is achieved by applying some techniques described in [26] . Then, we give an effective and algorithmic version of Seidenberg's proof of the existence of a primitive element (see [34] ) in our situation, reducing the problem to the computation of an eliminating polynomial in an algebraic-geometric context. Finally, we apply an elimination procedure based on [17] and [31] to make our main computations.. The approach to differential polynomial equation systems through resolvent representations has been known to be effective since its origins in [28] . Ritt's treatment of the subject as well as its subsequent generalizations (see, [5] , [4] ) are based on rewriting techniques, namely Gröbner bases and characteristic sets. Even though a single exponential complexity upper bound was proved in [9] for the computation of a resolvent representation using these methods in the algebraic (non-differential) context, no complexity analysis is presented in any of the works concerning its differential counterpart. However, the complexity results on the computation of characteristic sets in the differential setting given in [29] seem to yield single exponential complexity bounds for a probabilistic algorithm computing a resolvent representation (see [4] ) for the specific systems we consider. A different approach to effective elimination over ordinary differential fields can be found in [15] , where a general quantifier elimination procedure with doubly exponential complexity bounds is exhibited.. We point out that our algorithms do not require the computation of Gröbner bases or characteristic sets. Based on the computation of algebraic eliminating polynomials, our approach enables us to obtain complexity estimates in terms of a geometric invariant, which are more precise than those depending only on syntactic parameters (see Example 38). Complexity bounds depending on this kind of parameters appeared before in several algebraic elimination procedures (see for instance [13] , [17] , [14] , [12] ). We observe also that, in terms of the parameters n, m, r, d, the complexity of our algorithm is of order (nmr) O(1) d O((n+r) 2 ) , improving the complexity estimate (n+r) O((n+m)(n+r)) d O((n+m) 3 (n+r) 3 ) of the rewriting procedure presented in [29, Theorem 28] when applied to our particular equation systems.. We hope that our techniques and results would contribute to the symbolic treatment of systems where the parameters Y 's are replaced with given functions. We also expect that these results could be extended to more general cases such as partial derivative equation systems or positive characteristic differential fields (see [35] ).. The paper is organized as follows: in Section 2, we recall some basic notions and results from Differential Algebra and we present the algorithmic model we will adopt. In Section 3, we introduce the differential equation systems we will consider and we show some elementary facts about them. Section 4 deals with the computation of the differential Hilbert function of the ideal associated with the system and of a differential transcendence basis of the induced differential field extension. In Section 5 we recall the notion of a resolvent representation of a prime differential ideal and we prove upper bounds for the orders and degrees of the involved polynomials. Section 6 is devoted to the algorithmic computation of resolvent representations. Finally, in Section 7 we present a slight generalization of the algorithmic results stated in the previous sections.

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


A tuning framework for software-managed memory hierarchies Achieving good performance on a modern machine with a multi-level memory hierarchy, and in particular on a machine with software-managed memories, requires precise tuning of programs to the machine's particular characteristics. A large program on a multi-level machine can easily expose tens or hundreds of inter-dependent parameters which require tuning, and manually searching the resultant large, non-linear space of program parameters is a tedious process of trial-and-error. In this paper we present a general framework for automatically tuning general applications to machines with software-managed memory hierarchies. We evaluate our framework by measuring the performance of benchmarks that are tuned for a range of machines with different memory hierarchy configurations: a cluster of Intel P4 Xeon processors, a single Cell processor, and a cluster of Sony Playstation3's. We have presented a tuning framework that allows programs written in a portable language, Sequoia, to be automatically tuned for a wide range of machines with softwaremanaged memory hierarchies. Our framework matches the decomposition strategies to the memory hierarchies, and uses a search algorithm, specialized to software-managed hierarchies by intelligently choosing the initial search point and using a non-square grid, that achieves good performance quickly due to the smoothness of the search space. Since tunable mismatch penalties are greater on softwaremanaged hierarchies than on cache-based architectures, we apply a novel fusion algorithm that considers multiple outermost loop levels in a single step. The knowledge learned when searching the tunable space is used to guide the selection of a fusion configuration.. Our system, on top of a portable, structured language, with the profiling system matching the machine hierarchy and profiling results for each loop nest and each bulk operation, can provide valuable and easy-to-understand feedback to the user. The user can use the findings to deduce the bottlenecks of the application and to decide whether he/she should modify the Sequoia source code or external leaf implementations.. We have demonstrated the performance of our framework on a single Cell processor, on a cluster of Intel Xeon processors, and on a cluster of PS3s. Our framework gives similar or better performance than what is achieved by the bestavailable hand-tuned version coded in Sequoia. A number of empirically-tuned libraries deliver high performance for a range of architectures, such as FFTW [15] , SPIRAL [30] , ATLAS [35] and PhiPAC [4] . Both FFTW and SPIRAL use empirical techniques to