Real-coded crossover as a role of kernel density estimation This paper presents a kernel density estimation method by means of real-coded crossovers. Estimation of density algorithms (EDAs) are evolutionary optimization techniques, which determine the sampling strategy by means of a parametric probabilistic density function estimated from the population. Real-coded Genetic Algorithm (RCGA) does not explicitly estimate any probabilistic distribution, however, the probabilistic model of the population is implicitly estimated by crossovers and the sampling strategy is determined by this implicit probabilistic model. Based on this understanding, we propose a novel density estimation algorithm by using crossovers as nonparametric kernels and apply this kernel density estimation to the Gaussian Mixture modeling. We show that the proposed method is superior in the robustness of the computation and in the accuracy of the estimation by the comparison of conventional EM estimation. In applying Genetic Algorithms to function optimization in the continuous search space, Real-coded Genetic Algorithms (RCGAs) which use the real-number vector reprePermission 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. sentation have been proposed and reported to show better performance than bit-string GAs [4] [10] . In the background of the development of RCGAs, great efforts have been made not only in the improvement of the algorithms but also in the establishment of guidelines for designing real-coded crossovers.. In [6] , a guideline for the design of real-coded crossover, "Preservation of statistics" has been proposed. This guideline means that the distribution of offspring generated by crossovers should preserve the statistics such as the mean vector and the covariance matrix of the parental population. Several real-coded crossovers have been proposed following this guideline and the validity thereof has been verified [6] [5] . This guideline regards that a real-coded crossover is an operator which maps the probability distribution of parents to that of offspring.. As another evolutionary optimization techniques considering the probabilistic distribution of population, Estimation of Distribution Algorithms (EDAs) have also been developed. In EDAs, the probabilistic distribution is explicitly estimated by various methods and the sampling strategy is determined by the distribution. In this paper, we focus on the fact that the search framework of EDAs are mainly designed by the following two steps, (1) the explicit estimation of a parametric or semi-parametric probabilistic density distribution, (2) the sampling from the estimated distribution. To the contrary, the search algorithm of RCGAs is mainly designed by the following two steps, (1) the implicit estimation of non-parametric probabilistic density distribution, (2) the sampling from the estimated distribution.. In comparison of the two evolutionary algorithms, they are totally designed under a similar principal. Although great attentions have ever been paid only to the search performance of algorithms in conventional studies, we focus on the estimation performance of real-coded crossovers in this paper. Then, we show that real-coded crossovers satisfies the following facts:. • Real-coded crossovers can be interpreted as a nonparametric kernel density estimator (KDE). • If a crossover satisfies the preservation of statistics, the KDE using the crossover corresponds to the approximation of the maximum likelihood estimation of Gaussian distribution. Then we show that KDE can be actually designed from crossover Unimodal Normal Distribution Crossover (UNDXm) [6] and Simplex Crossover (SPX) [5] .. In [13] , a KDE using Constructive Elliptical Basis Function (CEBF) have been introduced and an EM algorithm using CEBF have been proposed. We show that CEBF and a kernel based on UNDX are geometrically equivalent in this paper. Then, we propose an EM algorithm using KDE based on crossovers for the Gaussian Mixture Model (GMM) by generalizing conventional EM algorithm.. Experiments show that EM estimation using KDE of crossovers is superior in robustness and the estimation accuracy. Add to this, it performs better than conventional EM in the sense that the estimation result does not tend to be captured in local optima. The effectiveness of EM using crossovers is shown by experiments of artificial data modeling problem and letter recognition problem.. RCGAs are widely used for large-scale applications and the performance thereof is superior even in the optimization of high dimension function. Though RCGAs do not estimate the density model in the procedure, it is considered that the performance of implicit density estimation does not degrades even in high dimensionality.. Based on the viewpoint shown above, our motivation in this paper is to show the applicability of RCGAs not only to optimization but also to density estimation. The probabilistic density estimation is often needed in the field of data analytics such as classification algorithms, clustering techniques and data compression methods.. Another motivation is to show an unified framework for RCGAs and EDAs based on the understanding that the probabilistic model estimated by real-coded crossovers is approximately corresponds to the maximum likelihood estimation of Gaussian model in a nonparametric manner. This framework contributes to bridge a gap between RCGAs and EDAs in continuous optimization.. In section 2, we clarify the role of real-coded crossovers by comparing the difference of the sampling strategy of RCGAs and EDAs in terms of probabilistic density function. Then, we show that real-coded crossovers can be interpreted as a kernel density estimator. In section 3, we explain algorithms of nonparametric kernels using two real-coded crossovers, UNDX-m and SPX. Section 4 describes a procedure of EM algorithm for the Gaussian Mixture Model using KDE of crossovers. Section 5 is experiments using benchmark problems and a letter recognition problem. Section 6 concludes this paper. We propose a kernel function CEBF that approximate Gaussian distribution in a nonparametric manner and construct crossover kernel EM that estimate the Gaussian Mix-ture. The appealing point of our proposal is that (1) the estimation results can escape form the local optima using the randomness in the selection of kernel construction set, (2) the procedure does not include the unstable computation and it gives a robust estimation result even in high dimension. In density modeling using the EM, the dimensionality is at most 10 in tradition. However, the dimensionality of the real world problem often reaches more than hundreds. Applying the proposal method to real-world application is also our future work.. The disadvantage of our algorithm is that the convergence property to the local optimum is not assured theoretically. Though we use a stopping condition heuristically, the time to convergence is highly dependent on the parameter, therefore, the improvement of the algorithm that theoretically assures local optimal convergence is our future work.. Our method can be applied to the optimization using the same framework of EDA in a straightforward manner. In the optimization of the multiple-peak function, the population forms several clusters and our method is expected to be the efficient sampler on these kinds of problem. In this section, we compare the estimation results of conventional EM and EM using crossover kernels for Gaussian Mixtures. Experiment 1 is the estimation of Gaussian mixture from artificially generated data sets, where the estimation accuracy and the computation time are compared. Experiment 2 is a letter recognition problem. EM algorithms estimate the classification model as Gaussian mixtures and the training error and the test error are compared. In both experiments, CEBF is used as a crossover kernel.

