ADMiRA: Atomic Decomposition for Minimum Rank Approximation In this paper, we address compressed sensing of a low-rank matrix posing the inverse problem as an approximation problem with a specified target rank of the solution. A simple search over the target rank then provides the minimum rank solution satisfying a prescribed data approximation bound. We propose an atomic decomposition providing an analogy between parsimonious representations of a sparse vector and a low-rank matrix and extending efficient greedy algorithms from the vector to the matrix case. In particular, we propose an efficient and guaranteed algorithm named atomic decomposition for minimum rank approximation (ADMiRA) that extends Needell and Tropp's compressive sampling matching pursuit (CoSaMP) algorithm from the sparse vector to the low-rank matrix case. The performance guarantee is given in terms of the rank-restricted isometry property (R-RIP) and bounds both the number of iterations and the error in the approximate solution for the general case of noisy measurements and approximately low-rank solution. With a sparse measurement operator as in the matrix completion problem, the computation in ADMiRA is linear in the number of measurements. Numerical experiments for the matrix completion problem show that, although the R-RIP is not satisfied in this case, ADMiRA is a competitive algorithm for matrix completion. R ECENT studies in compressed sensing have shown that a sparsity prior in the representation of the unknowns can guarantee unique and stable solutions to underdetermined linear systems. The idea has been generalized to the matrix case [1] with the rank replacing sparsity to define the parsimony of the representation of the unknowns. Compressed sensing of a low-rank matrix addresses the inverse problem of reconstructing an unknown low-rank matrix from its linear measurements 1 via a given linear operator . As in the vector case, the inverse problem is ill-posed in Manuscript received June 14, 2009 ; revised April 25, 2010. Date of current version August 18, 2010 . This work was supported in part by the National Science Foundation (NSF) under Grant CCF 06-35234. The material in this paper was presented in part at the IEEE International Symposium on Information Theory, Seoul, Korea, June 2009.. The authors are with the Coordinated Science Laboratory and the Department of Electrical and Computer Engineering, University of Illinois at Urbana-Champaign, Urbana, IL 61801-2307 USA (e-mail: klee81@illinois.edu; ybresler@illinois.edu).. Communicated by E. Serpedin, Associate Editor for Signal Processing. Color version of Figure 1 in this paper is available online at http://ieeexplore. ieee.org.. Digital Object Identifier 10.1109/ TIT.2010.2054251 the sense that the number of measurements is much smaller than the number of unknowns. Continuing the analogy with the vector case, the remarkable fact is that the number of measurements sufficient for unique and stable recovery is roughly on the same order as the number of degrees of freedom in the unknown low-rank matrix. Moreover, under certain conditions, the recovery can be accomplished by polynomial-time algorithms [2] . The problem of reconstructing a low-rank matrix from limited linear measurements arises in a wide range of applications. Low-order system identification can be formulated as a lowrank matrix recovery problem [3] , [4] . The order of a linear time invariant system determines the rank of the Hankel matrix formed from the system output and the linear measurement corresponds to the sampled response of the system obtained from a random (but known) input. Recently, the low-rank matrix recovery has been successfully applied to the reconstruction of dynamic MRI [5] , [6] . The sequence of vectorized image frames can be modeled as a low-rank matrix using a partially separable model [7] . The linear measurement in this case corresponds to the samples in the so-called -domain. Quantum state tomography is another application where the low-rank matrix model can be useful [8] . A particular form of the problem, known as the matrix completion problem, involves the recovery of a low-rank matrix when only a subset of its entries is known. Collaborative filtering, which is also better known as the Netflix problem [9] , aims to complete the rating matrix in order to provide a user-adaptive recommendation system. Since only a limited number of entries of the matrix are available, the completion of the matrix is a challenging problem. By modeling the matrix as a low rank, which is justified since the preference of a user for a particular item is determined by few factors, successful completion becomes possible. Global positioning from local distances is another application of matrix completion [10] . The entries of the matrix denote the intersensor distances in the sensor network. The rank is restricted to the dimension of the configuration, i.e., for the two dimensional case, the rank is at most .. One method to solve the inverse problem by exploiting the prior that is low rank is to solve the rank minimization problem , to minimize the rank within the affine space defined by and P1:. subject to. In practice, in the presence of measurement noise or modeling error, a more appropriate measurement model is 0018-9448/$26.00 © 2010 IEEE where the perturbation has bounded Euclidean norm . In this case, the rank minimization problem is written as P1 : subject to with an ellipsoidal constraint. In fact, rank minimization has been studied in the more general setting where the feasible set is not necessarily restricted to either an affine space or an ellipsoid. However, due to the nonconvexity of the rank function, rank minimization is NP-hard even when the feasible set is convex. Fazel et al. [3] proposed a convex relaxation of the rank minimization problem by introducing a convex surrogate of , which is known as nuclear norm and denotes the sum of all singular values of matrix .. Recht et al. [2] studied rank minimization in the framework of compressed sensing and showed that rank minimization for the matrix case is analogous to -norm (number of nonzero elements) minimization for the vector case. They provided an analogy between the two problems and their respective solutions by convex relaxation. In the analogy, -norm minimization for the -norm minimization problem is analogous to nuclear norm minimization for rank minimization. Both are efficient algorithms, with guaranteed performance under certain conditions, to solve NP-hard problems: -norm minimization and rank minimization, respectively. The respective conditions are given by the sparsity-restricted isometry property [11] and the rank-restricted isometry property (R-RIP) [1] , [2] , respectively. However, whereas -norm minimization corresponds to a linear program (or a quadratically constrained linear program for the noisy case), nuclear norm minimization is formulated as a convex semidefinite program (SDP). Although there exist polynomial time algorithms to solve SDP, in practice they do not scale well to large SDP problem instances.. Several authors proposed methods for solving large scale SDP derived from rank minimization. These include interior point methods for SDP, projected subgradient methods, and low-rank parametrization [2] combined with a customized interior point method [4] . These methods can solve larger rank minimization problems, which the general purpose SDP solvers cannot. However, the dimension of the problem is still restricted and some of these methods do not guarantee convergence to the global minimum. Other approaches are more direct, avoiding the SDP formulation. Cai et al. [12] proposed singular value thresholding (SVT), which penalizes the objective of nuclear norm minimization by the squared Frobenius norm weighted by a parameter . They solved the