An asymptotic-preserving method for highly anisotropic elliptic equations based on a Micro-Macro decomposition The concern of the present work is the introduction of a very efficient Asymptotic Preserving scheme for the resolution of highly anisotropic diffusion equations. The characteristic features of this scheme are the uniform convergence with respect to the anisotropy parameter 0 < ε << 1, the applicability (on cartesian grids) to cases of non-uniform and non-aligned anisotropy fields b and the simple extension to the case of a non-constant anisotropy intensity 1/ε. The mathematical approach and the numerical scheme are different from those presented in the previous work , arXiv:1008.3405v1] and its considerable advantages are pointed out. The numerical resolution of highly anisotropic physical problems is a challenging task. In particular, it is difficult to capture the behaviour of physical phenomena characterized by strong anisotropic features since a straight-forward discretization leads typically to very ill-conditioned problems. In the class of problems addressed in this paper the anisotropy is aligned with a vector field which may be variable in space/time. Such problems are encountered in many physical applications, for example flows in porous media [3, 10] , semiconductor modeling [14] , quasi-neutral plasma simulations [7] , the list of possible applications being not exhaustive. The motivation of this work is closely related to the magnetized plasma simulations such as atmospheric plasmas [12, 13] , internal fusion plasmas [4, 9] or plasma thrusters [1] . In this case the anisotropy direction is defined by a magnetic field confining the particles around the field lines, the anisotropy intensity 1/ε reaching orders of magnitude as high as 10 10 . The difficulty with these anisotropic problems is that they become singular in the limit ε → 0, where ε is a small parameter responsible for the strong anisotropy of the problem. A straightforward discretization of such problems (using, for example, finite difference methods) results in the inversion of a very badly conditioned linear system, which becomes unfeasible for ε << 1. In this paper we present a new approach based on the so called Asymptotic Preserving reformulation introduced initially in [11] . This work presents an important improvement to the method presented in the previous paper [6] and is aimed to treat in a precise manner a variety of strong anisotropies with low numerical costs.. The model problem we are interested in, reads. n · A∇u ε = 0 on ΓN ,. where Ω ⊂ R 2 or Ω ⊂ R 3 is a bounded domain with boundary ∂Ω = ΓD ∪ ΓN and outward normal n. The direction of the anisotropy is given by a vector field B, where we suppose divB = 0 and B = 0. The direction of B shall be denoted by the unit vector field b = B/|B|. The domain boundary is decomposed into ΓD := {x ∈ ∂Ω | b(x) · n = 0} and ΓN := ∂Ω\ΓD. The anisotropic diffusion matrix is then given by. The scalar field A > 0 and the symmetric positive definite matrix field A ⊥ are of order one while the parameter 0 < ε < 1 can be very small, provoking thus the high anisotropy of the problem. The system becomes ill posed if we consider the formal limit ε → 0. It is thus very ill conditioned for ε << 1. The goal of the present paper is to circumvent this difficulty and to propose a numerical scheme which is uniformly convergent with respect to the parameter ε. This model problem has been studied before in the Asymptotic Preserving context, see for example [8, 5, 6] . The key idea was to decompose the solution u ε into two parts: p ε , which is constant along the anisotropy direction and q ε , which contains the fluctuating part. The resulting modified linear system is bigger than the original problem but has the important feature of reducing, as ε → 0, to the so-called Limit model (L-model), which is a well-posed system satisfied by the limit solution u 0 = limε→0 u ε . In other words, this AP-procedure transforms a singularly perturbed problem in an equivalent regularly perturbed one.. In [8] , a special case of an anisotropy aligned with the z-axis was studied. The Asymptotic Preserving reformulation was obtained in the following way. Firstly, the original problem was integrated along the anisotropy direction, resulting in an ε-independent elliptic equation for the mean part p ε . Then, the mean equation was subtracted from the original problem giving rise to an elliptic equation for the fluctuating part q ε . A generalization of this approach was proposed in [5] , in the framework of curvilinear anisotropy fields b. The introduction of an adapted curvilinear coordinate system with one coordinate aligned with the anisotropy direction allowed to reduce the problem to the one studied in [8] and hence to address more realistic