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


Fast multilevel augmentation methods for nonlinear boundary value problems We develop a multilevel augmentation method for solving nonlinear boundary value problems. We first describe the multilevel augmentation method for solving nonlinear operator equations of the second kind which has been proposed in our recent paper Chen et al. (2011) [16], and then apply it to solving the nonlinear two-point boundary value problems of second-order differential equations. The theoretical analysis of convergence order and computational complexity are proposed. Finally numerical experiments are presented to confirm the theoretical estimates and illustrate the efficiency of the method. Many problems in physical, engineering and scientific applications, e.g., boundary layer theory, the study of stellar interiors, control and optimization theory, and flow networks, are modeled by two-point boundary value ordinary differential equations. There are many numerical methods for solving linear two-point boundary value problems (cf. [1] [2] [3] [4] [5] [6] [7] ), such as shooting, band matrix, multiple shooting, collocation, Ritz-Galerkin, sinc-Galerkin, etc.. But when we deal with nonlinear problems, a nonlinear system resulting by discretization needs to be solved. The typical suggestion is that this system be solved by a Newton method. In this case, the Jacobian matrices have to be established, inverted and possibly updated during the iteration. When high approximation accuracy is desired, it requires one to use sufficiently fine grids. Thus it demands a large amount of computational effort and a huge storage space, which becomes a bottleneck for solving nonlinear problems of large scale with high precision.. In this paper, we develop the multilevel augmentation method to solve nonlinear two-point boundary value problems. Multilevel and multiscale numerical methods received much attention recently (cf. [8] [9] [10] [11] [12] [13] [14] [15] ). It was proved in [10] that the multilevel augmentation method solving linear integral equations of the second kind enjoys optimal convergence order and linear computational complexity. The multilevel augmentation method for solving Hammerstein equations was developed in [11] . In our recent paper [16] , the multilevel augmentation method for solving sine-Gordon equations was proposed. This method is based on multilevel decompositions of approximate subspaces, aiming at efficiently solving nonlinear systems of large scale obtained from discretization of the nonlinear operator equations. The method begins with an initial approximate solution at a fixed lower level subspace, and obtains the approximate solution at a high level by two major steps: solving the nonlinear equation at an initial lower level, and compensating the error by solving a linear system at the high level.. The nonlinear boundary value problems considered in this paper are discretized by the multiscale Galerkin method, and the resulting nonlinear algebraic systems are solved by the multilevel augmentation method. Since this method only needs to solve a fixed lower level nonlinear system and compensate the high level component by matrix-vector multiplications, it reduces computational complexity greatly. Moreover, it saves plenty of storage space because we just need to store the Jacobian matrices of coarse level. We prove that this method enjoys optimal order of convergence and linear computational complexity.. We organize this paper in four sections. Section 2 is set to describe a general setting of the multilevel augmentation method for solving second kind nonlinear operator equations, and a result of convergence is presented. Section 3 is devoted to the discrete multilevel augmentation method based on the Galerkin method for solving nonlinear boundary value problems, and we provide the theoretical results for the convergence order and computational complexity for this special case. In Section 4, we present numerical experiments to confirm the theoretical estimates and demonstrate the efficiency and accuracy of the proposed method.

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Aggregated cross-media news visualization and personalization There is an increasing need for online news aggregation and visualization. Commercial systems, such as Google News and Ask.com, have successfully launched a portal aiming at providing an aggregated view of the top news events at a given time. However, these systems, as well as previous research projects, lack the ability to personalize events according to the user's need. Furthermore, users increasingly prefer to see multiple types of media to be presented when they follow a particular event of interest. In this paper, we describe a novel framework to allow the aggregation of online sources for text articles, images, videos and TV news into news stories, while the visualization enables the users to browse and select the news events based on semantic information. The experimental results have indicated some promising results. The vast amount of cross-media news resources generated each day can be overwhelming for casual readers. The tendency of journalists to extensively cover the same subjects using a variety of formats makes the overall information redundant and hard to filter for personalized needs.. Over the last years, many attempts have been made to propose an aggregated and visually rich interface to browse news contents. Among them, Google News 1 is certainly the most well known 1 news.google.com. 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, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. service. It constantly crawls a selection of more than 4500 sources [4] to extract the latest news, and then aggregate, illustrate and classify them into a standard set of categories. Its approach has been very successful, and it even allows people to personalize their front page based on certain keywords or, more recently, using the user's search history. However it still lacks the ability to quickly filter the news events along a large set of information facets such as people, companies, organizations, etc. Furthermore it does not provide other related contents such as videos or blogs. Ask.com at this time, is the only public company to have launched a news portal 2 that includes articles, images, videos and blogs related to a particular event. It also includes the concept of "Movers & Shakers", which consists of extracting a dozen of entities (mostly names of persons) from the events so that the user can click on one of them to search for any related news. However, the choice of an entity redirects to a search page result, which returns another vast amount of data that need to be browsed by the user. We believe that users should be able to dynamically filter any set of events by clicking on keywords that make sense to them. These keywords have to be automatically generated, ranked and displayed in a convenient way to the user. We thus propose a novel framework, which extends these state-ofthe-art systems with a high-level of semantic filtering that allows users to effectively select their topics of interest. Previous work in the area of news visualization includes the overview publication from MITRE team 8 summarizing several initiatives that are investigating the visualization of a range of content, including news stories. This research, as well as [7] and [8] were particularly aimed toward video news visualization and introduced the need of semantic information for a user to efficiently browse news stories. A lot of recent news visualization systems can be found in [5] . However most of them focused more on the graphical standpoint than the user-friendliness and effectiveness of browsing. Interesting examples include NewsMap [6] , which organizes news topics from Google news on a two dimensional rectangle, where the space allowed to each story is proportional to the number of related news pages; Buzztracker [1] , which draws on a world map the hot events; or Digg visualizations [7] , which display the top ranked news coming from the users' collaborative ratings as they appear on Digg over time. Pacific Northwest National Laboratory also published an interesting concept called "ThemeRiver" [9] , in which the themes in a collection are represented by a "river" that flows left to right through time. Finally, the recent LinkedFacts [10] application uses semantic content extracted from news articles to allow the user to dynamically filter the news presented on the screen. Our system is close to this concept in that it uses semantic content to dynamically filter the data presented to the user but, while LinkedFacts applies the filtering on raw text articles, we use it on aggregated resources combining text, images and videos, which cover the same events. Thus the browsing is much easier than having to scroll through a lot of (potentially) similar articles and provides an aggregated view that is close to state-of-the-art systems such as Google News and Ask News. Table 1 shows the similarities and differences between our system (OneStopNews) and state-of-the-art or research systems available on Internet. Previous work has shown that the task of aggregating news documents into news events is not trivial [11] [12] [13] . Such systems must be able to process rapidly changing text streams and have to deal with high dimensional data. Though not comparable in terms of scale to Google News or Ask News, our system has advanced features such as semantic filtering over a wide range of media content, including news articles, images, videos and TV content and experimental results show that we have comparable results to current major aggregated news providers.. The main contributions of this paper are: -A novel cross-modal news visualization allowing both easy browsing and in-depth understanding (via related articles, images and videos) on the top news of a particular period.. Details on the issues and solutions related to the implementation of such systems.. Experimental results showing the promising aggregation results obtained by the framework over 25 sources, as well as a user study confirming the effectiveness of the visualization. In this paper we presented a prototype and some early promising results from a project that aims to achieve aggregated cross-media news visualization with user personalization. The system was designed by maximizing the use of existing services and formats that are suitable to make the processing tasks easier. First, syndication feeds allowed us to overcome the problem of extracting text in raw web pages. Second, TV captions were extracted using existing tool from Source Forge. Third, Calais API provided the method to extract the named entities required for the semantic personalization of news articles. Using these resources, we have modified an existing incremental clustering algorithm to overcome some important issues in the aggregation of text streams from news domain. This clustering algorithm has also allowed us to automatically construct event timeline for each news event which has been covered extensively throughout a period of time.. The preliminary user evaluation, though limited, has shown promising results and will be used to drive some of the future work.. In particular, the use of different types of media (including text, images, and videos) to cover a news story seems to be a key feature of an aggregated news system. Moreover, the timeline provides an overview of the evolution of the topic over time.. User feedback showed that improvements are needed to reduce the amount of information presented on a page. We plan to address this issue by removing the separation into days and improving the ranking algorithm to present the breaking news as soon as they arrive, instead of having to wait for a breaking event to have a minimum number of resources to display it on top of the page.. Other future work aims to: 1) Improve the tag clouds to make them more understandable to users not familiar with the concept; 2) Improve the overall visualization to provide a more integrated and pleasant view of all the media related to each event; 3) Hide identical resources (published by different sources) to reduce the information noise resulting from too many similar resources; 4) Use name consolidation mechanism in addition to the entity extraction techniques to unify different names into one named entity (e.g. 'Hillary Clinton' == 'Hillary Rodham Clinton'). This could improve clustering results; 5) Include more sources of information in categories that do not have a good coverage in our evaluation. Blogs could also easily be added since we just need a syndication feed, which is publicly available on most of them; 6) Use the full text of articles to increase the performance of the clustering.