Lagrangian dual of the penalized problem by a projected subgadient method. For this particular problem, each iteration of the projected subgradient method can be computed efficiently by the truncated singular value decomposition (SVD). The sequence of solutions to the parameterized problems converges to the solution of the nuclear norm minimization problem as the penalty parameter goes to infinity. However, an analysis of the convergence rate is missing, and hence the quality of the solution by SVT with a particular is not guaranteed. Furthermore, the efficiency of SVT is restricted to the noiseless case where the constraint is affine (i.e., linear equality). Ma et al. [13] proposed a formulation of nuclear norm minimization using the Bregman divergence and solved the problem by an efficient fixed point algorithm based on the SVD. However, they did not provide a convergence rate analysis and like SVT the efficiency of this algorithm too is restricted to the noiseless, affine constraint case. Finally, Meka et al. [14] used multiplicative updates and online convex programming to provide an approximate solution to rank minimization. However, their result depends on the (unverified) existence of an oracle that provides the solution to the rank minimization problem with a single linear constraint in constant time.. An alternative formulation of the inverse problem of compressed sensing of a matrix is minimum rank approximation P2: subject to where denotes the minimum rank. The advantage of formulation P2 is that it can handle both the noiseless case and the noisy case in a single form. It also works for the more general case where is not exactly low rank but admits an accurate approximation by a low-rank matrix. When the minimum rank is unknown, an incremental search over will increase the complexity of the solution by at most factor . If an upper bound on is available, then a bisection search over can be used because the minimum of P2 is monotone decreasing in . Hence, the factor reduces to . Indeed, this is not an issue in many applications where the rank is assumed to be a small constant.. Recently, several algorithms have been proposed to solve P2. Haldar and Hernando [15] proposed an alternating least squares approach by exploiting the explicit factorization of a rank-matrix. Their algorithm is computationally efficient but does not provide any performance guarantee. Keshavan et al. [16] proposed an algorithm based on optimization over a Grassmann manifold. Their algorithm first finds a good starting point by an operation called trimming, and subsequently minimizes the objective of P2 using a line search and gradient descent over a Grassmann manifold. They provide a performance guarantee only for the matrix completion problem where the linear operator takes a few entries from . Moreover, the performance guarantee is restricted to the noiseless case.. For a fresh look at the problem, recall that minimum rank approximation, or rank-approximation for the matrix case, is analogous to -term approximation for the vector case. Like rankmatrix approximation, -term vector approximation is a way to find the sparsest solution of an ill-posed inverse problem in compressed sensing. For -term approximation, besides efficient greedy heuristics such as matching pursuit (MP) [17] and orthogonal matching pursuit (OMP) [18] , there are recent algorithms, which are more efficient than convex relaxation and also have performance guarantees. These include compressive sampling matching pursuit (CoSaMP) [19] and subspace pursuit (SP) [20] . To date, no such algorithms have been available for the matrix case.. In this paper, we propose an iterative algorithm for the rank minimization problem, which is a generalization 2 of the CoSaMP algorithm to the matrix case. We call this algorithm atomic decomposition for minimum rank approximation (AD-MiRA). ADMiRA is computationally efficient in the sense that the core computation consists of least squares and truncated SVDs, which are both basic linear algebra problems and admit efficient algorithms. Importantly, ADMiRA is the first algorithm that provides a performance guarantee for the minimum rank approximation problem. 3 Furthermore, ADMiRA provides a strong performance guarantee for P2 that covers the general case where is only approximately low rank and contains noise. The strong performance guarantee of ADMiRA is comparable to that of nuclear norm minimization in [1] . In the noiseless case, SVT [12] may be considered a competitor to ADMiRA. However, for the noisy case, SVT involves more than the simple singular value thresholding operation.. Matrix completion is a special case of low-rank matrix approximation from linear measurements where the linear operator takes a few random entries of the unknown matrix. It has received considerable attention owing to its important applications such as collaborative filtering. However, the linear operator in matrix completion does not satisfy the R-RIP [23] . Therefore, at the present time, ADMiRA does not have a guarantee for matrix completion. Nonetheless, empirical performance on matrix completion is better than SVT (for the experiments in this paper).. The remainder of this paper is organized as follows. The atomic decomposition and the analogy between the greedy algorithm for the vector case and the matrix case are introduced in Section II. The new algorithm ADMiRA and its performance guarantee are explained in Sections III and IV, respectively. Using the tools in Section V, the performance guarantees are derived in Sections VI and VII. Implementation issues and the computational complexity are discussed in Section VIII and numerical results in Section IX, followed by conclusions. Our exposition of ADMiRA follows the line of Needell and Tropp's exposition of CoSaMP [19] , to highlight, on the one hand, the close analogy, and on the other hand the differences between the two algorithms and their analysis. Indeed, there exist significant differences between the rank-approximation for the matrix case and the -term approximation for the vector case, which are discussed in some detail. We proposed a new algorithm, ADMiRA, which extends both the efficiency and the performance guarantee of the CoSaMP algorithm for -norm minimization to matrix rank minimization. By using the proposed generalized correlation maximization, greedy algorithms such as MP, OMP, and SP and their performance guarantees are also extended from the -term vector approximation problem to the rank-matrix approximation problem. ADMiRA can handle large scale rank minimization problems efficiently by using recent linear time algorithms for low-rank approximation of a known matrix.. Our numerical experiments demonstrate that ADMiRA is an effective algorithm even when the R-RIP is not satisfied, as in the matrix completion problem. While the performance guarantee in this paper relies on the R-RIP, it seems that a performance guarantee for ADMiRA without using the R-RIP might be possible. can be represented as (18) where and are defined by and respectively. As increases, the feasible sets of both problems increase and hence and are nondecreasing and nonincreasing, respectively. Therefore, (18) implies that is nondecreasing in . 2) Proof of Proposition 5.4: Let and let be an orthonormal basis of . 7 Then, is an isometry that satisfies . Since and for all , by the R-RIP (19) This implies that the operator norm of is bounded from above by . Since the adjoint operator has the same operator norm (20) Then, (9) follows from (20) . By the subadditivity of the rank, . By the orthogonality of and , . Therefore. In particular, the inequality holds for where . By the parallelogram identity Therefore 6) Proof of Corollary 5.9: For an arbitrary matrix and for all . Therefore, Proposition 5.7 implies. Since was arbitrary, we can take . Then

