Quantifying group problem solving with stochastic analysis Quantifying the relationship between group dynamics and group performance is a key issue of increasing group performance. In this paper, we will discuss how group performance is related to several heuristics about group dynamics in performing several typical tasks. We will also give our novel stochastic modeling in learning the structure of group dynamics. Our performance estimators account for between 40 and 60% of the variance across range of group problem solving tasks. We are interested in quantifying group problem solving performance by analysis of non-linguistic social signals. These pre-linguistic communication structures have been shown to capture a large fraction of the dynamics of group interaction, and to be predictive of performance and outcomes [1, 2] . We accomplish this by instrumenting group participants using Sociometric Badges [3, 2] , to record speaking dynamics, tone of voice, body motion, etc. These data are then analyzed by use of signal processing techniques including HMM, influence, and similar stochastic models.. The Interaction Process Analysis (IPA) [4] is a traditional approach for quantifying a general group problem-solving process based on fine time-grained analysis. In this approach, an interaction process is treated as a sequence of events of different categories -giving and analyzing facts, showing individual approaches for problem-solving, making group decisions, and releasing tensions developed in decisionmaking. The analysis proceeds in the following way: Two or more trained observers watch through a whole group problem-solving process and mark events at a resolution of 10˜15 events per minute; The sequences of events marked by 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. ICMI-MLMI'10, November 8-12, 2010, Beijing, China. Copyright 2010 ACM 978-1-4503-0414-6/10/11 ...$10.00. different observers are then compared and accessed for reliability; Heuristic scores about the interaction process are then computed by counting events in different categories and are related to group performance.. While they could quantitatively explain the relationship between the details of an interaction process and the corresponding group performance, the traditional methods are costly in terms of human expert time. As a result, there are many difficulties in applying these methods in explaining the fine differences about the interaction dynamics and performances of a large number of groups in solving a large number of different problems.. On the other hand, we argue that the traditional approaches could be complemented, automated and unified with a new approach based on the statistical learning methods and our capability to collect a massive amount of data about group interaction processes with embedded devices. Our reasoning is the following. Different types of activities in a group problem-solving process have different temporal and interaction statistics -Fact-giving often involves longer sentences and less parallel-speaking from other speakers while showing-opinions often involves shorter sentences and more parallel-speaking. Further, the solutions of many common problems often involve a limited amount of facts, opinions and voting and thus a limited amount of events of different categories in problem-specific proportions. Thus we could estimate group performance based on heuristics and stochastic methods about these non-semantic cues of the group process, and potentially find ways to improve it. In situations when we do not know the structure of the group problem-solving process, we could use latent-state stochastic models to "project" the time series of non-semantic cues along the direction of problem-solving performance and discover the structure of problem solving.. To illustrate our method in quantifying group interactiondynamics and problem-solving, we will refer to the interactiondynamics data collected by the Sociometric Badges in the Measuring Collective Intelligence (MCI) study 1 [5] . The goal of the MCI studies is towards finding the key components of collective intelligence, the relationship between group interaction and group performance, and the methods to increase collective intelligence. MCI Study 1 involves 42 groups solving 12 problems, with each problem costing a fixed amount of time ranging from 10 minutes to 1 hour and all 12 problems costing around 3 hours.. In the rest of the paper, we will summarize some key feature extraction steps, discuss some heuristics about quantifying group problem solving, and give our stochastic model-ing that learns the structure of group problem solving.

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


Towards system-mediated car passenger communication In this paper, we outline a system that supports the communication between passengers by transmitting speech (and maybe also video) of the communication partners back and forth. A study is presented that addresses the questions: 1. Is listening to noisy speech coming from the backseat really distracting the driver? Subjects are rating the truth of common-sense statements played from the back of the car (clear, noisy) while driving with a drive simulator. noisy is rated significantly more distracting than clear while objective driving performance only degrades for men but not for women. Research on automotive assistance and infotainment systems has traditionally focussed on one person: the driver. However, even with commuting to work, an average of 10.2 % chose to carpool in the US in 2004, as a study by American Community Survey revealed [1] . With leisure time traveling, the number of cars with more than one passenger can be expected to be much higher. Hence, taking passengers into account when designing in-car systems is a reasonable thing to do. In our research, we lay the foundations for a new generation of context-aware multimodal interfaces for car passengers that support the interaction of the passengers with the car, the interaction of the passengers and the road environment as well as the interaction between the passengers, mediated by the system. This study contributes to the latter aspect. We outlined a system that supports the communication between passengers by transmitting speech (and maybe also video) of the communication partners back and forth. We reported results of a study indicating that listening to noisy speech from the back is distracting drivers (subjective rating), especially men (subjective rating and drive simulator).