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


A framework for comparing task performance in real and virtual scenes In this paper, we describe a framework for comparing task performance in real and virtual environments. Realistic graphics, rear projection, haptics and rapid prototyping are used to match the virtual scene to the real scene. We describe some preliminary placement tasks which were evaluated using eye-tracking and discuss our future plans for this framework. Often it is necessary for computer graphics to operate under realtime constraints as well as maintaining realistic and dynamic scenes. Therefore it is useful to know what factors influence perception and can be allocated more resources at the expense of other aspects. In previous research we attempted to determine salient features of objects using eye-tracking. That research demonstrated that, if the salient features of natural objects are preserved during simplification, the visual fidelity of these models can be improved [Howlett et al. 2004] . However, we found that visually prominent features for man-made artifacts were not so easy to predict. A reason for this may be that man-made artifacts are generally related to a task and that prominent features may be defined by this task.. It is commonly known that the task performed on objects plays an important role in determining where attention is focused [Hayhoe et al. 2003 ], which leads us to the next step in our research. There are many factors that define a task, such as the environment, the nature of the task and the objects involved in the task. There has been much research in the field of psychology, examining eyemovements during a 3D task. However, there are further differences in performance between real and virtual environments.. The aim of our current work is to investigate these issues further by comparing tasks in the real and virtual world. To this end, we are building a framework using realistic graphics, rear projection, haptics, rapid prototyping and eye-tracking for evaluation. In this framework we attempt to replicate as accurately as possible a real world scene which we have created and the interaction with this world using haptics. Future plans for our framework include; investigating how attention is captured for a variety of tasks, determining the differences in performance and strategies between real * e-mail: Sarah.Howlett, Richard.Lee, Carol.OSullivan@cs.tcd.ie and virtual situations, and finding the limitations of carrying out similar tasks in a virtual environment. Our aim is to determine how the user experience can be improved, perhaps through previewing or by displaying salient object features [Howlett et al. 2004] or task related objects [Cater et al. 2003 ] in greater detail. This is work in progress, and the computer framework is not complete. We have carried out some preliminary studies on the real world scene and its virtual counterpart. The remainder of this paper describes the implementation of our framework and our efforts so far to match the two setups as accurately as possible, some preliminary tests and observations, followed by a discussion of our future plans for this framework. Our framework can be improved in a number of ways. Firstly, we experienced a major problem using the eye-tracker's scene camera with a single-chip DLP projector. These projectors beam white light through a spinning color wheel which filters it into red, green and blue components sequentially in time. Strobing effects result due to the insufficient sampling rate of the scene camera. We temporarily overcame this problem by instead using an overhead LCD projector. Note however that rear projection is greatly preferred to front projection as it allows participants to be seated directly in front of the virtual scene. Therefore, a better solution to this problem is to instead use a three-chip DLP projector which should prevent color cycling since red, green and blue color components are displayed simultaneously.. The most important discrepancy between our current real and virtual environments may be the lack of stereo vision in the virtual environment. We would like to address this by augmenting our framework with a rear projection stereoscopic display which will allow us to measure the effect of stereopsis on task performance in virtual environments. We have recently installed a Vicon optical motion capture system and will use this to examine motion parallax effects by tracking the head movement of participants, thereby allowing a dynamic viewpoint in our software. The influence of sound on task performance is another area of interest.. It is difficult to find a means of interacting with real world objects which can be faithfully reproduced in the virtual world. Options include the use of data gloves and motion capture. Hand [1997] examines some interaction techniques which have been developed for object manipulation, navigation and application control in 3D virtual environments. However, we chose the hand-held rod interface because it closely mimics the feel of the Phantom device when physically accurate feedback forces are applied to it, and we are very interested in examining the influence of haptics on task execution, including the use of non-physical forces to help "guide" the user during tasks. However, further tests to assess the faithfulness of the Phantom device in replicating the sensation of using the rod are needed.. Additionally, in the current set of experiments, the participants were seated directly in front of the scene, with the haptic device located to their right. This seemed the natural place to put it given their position and that they were all right handed. However, perhaps it would have felt more like the real world experience if it had been placed directly in front of the user. This will be considered in future experiments.. From an evaluation perspective, more experiments need to be carried out on the framework. So far, we have only examined eyemovements for a small number of participants during two placement tasks. Future experiments on the framework will involve more participants carrying out a wider variety of tasks e.g., passive, counting and memory, in addition to placement tasks.. The interesting observation about average fixation length merits further study. Perhaps in the future this could be used as a measure to compare how similar the real and virtual setups are. As more attention to the current object is needed to perform the same task in the virtual environment, this demonstrates that we need to come up with ways to facilitate the user. Possibilities would be to determine if enhancing the salient features of objects [Howlett et al. 2004] , or like Cater et al. [2003] , enhancing the task related objects could make it easier for the participant. Examining practices such as priming through previewing various aspects of objects would also be interesting. For example, Olds and Fockler [2004] compare the previewing of color and orientation, and show that conjunction previewing is most effective. Furthermore, Watson et al. [2003] demonstrated that, with previewing, more delay can be tolerated even when the task is difficult. Finally, the user's attention could be guided during a task. Halper et al. [2005] show that non-photorealistic rendering can play a subtle, yet effective, role in guiding judgement and subsequent interactions. We intend to examine whether additional cues can be used to augment the virtual environment, resulting in improved task performance.. A framework for comparing task performance in real and virtual scenes There is much research from the field of psychology suggesting that visual activity is largely controlled by task. Hayhoe et al. [2003] recorded participants' eye-movements while making a sandwich, and noted that almost all of the fixations focused on the task. Supporting this is work studying the eye-hand coordination in object manipulation [Johansson et al. 2001] . It was demonstrated that the salience of gaze targets arise from the functional sensorimotor requirements of the task, and therefore participants directed gaze almost exclusively towards objects involved in the task. Pelz et al. [2001] monitored participants' eye-movements during the familiar complex task of hand washing, which revealed a novel perceptual strategy involving task-dependent lookahead fixation. More recently, Ling et al. [2004] showed that color and size interact in a real 3D object similarity task.. From the field of computer graphics, recent work by Cater et al. [2003] also supports the suggestion that visual attention is largely controlled by the task. They show experimentally that it is possible to render scene objects not related to the task at a lower resolution without the viewer noticing any reduction in quality. Sundstedt et al. [2004] investigate to what level viewers fail to notice degradations in image quality, between task related areas and non-task related areas. Watson et al. [2003] investigated the relationship of delay to user performance in 3D object placement. They showed that delay has a greater impact on performance when difficulty is high. Furthermore, they demonstrated that, with previewing, more delay can be tolerated even when the task is difficult.. There have also been previous studies comparing performance in real and virtual setups. Thompson et al. [2004] have shown that participants are significantly less accurate at judging distances in visually immersive environments than in the real world. Moreover, Mohler et al. [2004] carried out studies using treadmill-based virtual environments to simulate the perceptual-motor effects of actually walking around in the real world. In task related research, Lok et al. [2003] pointed out that having interactions with real objects within a virtual world can increase the effectiveness of the environment.. In our research we wish to expand upon some of these approaches, by examining task performance in a truly interactive, multisensory environment. As described in the literature, we want to examine the eye-movements of participants while they carry out various 3D tasks in a real world situation, but we also extend this idea by comparing the eye-movement results to those found for a similar task carried out in a virtual environment.