choose among multiple implementations of the same problem. They recursively decompose a problem into simpler sub-problems using a set of rules, derived from mathematical properties of the signal processing algorithms. SPIRAL is more general than FFTW: it generates optimized code for a large class of signal transforms, while FFTW is a library for computing discrete Fourier transforms. PhiPAC and ATLAS both generate high performance matrix-matrix multiply by empirically searching a large space of parameter values. Our approach is different in that it does not exploit properties of any specific domain.. Empirically-based tuning methods have been used in general purpose compilers. In [17] , tile sizes and unroll factors of nested loops are empirically searched, and [6] considers tiling for each memory hierarchy level (from registers as the lowest level to main memory as the highest level), empirically searching tiling and prefetching parameters. [33] uses direct search to explore the space of tile sizes and unroll factors. Unlike the previous work that targets cache-based architectures, our tuning framework targets software-managed memory hierarchies; in particular, our search algorithm is tailored to the characteristics of the search space of tunables on software-managed memory hierarchies.. A fusion algorithm incorporating loop alignment, loop interchange, and a data regrouping step after fusion is presented in [11] ; their method considers the outermost loop level only at each step of the algorithm, and the selection of loop order is driven by number of fusions. Our integrated fusion algorithm differs in that it looks at multiple outermost loop levels at each algorithmic step and the profitability measurement considers mismatch of the tuning parameters. Several loop transformations including loop fusion and tiling are evaluated in [36] , but only static models are used to determine profitability and tiling decisions are made after loop fusion and loop distribution.. In [31] , a profitability model based on reuse analysis targeting cache-based architectures is presented for loop fusion, and several architectural parameters in the profitability model are empirically searched. When those parameters are changed, a different fusion configuration can be generated from a greedy fusion algorithm. This work is extended to tiling and fusion in [32] . With this approach less speedup is observed for more complex machines, since its effectiveness depends on how well the model matches the underlying architecture, to some degree. Our tuning framework calculates the profitability of a fusion configuration with information collected when exploring the search space of tunables.. Steady progress has been made in the past decade on dependence analysis, transformations, and code generation in the polyhedral model [34, 2, 27] . The cost function used to select a transformation must be simple to be tractable mathematically. In addition to model-based approaches, semiautomatic and search-based frameworks also exist [8, 19, 16, 29, 28] . The search space of finding a set of transformation coefficients for each statement can be huge, thus heuristics are used to bound the search space and to guide the search [16, 29, 28] . Our approach depends on the programmer to decompose a program and to pick parameters as tunables, while those information is automatically extracted from the program in the polyhedral model. The polyhedral model is applicable to affine loop nests only, but our framework works for non-affine programs as well.

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


Query relaxation by structure and semantics for retrieval of logical web documents AbstractÐSince the Web encourages hypertext and hypermedia document authoring (e.g., HTML or XML), Web authors tend to create documents that are composed of multiple pages connected with hyperlinks. A Web document may be authored in multiple ways, such as, 1) all information in one physical page, or 2) a main page and the related information in separate linked pages. Existing Web search engines, however, return only physical pages containing keywords. In this paper, we introduce the concept of information unit, which can be viewed as a logical Web document consisting of multiple physical pages as one atomic retrieval unit. We present an algorithm to efficiently retrieve information units. Our algorithm can perform progressive query processing. These functionalities are essential for information retrieval on the Web and large XML databases. We also present experimental results on synthetic graphs and real Web data. T O find the announcements for conferences whose topics of interests include WWW, a user may issue a query ªretrieve Web documents which contain keywords WWW, conference, and topics.º We issued the above query to an Internet search engine and surprisingly found that the returned results did not include many relevant conferences, such as the Eighth WWW and VLDB '1998 Conferences. The main reason for this type of false drops is that the contents of HTML documents are often distributed among multiple physical pages, as illustrated in Fig. 1a . Furthermore, many Web pages are authored using frames. As the Web page shown in Fig. 1b , these pages are displayed to the user as one page although the source for the page are four separate HTML files. Since WWW encourages hypertext and hypermedia document authoring (e.g., HTML or XML), authors might prefer to create Web documents that are composed of multiple pages connected with hyperlinks. Consequently, a Web document for conferences whose topics of interests include WWW may be authored in multiple ways, such as 1) all information in one physical page, 2) general announcement for venue in the main page and the topics of interests in a separate linked page, or 3) a main page, a linked page for call for papers, and a linked page for topics of interests. We illustrate the document authoring styles of the Eighth WWW Conference and VLDB '1998 Conference as in November 1998 in Fig. 1a .. Using the current Web indexing and search technologies, search engines can retrieve only those physical pages that have all of the above three keywords. As is clear from the above example, individual