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


Document dependent fusion in multimodal music retrieval In this paper, we propose a novel multimodal fusion framework, document dependent fusion (DDF), which derives the optimal combination strategy for each individual document in the fusion process. For each document, we derive a document weight vector by estimating the descriptive abilities of its different modalities. The document weight vector also enables our framework to be easily integrated with existing multimodal fusion schemes, and achieve a better combination strategy for each document given a query. Experiments are conducted on a 17174-song music database to compare the retrieval accuracy of traditional query independent fusion and query dependent fusion approaches, and that obtained after integrating DDF with them. Experimental results indicate that DDF can significantly improve the retrieval performance of current fusion approaches. Since most documents (e.g., music, images, text documents) contain information or cues in different modalities, multimodal fusion, which aims to combine these modalities to better meet users' information needs, has been regarded as an effective approach to improve IR performance. Intensive research has been carried out aiming to estimate the optimal combination strategy of different modalities. Existing * Area Chair: Alexander Hauptmann 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. query independent fusion (QIF) and query dependent fusion (QDF). In the QIF scheme, the same fusion strategy is applied to combine different modalities for every query regardless of the query content and diversity. An example work of this category is CombSUM/CombMNZ method found in meta search [5] . However, this strategy is inadequate due to the fact that all queries are not equally created and they may have different information focuses. QDF emerges with the goal to improve the retrieval performance by adopting different fusion strategies for each query class (e.g., [1, 2, 7, 6] ) or individual query (e.g., [9] ). It is noted that these approaches focus on deriving the optimal fusion strategy by only considering queries. Once the fusion strategy is determined (either in QIF or QDF), all the documents adopt the same strategy to combine its modalities.. In this paper, we propose a document dependent fusion (DDF) framework to derive the optimal fusion strategy for each document by considering influences of both queries and documents on the retrieval performance of IR applications. The structure of the framework is illustrated in Fig. 1 . A document weight vector is derived for each document by learning the descriptive abilities of different modalities. This weight vector can be then integrated with QIF and QDF approaches. Confirmed by our experimental results, DDF significantly improves the performance of multimodal music retrieval.. The rest of the paper is organized as follows: Section 2 describes our approach from three main aspects: framework overview, document weight deviation, and document dependent fusion. Section 3 describes configurations of our experiments. Experimental results are presented and analyzed in Section 4, followed by the conclusion in Section 5. We have introduced a novel multimodal fusion framework, document dependent fusion (DDF), to derive the optimal fusion strategy for each individual document. We derive a document weight vector for each document, and integrate it into the fusion process. Confirmed by the experimental results, our proposed framework has significantly improved current multimodal fusion approaches. Moreover, in the process of DA derivation, relative scores of different modalities are learned from the retrieval results of a large number of user queries. By combining with the DA of textual modalities, this method can derive DAs for modalities with various formats. Therefore, it can also be extended to other media documents in different multimodal retrieval applications, such as meta search, and video/image retrieval.

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


Unsupervised Segmentation of Color-Texture Regions in Images and Video A new method for unsupervised segmentation of color-texture regions in images and video is presented. This method, which we refer to as JSEG, consists of two independent steps: color quantization and spatial segmentation. In the first step, colors in the image are quantized to several representative classes that can be used to differentiate regions in the image. The image pixels are then replaced by their corresponding color class labels, thus forming a class-map of the image. The focus of this work is on spatial segmentation, where a criterion for "good" segmentation using the class-map is proposed. Applying the criterion to local windows in the class-map results in the "Jimage," in which high and low values correspond to possible boundaries and interiors of colortexture regions. A region growing method is then used to segment the image based on the multiscale J-images. A similar approach is applied to video sequences. An additional region tracking scheme is embedded into the region growing process to achieve consistent segmentation and tracking results, even for scenes with non-rigid object motion. Experiments show the robustness of the JSEG algorithm on real images and video.Final Manuscript to PAMI (regular paper) Image and video segmentation is useful in many applications for identifying regions of interest in a scene or annotating the data. The MPEG-4 standard needs segmentation for object based video coding. However, the problem of unsupervised segmentation is ill-defined because semantic objects do not usually correspond to homogeneous spatio-temporal regions in color, texture, or motion. Some of the recent work in image segmentation include stochastic model based approaches [1] , [6] , [13] , [17] , [24] , [25] , morphological watershed based region growing [18] , energy diffusion [14] , and graph partitioning [20] . The work on video segmentation include motion based segmentation [3] , [19] , [21] , [23] , spatial segmentation and motion tracking [8] , [22] , moving objects extraction [12] , [15] , and region growing using spatio-temporal similarity [4] , [16] . Quantitative evaluation methods have also been suggested [2] .. Many of the existing segmentation techniques, such as direct clustering methods in color space [5] and [9] , work well on homogeneous color regions. Natural scenes are rich in color and texture.. Many texture segmentation algorithms require the estimation of texture model parameters.. Parameter estimation is a difficult problem and often requires good homogeneous region for robust estimation. The goal of this work is to segment images and video into homogeneous colortexture regions. A new approach called JSEG is proposed towards this goal. This approach does not attempt to estimate a specific model for a texture region. Instead, it tests for the homogeneity of a given color-texture pattern, which is computationally more feasible than model parameter estimation.. In order to identify this homogeneity, the following assumptions about the image are made:. • Each image contains a set of approximately homogeneous color-texture regions. This assumption conforms with our segmentation objective.. • The color information in each image region can be represented by a set of few quantized colors. In our experience with a large number of different image datasets, including thousands of images from the Corel stock photo gallery, we have found that this assumption is generally valid.. • The colors between two neighboring regions are distinguishable --a basic assumption in any color image segmentation algorithm.. The basic idea of the JSEG method is to separate the segmentation process into two stages, color quantization and spatial segmentation. In the first stage, colors in the image are quantized to several representative classes that can be used to differentiate regions in the image. This quantization is performed in the color space without considering the spatial distributions of the colors.. Then the image pixel values are replaced by their corresponding color class labels, thus forming a class-map of the image. The class-map can be viewed as a special kind of texture composition. In the second stage, spatial segmentation is performed directly on this class-map without considering the corresponding pixel color similarity. The benefit of this two-stage separation is clear. It is a difficult task to analyze the similarity of the colors and their distributions at the same time. The decoupling of color similarity from spatial distribution allows development of more tractable algorithms for each of the two processing stages. In fact, many good color quantization algorithms exist and one of them [9] has been used in this work .. The main focus of this work is on spatial segmentation and the contributions can be summarized as:. • We introduce a new criterion for image segmentation (Section 2). This criterion involves minimizing a cost associated with the partitioning of the image based on pixel labels.. • A practical algorithm is suggested towards achieving this segmentation objective. The notion of "J-images" is introduced in Section 2. J-images correspond to measurements of local homogeneities at different scales, which can indicate potential boundary locations.. • A spatial segmentation algorithm is then described in Section 3, which grows regions from seed areas of the J-images to achieve the final segmentation. Fig. 1 shows a schematic of the JSEG algorithm for color image segmentation. Extensions to video segmentation are discussed in Section 4. We conclude with experimental results and discussions in Section 5. In this work, a new approach called JSEG is presented for fully unsupervised segmentation of color-texture regions in images and video. The segmentation consists of color quantization and spatial segmentation. A criterion for "good" segmentation is proposed. Applying the criterion to local image windows results in J-images, which can be segmented using a multi-scale region growing method. For video, region tracking is embedded into segmentation. Results show the robustness of the algorithm on real images and video. Future research work is on how to handle the limitations in the algorithm and improve the results.