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Fast Image Recovery Using Variable Splitting and Constrained Optimization Abstract-We propose a new fast algorithm for solving one of the standard formulations of image restoration and reconstruction which consists of an unconstrained optimization problem where the objective includes an ℓ2 data-fidelity term and a nonsmooth regularizer. This formulation allows both wavelet-based (with orthogonal or frame-based representations) regularization or total-variation regularization. Our approach is based on a variable splitting to obtain an equivalent constrained optimization formulation, which is then addressed with an augmented Lagrangian method. The proposed algorithm is an instance of the so-called alternating direction method of multipliers, for which convergence has been proved. Experiments on a set of image restoration and reconstruction benchmark problems show that the proposed algorithm is faster than the current state of the art methods. We have presented a new algorithm for solving the unconstrained optimization formulation of regularized image reconstruction/restoration. The approach, which can be used with different types of regularization (wavelet-based, total variation), is based on a variable splitting technique which yields an equivalent constrained problem. This constrained problem is then addressed using an augmented Lagrangian method, more specifically, the alternating direction method of multipliers (ADMM). The algorithm uses a regularized version of the Hessian of the ℓ 2 data-fidelity term, which can be computed efficiently for several classes of problems. Experiments on a set of standard image recovery problems (deconvolution, MRI reconstruction, inpainting) have shown that the proposed algorithm (termed SALSA, for split augmented Lagrangian shrinkage algorithm) is faster than previous state-of-the-art methods. Current and future work involves using a similar approach to solve constrained formulations of the forms (3) and (4).

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Analytic Constructions of Periodic and Non-periodic Complementary Sequences An analytic approach for the generation of non-periodic and periodic complementary sequences is advanced for lengths that are powers of two. The periodic complementary sequences can be obtained using symmetric or anti-symmetric extensions. The properties of their autocorrelation functions are studied. The non-periodic complementary sequences are the intersection between anti-symmetric and symmetric periodic sequences. These non-periodic and periodic complementary sequences are identified to be special cases of non-periodic and periodic (or cyclic) orthogonal wavelet transforms. This relationship leads to the novel approach. There is a wealth of literature on the theory and design of pseudo-random (or pseudo-noise) sequences for communications with different properties of their autocorrelation and cross-correlation functions (ACF and CCF) [1] - [5] , [12] - [27] .. Perfect-reconstruction (PR) filter banks have been intensely studied over the last twenty years. Orthogonal filter banks provide orthogonal bases for the Hilbert space of square-summable sequences [6] . Furthermore provided that the filters satisfy constraints additional to PR, regular (or smooth) continuous-time functions (scaling functions and wavelets) can be obtained, which are orthogonal bases for the space of square-integrable functions [6] .. The main purpose of this paper is firstly to demonstrate the relationship between wavelet transform theory and the theory of complementary sequences, and secondly to develop novel formulae for the analytic construction of complementary sequences using wavelet (or filter bank) theory. We shall consider one important class of sequences, namely complementary sequences. These sequences were recently found to be efficient in a new modulation for wireless communications, called spread-signature CDMA [11] . The connection between two-channel orthogonal FIR filter banks and aperiodic complementary sequences was observed by Manuscript several researchers [8] , [10] and is not novel. Periodic complementary sequences were advanced in [27] . It is shown here that they can be approached using the cyclic wavelet transform. This allows us to develop systematic algorithms for their generation. These two new sets of orthogonal sequences are generalizations of the Golay sequences in the sense that the Golay sequences are members of both of these sets. The novel approach allows to derive explicit formulas for the systematic generation of Golay sequences, when the length is a power of two. Previously these sequences could only be generated using computer searches. The paper is organized as follows. In Sect. 2 we review filter bank theory and complementary sequences. Section 3 is devoted to orthogonal periodic symmetric codes, and Sect. 4-to anti-symmetric codes. Section 5 is devoted to explicit formulas for Golay complementary pairs. We have developed novel analytic solutions for periodic and aperiodic complementary sequences. These analytic solutions allow the generation of all periodic and non-periodic complementary sequences when the length is a power of two. Previously this could only be accomplished with computer searches. The approach that has been proposed here can be used, in principle, for other complementary sequences, like ternary complementary sequences, advanced in [21] .. The novelty in this work from the point of view of wavelet transforms is that non-regular wavelets are constructed here. Note that filter banks have always been designed so that in addition to perfect reconstruction the filters have "good" frequency responses; e.g. H 0 (z) has always been required to be a good low pass filter and H 1 (z) is to be a good high pass filter [7] . This requirement is equivalent to requiring that the filter bank offer energy concentration and perform well in applications which require energy concentration like compression. Complementary sequences correspond to filter banks where the filters H 0 (z) and H 1 (z) are not "good" filters in this traditional sense, i.e. these filters have pseudo-random frequency responses. These filters offer energy spreading as opposed to energy compaction. This property is not desirable in data compression, but very desirable in CDMA wireless communication systems [11] .