pages on the Web may not contain complete information for answering queries. It is crucial that the structure of Web documents (which may consist of multiple pages) is taken into consideration for information retrieval.. In order to observe what kind of a document structure is preferred by the authors on the Web, we used a crawler to retrieve and index all call for paper pages announced on the DBWORLD [1] (a well-known database mailing list) for a period of two years, from January 1997 to November 1998. There were a total of 1,640 messages posted during this period, out of which, 473 were call for papers (CFPs). Each announcement had one or more related information links attached. We used WebDB, a Web search engine we developed at NEC C&C Research Laboratories [2] , to search the links to see how many of them are conference CFPs with topics of interest including WWW. The result indicated that if we simply search all the CFP home pages with both keywords ªconferenceº and ªwwwº in them, only 79 satisfied the query. Most interestingly, most expected conferences, such as WWW8 and VLDB98 were not among the resulting 79 CFP home pages. Alternatively, we relaxed the query to include a pair of pages containing the keyword WWW and Conference connected with a direct hyperlink. In this case, 221 pairs of pages satisfied the query, with most related ones, such as WWW8 and VLDB98, included. This empirical observation establishes the need for document retrieval by information units beyond current physical page-based information retrieval.. In this paper, we introduce the concept of information unit, which can be viewed as a logical Web document, which may consist of multiple physical pages as one atomic retrieval unit. The algorithms described in this paper have been deployed in conjunction with the WebDB which keeps snapshots of the Web, in terms of the textual content of the pages and the link structure.. With a huge amount of information available on the Web, a query tends to generate a large number of results, including exactly matched ones containing all keywords and partially matched ones containing some but not all keywords. The concept of information units does not attempt to produce additional results that are likely to be more than users can browse. Instead, our approach is to keep those exactly matched pages at the top of the ranked list, while merging a group of partially matched pages into one unit in a more organized manner for easy visualization and access for the users. In other words, unlike the traditional keyword-based query relaxation, the information unit concept enables Web-structure based query relaxation in conjunction with the keyword-based relaxation.. In this paper, we present a framework for retrieval of such information units over the Web as well as on hypermedia databases, such as XML document databases. Below, we provide a simple overview of the concept of retrieval by information unit. For the sake of clarity, we informally introduce some terminology in this example. The formalism used in this example will be described in greater detail later in the paper. Example 1.1. Let us denote the set of Web pages containing a given keyword, u i , as i . Furthermore, for a given i , let us define 3 i as the set of Web pages that contain a link to at least one of the pages in i . Similarly, let us denote i 3 as a set of pages that are linked from at least one of the pages in i . For instance, in Fig. 2, I , P 3, and 3 Q represent fvIY vQY vRY vSgY fvTY vRY vSY vUgY and fvIY vPg respectively. Fig. 3 illustrates the query results that are generated progressively for a query with two keywords. In this figure, we denote class 0 information units as documents which contain both u I and u P , and class i information units as pairs of documents such that one contains u I and the other contains u P and there is a path of length i between them. Note that, 1) the intermediate query results of Class 0, I and P, are reused while processing the query for Class 1, 2) I 3 and P 3 are derived using Class 0 results, and 3) computation of (I 3 P) and (I P 3) can be parallelized.. Note that, in order to find information units, we may constrain that a pair of pages in must be in the same Web domain. This is different from link analysis in ªtopic distillationº [3] . The motivation of topic distillation is to find important sites on the Web or from query results. The important sites can be hubs and authorities. Hubs are good sites that cite to many good authorities and good authorities are sites that are cited by many good hubs. Hubs and authorities need to be in different domains [4] so that the links between them can be validated as ªcitation.º In contrast, links between two documents in the same domain are for authoring instead of citation. Therefore, in retrieval by information unit, in most cases it is enough to consider only the links connecting two pages within the same domain. This is useful since our algorithm requires consideration of only a substantially smaller connection graph within a single domain rather than the whole Web. The example described earlier highlights the three essential requirements of information unit-based retrieval on the Web:. . Users are not just interesed in a single result, but the top k results. . While generating the ith result, we want to reuse existing i À I results. . And, since the Web is large and usually a simple search results in thousands of hits, preprocessing and any computation which requires touching or enumerating all pages is not feasible. In the rest of the paper, we present our research on progressive query processing for retrieving information units. We present experimental results on both synthetic graphs and real Web data and discuss the application of this technique in query result organization and XML database proximity queries.. The rest of the paper is organized as follows: In Section 2, we provide formal definitions of the more general problem of information unit-based retrieval. In Section 3, we describe the query processing techniques and generalize the framework to more complex scenarios. In Section 4, we describe how our technique can be extended to deal with fuzziness in keyword-based retrieval, such