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


Weblog Campaigning in the German Bundestag Election 2005 Election campaigns are catalysts for new forms of political communication. They are a field of experimentation for new techniques and technologies to reach target groups and influence voters. This article explores how weblogs were used in the 2005 Bundestag election campaign in Germany, examining their effect on the mediatized political field. It is based on an empirical analysis of 317 campaign weblogs. Building on mediatization theory and research on campaign weblogs in other countries, weblog usage is examined along the dimensions of activity, interactivity, and connectedness. The results of the study indicate that weblog communication largely follows the dominant logic of mass media. But weblogs also offer forms of communication that allow political actors to bypass established media practices. Although the results are limited by the fact that the political blogosphere in Germany is still under construction, they reveal the potential of weblogs to enrich campaigns.Weblogs; campaign; political communication; election; Germany; network analysis E lection campaigns are an extreme form of political communication. During these periods, the mass media and the electorate devote more attention to the statements of politicians and their parties than at any other time. The stakes are high, indeed; elections are at the core of the political process: the allocation of political power. Because of their importance, campaigns can act as catalysts for new forms of political communication.This article examines how campaign communication is being changed by a new technological medium: weblogs. By offering easy-to-use content-management software and an attractive presentation, weblogs have revolutionized the way information is distributed on the Internet. In contrast to traditional mass media, weblogs support the interaction of authors-bloggers-with their readers by offering services to comment on articles (socalled "blog posts"). Furthermore, they support the interaction with other bloggers by facilitating hyperlinking to other blogs and blog posts. The totality of weblogs, the "blogosphere," today forms a new communicative space on the Internet.Although research in political communication has shown that changes in communication technology strongly influence campaigns (Mancini & Swanson, 1996; Schulz, Zeh, & Quiring, 2005) , little is known about the effects of weblogs yet. On one hand, authors view weblogs as an alternative channel for the distribution of information as well as a mobilization tool due to their ability to spread news very quickly (Ito, 2004; Kahn & Kellner, 2004) .The authors would like to thank Björn Greve, Jan Hildebrandt, Judith Muster, Marco Schmitt, and Dr. Klaus Stein for their assistance in conducting the empirical research.Bloggers are seen as a "fifth power" that increasingly occupies the control function of the mass media (Gillmor, 2004; Himmelsbach, 2005) , contrasting established news values with a more personal, direct, and often location-specific style of reporting. Blogs can be a tool for opinion formation, as they are said to influence agenda setting and framing processes (Drezner & Farrell, 2004) .On the other hand, hyperlinking on weblogs might foster political fragmentation by connecting only like-minded bloggers, who, as a consequence, avoid dealing with diverging views (Howard, 2005) . Blogs are said to destroy the reflective quality of public political communication by letting anybody share their more or less concise thoughts. Blogs are also expected to worsen the inequality of voices in the public sphere by supporting a star culture with few prominent authors (so-called "A-listers") and a large number of unknown bloggers (Shirky, 2003) .This article tries to further the state of research by empirically analyzing political communication with weblogs in the campaign for the German Bundestag election in 2005. Starting from mediatization theory (section two), it explores how the logic of the mediatized political field collides with the logic of the weblogging culture in the campaign blogosphere. In section three, we introduce our research methodology and provide information about the study case. Section four discusses the empirical results and section five presents the conclusions. According to a survey of German weblog users (Schmidt & Wilbers, 2006) , weblogs are expected to be updated daily or at least several times a week. Weblog readers expect to be able to comment, though in practice, few posts are commented on. About half of the bloggers consider blogrolls typical elements of a weblog, and a slight majority has a blogroll. This combination of blogging routines and users' expectations shapes a certain practice that establishes a new format of public expression. This format, in turn, follows its own logic: It rewards active involvement in web publishing, orientation toward dialogue, and efforts to establish lasting social relations. Our hypothesis is that this blogging logic overrides the dominant logic of media democracies in shaping campaign communication. Our case study shows that weblogs played an important role in the Bundestag campaign as far as we consider their active usage. All major parties and many candidates used this new mode of communication, though only a few attracted much attention. Campaign weblogs were found to have a limited reach, at least with regard to the number of comments they provoke. Thus, our study confirms the results of previous studies on campaign weblogging that weblogs fill a niche in campaign communication.. Furthermore, we wanted to find out whether this niche position corresponds to a specific form of communication, a specific "weblog logic" contrasting with the "media logic" This is in contrast to the media logic of gatekeepers limiting the scope of actors that appear on the public stage. On the other hand, weblogs were mainly used as a campaign instrument with a short-term perspective, which is in line with the time horizon of mediatized politics. Along the dimension of interactivity, the results clearly indicate that the campaign blogosphere has adopted the media logic. Weblogs of prominent actors or weblogs hosted by well-known online portals receive the largest share of attention independent of their authors' activity. We confirmed this result with two different measures of attention, the number of comments per post and the indegree centrality score. Only a few weblogs with other characteristics were able to receive much attention from readers, indicating that sincerity and long duration of blogging can lead to higher levels of interaction with readers.. Finally, along the dimension of connectedness, the hyperlink structure of the campaign blogosphere resembled very much the ideological structure of the political field in general. This result supports the view of weblogs as a mirror of the offline world. It rejects both the skeptical thesis implying weblogs worsen political fragmentation and the optimistic thesis implying weblogs foster dialogue across ideological divides.. In our interpretation, these results are an indicator that the logic of mediatized politics is strongly affecting weblog communication in the campaign. But under certain circumstances, the distinctive logic of weblogs interferes with this dominant logic, allowing actors from the periphery of the political field to gain a more prominent position. Based on our explorative study, we suggest that the decisive condition for this to happen is that the blogger conforms with the cultural norms of blogging. This includes to post regularly and with a long-term perspective to build social relationships, to engage in discussions with the readers who comment, and to connect to other bloggers by hyperlinking. Further studies are required to confirm this tentative conclusion.. As an advice to political actors with small reputations, we recommend that they try to play against the rules of the mediatized political field. These actors will profit from using weblogs if they adopt established blogging practices and persistently engage in communication with readers and fellow bloggers. At least, such a strategy was evident in the few cases in our study when weblog logic prevailed over media logic and allowed actors to bypass gatekeepers in media and party organizations.. Assuming that campaigns act like a prism in making visible the special features of political communication (Holtz-Bacha 2004, p. 468) , our findings are relevant not only for campaigns, but also for the political process more generally. However, the novelty of blogging as a mode of communication limits the generalizability of the results. The field of campaign weblogs was still under construction in Germany at the time of the Bundestag campaign 2005. Observations of the campaigns in the United Kingdom, New Zealand, and Denmark, where weblog diffusion was at a comparable stage, support our findings; with more time and widespread adoption, the practices might come to resemble the pattern found in the United States, where the dominance of media logic was more evident.. To estimate the influence of weblogs for political communication, one has to consider the whole public sphere and not just the political actors. Weblog use will increase the personalization of campaigns and speed up political communication. Politicians who report about their daily life and interact with their readers work against the impression of a disconnected political 518 Social Science Computer Review caste (Coenen 2005) . Bloggers scrutinizing media reports and campaign information and engaging in political discussions across the blogosphere offer an alternative to highly professionalized campaigns. The impact of weblogs on campaigns, and on political communication more generally, will depend on actual usage once campaign blogging reaches maturity. More comparative and follow-up studies are necessary to make assertions about these future developments.