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


Tool support for data validation by end-user programmers End-user programming tools for creating spreadsheets and webforms offer no data types except "string" for storing many kinds of data, such as person names and street addresses. Consequently, these tools cannot automatically validate these data.To address this problem, we have developed a new userextensible model for string-like data. Each "tope" in this model is a user-defined abstraction that guides the interpretation of strings as a particular kind of data, such as a mailing address. Specifically, each tope implementation contains software functions for recognizing and reformatting that tope's kind of data.With our tools, end-user programmers define new topes and associate them with fields in spreadsheets, webforms, and other programs. This makes it possible at runtime to distinguish between invalid data, valid data, and questionable data that could be valid or invalid. Once identified, questionable and/or invalid data can be double-checked and possibly corrected, thereby increasing the overall reliability of the data. Already, over 50 million people create spreadsheets, databases or webforms to collect and organize data [13] . One study of spreadsheets showed that nearly 40% of this data is short, humanreadable strings of text, such as phone numbers, email addresses and person names, rather than numbers or formulas [2] .. Unfortunately, just as several percent of a spreadsheet's formulas typically contain errors [6] , string data has many errors. Common examples include using a field to store data of the wrong kind (such as putting a person's first and middle name in a field that should just have a first name [14] or even putting an age into an address field [11] ), or storing valid data in the wrong format (such as a phone number with unexpected parentheses around the area code).. These errors occur in part because spreadsheets and webform development tools require programmers to use regular expressions (regexps) or even scripts to validate data. Regexps can only accept or reject a string, with no shades of grey in between. Yet many kinds of data are not well-described in this binary manner. For example, suppose a web application validates email addresses using a regexp based on the official specification [3] . Then it would allow users to enter email addresses with 64 characters in the address's username (since the specification allows this), but obviously such a long username is highly unusual and questionable: it might be valid, but it probably is invalid. Regexps can only categorize data as valid or invalid, offering no third category for data that theoretically might be valid but still could benefit from manual double-checking by the person who entered that email address (or by some other person). Aside from this expressiveness problem, regexps are also hard to read and write for enduser programmers, who lack professional programming training [1] . Validation scripts are even more time-consuming and difficult to write than regexps, even for professional programmers, who consequently often choose to omit validation on webforms [11] .. The second obstacle to more thorough validation is that valid data appear in multiple formats. For example, mailing addresses may specify a full street type such as "Avenue" or an abbreviation such as "Ave.", and books may be referenced by title or ISBN. Prior to using data, an application typically must put data into a consistent format. Even if a programmer could write a regexp (with many disjunctions) to recognize multi-format data, the regexp still would leave inputs in multiple formats at the end of validation. Ideally, validation should help transform data into the format needed by the main application.. Based on these considerations, we present a tool set supporting a technique for recognizing questionable data and putting data into a consistent format. Our technique enables end-user programmers to define new abstractions called "topes", each of which robustly describes one kind of data (such as a mailing address) independently of any particular software application and which is reusable across applications and across software development platforms. A tope contains multiple explicitly distinguished formats that recognize valid inputs on a non-binary scale, and it contains transformation functions to map values from one format to another.