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Automatic determination of envelopes and other derived curves within a graphic environment Dynamic geometry programs provide environments where accurate construction of geometric configurations can be done. Nevertheless, intrinsic limitations in their standard development technology mostly produce objects that are equationally unknown and so can not be further used in constructions. In this paper, we pursue the development of a geometric system that uses in the background the symbolic capabilities of two computer algebra systems, CoCoA and Mathematica. The cooperation between the geometric and symbolic modules of the software is illustrated by the computation of plane envelopes and other derived curves. These curves are described both graphically and analytically. Since the equations of these curves are known, the system allows the construction of new elements depending on them. Considerable attention and efforts are being given to an emerging field which can be termed SymbolicDynamic Geometry Environments (SDGE), a synthesis of Dynamic Geometry Software (DGS) and Computer Algebra Systems (CAS). We will not give a definition of CAS, but a few words must be said about the dynamic geometry paradigm. DGS offers virtual environments where accurate construction of geometric configurations can be carried out. The key characteristic of these systems is that unconstrained parts of the construction can be moved and, as they do, all other elements automatically self-adjust, preserving all dependent relationships and constraints [13, 5] .. Several authors have postulated a deeper cooperation between both types of systems in order to enhance the abilities of dynamic geometry programs with sophisticated algebraic algorithms. Recio and Vélez [16, 17] have extended the automatic theorem-proving method proposed by Kapur [11] to deal with automatic discovery in elementary geometry. They conclude that their method can "be regarded as the core of a future program [· · · ] that allows, when linked simultaneously with a tool for displaying geometric constructions and a symbolic computation package, the interactive exploration of geometric properties". We have developed such a program, Discovery [1] , where a dynamic geometry environment written in Prolog cooperates with Mathematica in order to automatize geometric discovery. Another piece of software using the above method is Lugares [2] . Lugares specializes in computing plane loci, and it uses CoCoA [3] in order to override current limitations of Mathematica when dealing with Groebner bases computations. Roanes [20] has also claimed boosting the cooperation betweeen DGS and CAS, having coauthored ParamGeo, a package that links Maple and Derive with The Geometer's Sketchpad (GSP) [10] , currently at a beta-level version. Kortenkamp reports in [14] some experiments about integrating its dynamic geometry package Cinderella [19] with other software. Cinderella is used to visualize a simulation driven by a Mathematica notebook, or talks to JavaView [12] using its automatic loci generation to display a surface.. This paper describes our last findings in the development of a symbolic-dynamic geometry environment. While the loci computed by Lugares are special objects in the graphic environment (in the sense that they do not respond to dragging and do not support the construction of new points on them), the actual version of the program deals with such loci as full dynamic objects: the loci are recomputed with no appreciable delay whenever some part of a construction is moved. Furthermore, symbolic algorithms for computing envelopes, pedals and caustics have been added. Both enhancements conclude the development of our SDGE, now called GDI, a Spanish acronym for Intelligent Dynamic Geometry.. The structure of this paper is as follows. Section 2 compares four well-known dynamic geometry environments and GDI when computing a single envelope, the deltoid of Steiner. We recall the basic mathematical machinery necessary for the computation of plane envelopes and we illustrate the developed algorithms for some curve families in Section 3. Section 4 describes how caustics and pedals can also be computed in the system. We described how envelopes of family curves and other derived curves can be automatically computed within a graphical interface. We found that the implementation of the algorithm of Buchberger in CoCoA is efficient for common elimination tasks in the domain of plane geometry with numeric coordinates. Nevertheless, the complexity of some problems involving more than a few variables exceeds the capabilities of current elimination algorithms.. In this paper, we complete the description of GDI, a dynamic geometry environment which uses the symbolic abilities of two computer algebra systems, CoCoA and Mathematica. The system may be downloaded (for academic purposes) from José L. Valcarce by writing to the given e-mail address.

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Editorial process in scientific journals: analysis and modeling Abstract The editorial handling of papers in scientific journals as a human activity process is considered. Using recently proposed approaches of human dynamics theory we examine the probability distributions of random variables reflecting the temporal characteristics of studied processes. The first part of this paper contains our results of analysis of the real data about papers published in scientific journals. The second part is devoted to modeling of time-series connected with editorial work. The purpose of our work is to present new object that can be studied in terms of human dynamics theory and to corroborate the scientometrical application of the results obtained. Nowadays new possibilities for quantitative studying of human activity processes appear. Modern computer technologies allow to collect and to process large volumes of statistical data. It is possible to fix the time of each performed operation from large flow of human (customer/user/client) actions and to obtain the data set representing whole picture. Therefore, new methods for data analysis and knowledge discovering could be applied. In particular, this allows quantitative analysis of psychological, social and other aspects of human behavior.. The sequences of human actions (telephone calls, information queries or stock exchanges) are not new subject to study. But contrary to generally accepted opinion about human actions randomly distributed in time and thus well approximated by Poisson processes (interevent times are exponentially distributed), the comparatively recent results of human dynamics analysis show the presence of power laws which nature and origin are unexplained up till now [1, 2, 3] . This discovery attracts an interest and provokes analysis of new processes involving human actions in different fields of our life. The analysis of time statistics of human activity patterns can be useful for different optimization and control tasks in spheres of mass service, communication, information technologies, resource distribution, etc. Besides, this approach can give a new possibility to understand human behaviour and to get its additional quantitative measure.. The continuous human behaviour can be considered as the set of consecutive actions in time. In this case it is convenient to examine two characteristic random variables: the time interval between two consecutive actions (called the interevent time t int ) and the time a task is waiting for an execution (the so-called waiting time tw). The power-law nature of corresponding distributions. arises from the analysis of real processes that involve human actions such as browsing the Internet, data downloading, electronic and mail communication, initiating financial transactions etc. [1, 2, 4] . On the other hand, the processes with execution of tasks in queue are the typical objects of study in the queueing theory which can be seen as the subfield of the so-called theory of mass service or, generally speaking, of applied probability theory [5, 6] . So, it is natural to use some general terminology to describe such kinds of processes. An empirical analysis results in a variety of values of the exponents governing (1) [3, 5] , however an observed tendency when similar values of the exponents describe different processes gives rise to an analogy with the "universality classes" found in physics of critical phenomena [5] . Different models have been proposed to gain insight about an origin of power laws (1) [3] . Some of the proposed models are based on the assumption about the key role of priority-based (decision-based) queuing process [5] . The situation when an individual has to perform a list of tasks and chooses a task from this list using some internal priority is very natural. It is important, that power-law-like distributions (1) appear only in the so-called critical and supercritical regimes of service, when its traffic intensity ρ:. is greater than 1. In (2) λ is the tasks arrival rate and µ is the execution rate, respectively [5] . In other words, the probability distribution functions of human activity processes are close to power law only when the queue of tasks is not exhausted [5] . This class of human activity can be described by the so-called "task-driven" models [3] . On the other hand, the "interest-driven" models explain the existence of power laws in human dynamics in a different way. There, the power laws may be observed also for the processes without any possibility to determine the queue of tasks, for example visiting of web-sites by different users [3] . Thus, we can conclude that human dynamics theory is the issue of current importance. Often besides academic interest there is an obvious great practical value of the results obtained.. The main purpose of this paper is to gain insight on the editorial process in scientific journals using tools and concepts of the human dynamics theory. In the first part (section 1) we show our empirical results obtained during the data analysis about distributions of waiting times of papers in several scientific journals. The simple simulation model of editorial processing of scientific manuscripts is presented in the second part of this paper (section 2). We have found that both log-normal and power-law function with exponential cutoff and exponent α = 1 can be the probable functions of waiting time distributions P (tw) for manuscripts in scientific journals. In fact, both log-normal and power-law functions predict exactly the same leading power behavior t −1 , differing only in the functional form of the exponential correction [10] . In this sense, process considered here is governed by similar probability distributions as other examples of human activities [1, 2, 3, 4, 5, 9] . The observed data fluctuations can be explained by relatively small statistics but such situation is usual for the majority of real-world data bases. Thus, we consider the obtained form of probability distributions P (tw) as the typical one that can be used for scientometrical analysis of editions. The length of waiting times is an important characteristic of Editorial Board's activity. The publication delay effects journal rankings according to the impact factor [12] as well as personal citation rating of authors.. The simple model of Editorial Board work was created to verify the hypothesis about the important role of peer-reviewing in the waiting times distributions P (tw) shaping. In general, the obtained results can be considered as the support of our previous conclusions.. In conclusion it is worth to mention some peculiarities of scientific editorial process that were not taken into consideration in our work. Here the main idea is connected with emphasizing of the meaning of natural human activity within the complex processes taking place in the Editorial Boards working. But these natural human activity patterns could be also affected by different situations or rules. For example, journal policy could be very different concerning the strictness of time deadlines for peer-reviewing or concerning the manuscripts with one "positive" and one "negative" referee reports. In addition to peer review we can mention other processes as the examples of natural human activity: technical work with raw manuscripts, communication between the editors and other participants of the editorial processes, etc. Moreover, one can distinguish several human activity sub-processes within peer reviewing such as pure referee work with manuscript, communication processes between referee, editorial office and authors, and, eventually, the manuscript revision by authors according to the referee remarks. It is very complex problem to account all these aspects in one model. So, it could be the worth challenge for the future analysis.