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


On the Monadic Second-Order Transduction Hierarchy Abstract. We compare classes of finite relational structures via monadic second-order transductions. More precisely, we study the preorder where we set C ⊑ K if, and only if, there exists a transduction τ such that C ⊆ τ (K). If we only consider classes of incidence structures we can completely describe the resulting hierarchy. It is linear of order type ω+3. Each level can be characterised in terms of a suitable variant of tree-width. Canonical representatives of the various levels are: the class of all trees of height n, for each n ∈ N, of all paths, of all trees, and of all grids. Monadic second-order logic (MSO) is one of the most expressive logics for which the theories of many interesting classes of structures are still decidable. In particular, the infinite binary tree and many linear orders have a decidable MSO-theory [Rab69, She75] and the same holds for many classes of (finite or infinite) structures with bounded tree-width [BCL07, RS86] . Furthermore, for every fixed MSO-sentence ϕ and every class C of finite structures with bounded tree-width, there is a linear-time algorithm that checks whether a given structure from C satisfies ϕ [Bod96, FG06] . Examples of monadic second-order expressible graph properties are k-colourability, various types of connectivity, and planarity (via Kuratowski's well-known characterisation by forbidden configurations).. A variant of monadic second-order logic called guarded second-order logic (GSO) allows quantification not only over sets of elements but also over sets of edges (i.e., tuples from the relations) [GHO02] . The above mentioned linear-time algorithms can be adapted to this logic. There are tight links between guarded second-order logic and tree-width: every class of (finite or infinite) relational structures with a decidable GSO-theory has bounded tree-width. This gives a sort of converse to the above mentioned decidability results [See91, Cou95] . The proof of this result uses a deep theorem of graph minor theory by Robertson and Seymour: a set of graphs has bounded tree-width if and only if it excludes some planar graph as a minor [RS86] .. To compare the MSO-theories or GSO-theories of two classes of structures we can use monadic second-order transductions, a certain kind of interpretations suitable both, for monadic second-order logic and, using a detour via incidence structures, also for guarded second-order logic [BCL07, Cou91, Cou95, Cou03] .. In the present article we classify classes of finite structures according to their 'combinatorial complexity'. (Note that we do not consider decidability issues.) We will consider two ways to measure the complexity of such classes. On the one hand, we can use their tree-width and its variants. On the other hand, we can compare them via transductions. As it turns out, these two approaches are equivalent and they give rise to the same hierarchy. This indicates the robustness of our definitions and their intrinsic interest. Other possible hierarchies, based on different logics, will be briefly mentioned in Section 9.. Let us give more details. An MSO-transduction is a transformation of relational structures specified by monadic second-order formulae. As graphs can be represented by relational structures, we can use MSO-transductions as transformations between graphs. An MSO-transduction is a generalisation of the following kind of operations (see Definition 3.4):. (i) the definition of a relational structure "inside" another one (in model theory this is called an interpretation);. (ii) the replacement of a structure A by the union of a fixed number of disjoint copies of A, augmented with appropriate relations between the copies; (iii) the expansion of a given structure A by a fixed number of unary predicates, called parameters. Usually, these predicates are arbitrary subsets of the domain, but we also may have a formula imposing restrictions on them.. Because of the possibility to use parameters, a transduction τ is a many-valued map in general. (We may also think of it as non-deterministic.) Each relational structure A has several images τ (A, P 1 , . . . , P n ) depending on the choice of the parameters P 1 , . . . , P n ⊆ A. If B = τ (A, P 1 , . . . , P n ) we can consider the tuple P 1 , . . . , P n as an encoding of B in A. The transduction τ is the corresponding decoding function.. Each transduction τ extends in a canonical way to a transformation between classes of structures. If C and K are classes of relational structures with C ⊆ τ (K), we can think of τ as a way of encoding the structures in C by elements of K. For instance, every finite graph can be encoded in a sufficiently large finite square grid (by a fixed transduction τ ). Every finite tree of height at most n (for fixed n) can be encoded in a sufficiently long finite path. But it is not the case that all finite trees can be encoded by paths (by a single transduction).. The purpose of this article is to classify classes of finite relational structures according to their encoding powers. We will compare classes C and K of structures by the following preorder:

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The sociological turn in information science This paper explores the history of 'the social' in information science. It traces the influence of social scientific thinking on the development of the field's intellectual base. The continuing appropriation of both theoretical and methodological insights from domains such as social studies of science, science and technology studies, and socio-technical systems is discussed. Robert Merton, as it happens, was one of the sociologists identified by Howard Rosenbaum and Inna Kouper in their preliminary analysis of major sociological influences on information science [80] . They conducted a content analysis of all chapters in volumes 36-40 of ARIST -whose founding editor, by the way, was a social/behavioral scientist: Carlos Cuadra held a PhD in clinical/experimental psychology from the University of California at Berkeley -to determine which sociologists, both classical and contemporary, and also which sociological theories, had been imported into information science within the recent past. Among the most frequently cited names were Pierre Bourdieu (social and cultural capital), Manuel Castells (networked society), Harold Garfinkel (ethnomethodology), Anthony Giddens (structuration), Bruno Latour (Actor-Network theory) and Robert Merton (Matthew effect). These names and others of that ilk are not only to be found in ARIST -and not only for the five years covered by Rosenbaum and Kouper's surveybut also appear regularly in the pages of JIS, JASIST and other core information science journals. In some cases, the theories, methods and terminology associated with these eminences, a few of which I have listed parenthetically above, have become standard elements of our field's scholarly apparatus and professional discourse.