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


Eye-tracking for avatar eye-gaze and interactional analysis in immersive collaborative virtual environments Participants' eye-gaze is generally not captured or represented in immersive collaborative virtual environment (ICVE) systems. We present EyeCVE, which uses mobile eye-trackers to drive the gaze of each participant's virtual avatar, thus supporting remote mutual eye-contact and awareness of others' gaze in a perceptually unfragmented shared virtual workspace. We detail trials in which participants took part in three-way conferences between remote CAVE TM systems linked via EyeCVE. Eye-tracking data was recorded and used to evaluate interaction, confirming the system's support for the use of gaze as a communicational and management resource in multiparty conversational scenarios. We point toward subsequent investigation of eye-tracking in ICVEs for enhanced remote social-interaction and analysis. In a face-to-face meeting, the surrounding environment is a contiguous space in which participants are able to use a fullrange of non-verbal communicational resources: they can move their eyes and head to look at others, change facial expression, gesture, posture, and position themselves as desired. Despite development of highly sophisticated CSCW systems, there is no substitute for such co-located interaction which supports rich non-verbal communication while allowing free movement in a perceptually unfragmented workspace.. Video-mediated communication (VMC) systems add a video channel to audio, and have been found to improve participants' ability to show understanding, forecast responses, give non-verbal information, enhance verbal descriptions, * W.Steptoe@cs.ucl.ac.uk 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. CSCW'08, November 8-12, 2008 , San Diego, California, USA. Copyright 2008 ACM 978-1-60558-007-4/08/11...$5.00. manage pauses and express attitudes [13] . However, VMC compresses the representation of 3D space, constraining rich cues available in co-located collaboration such as depth, resolution and field of view, and thereby limiting awareness and ability to point at and manipulate objects [10] .. Immersive Collaborative Virtual Environments (ICVEs) connect remote or co-located users of immersive display systems (such as the CAVE) within a spatial, social and informational context, with the aim of supporting high-quality interaction [19] . ICVEs generally represent participants as avatars (a graphical representation of a human) in a shared computer-generated virtual environment [5] . Head-orientation and pointing gestures are animated by head and hand trackers worn by participants, and significantly contribute toward perception of other's visual attention [14] . However, ICVEs currently fail to track participant gaze. Murray and Roberts determined that augmenting avatar head-orientation with gaze (replayed from pre-recorded eye-tracking data) is of vital importance for observers to be able to correctly identify where an avatar is looking (gaze target) [17] . Uses of gaze which are particularly relevant to interaction in ICVEs include indicating and determining focus of attention, addressing, prompting, and when describing and handling objects.. We addressed the lack of participant gaze capture and representation in ICVEs by developing EyeCVE: a novel system with integrated mobile eye-trackers that drive avatar gaze in real-time, thus supporting natural awareness of other's visual attention and allowing eye-contact (mutual gaze) to be established between participants. Although the primary motivation for this work is to accurately represent gaze for enhanced remote social-interaction in ICVEs, the use of eyetrackers grant other opportunities directly and through data collection. This paper demonstrates interactional analysis to measure the system's ability to support remote multiparty virtual conferencing scenarios. We cover initial use, evaluation, and potential of EyeCVE as opposed to technical implementation described in [26] . We presented EyeCVE, our multiparty CAVE-based system using mobile eye-trackers to drive avatar gaze, thus supporting communicational gaze in an unfragmented workspace. The capture of nonverbal behaviour is considered essential in order to support collaborative interactions that are more similar to those in the real world [21] , and the system augments standard ICVE replication of head and hand movement with gaze. While further investigation and addressing current shortfalls is required, our system enables communicational gaze and free movement in an unfragmented workspace, in which multiple participants can be co-present together with virtual objects and documents, thus supporting remote cooperative working.. Future work will focus on content outlined in Figure 2 , and will be evaluated in dynamic and object-focused tasks common to CSCW. We will enhance our software framework and robustness of eye-tracking in the CAVE to reduce gaze target ambiguities. High-fidelity avatars as detailed in [22] featuring facial expression, lip-movement and accurate eyeanimation will be integrated, allowing investigation into behavioural and representational fidelity. Finally, we will explore the impact of gaze communication in ICVEs, establishing situations where it is critical for remote collaboration and its use as a tool for interactional analysis. In combination with gaze data from the three eye-trackers, our qualitative analysis of participants' interactional behaviour draws primarily on conversation analysis: an inductive process for analysing how human interaction is organised into sequences of action or systematic practices [20] . We limit analysis to the interviewees, although it will also be necessary to consider some of the interviewers' behaviour. Due to space limitations, we can only show one data extract, but full transcripts and videos will be made available online. In the extract, reference numbers relate to speech from the adjacent name. Various symbols and spellings are used to capture aspects of the sound of the talk. The interviewee's gaze is indicated by labeled lines below and parallel to the related transcribed talk. We consider the exchange of information and involvement of participants, including the ability to interpret attention from gaze as well as maintaining mutual gaze with others during conversation. Avatar gaze mimicked participant gaze, which was generally found to follow standard gaze practices. Therefore, EyeCVE allowed participants to use gaze for bidirectional feedback and signaling similarly to face-to-face interaction. While being asked a question, participants gazed at the questioner in 66.7% of cases. This figure seems to have been deflated due to eye-tracker noise, which contributed to the 11.1% of ambiguous cases in which there was no agreement between raters as to where to the participant was looking. In any case, this frequency is comparable to Argyle's time-range of 70-75% that listeners gaze at speakers during dyadic faceto-face conversation [2] .. Although our quantitative analysis did not expose obvious within-session effects, conversation analysis revealed behavioural changes in participants who initially gazed generally towards other avatars, but began to consistently target fellow avatar's eyes as the interview progressed. This suggests that some participants realised the significance of gaze information, and responded with interactionally relevant behaviour, despite not having been told that gaze was being captured for real-time representation. Gesture was important for conversation management and speaker transition, and was employed by interviewers to compensate for the lack of avatar lip-movement and spatialised audio. Participant gaze was sensitive to gesture, and conversation flowed smoothly. Eye-CVE's support for such observed emergent learning and communicative behaviour will be explored in future work. Evidence from referenced studies suggests that capturing and representing participant gaze will facilitate more natural social interaction in ICVEs. Although not specifically investigated in this experiment, the use of mobile head-mounted eye-trackers allow free-movement within the CAVE while maintaining communicational gaze between multiple participants without the parallax problematic to VMC systems. Integrating eye-tracking and ICVEs also invites exploration of other possible uses as illustrated in Figure 2 . Figure 2 's shaded boxes, this paper focuses on communicational avatar gaze and analysis, while the unshaded boxes will be addressed in future work. Here, we differentiate communicational from attentional gaze by classifying the former as behaviour from raw eye-tracker data, while the latter will apply filters to the data to recognise eyefixations and saccades in order to selectively represent focus of attention in a more iconic manner. Inferred from Hindmarsh et al. [12] and Garau et al. [8] respectively, we predict that varying gaze fidelity will benefit interaction depending on task (i.e. conversational or object-focused) and avatar quality. Augmented gaze refers to communicating information not usually available in face-to-face interaction, such as indicating gaze target or manipulating perceived attention as seen in Bailenson et al. [3] . Advanced gaze models informed by multiparty analysis will subsequently be used to drive avatar gaze, allowing performance comparison with tracked gaze. Natural object selection and navigation in 3D space is also granted by using eye-trackers as an input device.