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


Lark: Coordinating Co-located Collaboration with Information Visualization Abstract-Large multi-touch displays are expanding the possibilities of multiple-coordinated views by allowing multiple people to interact with data in concert or independently. We present Lark, a system that facilitates the coordination of interactions with information visualizations on shared digital workspaces. We focus on supporting this coordination according to four main criteria: scoped interaction, temporal flexibility, spatial flexibility, and changing collaboration styles. These are achieved by integrating a representation of the information visualization pipeline into the shared workspace, thus explicitly indicating coordination points on data, representation, presentation, and view levels. This integrated meta-visualization supports both the awareness of how views are linked and the freedom to work in concert or independently. Lark incorporates these four main criteria into a coherent visualization collaboration interaction environment by providing direct visual and algorithmic support for the coordination of data analysis actions over shared large displays. Real-world information continues to grow in size and complexity, creating ever increasing challenges for information workers. Both information visualization and collaborative team work have been suggested as important factors in addressing these information complexity challenges [17] . Information visualization has the potential to provide different ways of examining and exploring the data. Collaborative data analysis scenarios can combine the analytic power of multiple individuals, with the possibility of including varying types and levels of expertise, potentially leading to increased quality of solutions and discoveries. However, while considerable research is being conducted in both information visualization and computer supported cooperative work, comparatively less research examines the interplay between them. This is especially true for co-located collaborative scenarios. It is this problem we address: how to best support co-located collaboration among information workers who are making use of information visualizations in their analysis process.. Large multi-touch wall and tabletop displays offer new opportunities to support face-to-face collaboration, discussion, interpretation, and analysis around information displays. These displays have the potential to expand the possibilities of desktop-based data analysis environments as large displays allow multiple people to stand comfortably around a shared workspace with sufficient room for individual and group work. Multi-touch capabilities offer the opportunity for team members to manipulate both shared and individual instances of data representations concurrently, while large multi-touch displays offer new opportunities for information visualization collaboration support. Fully realizing this potential requires careful consideration of the design of information visualization workspaces, representations, and interaction techniques. One important aspect of designing for concurrent interaction with information visualizations is the coordination of collaborators' interactions with individual views of the data. Since this coordination can take place at several different stages of the visualization pipeline-data, representations, presentation, or view level [6] making the stage at which coordination is taking place visually explicit may help provide awareness, which collaborators can use to flexibly coordinate their activities. We present Lark, an information visualization system for hierarchical data that supports this type of coordi- nation by integrating a representation of the information visualization pipeline into the shared workspace, thus indicating coordination points for data, representation, presentation, and view levels. This visualized pipeline supports both the awareness of how views are linked and the freedom to work in concert or independently. Our goal is to provide a multiple view information visualization system in which the views are linked and coordinated by a meta-visualization offering a mechanism for integrating individual and team work, helping team members to switch between degrees of cohesion in their work, and allowing them to build on each others' findings. In this paper we have presented Lark a collaborative information visualization system that provides active support for collaboration by setting the data-visualization within a meta-visualization. This metavisualization is based on the information visualization pipeline and uses the levels within the pipeline to create collaboration coordination points. Specifically, Lark supports: Changing Collaboration Styles: Lark supports changing collaboration styles by allowing people to switch between tightly and loosely coupled work within a multiple coordinated view system. Temporal Flexibility: Lark requires no specific temporal flow of activities, letting team members follow their own unique analysis approaches. Spatial Flexibility: Lark's views can be individually placed, scaled, and organized through out the workspace. This flexible approach to space usage supports mobility among team members, which is a common factor in changing collaboration cohesion during work. Scoped Interaction: Lark's interactions are scoped in the datavisualization gestures and commands all occur within individual viewpanes. The scope of Lark's meta-visualization interactions is explicitly set via the collaboration coordination point icons in the local view window. The choice of CCP setting specifies which view-panes will be affected. Our research was motivated by the benefits and requirements of face-to-face collaboration with information visualizations. With the possibility of simultaneous, concurrent interaction with a visualization on a shared large display comes the need to support the coordination of joint data analysis efforts. Lark was designed to support a range of collaboration styles by providing collaborative coordination mechanisms in an extended multiple-coordinated view system. For the individual information worker this provides a new type of interacting with multiple views of the same data that are near to hand. For team work, the view structure can inform collaborators about not only what they have done but how their work relates to what their team members have done and the locally scoped interaction controls help coordinate collaboration. Our primary goal is to provide an effective visual analysis mechanism for both individual as well as team work, help team members to switch between both types of work, and build on each others' findings. Early work in Computer-Supported Cooperative Work (CSCW) has indicated that many group activities, such as brainstorming or planning, involve phases of mixed-focus collaboration in which group members transition from loosely coupled, parallel work to closely coupled, group work [5] . We also know that these transitions require the coordination of group members' activities. Mixed-focus collaboration has recently been shown to apply to our work scenario: synchronous co-located collaboration with information visualizations over shared displays [9, 16] . In Tang et al. [16] different types of lenses and filters were studied to understand different types of group cohesion. It was noted that a tradeoff is necessary between providing only a single or multiple independent instances of data views. With a single shared representation individuals' abilities to work independently may be compromised, yet using separate copied views may prevent many group collaborative dynamics from emerging. Several collaborative information visualization and analysis systems have dealt with the problem of trading off individual and joint work with visual data representations and offered different solutions for coordinating among both types of work. Brennan et al. [1] proposed a distributed collaborative visual analytics framework that represents individual viewpoints as distinct from shared viewpoints. Individual views could be explicitly shared with others and were algorithmically merged to aid group analysis. In Keel's distributed analysis system [11] , computational agents were used to identify when an individual had uncovered potential relationships between information items in his/her workspace; this insight was then automatically relayed to the larger group of collaborators. We share these goals of providing explicit logical and graphical support for sharing information and translating among different views. Yet, their execution is quite different as individual perspectives are emphasized and spontaneous interactions are not easily possible. We want to support the coordination of views and interactions so that team members can follow a momentary insight, glance at another's views, and transition quickly and effortlessly between different views of the data. This goal has been examined in two previous systems for co-located data analysis [7, 8] . In a co-located collaborative tree comparison system [7] , group members could create multiple view instances and interact with these as separate entities. Yet, coordination among views was limited to a tree comparison operation and did not allow for group members to easily coordinate data annotations or other data modifications. In Cambiera [8] , group members were provided with coordinated visualizations of their search results through text document collections. Through "collaborative brushing and linking" individual search results and text document representations were linked and joint interactions and search overlap were explicitly visualized. Lark takes a different approach to the coordination of activities through explicit coordination points that use a representation of the information visualization pipeline.. Our implementation of coordination points relates to Heer and Agrawala's idea of using the information visualization reference model as "entry points for collaborative activity" [6] . In earlier work, Wood et al. [20] used the idea of coordinating collaboration around the visualization pipeline in a distributed system. This work is conceptually close to ours but the implementation was limited to an architectural design whereas our approach focuses on making different coordination points in the pipeline visually accessible and understandable. We base our work on Chi and Riedl's [3] operator interaction framework as a conceptual model for visualization operations. One of the main problems described in Chi and Riedl's work is the gulf of execution or the difference between intended and possible interactions in a system, explaining the view vs. value property as a fundamental classification for system operations. This is a critical distinction if people are to be allowed to distinguish between view and value operations when multiple views and multiple group members' interactions need to be coordinated. For example, interactions such as filters can apply to one or many visual representations (views) or propagate to the underlying data (value). A value operation would have a global scope and extend to all views attached to a specific data source, independent of which collaborator issued the operation. A view operation could have a more local scope, affecting only specific views of the data. The connections between our use of the visualization pipeline and the model proposed by Chi and Riedl are described in more detail in Section 4.