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Server-side detection of malware infection We review the intertwined problems of malware and online fraud, and argue that the fact that service providers often are financially responsible for fraud causes a relative lack of incentives for clients to manage their own security well. This suggests the need for a server-side tool to determine the security posture of clients before letting them transact.We introduce an exceedingly lightweight audit mechanism to address this need -permitting for post-mortem infection analysis -and prove its security properties based on standard cryptographic hardness assumptions. We describe a deployment architecture that aligns the incentives of participants in order to facilitate quick adoption and widespread use of the technology. Our approach is flexible enough to protect even low-end computing devices like mobile handsets, which future malware will target heavily, but whose power and bandwidth limitations result in poor effectiveness for traditional anti-virus solutions.A contribution of independent potential value is the enabling of a centralized analysis of malware-related events, which promises to extend the power of detection in comparison to what today's decentralized paradigm allows. Currently, industry sources estimate that 0.25% of infected computers are directly involved in financial fraud [3] . But with malware penetrating 10-15% [15] of all computers connected to the Internet, converting these computers into tools for committing financial fraud (which can easily happen) would result in an instant fifty-fold increase of fraud. To put this in perspective, most businesses would fail or fold their Internet operations long before this happened. This situation urgently calls for a change in malware-combatting strategies, or the Internet will wither along with the economy that supports it.. As worrisome as this is, the problem is even more acute in the context of mobile malware. A problem first given attention in 2006 [20] , it has recently been identified [35, 18] as a likely game changer within two to three years, at which time it is expected that there will be a comparable number of smart phones and laptops/desktops computers in use. The expected escalation of the problem is both due to the explosive adoption rates of smartphones, and due to their inherent limitations -such as power, memory, and bandwidth. The latter makes current Anti-Virus (AV) tools unsuitable once the rate of new or mutated malware instances reaches a threshold beyond which it is not reasonable to push updates. (Currently, there are close to forty thousand new instances of Windows malware a day and updates to AV filter rules several times an hour. This volume is not easy for a smartphone to manage.) Finally, phones may be more desirable platforms to attack, given the rich data they hold, and the fact that they inherently are payment platforms [22] . Even with today's relatively contained problem, consumers are wary [17] .. Looking beyond the technical parameters of the problem, we see that this pending catastrophe owes much to poor alignment of incentives. Financial service providers commonly bear the full financial responsibility for fraud 1 , while most of the available malware countermeasures are designed for client-side use. To come to terms with malware-fueled fraud, financial service providers need access to information allowing them to better evaluate a client's security posture. This type of information is sometimes available to network nodes -ISPs and backbone nodes -whose identification of corruption can be made using traffic analysis (observing patterns of communication) and sometimes by analysis of packet contents. However, network nodes are often not able to attribute traffic to a given originating machine, given that the network nodes cannot distinguish between different machines behind one IP address. Accurate information about a client's security posture is available to the client itself, though. The dilemma is that it is not trivial to extract this information in a reliable manner, in view of the fact that a corrupted machine will do anything it can to cover up the corruption. We believe that we are close to a tipping point at which malware costs will upset the fragile balance of attack and defense within which Internet commerce remains sustainable today. Malware also threatens to erupt as a dominant threat on mobile handsets as these devices grow more open and sophisticated. We do not believe that the current anti-virus paradigm can control this alarming situation much longer: Mobile handsets are too limited to run AV software, and mutating malware is blunting the power of AV even on more powerful computing platforms.. In this paper, we have proposed a new paradigm that uses a server-or cloud-based post-mortem detection of client in-fection. Having argued that our proposal is both sound and practical, we hope to see other challenges to and improvements of traditional malware defenses. In our view, they are long overdue. There are four principal approaches to combating malwarebased fraud. The first, and currently most popular approach, is technical. This can be done as a server-side measure, typically as back-end anomaly detection (e.g., RSA FraudAction, 41st parameter and Mark Monitor). It can also be done as a client-side measure, as in the case of traditional anti-virus (AV) software. It is worth noting that -as simple as having an up-to-date AV filter may seemit is believed [29] that less than 50 percent of networked computers in the developed world do. Consumer education (see, e.g., [25, 32] ), which is a second principal approach, can help boost those numbers and suppress the rate of userapproved malware installations, but hardly eliminate the problem. Policy measures offer a third approach entailing the creation of legislative and regulatory frameworks that favor stronger computer security. Policies may range from regulation to encourage ISPs to block traffic from apparently infected machines [1] , to providing tax incentives for deployment of AV services, to legislation such as the CAN-SPAM Act in the U.S. A fourth principal approach is to step up law enforcement efforts to make online fraud less appealing to criminals by pursuing perpetrators. This includes efforts to infiltrate criminal networks and trace traffic to its sources. These four main approaches are symbiotic to a large extent, with technical measures playing a main and often enabling role.. It is starting to become commonly recognized that the traditional AV paradigm is poorly suited for mobile platforms, due to their resource constraints. The limitations in terms of battery power, memory resources and bandwidth make both signature-based technologies and behavioral technologies problematic for resource-constrained devices -at least when the detection software is run on the client machine. This is true even for any plausible or foreseeable advances in battery, memory and communications technology. One approach to address the problem could therefore be to run detection software on the network (see, e.g., [30] ), using information indicating the security posture of the client device. If done right, this approach may mitigate the problems arising from end-device limitations. It is non-trivial to perform remote audits, though, as infected client machines can misrepresent their security posture, fabricating transcript evidence of having no infection.. Our solution lets a server efficiently audit the security posture of a client machine. Port-scanning is a common example of this general approach. Port-scanning can be used to detect the use of communication protocols that are likely to indicate vulnerability; for example, sending a DNS query to port 53 will tell whether the probed machine has a DNS server. Network Access Control (NAC) is a technique that allows a network to control access by verifying that connecting nodes satisfy certain minimum requirements, such as having AV software, an approved update level, and an appropriate configuration. This type of audit allows the endpoints to quarantine a connecting node that does not meet the requirements. Both of these techniques are commercially useful, but offer no guarantees against infection. In fact, it is possible for malware to communicate via commonly used ports (or simply not communicate while being audited), and compliance with requirements is in no way an assurance of security. Similarly, while so-called browser-recon [23] can be used to inspect the browser history of a target machine for signs of corruption, it is trivial for a malware agent to erase incriminating portions of the browser history once a machine has been corrupted.. Stronger assurance is obtainable in principle by the use of trusted hardware. Trusted Platform Modules (TPMs) are widely deployed hardware devices that generate remotely consumable attestations to the software stack executed by a client [34] . They can support rigorous enforcement of NAC policies requiring clients to run approved software configurations. Despite hundreds of millions of shipped units, however, TPMs have seen little application [36] . Implementation complexity, key-management challenges, and concerns about aggressive application to digital-rights management have stymied their use, but so too have more fundamental elements of their design. TPM attestations support only a whitelisting approach, and do not gracefully handle the dynamically changing nature of software configurations resulting from patches, driver updates, and so forth. Additionally, TPMs attest to the presence of an ostensibly trustworthy software configuration, but in their standard and intended modes of use provide no assurance against runtime attacks on software vulnerabilities-e.g., exploits of OS bugs.. We propose a solution in which a server can audit a client machine, avoiding the shortcomings of the approaches just described. Our technique combines client-side logging with server-side auditing. This general architecture was first proposed by Bellare and Yee [7, 8] to record important system events, such as crashes, resource exhaustions, and failed login attempts. Bellare and Yee do not mention detection of malware corruption among their motivations, though, nor is their solution geared toward this type of attack. In its basic instantiation, their solution is vulnerable to what we may term a limited "roll-back" attack, in which a malware agent erases the latest log entry (or entries) immediately upon infecting a client machine. This is the entry that provides evidence of corruption. The attack works due to the fact that the log remains open until explicitly closed -whether at the end of a time epoch or at the request of a server -and the latest log entries can be manipulated during this time period.. Independently of Bellare and Yee, Schneier and Kelsey [31] also proposed an audit mechanism, which is similar in flavor, but has privacy-preserving enhancements. Their solution is similarly vulnerable to roll-back attacks due to the need for explicit log closing, and also lacks formal security analysis. The same shortcomings exist in the schemes proposed by Jin, Myles, and Lotspiech [26, 27] , who propose an audit structure aimed to improve software tamper resistance.. We describe two solutions -one based on symmetric-key cryptography alone, and one based on public-key cryptography, both of them provably secure against roll-back attacks. Both are exceedingly simple -the symmetric-key solution authenticates pending events using a simple construction based on message authentication codes, and the public-key version -a simple but crucial modification of Bellare and Yee's scheme -uses a forward-secure signature scheme to authenticate pending events.. Our approach might be viewed loosely as an enabler of server-side execution of AV software [30] . Centralized analysis of events is not only a matter of moving the computational burden of detection from clients to servers, but also enables new pattern-based detection approaches [21] . For example, Bluetooth malware exhibits a strong geographic component in terms of how it spreads, whereas installation of a system patch is likely to instead depend on the local time of the day, and the time the patch was released.. Our solution allows for detection of corruption of typical user computers and mobile phones. This is in contrast to the more specialized solution proposed by Choi, Golle and Jakobsson [9, 10] , in which deviation of the behavior of a client machine could be detected by a third-party auditor -but only if the audited client only performs publicly verifiable computation, such as the computation of a digital signature or the mixing of ciphertexts.. Durfee, Smetters and Balfanz's [13] recent work on posturebased data protection describes a mechanism by which a client machine can protect its contents using encryption using a key released by a third party -the trusted audit server -after this server has verified that the client machine passes a security audit. Their solution addresses a different problem than we do; it does not describe the audit process, but treats that as an issue orthogonal to the question of how to protect the data on the machine against attack.. Although it is not explicitly discussed in the context of previous audit proposals (as listed above), it is evident that secure audit requires timely erasure of keys. Erasure is known to be a complicated problem -see e.g., [12, 16, 19] . However, we note that since our adversary is a software agent, it cannot access data on the physical layer, as a human adversary might. Therefore, it suffices to simply overwrite the old contents of the cells that were used to store the old secret key, along with intermediate values that were generated as the new secret key was computed. Thus, while the erasure component of the problem must be carefully attended to in general audit contexts, it is straightforwardly addressed in the context of malware detection.