as partial match and different importance of query keywords. In Section 5, we present experimental results for evaluating the proposed algorithm on both synthetic graphs and actual Web data. In Section 6, we highlight two applications of the information unit retrieval. In Section 7, we review related work and compare it with our work. Finally, we present concluding remarks in Section 8. We have discussed existing work on group Steiner trees in Section 3. In this section, we give an overview of work in the area of integrating content search on the Web and Web structure analysis.. Although search engines are one of the most popular method to retrieve information of interest from the Web, they usually return thousands of URLs that match the user specified query terms. Many prototype systems are built to perform clustering or ranking based on link structures [3] , [19] , and links and context [20] , [21] , [22] . Another solution to the above problem is the topic distillation [23] , [24] , [20] , [3] approach. This approach aims at selecting small subsets of the authoritative and hub pages from the much larger set of domain pages. An authoritative page is a page with many inward links and a hub page is a page with many outward links. Authoritative pages and hub pages are mutually reinforcing: A good authoritative page is linked by good hub pages and vice versa. In [4] , Bharat and Henzinger, present improvements on the basic topic distillation algorithm [23] . They introduce additional heuristics, such as considering only those pages which are in different domains and using page similarity for mutual authority/hub reinforcement.. Similar techniques for improving the effectiveness of search results are also investigated for database systems. In [18] , Goldman et al. propose techniques for performing proximity searches over databases. In this work, proximity is defined as the shortest path between vertices (objects) in a given graph (database). In order to increase the efficiency of the algorithm, authors also propose techniques for constructing the indexes that help find the shortest distances between vertices. In our work, in the special case of two keywords, we also use shortest distances. In the more general case, however, we use minimal group Steiner trees to gather results. Note that minimal group Steiner trees reduce to the shortest paths when the number of groups, that is keywords, is limited to two. DataSpot, described in [25] , aims at providing ranked results in a database which uses a schema-less semistructured graph called a Web View for data representation.. Compared with existing work, our work aims at providing more efficient graph search capability. Our work focuses on progressive query processing without the assumption that the complete graph is known. Our framework considers queries with more than two keywords, which is significantly more complex. In this paper, we introduced the concept of information unit, which is as a logical document consisting of multiple physical pages. We proposed a novel framework for document retrieval by information units. In addition to the results generated by existing search engines, our approach further benefits from the link structure retrieving results consisting of multiple relevant pages associated by linkage and keyword semantics. We proposed appropriate data and query models and algorithms that efficiently solve the retrieval by information unit problem. The proposed algorithms satisfy the essential requirement of progressive query processing, which ensures that the system does not enumerate an unnecessarily large set of results when users are interested only in top matches.. We discussed extensions to the basic algorithms for many variations of this problem, such as partial match queries and similarity-based keyword matching. We also discussed application of this framework and techniques to the data retrieval in XML form. Since XML documents can be formulated as (mostly tree-like) graphs [26] XML queries can benefit from the formulation we proposed in this paper.. We presented a set of experiment results conducted on synthetic as well as real data. These experiments show that although the algorithm we propose is suboptimal (the optimal version of the problem is NP-hard), its is efficient and provides adequate accuracy.. K. Selc Ë uk Candan received the BS degree, first ranked in the department, in computer science from Bilkent University in Turkey in 1993, and the PhD degree from the Computer Science Department at the University of Maryland at College Park. He is a tenure track assistant professor at the Department of Computer Science and Engineering at Arizona State University. He joined the department in August 1997 after receiving his PhD. His dissertation research concentrated on multimedia document authoring, presentation, and retrieval in distributed collaborative environments. He received the 1997 ACM DC Chapter award of a Samuel N. Alexander Fellowship for his PhD work. His research interests include development of formal models, indexing schemes, retrieval algorithms for multimedia and Web information, and development of novel query optimization and processing algorithms. He has published various articles in respected journals and conferences in related areas.. Quoc Vu received the MS degree in computer science from the University of Montreal in 1995. He is currently a staff engineer at Selectica Inc. an eCommerce software provider. At the NEC C&C Research Laboratories and IBM Almaden Research Center, he was involved in several research projects related to data mining, information retrieval, and internet-based data/knowledge management.. Divyakant Agrawal received the PhD degree from State University of New York, Stony Brook. He is a visiting senior research scientist at C&C Research Laboratories, NEC USA, Inc. in San Jose. His current research interests are in the area of distributed hypermedia databases, multimedia information storage and retrieval, and Web-based technologies. He is a member of the IEEE.. F For more information on this or any computing topic, please visit our Digital Library at http://computer.org/publications/dlib.

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