problems, as for example the ionospheric plasma simulations.. In [6] , the original method of [8] is generalized for arbitrary fields b in a different manner. Instead of performing a coordinate-system transformation and integrating along the anisotropy direction, the new technique uses a Cartesian grid in combination with an adapted mathematical framework. The mean part p ε is forced to be in the space of functions constant along the b field by means of a Lagrange multiplier technique. Similarly, the fluctuating part q ε is forced to be in the orthogonal space (with respect to the L 2 -norm). This approach requires the introduction of three Lagrange multipliers and results in a system with five unknowns. The advantage of this method lies in its generality. Since no change of the coordinate system is needed, no computation of the field lines, no integration along them as well as no mesh adaptation is required, this numerical method is easy to implement even for anisotropies varying in time. The method works well on Cartesian grids even for strongly varying b fields. We will refer to the method of [6] as the Duality-Based (DB) Asymptotic Preserving reformulation or simply as the DB-method, to emphasize the extensive use of Lagrange multipliers in its derivation.. In the present paper we introduce a novel approach. It is as general as the DB-method, i.e. no change of coordinate system nor mesh adaptation is required. It is however much more efficient in terms of computational cost. The new idea arises from the following questions: does p ε need to be the average of u ε along the anisotropy direction? Does q ε need to be orthogonal to p ε , with respect to the L 2 -norm? Is u ε = p ε + q ε an optimal decomposition? In this paper we exploit a different decomposition: u ε = p ε + εq ε , with q ε not being orthogonal to p ε . Instead, q ε belongs to the space of functions vanishing on the "inflow" part of the boundary, i.e. where b · n < 0. This space is easy to discretize without introducing any additional Lagrange multiplier. As a result, p ε is no longer an average of u ε , however we still choose it to be constant along the anisotropy direction. The AP reformulation of the original equation is then obtained in terms of u ε and q ε . We use first the fact that the only component of u ε that varies along the anisotropy direction is εq ε , and thus replace ∇ || u ε by ε∇ || q ε in the term of order 1/ε. We obtain thus an equation whose coefficients are all of order one. We should add also a second equation assuring than p ε = u ε − εq ε is indeed constant along the field lines. The resulting system consists of only two equations compared to the five equations of the DB-method. It should be noted that, while keeping the advantages of the DB-method (no need of mesh-or coordinate-system-adaptation with respect to the anisotropy direction, uniform convergence with respect to ε), the new method is far more efficient in terms of memory requirements as well as computational time. The new method will be referred to as the Micro-Macro (MM) Asymptotic Preserving reformulation or simply as the MM-method, to emphasize the fact that the fluctuating part q ε of the solution is now rescaled by ε. We will prove, in particular, that q ε does not explode as ε → 0, so that the ansatz u ε = p ε + εq ε does indeed introduce a proper rescaling for the "micro"-fluctuations over the "macro" part of the solution contained in p ε . The paper is organized as follows. Section 2 introduces the Singularly Perturbed elliptic problem (P-model) and the new Asymptotic Preserving reformulation (MM-method). We also perform a mathematical study of this reformulation, in particular, of the convergence towards the Limit model, as ε → 0. In Section 3 we present the discretization and the numerical results of various test cases for constant and variable anisotropy fields b. We compare the efficiency of the new MM-method with the previously proposed DB-method. Finally, in Section 4 we propose a generalization of the MM-method to the case of a non-constant anisotropy parameter ε. The detailed numerical analysis of the MM-method is postponed to a forthcoming work. The construction of the here introduced Micro-Macro based Asymptotic-Preserving scheme for the resolution of an anisotropic diffusion equation was based on a different reformulation of the initial Singular Perturbation problem as compared to the earlier work [6] . The advantages of the new MM-verison were shown numerically, in particular the considerable gain in simulation time and the simplicity to treat variable ε-intensities within the domain. The rigorous numerical analysis of both AP-reformulations will be the aim of a futur work, in particular the AP-property shall be shown, i.e. the uniform convergence of the scheme with respect to ε.