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


Principles of Scatter Search Scatter search is an evolutionary method that has been successfully applied to hard optimization problems. The fundamental concepts and principles of the method were first proposed in the 1970s, based on formulations dating back to the 1960s for combining decision rules and problem constraints. In contrast to other evolutionary methods like genetic algorithms, scatter search is founded on the premise that systematic designs and methods for creating new solutions afford significant benefits beyond those derived from recourse to randomization. It uses strategies for search diversification and intensification that have proved effective in a variety of optimization problems.This paper provides the main principles and ideas of scatter search and its generalized form path relinking. We first describe a basic design to give the reader the tools to create relatively simple implementations. More advanced designs derive from the fact that scatter search and path relinking are also intimately related to the tabu search (TS) metaheuristic, and gain additional advantage by making use of TS adaptive memory and associated memory-exploiting mechanisms capable of being tailored to particular contexts. These and other advanced processes described in the paper facilitate the creation of sophisticated implementations for hard problems that often arise in practical settings. Due to their flexibility and proven effectiveness, scatter search and path relinking can be successfully adapted to tackle optimization problems spanning a wide range of applications and a diverse collection of structures, as shown in the papers of this volume. Scatter search (SS) was first introduced in Glover (1977) as a heuristic for integer programming. In the original proposal, solutions are purposely (i.e., non-randomly) generated to take account of characteristics in various parts of the solution space. Scatter search orients its explorations systematically relative to a set of reference points that typically consist of good solutions obtained by prior problem solving efforts, where the criteria for "good" are not restricted to objective function values, and may apply to subcollections of solutions rather than to a single solution, as in the case of solutions that differ from each other according to certain specifications.. Weighted linear combinations provide the main mechanism to generate new trial points within the space containing the reference points, accompanied by a generalized (successively iterated) rounding mechanism to assure these trial points satisfy integer feasibility conditions in the case where some variables are required to receive integer values. These mechanisms are oriented toward the goal of creating weighted centers of selected sub-regions, including regions external to the convex hull of the reference points.. The scatter search template (Glover 1998 ) has served as the main reference for most of the scatter search implementations to date. The dispersion patterns created by these designs have been found useful in several application areas. Section 2 gives a comprehensive description of the elements and methods of this template based on the formulation given in Laguna and Martí (2003) . Following this, section 3 examines different advanced scatter search designs, including some recent features as the 3-Tier reference set update and associated uses of memory. Section 4 is devoted to the path relinking methodology that extends scatter search to the setting of neighborhood spaces, including both basic and advanced implementations, and the paper ends with concluding observations. The focus and emphasis of scatter search and path relinking have a number of implications for the goal of designing improved optimization procedures. These research opportunities carry with them an emphasis on producing systematic and strategically designed rules, rather than following the policy of relegating decisions to random choices, as often is fashionable in evolutionary methods. The strategic orientation underlying scatter search and path relinking is motivated by connections with the tabu search setting where the path relinking ideas were first proposed, and invites the use of adaptive memory structures in determining the strategies produced.