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


Design of on-line algorithms using hitting times AbstractRandom walks are well known to play a crucial role in the design of randomized off-line as well as on-line algorithms. Symmetry of the costs is very crucial to the basic technique used in [6] in designing the appropriate random walk, and thus left open an interesting question on stretch under asymmetric costs -equivalently, the stretch of random walks on directed graphs. In this work we prove close to optimal lower and upper bounds on stretch without the symmetry assumption.. Moreover, under symmetry our results imply those of [6] . In a recent paper, Coppersmith et al [6] made clever use of results from synthesis of electrical networks to design reversible random walks useful for certain randomized on-line algorithms.. At the heart of their methods lies the following problem on random walks. We are given a weighted (undirected) graph with n vertices, and with weight Cij on edge {i, j}, for 1 5 i, j 5 n. Assume that the weights are symmetric and that they satisfy the triangle inequality.. Every traversal of an edge {i, j} costs Cij. We say a random walk has stretch c if, for any sequence of vertices '~0, . . . , vk, the expected cost of the random walk to traverse these nodes in the prescribed order is at most c times the optimal cost, upto an additive constant. Let eU," denote the expected cost of the walk to go from vertex u to vertex v. Then, if for every vc, . . .Vk, cfcl ev;-lvi 5 C~~zl cu,-,v; + a, where a > 0, then the walk is said to have stretch c. Given the cost matrix C, the problem is to design a random walk with as low a stretch as possible. Coppersmith et al proved the following tight result for all symmetric cost matrices.. Any random walk on a weighted (undirected) graph with n vertices has stretch 2 (n-l), and every weighted (undirected) graph h as a random walk with stretch 5 (n -I).. Coppersmith et al justified the relevance of this problem by providing bounds for the cut and mouse game, which they showed was central to the analysis of on-line algorithms for well-known problems such as the metrical task system problem, and also bounds for In a nutshell, Coppersmith et al interpret a given cost matrix as an effective resistance matrix of a resistive network, and then they synthesize an actual network that has the desired properties. Classical analogs between resistive networks and reversible Markov chains yield a corresponding random walk that achieves the optimal stretch. We use a different way of synthesizing a random walk, the advantage being that we do not need reversibility of the walk ( i.e symmetry of the costs) for our techniques to work. We interpret the cost matrix as the hitting time (first passage time) matrix of an ergodic (not necessarily reversible) Markov chain, and then describe how to find the unique chain that yields the desired hitting times. i.e. design the transition probabilities which yield the desired hitting times. While such a synthesis of an ergodic chain from a valid hitting time matrix is unique and efficient, it is not true that an arbitrary cost matrix is always a hitting time matrix'. (The consolation, however, is that we can check for the latter condition with essentially one matrix inversion.) We call a cost matrix ergodic if it can be interpreted as a hitting time matirx and we call the corresponding random walk an ergodic walk. We show that this walk achieves optimal stretch when the costs are symmetric, and close to optimal when the costs are asymmetric. This approach also extends several other results proved in [6] .. Given a weighted (directed) graph with a weight (or cost) matrix C = {Cai}, define the cycle offset ratio Q(C) as follows. q(C) is the maximum over all 403 sequences vo, . . . , Vk = v. of ok CL G-I,%~ (Note that n tic1 ~Vi,U,-1 1 I Q'(C) I (n -I>, since the costs satisfy the triangle inequality.). We prove the following result. Any random walk on a weighted graph with n vertices has stretch _> (n -l)/*(C), and the ergodic walk has stretch < (n -l), with equality under a symmetric C. While we show examples that achieve equality in the lower bound, any tightening of the upper bound seems quite hard. However, it is interesting that the stretch of random walks on directed graphs can be brought down below n -1, while the counterpart on undirected graphs has an optimal bound of n -1.. The first application, for the cut and mouse game (see Section 3), follows immediately from the above. It was mentioned in [6] that the cat and mouse game is at the core of several on-line algorithms.. We show that for any n x n cost matrix C and any "blind" cat strategy (i.e. a random walk strategy), there is a mouse strategy that forces the competitiveness of the cat to be at least (n -1)/Q!(C), and the ergodic walk by the cat achieves a competitive ratio < (n -1), on ergodic C. The second and more interesting application is for the notoriously hard k-server problem (see [ll] , [16] , [19] ).. The Ic-server problem (defined in [19] ) is as follows. There are rE mobile servers located on k vertices of a graph G with positive, real costs on the edges. (The costs can be thought of distances between the positions.) An on-line algorithm manages the servers in such a way as to satisfy an on-line sequence of requests for service at vertices vi, i = 1,2, . . . -servicing a request corresponds to moving a server to the requested vertex, whenever there isn't a server there.. The algorithm pays a cost equal to the cost on the edge traversed by the server.. The competitiveness of the algorithm is measured with respect to the cost an adversary pays, wherein the adversary moves the servers, but also gets to choose the request sequence.. Due to the hardness of the k-server problem, it is significant to prove competitive ratios even for special cases such as special classes of graphs (e.g. [6] p rovide one such example class. They use random walks to design optimal randomized k-competitive server algorithms when the cost matrix has a resistive inverse. We extend this class by allowing asymmetric costs, or equivalently, weighted directed graphs, with ergodic cost matrices.. Define edge offset ratio W(C) to be rnaxij 2.. (Note that q(C) 5 @'(C), and that q(C) = Q'(C) ='i, for symmetric C.) We prove the following result