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


A Symmetry Preserving Alternating Projection Method for Matrix Model Updating The Matrix Model Updating Problem (MMUP), considered in this paper, concerns updating a symmetric second-order finite element model so that the updated model reproduces a given set of desired eigenvalues and eigenvectors by replacing the corresponding ones from the original model, and preserves the symmetry of the original model. In an optimization setting, this is a constrained nonlinear optimization problem. Taking advantage of the special structure of the constraint sets, it is first shown that the MMUP can be formulated as an optimization problem over the intersection of some special subspaces and linear varieties on the space of matrices. Using this formulation, an alternating projection method is then proposed and analyzed. The projections onto the involved subspaces and linear varieties are characterized. To the best of our knowledge, an alternating projection method for MMUP has not been proposed in the literature earlier. A distinct practical feature of the proposed method is that it is implementable using only a few measured eigenvalues and eigenvectors. No knowledge of the eigenvalues and eigenvectors of the associated quadratic matrix pencil is required. The results of our numerical experiments on both illustrative and benchmark problems show that the algorithm works well. The paper concludes with some future research problems. It is well-known that vibrating structures, such as bridges, highways, buildings, etc., can be mathematically modelled by a system of differential equations of the form:. where M , D and K are n × n matrices; andẋ(t) andẍ(t) denote the first and second derivatives of the time-dependent vector x(t), respectively. Equation (1) is usually obtained by discretization of a distributed parameter system with finite element techniques, and therefore, known as the finite element model. The matrices M , D, and K are known as mass, damping and stiffness matrices, respectively. They are often very large and sparse, but have some nice structures, such as, M is symmetric and positive definite (M = M . Through out the whole paper, such assumptions will be made.. Assuming that the solutions x(t) of (1) . The eigenvalues of P (λ) are related to the natural frequencies of the homogeneous system and the eigenvectors are the mode shapes of the vibration of the system (see, e. g., [11] , [12] , [30] ). The dynamics of the system are modelled by these eigenvalues and eigenvectors. For example, sometimes the vibrating structures experience dangerous vibrations, called resonance, when a natural frequency becomes close or equal to a frequency of an external force, such as earthquake, gusty wind, weights of the human bodies, etc. Similarly, the stability of a vibrating system is determined by nature of a few dominating natural frequencies. The solutions of these problems naturally lead to the following inverse eigenvalue problem for the quadratic matrix pencil: Given The last requirement, namely, the invariance of the last 2n − p eigenvalues and the corresponding eigenvectors, is known as the no spill-over in vibration literature. The problem is called Quadratic Eigenvalue Assignment Problem(QPEVAP), when it is solved using feedback control techniques. A usual approach for solving the QPEVAP is to transform the problem to a standard first-order state space problem and then apply some of the specialized techniques for first-order partial eigenvalue assignment problem (see Chapter 11 of the book [12] ). However, because of several serious computational difficulties, including the inversion of a possible ill-conditioned mass matrix M and the complete loss of the exploitable structures of the matrices, M , K and D , such as the symmetry, sparsity, and definiteness, this approach is not practical. In view of these considerations, in recent years, several techniques for QPEVAP, which work directly in second-order setting and requires the knowledge of only those few eigenvalues and eigenvectors that need to be reassigned, have been developed in (e.g., [9] , [15] , [13] , [14] , [17] , [18] ). Unfortunately, the use of feedback control destroys the symmetry of the updated model. While solution of the QPEVAP does not require that the symmetry is preserved, one of the fundamental requirements of the closely related Matrix Model Updating Problem (MMUP) is that the updated model remains symmetric. The MMUP concerns updating of a finite element model in such a way that a set of "unwanted eigenvalues and eigenvectors" from the original model is replaced by suitably given ones and the symmetry of the original model preserved.. The MMUP has been well studied and there exists a large amount of literature on its solution. For an account of the earlier methods, see the authoritative book by Friswell and Mottershead [26] . References to some of the more recent work can be found in [7] . Most of these methods, except the one in [7] , are optimization based. The idea is to formulate the problem as a constrained optimization problem and then use some of the existing optimization techniques. In many cases, especially when the problem is solved for an undamped model, explicit solutions can be given (see [26] . The direct method proposed in [7] has the additional feature that it can mathematically guarantee the no spill-over in the updated model. The last paper, however, concerns updating of an undamped model. In [7] , a symmetry preserving eigenvalue embedding scheme for a damped model has been proposed and the scheme there is capable of preserving the no spill-over. However, that paper considers assigning only of a given set of eigenvalues but not the eigenvectors. It is to be noted in this context that it is not critically important from practical view point to preserve the no spill-over per say. What is important is to guarantee that spurious modes are not introduced into the frequency range of interests (see [26] ).. In this paper, the optimization problem for MMUP for a damped model is formulated in such a way that the well-known "Alternating Projection" technique can be used to our advantage. This has been done by exploiting the special structure offered by the constraint set. Using this technique, a new method for the damped MMUP is proposed. A distinct practical feature of our proposed alternating project method is that it can be implemented using only those few eigenvalues and eigenvectors that are needed to be reassigned. No knowledge of the spectrum and the eigenvectors of p(λ) is needed. It is to be noted in this context that most of the eigenvalues and eigenvectors of p(λ),in the case when the number of degrees of freedom is quite large, are neither computable using the state-of-the-art computational techniques nor are experimentally measurable. The results of numerical experiments, both on illustrative and benchmark examples, shown that the algorithm is working well.

O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 optimal low rank Tucker approximation for tensors: the case for an adjustable core size Approximating high order tensors by low Tucker-rank tensors have applications in psychometrics, chemometrics, computer vision, biomedical informatics, among others. Traditionally, solution methods for finding a low Tucker-rank approximation presume that the size of the core tensor is specified in advance, which may not be a realistic assumption in many applications. In this paper we propose a new computational model where the configuration and the size of the core become a part of the decisions to be optimized. Our approach is based on the so-called maximum block improvement (MBI) method for non-convex block optimization. Numerical tests on various real data sets from gene expression analysis and image compression are reported, which show promising performances of the proposed algorithms. In this paper we study the problem of finding a proper Tucker approximation for a general tensor without a pre-specified size of the core tensor, which addresses an important practical issue for real applications. The size of the core tensor is assumed in almost all the existing methods for tensor Tucker decomposition. The approach that we propose is based on the so-called maximum block improvement (MBI) method. Our numerical experiments on a variety of instances taken from real applications suggest that the proposed methods perform robustly and effectively.