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


A general two-pass method integrating specular and diffuse reflection We analyse some recent approaches to the global illumination problem by introducing the corresponding reflection operators, and we demonstrate the advantages of a two-pass method. A generalization of the system introduced by Wallace et al. at Siggraph '87 to integrate diffuse as well as specular effects is presented. It is based on the calculation of extended form-factors, which allows arbitrary geometries to be used in the scene description, as well as refraction effects. We also present a new sampling method for the calculation of form-factors, which is an Mternative to the hemi-cube technique introduced by Cohen and Greenberg for radiosity calculations. This method is particularly well suited to the extended form-factors calculation. The problem of interactive display of the picture being created is also addressed by using hardware-assisted projections and image composition to recreate a complete specular view of the scene. The problem of light interreflection has been one of the main issues for realistic image synthesis during the last few years. It is now widely known that local lighting models are not sufficient to corn- Permission to copy without fee all or part of this material is granted provided that the copies are not made or distributed for direct commercial advantage, the ACM copyright notice and the title of the publication and its date appear, and notice is given that copying is by permission of the Association for Computing Machinery. To copy otherwise, or to republish, requires a fee and/or specific permission. The two-pass approach is certainJy a good compromise between image fidelity and CPU cost, as it uses the respective strength of ray tracing and radiosity to compute the different components of light. Although it involves the computation of extended form factors, which requires more CPU than the computation of diffuse form factors, this method has a number of advantages against Shao e~ al.'s method :. • It is independent of light distribution. If the extended form factors are stored in a file, a new picture can be generated with new lighting conditions, at the only expense of the radiosity solution and the second pass (see last section of this paper for a method to display the final images more quickly).. • There is no need to store the hemi-cubes for the specular patches.. • Specular patches do not have to be finely subdivided. A problem that appears when studying the reflection of light on a specular surface is that directions of interest vary rapidly on the surface (fig. 4) . Therefore, all specular patches should be finely subdivided in order for Shao et al.'s method to produce accurate results. On, the other hand, Wallace's "image method" (though restricted to plane mirrors) and our ray tracing technique, allow specular patches to be treated as a whole, without further substruct uring.. This lack of precision for specular reflection is precisely the reason that makes Shao et al. use a ray-traced second pass, and one can wonder if the precision of specular transfers is not as important during the first pass than during the second. Actually, it would make more sense to either use Shao's method as one pass, with finely subdivided specular patches (but then there will be a huge number of hemi-cubes to store), or a complete two-pass method like the one presented here.. However, Shao's method could prove very useful for simple environments, if a complex reflectance function is to be used. 4 An alternative to the hemi-cube sampling technique.. A new sampling method using adaptive subdivision is introduced for the calculation of form-factors, which is an alternative to the hemicube technique [3] . The use of an adaptive subdivision scheme proves especially useful when extended form-factors are to be computed, as it reduces the number of rays to be shot, but our statistics show that the approach is efficient even for the diffuse case, especially for high sampling resolutions. We shall first explain the method in the diffuse case, and then show hew it can be used for extended form factors.

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


Anomalous diffusion modeling by fractal and fractional derivatives This paper makes an attempt to develop a fractal derivative model of anomalous diffusion. We also derive the fundamental solution of the fractal derivative equation for anomalous diffusion, which characterizes a clear power law. This new model is compared with the corresponding fractional derivative model in terms of computational efficiency, diffusion velocity, and heavy tail property. The merits and distinctions of these two models of anomalous diffusion are then summarized. In recent years, the phenomena of anomalous diffusion have been observed in many fields, such as those of turbulence, seepage in porous media, pollution control [1] [2] [3] [4] [5] . Although the demand for appropriate mathematical models is high from biomechanics to geophysics to acoustics, the differential equation modelling of anomalous diffusion has long been a perplexing mathematical physics issue.. Nonlinear modelling is a popular approach to depicting a variety of complex anomalous diffusion phenomena. However, it is mathematically very difficult to analyze and computationally very expensive to simulate. In addition, the nonlinear models often require some parameters unavailable from experiment or field measurements. As alternative approaches, in recent decades the fractal and fractional derivatives have been found effective in modelling anomalous diffusion processes [2, 3] . The advantage of the fractal or the fractional derivative models over the standard integer-order derivative models is in that the former can describe very well the inherent abnormal-exponential or heavy tail decay processes.. From the viewpoint of statistical physics, the normal diffusion underlies the well-known Brownian motion of the particles. The probability density function (PDF) in space, evolving in time, which governs the Brownian motion, is of the Gaussian type whose variance is proportional to the first power of time. In contrast, a number of evolution equations have been proposed in recent decades for describing anomalous diffusion, in which the variance is no longer proportional to the first power of time. One of the most popular statistical models of anomalous diffusion is the continuous time random walk model (CTRW), which corresponds to the fractional diffusion equation underlying the Lévy diffusion process [6, 7] . It is worthwhile to note that the parameters of the fractional derivative models have clear physical significance and are easy to get from a data fitting of experimental or field measurements. In addition, the models of this type are also mathematically easy to analyze. However, like nonlinear equation models, these models are not computationally cheap and are also of a phenomenological description which does not necessarily reflect the physical mechanism behind the scenes. On the other hand, Chen [8] recently introduced a fractal derivative from the fractal concept and applied it to model a variety of power law scaling phenomena, such as turbulence, fractional quantum mechanics, and anomalous diffusion. It was found that the well-known stretched Gaussian distribution is the analytical solution of the fractal derivative anomalous diffusion equation [9, 10] .. However, to the best of our knowledge, in-depth analysis and comparisons of the fractal and the fractional derivative models of anomalous diffusion have not been reported in the literature. Through theoretical analysis and numerical experiments, this study makes an attempt to investigate the merits and demerits of these two modelling approaches. From a statistical viewpoint, the fractal diffusion equation underlies the stretched Gaussian process, while the fractional diffusion equation reflects the Lévy process. Although both models can characterize the power law phenomena of anomalous diffusion, this study has observed some notable differences in diffusion rate and heavy tail behaviours, etc. Since the fractal derivative is a local operator, unlike the global fractional derivative operator, the numerical solution of fractal derivative equations can be carried out by standard numerical techniques for the integer-order derivative equations and thus is far more mathematically simple and computationally efficient than that of fractional derivative equations.. It should be noted that both models can depict a variety of kinds of anomalous diffusion processes, but the particular application areas of the two modelling approaches are still unclear. There are also some unresolved issues in this study such as the complete mathematical foundation of the fractal derivative, the physical mechanism of the descriptive models, to mention but a few. Therefore, further study of these open problems is still under way.