for the asymmetric &server problem.. (This implies the result of F%). Let C be a cost matrix on n nodes. If every submatrix on k + l-nodes is ergodic, then we have a randomized kW(C)-competitive strategy for the kserver problem on C.. The final application is to the task system problem, defined as follows.. We have a task system (S, C) for processing sequences of tasks wherein S is a set of states, and C is a cost matrix, describing the cost of changing from state i to state j. We assume that the costs satisfy the triangle inequality, and that there is no cost of staying in the same state (Cii = 0). Furthermore, when the costs are symmetric we refer to the task system as a metrical task system (MTS). Each task T has a cost vector VT, where VT(i) is the cost of processing T in state i. A schedule for a given sequence of tasks Tl, . . . , Tk, is a sequence of states si, . . . , Sk, where si is the state in which Ti is processed.. The task system problem is to design an on-line schedule (choose si only knowing Z, . . . . Z) so that the algorithm is ur-competitive -on any input sequence of tasks, the cost of the on-line algorithm is, barring an additive constant, at most w times that of the optimal off-line algorithm.. Borodin et al.. [5] designed a deterministic algorithm with a competitive ratio of at most (2n-l)@(C) for the task systems problem with asymmetric costs. If the costs are symmetric (i.e. an MTS), they prove a matching lower bound of (2n -1). It is straight forward to extend their lower bound proof for the asymmetric case to get a lower bound of (2n -1)/9(C).. Coppersmith et al. provided a simpler, memoryless, (2n -l)-competitive, randomized algorithm for any MTS, and also showed that no randomized algorithm can do better against an adaptive on-line adversary.. We extend the results of [6] for the task systems with ergodic cost matrices.. In particular, we prove a lower bound of (2n -1)/4(C) f or any randomized on-line scheduler. We also provide a randomized on-line scheduler with a competitive ratio of at most (2n -1). This suggests that the deterministic algorithm of [5] may also have a competitive ratio of at most (2n -1); however, at this time it is not clear how to tighten the analysis in [5] .. Thus the novel technique of using the synthesis of random walks from hitting times for the design of online algorithms, while yielding the results of [6] for undirected graphs in a natural and simpler way, also yields results for directed graphs. We conclude this work with an interesting question on "approximating" an ergodic Markov chain, which will have useful implications in terms of extending our results to all cost matrices.

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


THE OPTIMIZED MODEL OF MULTIPLE INVASION PERCOLATION We study the optimized version of the multiple invasion percolation model. Some topological aspects as the behavior of the acceptance profile, coordination number and vertex type abundance were investigated and compared to those of the ordinary invasion. Our results indicate that the clusters show a very high degree of connectivity, spoiling the usual nodes-links-blobs geometrical picture. When a nonviscous liquid is injected into a porous medium already filled with a viscous fluid the system can be found in two different regimes: one where the dominant forces are of capillary nature and another where the viscous forces are predominant. The theoretical description of such system is based on two models: diffusion-limited aggregation (DLA) 1 and invasion percolation 2 . DLA describes the fast displacement situation when the viscous forces are dominant. The invasion percolation model is applied to a slow fluid flow, where the leading forces are of capillary nature. The fluid displacement follows minimum resistance paths: the smaller pores are filled or invaded first.. The original invasion percolation model have been modified in order to bring it as close as possible to real world. So, the action of an external gravitational field 3, 4, 5 and the flux with a privileged direction 6, 7 were incorporated into the model. Recently 8 the multiple invasion percolation model was proposed. In this model a certain number of lattice sites can be simultaneously invaded. It is always important to have in mind that invasion percolation is a dynamical model, that is, it intends to explain not only static properties like the clusters fractal dimensions but also how these clusters evolve in time. The lack of a meaning on associating or trying to make a correspondence between one step growth interval (of the algorithm) and one time interval separating two sucessives pore's invasions (of the real world) is what we were concerned by the time we formulated the multiple invasion percolation model 8 . In our models, one real time interval corresponds exactly to one growth step and it is, in this sense, more realistic. When water penetrates layered soil, in some cases, a fingering formation is detected. The multiple invasion percolation not only describes successfully the fingers dynamics but also led us to a more ambitious program -to obtain the experimental pores size distribution of the soil 6 . Briefly, the multiple invasion percolation model is useful not only to explain experimental results but also to predict them.. There are two kinds of multiple invasion percolation: the perimeter and optimized models. In the first model the cluster growth is controlled by the flux through the perimeter. The optimized model is governed by a scaling relation between the mass and the gyration radius of the cluster. Both types of invasion were studied in their site versions. For the perimeter model, the acceptance profile, mean coordination number and abundance of vertice type were investigated. In this paper we discuss the acceptance profile and some topological properties of the optimized model clusters. We studied the optimized model of multiple invasion percolation by comparing its topological properties with those of the ordinary invasion percolation. The high connectivity of the clusters produced by the optimized model together with the almost disappearance of the red sites, led us to conclude that the nodes-links-blobs model is not well suited to describe the backbones of the optimized model.

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