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Algorithms on ensemble quantum computers In ensemble (or bulk) quantum computation, all computations are performed on an ensemble of computers rather than on a single computer. Measurements of qubits in an individual computer cannot be performed; instead, only expectation values (over the complete ensemble of computers) can be measured. As a result of this limitation on the model of computation, many algorithms cannot be processed directly on such computers, and must be modified, as the common strategy of delaying the measurements usually does not resolve this ensemble-measurement problem. Here we present several new strategies for resolving this problem. Based on these strategies we provide new versions of some of the most important quantum algorithms, versions that are suitable for implementing on ensemble quantum computers, e.g., on liquid NMR quantum computers. These algorithms are Shor's factorization algorithm, Grover's search algorithm (with several marked items), and an algorithm for quantum fault-tolerant computation. The first two algorithms are simply modified using a randomizing and a sorting strategies. For the last algorithm, we develop a classical-quantum hybrid strategy for removing measurements. We use it to present a novel quantum fault-tolerant scheme. More explicitly, we present schemes for fault-tolerant measurement-free implementation of Toffoli and r 1=4 z ; as these operations cannot be implemented ''bitwise'', and their standard fault-tolerant implementations require measurement. To summarize, various conventional algorithms cannot run on ensemble (bulk) computers, such as NMR quantum computers, since individual qubit measurement is not available. We explained in details why running various algorithms on ensemble computers is not always straightforward. We modified Shor's algorithm, Grover's algorithm (in the case of more than one solution), and fault tolerance protocols so that they can run on ensemble computers.. A very preliminary version of this work appears in the Los-Alamos archive, quant-ph/ 9907067. A partial version describing the algorithm for fault-tolerant quantum computing appears in the DSN'04 conference proceedings (Boykin et al. 2004) .. In a prior work, addressing fault tolerant computation, Aharonov and Ben-Or (1996) have observed that the measurements required for fault tolerant computation can be substituted by reversible classical circuits performing controlled operations. D. Aharonov also sent us a manuscript (Aharonov D, private communication) with results regarding Toffoli gate which are very similar to those obtained here. Knill et al. (1996) followed a different approach that potentially does not require measurements. However, to the best of our knowledge, a proof of universal fault tolerant computation via their approach is not available. In particular, a measurement-free implementation of the Hadamard gate using that approach has not been demonstrated. Finally, Peres (1998) also discusses the possibility of measurement-free encoding and decoding procedures in quantum error-correction. However, in his scheme the quantum information is transformed to a single qubit, and his method is not suitable for fault tolerant computation.

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Power grid voltage integrity verification Full-chip verification requires one to check if the power grid is safe, i.e., if the voltage drop on the grid does not exceed a certain threshold. The traditional simulation-based solution to this problem is computationally expensive, because of the large variety of possible circuit behaviors that would need to be simulated; it also has the disadvantage that it requires full knowledge of the details of the circuit attached to the grid, thereby precluding early verification of the grid. We propose a power grid verification technique that can be applied before the complete circuit has been designed and without exact knowledge of the circuit currents. We use current constraints, which are upper bound constraints on the currents that can be drawn from the grid, as a way to capture the uncertainty about the circuit details and activity. Based on this, we propose two solution approaches. One approach gives an upper-bound on the worst-case voltage drop at every node of the grid. Another, less expensive approach, applies a sufficient condition (thus, this becomes a conservative approach) to check if the drop on the grid exceeds a given voltage threshold. As the supply and threshold voltages are decreasing with technology scaling, full-chip verification is becoming more and more challenging. In particular, checking the integrity of the voltage on the power grid is becoming crucial. With lower supply voltages, smaller voltage drops become more significant and can cause longer circuit delays and lead to soft errors. Thus, supply voltage integrity verification is an integral part of both timing verification and noise immunity checking.. Voltage drop on the grid is mainly due to IR drop and Ldi/dt drop. IR drop is due to the resistance of the metal lines of the power network. The Ldi/dt drop is due to the self and mutual inductances of the power lines. In practice, the effect of inductance in the power grid is only significant at frequencies above a GHz or so, and it can therefore be ignored in many circuits. In this paper, we will use an RC model of the power grid, ignoring the inductance effects and focusing on IR drop.. Power grid verification via traditional circuit simulation requires full knowledge of the current waveform drawn by every 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. circuit block attached to the grid. These current waveforms would be used to simulate the grid and get the voltage drop at every grid node. This drop is then compared to a maximum allowable voltage drop threshold to check if any node on the grid is unsafe (the voltage drop at this node is higher than the threshold). To verify the grid in this way requires a comprehensive set of current waveforms to make sure all the regions on the grid are simulated, and that the obtained voltage drop is a worst-case drop. Also, this method requires full knowledge of the circuit, which is a concern if one would like to verify the grid early in the design flow, before all the circuit details are available.. To overcome these problems, we will use the concept of current constraints [1] to capture the uncertainty about the circuit details and circuit behavior. These current constraints are a set of upper-bounds on the currents that would be drawn by the circuit. They can be obtained from simulations of the circuit or from knowledge of the overall power dissipation of the circuit blocks. Using these upper-bound constraints, we will show how to check if the maximum voltage drop on the power grid, under all possible transient current waveforms that satisfy the constraints, exceeds a certain voltage threshold.. A similar verification problem was previously formulated and solved in [1] , but under the assumption that the currents on the grid are DC, which can under-estimate the worst-case drop. In this paper, we present a general solution to the problem, in which the currents are allowed to be arbitrary transient waveforms. We will present two solution approaches. First, we present an algorithm that computes an upper bound on the worst-case drop at every node of the grid. We give empirical data that shows that the upper bound can be tight, and that therefore the pessimism in the first approach is not too significant. In the second approach, we will present a method to check if the grid is safe with respect to a given voltage threshold, without attempting to find the exact maximum drop on the grid. This method applies a sufficient condition to perform the check, thereby leading to a conservative approach by which some grids which are declared unsafe may actually be safe, but no unsafe grid would be declared safe. The method does provide an indication of the nodes that did not pass the safety check, which allows one to focus on specific regions of the grid to perform more detailed analysis.. The rest of the paper is organized as follows. In the next section, a standard RC model of the power grid is adopted and the system equations explained, followed by a brief section 3 that describes a time discretization of the system equations. Current constraints are introduced in section 4 and our first solution approach is then given in section 5, whereby the worst-case voltage drop at every node is sought. Section 6 describes our second solution approach, which efficiently provides a safety check of the grid, and is followed by our conclusion. Checking the safety of the power grid is an essential part of chip verification. To do this by circuit simulation requires gathering complete information about the circuit and doing expensive simulation. Instead, we propose a verification approach based on a set of current constraints (upper bounds on the current sources attached to the grid). We first gave a conservative algorithm to get an upper bound on the maximum voltage drop at every node of the grid, we then offered two simple safety check algorithms.