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


Predicting the volume of comments on online news stories On-line news agents provide commenting facilities for readers to express their views with regard to news stories. The number of user supplied comments on a news article may be indicative of its importance or impact. We report on exploratory work that predicts the comment volume of news articles prior to publication using five feature sets. We address the prediction task as a two stage classification task: a binary classification identifies articles with the potential to receive comments, and a second binary classification receives the output from the first step to label articles "low" or "high" comment volume. The results show solid performance for the former task, while performance degrades for the latter. As we increasingly live our life online, in the form of blogs, discussion forums, comment facilities, etc., new types of data become available that can be mined for valuable knowledge. E.g., online chatter can be used to predict sales ranks of books [4] . Online news is an especially interesting data type for mining and analysis purposes. Much of what goes on in social media is a response to news events, as is evidenced by the large amount of news-related queries users submit to blog search engines [9] . Tracking news events and their impact as reflected in social media has become an important activity of media analysts [1] . We focus on online news articles plus the comments they generate, and attempt to predict news article comment volume prior to publication time.. One might raise the question why one should be interested in commenting behavior and the factors contributing to it. We enPermission 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. visage three types of application for predicting the volume of comments generated by news articles. First, media and reputation analysis is dependent on what users think of topics covered in the media. Predicting the comment volume might help in determining the desirability of an article (e.g., regarding the influence on one's reputation) or the timing of its publication (e.g., generate publicity and discussion during election time). Second, pricing of news articles by news agencies and ad placement strategies by news publishers could be made dependent on the expected comment volume; articles that are more likely to generate comments could be priced differently. Finally, news consumers could be served only news articles that are most likely to generate many comments; news sources can thus provide new services to their customers and can save consumers' time in identifying "important" articles.. Our aim in this paper is to predict comment volume of news articles prior to publication. To this end, we seek to answer the following two questions: (i) What are the dynamics of user generated comments on news articles? We look at article and comment statistics per source. (ii) Can we predict, prior to publication, whether a news story will receive any comments at all, and if so, whether it will receive few or many comments?. This work makes several contributions. First, it explores the dynamics of user generated comments in on-line Dutch media. Second, it introduces the problem of predicting the comment volume of a news article. Third, it provides a set of surface, cumulative, textual, semantic, and real-world features that can be used to predict the number of comments of a news story prior to publication. Fourth, it provides an evaluation of the introduced features. Fifth, an error analysis identifies possible causes for classification failure.. Section 2 contains related work; we explore news comments in Section 3; our feature sets are introduced in Section 4; predicting comment volume is done in Section 5; Section 6 contains discussion, error analyses, conclusions, and future work. Different aspects of the comment space dynamics have been explored in the past. Schuth et al. [11] explore the news comments space of four on-line Dutch media, while Mishne and Glance [10] explored the weblog comment space. Kaltenbrunner et al. [6] measured community response time in terms of comment activity on Slashdot stories, and discovered regular temporal patterns on people's commenting behaviour. Recently, various prediction tasks and correlation studies have been considered in social media. Mishne and de Rijke [8] use textual features as well as temporal metadata of blog posts to predict the mood of the blogosphere. De Choudhury et al. [3] correlate blog dynamics with stock market activity, and Gruhl et al. [4] perform a similar task with blogs/reviews and book sales. Szabó and Huberman [12] predict the popularity of a story or a video on Digg or YouTube, given an item's statistics over a certain time period after publication. Lerman et al. [7] forecast the public opinion of political candidates from objective news articles. Finally, Tsagkias et al. [13] predict podcast preference using surface features extracted from podcast RSS feeds.. To our knowledge, no prediction tasks have been published that concern the volume of comments generated by online news articles.