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


The LOGIC negotiation model Successful negotiators prepare by determining their position along five dimensions: Legitimacy, Options, Goals, Independence, and Commitment, (LOGIC). We introduce a negotiation model based on these dimensions and on two primitive concepts: intimacy (degree of closeness) and balance (degree of fairness). The intimacy is a pair of matrices that evaluate both an agent's contribution to the relationship and its opponent's contribution each from an information view and from a utilitarian view across the five LOGIC dimensions. The balance is the difference between these matrices. A relationship strategy maintains a target intimacy for each relationship that an agent would like the relationship to move towards in future. The negotiation strategy maintains a set of Options that are in-line with the current intimacy level, and then tactics wrap the Options in argumentation with the aim of attaining a successful deal and manipulating the successive negotiation balances towards the target intimacy. In this paper we propose a new negotiation model to deal with long term relationships that are founded on successive negotiation encounters. The model is grounded on results from business and psychological studies [1, 16, 9] , and acknowledges that negotiation is an information exchange proPermission 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. cess as well as a utility exchange process [15, 14] . We believe that if agents are to succeed in real application domains they have to reconcile both views: informational and gametheoretical. Our aim is to model trading scenarios where agents represent their human principals, and thus we want their behaviour to be comprehensible by humans and to respect usual human negotiation procedures, whilst being consistent with, and somehow extending, game theoretical and information theoretical results. In this sense, agents are not just utility maximisers, but aim at building long lasting relationships with progressing levels of intimacy that determine what balance in information and resource sharing is acceptable to them. These two concepts, intimacy and balance are key in the model, and enable us to understand competitive and co-operative game theory as two particular theories of agent relationships (i.e. at different intimacy levels). These two theories are too specific and distinct to describe how a (business) relationship might grow because interactions have some aspects of these two extremes on a continuum in which, for example, agents reveal increasing amounts of private information as their intimacy grows. We don't follow the 'Co-Opetition' aproach [4] where co-operation and competition depend on the issue under negotiation, but instead we belief that the willingness to co-operate/compete affect all aspects in the negotiation process. Negotiation strategies can naturally be seen as procedures that select tactics used to attain a successful deal and to reach a target intimacy level. It is common in human settings to use tactics that compensate for unbalances in one dimension of a negotiation with unbalances in another dimension. In this sense, humans aim at a general sense of fairness in an interaction.. In Section 2 we outline the aspects of human negotiation modelling that we cover in this work. Then, in Section 3 we introduce the negotiation language. Section 4 explains in outline the architecture and the concepts of intimacy and balance, and how they influence the negotiation. Section 5 contains a description of the different metrics used in the agent model including intimacy. Finally, Section 6 outlines how strategies and tactics use the LOGIC framework, intimacy and balance. In this paper we have introduced a novel approach to negotiation that uses information and game-theoretical measures grounded on business and psychological studies. It introduces the concepts of intimacy and balance as key elements in understanding what is a negotiation strategy and tactic. Negotiation is understood as a dialogue that affect five basic dimensions: Legitimacy, Options, Goals, Independence, and Commitment. Each dialogical move produces a change in a 2×5 matrix that evaluates the dialogue along five information-based measures and five utility-based measures. The current Balance and intimacy levels and the desired, or target, levels are used by the tactics to determine what to say next. We are currently exploring the use of this model as an extension of a currently widespread eProcurement software commercialised by iSOCO, a spin-off company of the laboratory of one of the authors.

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


Automatic adaptation of proper noun dictionaries through cooperation of machine learning and probabilistic methods Abstract Current methods for Proper Noun (PN) recognition and classification perform well, hut are admittedly sensitive to domain and language shifts. Though it may be possible to produce (especially using the Web) an initial dictionary of domain-specific PNs, often to achieve an adequate coverage some non-trivial amount of manual work is necessary, for dictionary extension, rule writing and manual tagging of texts.. In this paper we presented an integrated classification method for the automatic extension of a PN dictionary. The method combined two learning approaches: sup~vised learning of decision-tree classifiers and unsupervised probabilistie learning of syntactic and semantic context. The supervised learning algorithm used the information in the initial PN dietionary and a training corpus to construct a decision tree that assigned semantic categories to PNs, which were not in the initial dictionary. Only high-confidence classifications were accepted, imposing a bias for high precision. Despite this fact, performance in terms of recall was also good. In a second phase, unsupervised learning was used to increase recall and assign a semantic category to those PNs that were still unclassifted. In this phase, we investigated the effectiveness of using syntactic contexts and semantic generalization for categorizing unknown PN in running text. Similar techniques have been applied (alone or in combination) to the more general task of word sense disambiguation, with no clear-cut results. In the case of PNs, however, certain favourable conditions (especially the applicability of the one-sense-per-domain hypothesis) favour the good performance of this technique. Remarkably, our combined method achieved both high recall (86.97%) and precision (89.66%), while imposing limited requirements on the coverage of the initial PN dictionary. These results are among the highest reported in the literature and were achieved on three PN categories that are considered hard to recognize: person, organization and location. But the main advantage of our method is the low initial requirement, that is a 50% coverage PN dictionary, while all MUC systems require more or less heavy manual work for rule writing or text tagging.. The results presented here suggest that the combined method that we presented is appropriate for PN recognition. However, we need to evaluate the method further and compare it directly to some of the existing high-performing systems, possibly on the data used for the MUC comparisons. Before doing that, though, we would like to improve on the simple method that we are currently using for the identification of PNs in text. This step is essential, in order to construct a complete NERC system. An alternative direction that we are examining is to apply the method to other problems, such as word sense disambiguation. If the good performance that we achieved on PN recognition carries over to these other problems, we might be able to propose it as a more general method for sense tagging.

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