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


Path computation in multi-layer multi-domain networks: A language theoretic approach Multi-layer networks are networks in which several protocols may coexist at different layers. The Pseudo-Wire architecture provides encapsulation and decapsulation functions of protocols over Packet-Switched Networks. In a multidomain context, computing a path to support end-to-end services requires the consideration of encapsulation and decapsulation capabilities. It appears that graph models are not expressive enough to tackle this problem. In this paper, we propose a new model of heterogeneous networks using Automata Theory. A network is modeled as a Push-Down Automaton (PDA) which is able to capture the encapsulation and decapsulation capabilities, the PDA stack corresponding to the stack of encapsulated protocols. We provide polynomial algorithms that compute the shortest path either in hops or in the number of encapsulations and decapsulations along the inter-domain path, the latter reducing manual configurations and possible loops in the path. Most carrier-grade networks comprise multiple layers of technologies (e.g. Ethernet, IP, etc.). These layers are administrated by different control and/or management plane instances. The Pseudo-Wire (PWE3) architecture [2] unifies control plane functions in heterogeneous networks to allow multi-layer services (e.g. Layer 2 VPN). To this end, it defines encapsulation (a protocol is encapsulated into another) and decapsulation (a protocol is unwrapped from another) functions, called adaptation functions further in this paper. These functions in a PDA respectively, the PDA stack allowing to memorize the nested protocols. If the goal is to minimize the number of adaptation functions, the PDA is transformed in order to bypass sub-paths without adaptation functions. The PDA or transformed PDA is then converted into a Context-Free Grammar (CFG) using a method of [13] . A shortest word, either corresponding to the shortest path in nodes or in adaptation functions, is generated from this CFG.. This paper extends the work published in [15] , providing the detailed proofs of the correctness of the algorithms and including new algorithms (transforming the PDA, converting the PDA to a CFG, generating the shortest word). Furthermore, the complexity analyses are refined and the total worst case complexity of the path computation is significantly reduced.. This paper is organized as follows: Section 2 recalls the context of multilayer multi-domain networks and the related work on path computation in such networks and presents the proposed approach; Section 3 provides a model of multi-layer multi-domain networks and a formal definition of the problem; Section 4 explains how a network is converted into a PDA and provides the complexity of this transformation; finally, Section 5 gives the different methods that compute the shortest path in nodes or in encapsulations/decapsulation.. In order to ease the paper reading, a table summarizing the used notations is provided in Appendix A. The problem of path computation in a multi-layer network has been studied in the field of intra-domain path computation but is less addressed in the interdomain field with consideration of the Pseudo-Wire architecture. There was no polynomial solution to this problem and the models used were not expressive enough to capture the encapsulation/decapsulation capabilities described in the Pseudo-Wire architecture.. In this paper, we provide algorithms that compute the shortest path in a multi-layer multi-domain network, minimizing the number of hops or the number of encapsulations and decapsulations. The presented algorithms involve Automata and Language Theory methods. A Push-Down Automaton models the multi-layer multi-domain network. It is then transformed in order to bypass passive transitions and converted into a Context-Free Grammar. The grammar generates the shortest protocol sequence, which allows to compute the path matching this sequence.. The different algorithms of our methodology have polynomial upper-bound complexity as summarized by Table 1 . Compared to the preliminary version of this work, the proofs of correctness of the algorithms are detailed and the complexity analysis is significantly refined (the highest algorithm complexity is in O(|A| 8 × |V| 7 ) instead of O(|A| 11 × |V| 7 × |E| 2 )). In order to figure out the whole problem of end-to-end service delivery, we plan to extend our solution to support end-to-end Quality of Service constraints and model all technology constraints on the different layers (conversion or "mapping" of protocols). As a future work, we also plan to investigate which part of our algorithms can be distributed (e.g., Can the domains publish their encapsulation/decapsulation capabilities without disclosing their internal topology?) and how such a solution can be established on today's architectures.