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


Does the use of structured reporting improve usability? A comparative evaluation of the usability of two approaches for findings reporting in a large-scale telecardiology context One of the main reasons that leads to a low adoption rate of telemedicine systems is poor usability. An aspect that influences usability during the reporting of findings is the input mode, e.g., if a free-text (FT) or a structured report (SR) interface is employed. The objective of our study is to compare the usability of FT and ST telemedicine systems, specifically in terms of user satisfaction, efficiency and general usability. We comparatively evaluate the usability of these two input modes in a telecardiology system for issuing electrocardiography reports in the context of a statewide telemedicine system in Brazil with more than 350.000 performed tele-electrocardiography examinations. We adopted a multiple method research strategy, applying three different kinds of usability evaluations: user satisfaction was evaluated through interviews with seven medical professionals using the System Usability Scale (SUS) questionnaire and specific questions related to adequacy and user experience. Efficiency was evaluated by estimating execution time using the Keystroke-Level Model (KLM). General usability was assessed based on the conformity of the systems to a set of e-health specific usability heuristics. The results of this comparison provide a first indication that a structured report (SR) input mode for such a system is more satisfactory and efficient with a larger conformity to usability heuristics than free-text (FT) input. User satisfaction using the SUS questionnaire has been scored in average with 58.8 and 77.5 points for the FT and SR system, respectively, which means that the SR system was rated 18.65 points higher than the FT system. In terms of efficiency, the completion of a findings report using the SR mode is estimated to take 8.5 s, 3.74 times faster than using the FT system (31.8 s). The SR system also demonstrated less violations to usability heuristics (8 points) in comparison to 14 points observed in the FT system. These results provide a first indication that the usage of structured reporting as an input mode in telecardiology systems may enhance usability. This also seems to confirm the advantages of the usage of structured reporting, as already described in the literature for other areas such as teleradiology. telecardiology is one of the most traditional applications of telemedicine. It has been widely used for more than 15 years and encompasses a wide range of application areas, being one of the fastest growing telemedicine fields [1] . A successful example of a telemedicine network offering telecardiology services is the STT/ SC -Santa Catarina State Integrated Telemedicine and Telehealth System [2] . The STT/SC is an essentially asynchronous telemedicine system, also referred to as a store-and-forward (SF) system, which offers, among other modalities, telecardiology services through the provision of findings reports to EKG examinations. These are performed mostly at upstate primary healthcare facilities and sent to a central portal via a web interface. Telecardiology findings reports are provided by cardiologists accessing the portal using specially developed web and mobile applications. The findings are stored at the same portal, where the requesting physician and the patient can access the results. To date, more than 370,000 telecardiology examinations have been performed online, employing different versions of the system. The first version of the system, shown in Fig. 1 , offered free text insertion (FT) for the provision of the findings reports.. Various disadvantages, however, were observed with this kind of interaction and its usability, which could have negative implications on the clinic context [3] . This includes a higher probability of user errors that could not only affect the patient but also lead to setbacks in the degree of acceptance of the service. Therefore, a new version was developed, in which the use of structured reporting (SR) has been employed for the provision of findings reports, as shown in Fig. 2 .. The existence of a telemedicine operation on the scale of STT, raises questions about the adequacy of its model, based on a single and specifically developed software platform and its impact on both, patients and health professionals. There exists evidence that the most frequently cited reasons for the low adoption rate of Electronic Health Records (EHRs) -security, privacy and systems integration -are surpassed by the issues of productivity and usability [4, 5] . Besides, many authors have commented that the usability situation of most EHR systems is not satisfactory [6] [7] [8] . Usability problems are considered a factor that can lead to the implementation of a healthcare IT system to fail [5] . On the other side, the majority of medical device incident reports can primarily be attributed to user error, implying that greater attention to human factors and usability during development of a medical devices and software could improve this situation [9] . Thus, the enhancement of the usability of EHR-related software seems to be critical for the continuous diffusion and success of this technology [10] .. In this context, an earlier investigation into user satisfaction with the STT's service has already shown a very high degree of acceptance [11] . The adequacy of the software tools being offered, however, has not yet been systematically investigated. Therefore, the study described here represents a first step into this direction by analyzing usability. The quality usability is directly related to how users interact with software and with which levels of efficacy, efficiency and satisfaction a user is able to execute a particular task [12] .. In this regard, the adoption of a new structured reporting (SR) input mode, particularly in a specialized and well established field of telemedicine, such as, telecardiology, leads to the question on how SR compares to FT reporting with respect to usability as perceived by the healthcare professionals. Is it easier and more comfortable to provide a findings report using structured reporting? Is it faster? It is also important to question, if the modification from FT to SR has improved the quality of the telecardiology system from the users' point of view.. To effectively measure usability involves a combination of heuristics and observations of user interaction situations, along with expected patterns. The complexity of the clinical environment, however, is difficult to be reproduced in laboratory and ethics/privacy issues can prevent the execution of some kinds of usability evaluations [13] . The inclusion of usability specialists in healthcare IT development teams, on the other side, has not been common and end-users do not have the abilities or the training required to help in the usability design [14] . As a consequence, wellestablished and rigorous usability research strategies should be employed when performing usability research in the healthcare IT domain [15, 16] . This paper focuses on comparing the usability of FT and ST systems for reporting findings on electrocardiograms from the viewpoint of a cardiologist, based exemplarily on the STT/SC. We specifically analyze if user satisfaction, efficiency and general usability vary depending on the different input modes. The paper is organized as follows: Section 2 focuses on the study context providing background information on the STT/SC. Section 3 presents and discusses related work. In Section 4, we detail the adopted research methodology and in Section 5 we present the results of our study. A conclusion is given in Section 6. We performed an original comparison with respect to usability of two different interaction modes, free text versus structured reporting, for the task of the description and publication of findings reports of electrocardiography examinations. The results of this work provide evidence that seems to confirm the benefits of the usage of structured reporting in telecardiology as observed already for other areas such as radiology [39] . The results we obtained indicate that also in the area of telecardiology the usage of structured reporting as an interaction mode enhances the system usability, mainly in terms of efficiency and satisfaction. Among the factors that contributed to this result are the fact that the SR system possesses clean screens, showing only information necessary to execute the task, and requires fewer steps by eliminating the need for typing the report. The results of this study, even if performed with a relatively small user group, clearly point out the benefits of the structured reporting mode. In this context, the use of structured reporting can strengthen the advantages of the usage of telecardiology systems through the reduction of the work load of healthcare professionals and promoting a better acceptance of this kind of system. This research work also provides a starting point for further studies of structured reporting systems aimed at other questions such as if findings report texts rendered from structured reports are easier to read or if they have a more significant content. Usability is an important issue for telemedicine systems, as it is one of the most contributing factors to their success [4, 5] .. Systematically adopting usability engineering in the development of healthcare systems can minimize the number of user errors that may lead to wrong diagnosis and consequently harm patients [19] .. In order to assess the state of the art in the field of usability of telecardiology systems, we performed a systematic literature review. This review explicitly focused on papers addressing usability related to data entry modes in various fields of telemedicine. We considered articles published in English in the period from 2006 to 2014 that discuss usability (specifically efficiency and user satisfaction) for the task of providing a remote findings report for an examination adopting FT or SR data entry. We excluded articles that discussed aspects unrelated to usability. We searched the IEEE, ACM, PubMed and Google Scholar bases using the search string ''usability AND cardiology AND (structured OR free-text) AND report''.. Analyzing the search results, only five articles relevant to our research focus were encountered (Table 1) . Other articles initially found only discussed the FT/SR data entry modes from the point of view of the data storage efficiency, quality of obtained information and ease of extraction of clinical information, and did not address usability questions. No articles addressing usability or user acceptance questions related to FT/SR data entry modes in the field of telecardiology were encountered. We only identified articles discussing FT/SR acceptance and usability questions in teleradiology.. The analysis of these teleradiology articles reveals a lack of consensus between authors concerning the efficiency and acceptance of SR input modes. Besides, the interfaces and input modes of the analyzed SR systems are not uniform, ranging from lists and selection boxes to input via menus [25] . These are very different input forms, which present different usability characteristics and vary widely in user-friendliness, providing different user experiences, which could justify the observed lack of consensus about the advantages and acceptance of SR. All articles have in common that a preexisting or newly developed SR system was taken and compared to the user experience with an also preexisting FT system. The test concluded that the use of the structured reporting system resulted in statistically significant decreases in user dissatisfaction. Results of an accompanying survey of the intervention group reveal that users thought the structured reporting system was overly constraining and time-consuming to use Authors highlight that the system studied was first designed more than 10 years ago and many system shortcomings were due to the technologic limitations of the time There is no evidence in the articles that the SR system used for comparison was systematically developed taking into consideration usability issues or the working culture already established with the previous FT system.