O O O O O O O O O O B I 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 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 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 O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 discriminative framework for clustering via similarity functions Problems of clustering data from pairwise similarity information are ubiquitous in Computer Science. Theoretical treatments typically view the similarity information as ground-truth and then design algorithms to (approximately) optimize various graph-based objective functions. However, in most applications, this similarity information is merely based on some heuristic; the ground truth is really the unknown correct clustering of the data points and the real goal is to achieve low error on the data. In this work, we develop a theoretical approach to clustering from this perspective. In particular, motivated by recent work in learning theory that asks "what natural properties of a similarity (or kernel) function are sufficient to be able to learn well?" we ask "what natural properties of a similarity function are sufficient to be able to cluster well?"To study this question we develop a theoretical framework that can be viewed as an analog of the PAC learning model for clustering, where the object of study, rather than being a concept class, is a class of (concept, similarity function) pairs, or equivalently, a property the similarity function should satisfy with respect to the ground truth clustering. We then analyze both algorithmic and information theoretic issues in our model. While quite strong properties are needed if the goal is to produce a single approximatelycorrect clustering, we find that a number of reasonable properties are sufficient under two natural relaxations: (a) list clustering: analogous to the notion of list-decoding, the algorithm can produce a small list of clusterings (which a user can select from) and (b) hierarchical clustering: the algorithm's goal is to produce a hierarchy such that desired clustering is some pruning of this tree (which a user could navigate). We develop a notion of the clustering complexity of a given property (analogous to notions of capacity in learning theory), that characterizes its information-theoretic usefulness for clustering. We analyze this quantity for several natural game-theoretic and learning-theoretic properties, as well as design * Supported in part by the National Science Foundation under grant CCF-0514922, and by a Google Research Grant.† Supported in part by the National Science Foundation under grant CCF-0721503, and by a Raytheon fellowship.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. Clustering is an important problem in the analysis and exploration of data. It has a wide range of applications in data mining, computer vision and graphics, and gene analysis. It has many variants and formulations and it has been extensively studied in many different communities.. In the Algorithms literature, clustering is typically studied by posing some objective function, such as k-median, min-sum or k-means, and then developing algorithms for approximately optimizing this objective given a data set represented as a weighted graph [12, 24, 22] . That is, the graph is viewed as "ground truth" and then the goal is to design algorithms to optimize various objectives over this graph. However, for most clustering problems such as clustering documents by topic or clustering web-search results by category, ground truth is really the unknown true topic or true category of each object. The construction of the weighted graph is just done using some heuristic: e.g., cosine-similarity for clustering documents or a Smith-Waterman score in computational biology. In all these settings, the goal is really to produce a clustering that gets the data correct. Alternatively, methods developed both in the algorithms and in the machine learning literature for learning mixtures of distributions [1, 5, 23, 36, 17, 15] explicitly have a notion of ground-truth clusters which they aim to recover. However, such methods are based on very strong assumptions: they require an embedding of the objects into R n such that the clusters can be viewed as distributions with very specific properties (e.g., Gaussian or log-concave). In many real-world situations (e.g., clustering web-search results by topic, where different users might have different notions of what a "topic" is) we can only expect a domain expert to provide a notion of similarity between objects that is related in some reasonable ways to the desired clustering goal, and not necessarily an embedding with such strong properties.. In this work, we develop a theoretical study of the clustering problem from this perspective. In particular, motivated by work on learning with kernel functions that asks "what natural properties of a given kernel (or similarity) function K are sufficient to allow one to learn well?" [6, 7, 31, 29, 21] we ask the question "what natural properties of a pairwise similarity function are sufficient to allow one to cluster well?" To study this question we develop a theoretical framework which can be thought of as a discriminative (PAC style) model for clustering, though the basic object of study, rather than a concept class, is a property of the similarity function K in relation to the target concept, or equivalently a set of (concept, similarity function) pairs.. The main difficulty that appears when phrasing the problem in this general way is that if one defines success as outputting a single clustering that closely approximates the correct clustering, then one needs to assume very strong conditions on the similarity function. For example, if the function provided by our expert is extremely good, say K(x, y) > 1/2 for all pairs x and y that should be in the same cluster, and K(x, y) < 1/2 for all pairs x and y that should be in different clusters, then we could just use it to recover the clusters in a trivial way. 1 However, if we just slightly weaken this condition to simply require that all points x are more similar to all points y from their own cluster than to any points y from any other clusters, then this is no longer sufficient to uniquely identify even a good approximation to the correct answer. For instance, in the example in Figure 1 , there are multiple clusterings consistent with this property. Even if one is told the correct clustering has 3 clusters, there is no way for an algorithm to tell which of the two (very different) possible solutions is correct. In fact, results of Kleinberg [25] can be viewed as effectively ruling out a broad class of scale-invariant properties such as this one as being sufficient for producing the correct answer.. In our work we overcome this problem by considering two relaxations of the clustering objective that are natural for many clustering applications. The first is as in list-decoding to allow the algorithm to produce a small list of clusterings such that at least one of them has low error. The second is instead to allow the clustering algorithm to produce a tree (a hierarchical clustering) such that the correct answer is approximately some pruning of this tree. For instance, the example in Figure 1 has a natural hierarchical decomposition of this form. Both relaxed objectives make sense for settings in which we imagine the output being fed to a user who will then decide what she likes best. For example, with the tree relaxation, we allow the clustering algorithm to effectively say: "I wasn't sure how specific you wanted to be, so if any of these clusters are too broad, just click and I will split it for you." We then show that with these relaxations, a number of interesting, natural learningtheoretic and game-theoretic properties can be defined that each are sufficient to allow an algorithm to cluster well.. At the high level, our framework has two goals. The first is to provide advice about what type of algorithms to use given certain beliefs about the relation of the similarity function to the clustering task. That is, if a domain expert handed us a similarity function that they believed satisfied a certain natural property with respect to the true clustering, what algorithm would be most appropriate to use? The second goal is providing advice to the designer of a similarity function for a given clustering task (such as clustering web-pages by topic). That is, if a domain expert is trying up to come up with a similarity measure, what properties should they aim for? 1 Correlation Clustering can be viewed as a relaxation that allows some pairs to fail to satisfy this condition, and the algorithms of [10, 13, 33, 2] show this is sufficient to cluster well if the number of pairs that fail is small. Planted partition models [4, 28, 16] allow for many failures so long as they occur at random. We will be interested in much more drastic relaxations, however.

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