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


A Split-Step Numerical Method for the Time-Dependent Dirac Equation in 3-D Axisymmetric Geometry A numerical method is developed to solve the time-dependent Dirac equation in cylindrical coordinates for 3-D axisymmetric systems. The time evolution is treated by a splitting scheme in coordinate space using alternate direction iteration, while the wave function is discretized spatially on a uniform grid. The longitudinal coordinate evolution is performed exactly by the method of characteristics while the radial coordinates evolution uses Poisson's integral solution, which allows to implement the radial symmetry of the wave function. The latter is evaluated on a time staggered mesh by using Hermite polynomial interpolation and by performing the integration analytically. The cylindrical coordinate singularity problem at r = 0 is circumvented by this method as the integral is well-defined at the origin. The resulting scheme is reminiscent of non-standard finite differences. In the last step of the splitting, the remaining equation has a solution in terms of a time-ordered exponential, which is approximated to a higher order than the time evolution scheme. We study the time evolution of Gaussian wave packets, and we evaluate the eigenstates of hydrogenlike systems by using a spectral method. We compare the numerical results to analytical solutions to validate the method. In addition, we present three-dimensional simulations of relativistic laser-matter interactions, using the Dirac equation. In this work, a numerical method based on a splitting scheme was developed to solve the time-dependent This numerical scheme is an extension of the one presented in [25, 26] and thus, shares some of its main properties:. 1. There is no fermion-doubling problem in the discretization process. Indeed, each step of the splitting is solved in a way that does not modify drastically the continuum dispersion relation, apart from small errors related to the splitting and the radial spatial discretization. A careful analysis of this issue would require a Von Neumann analysis, as in [26] for Cartesian coordinates, where the continuous and discretized Dirac equation are Fourier transformed 5 to obtain their respective dispersion relations (similar calculations are found in [26, 24] ). This will be the subject of future investigation.. 2. The numerical scheme can be parallelized very efficiently using a domain decomposition method because the algorithm obtained is local in space. Thus, the domain can be separated into subdomains which can be solved independently on different processors: only the information at the subdomain boundaries is exchanged between neighbour processes. This leads to a quasi-linear speedup as the number of processors is increased [26] . This was not considered explicitly in this article, but was verified numerically in some calculation.. The method was tested by looking at the dynamics of wave packets in 2-D. It was shown that the numerical results were in agreement with the analytical result. Moreover, it was tested that the order of convergence of the method in the radial direction is similar to the Cartesian case. Then, a more interesting 5 For the radial part, we should use the Hankel transform. We are interested first in solving the following equation:. with an initial condition given by. In the first step, the matrix α z is diagonalized to decouple the spinor components. This is performed by a similarity transformation as. where P z is a unitary matrix and Λ z = Diag[1, 1, −1, −1] = β is a diagonal matrix. Starting with α z in the Dirac representation, the explicit expression of the transformation matrix is. The resulting Dirac equation is then i∂ tψ (t, r, z) = −icβ∂ zψ (t, r, z) (A.5). where we definedψ := P † ψ. It is convenient here, for notational purposes, to split the four-spinor into two bi-spinors asψ = (φ,χ) T to get. Therefore, the Dirac equation clearly becomes a set of four uncoupled first-order differential equations in this representation. Their solution is well-known and can be obtained from the method of characteristics.. The solution is given byφ . 2 (t n+1 , 0, z k ) = 1 2πa . 2,4 (t n+1 , 0, z k ) = 0. Using the same strategy as above, the cubic Hermite interpolation becomes g h ,1 (r, z k ) = g h ,1 (0, k)S 1 (ξ(r)) + g h ,1 (1, k)S 2 (ξ(r)) + r There is no known analytical form for these integrals in the general case [55] . However, using high accuracy numerical integration, this result can be used to validate our numerical method and to analyze the operator splitting.

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


Line width optimization for interdigitated power/ground networks Higher operating frequencies have increased the importance of inductance in power and ground networks. The effective inductance of the power and ground network can be reduced with an interdigitated structure. A closed-form solution for determining the optimal power and ground wire width is described, producing the minimum impedance within an interdigitated structure. The optimal wire width is determined under different physical network dimensions and signal frequencies, suggesting useful trends for interdigitated power and ground networks. In addition, a closed-form expression for the optimal wire width is determined that minimizes the voltage drop over a single metal layer of an interdigitated power/ground network. With high operating frequencies and scaled geometries, the power and ground (P/G) distribution network requires enhanced optimization to provide significant current flow. The higher currents increase voltage losses within the P/G network, while decreasing power supply voltages provide lower noise margins. With flip-chip packaging, the package inductance is reduced [1] , making the on-chip inductance more significant. Since the voltage variations within a P/G network are due to IR [2, 3] and L di dt [4] voltage drops, the effective resistance and inductance are the primary foci of the optimization process. At higher frequencies, the inductive impedance is dominant, requiring accurate estimation of the effective inductance.. An interdigitated P/G distribution network structure where a few wide lines are replaced by a large number of narrow lines is often used to reduce the inductive effect [5, 6] . Different P/G structures have been compared in [7, 8] , where an interdigitated structure is shown to achieve the greatest reduction in inductance.. Each layer of a multi-layer interdigitated structure consists of individual interdigitated power and ground wires, as depicted in Fig. 1 . Routing flexibility and reduced inductance are two primary advantages of an interdigitated P/G distribution structure.. The need for efficient P/G networks has been recognized, and several techniques to optimize the P/G distribution network have been developed [9, 10] . More advanced techniques for designing power networks have been described [11, 12] ; however, only the package inductance is considered, neglecting the on-chip inductance. With more advanced packaging techniques (such as flipchip), the on-chip inductive noise (L di dt ) is also important [1, 13] . To consider on-chip inductance in power supply networks, a technique to simplify the mesh model of an RLC power network is proposed [14] , assuming the loads are treated as identical current sources. The significance of the on-chip inductance within paired and interdigitated power/ground network structures is described in [15] , where the inductance is treated as a local effect. In [16] , the inductance model considers the mutual inductance between close and distant power/ground wires in interdigitated structures. Based on this model, a closed-form expression characterizing a single layer of an interdigitated P/G network structure is utilized, permitting the optimal width of a power/ground network that minimizes the network impedance to be determined.. The paper is organized as follows. The problem is formulated in Section 2. The resistance and inductance of an interdigitated power and ground structure are discussed in Section 3. In Section 4, a closed-form expression for the line width that produces the minimum impedance for a single metal layer is presented. The accuracy of the optimal line width and related issues are discussed in Section 5. The paper is concluded in Section 6. The characteristics of an interdigitated power and ground network are investigated in this paper. The effect of resistive and inductive impedances under a constant area constraint is observed for different wire widths (or number of interdigitated pairs).. Under a constant area constraint, conflicting behavior of the effective resistive and inductive impedances is observed with increasing wire width. This conflicting behavior is explored to achieve the minimum impedance of a single interdigitated metal layer. A closed-form expression for the line width is determined, achieving high accuracy for small spacings as compared to FastHenry. The accuracy of the optimal width is enhanced over a wide range of spacings utilizing iterative approaches (up to four iterations). The effect of different spacings, thicknesses, and frequencies on the optimal width is reviewed. A design methodology that considers the network resistance and inductance (both self and mutual) of a single interdigitated metal layer network that produces the minimum impedance is presented in this paper. In addition, a closed-form expression for determining the optimal wire width is described that minimizes the voltage drop over a single metal layer of an interdigitated power/ground network.

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


Parallel evaluation of multi-join queries A number of execution strategies for parallel evaluation of multi-join queries have been proposed in the literature; their performance was evaluated by simulation. In this paper we give a comparative performance evaluation of four execution strategies by implementing all of them on the same parallel database system, PRISMA/DB. Experiments have been done up to 80 processors. The basic strategy is to first determine an execution schedule with minimum total cost and then parallelize this schedule with one of the four execution strategies. These strategies, coming from the literature, are named: Sequential Parallel, Synchronous Execution, Segmented Right-Deep, and Full Parallel. Based on the experiments clear guidelines are given when to use which strategy. For years now, research has been done on the design, implementation, and performance of parallel DBMSS.. Teradata [CaK92], Bubba [BAC90] , HC1 86-16 [BrG89] , GAMMA [DGS90] , and XPRS [SKP88] are examples of systems that actually were implemented, and many papers were written on their performance. The performance evaluation of these systems is mainly limited to simple queries that involve no more than one or two join operations.. Recent developments in the direction of support of nonstandard applications, the use of complex data models, and the availability of high-level interfaces tend to generate complex queries that may contain larger numbers of joins between relations. Consequently, the development of execution strategies for the parallel evaluation of multi-join queries has drawn the attention of the scientific community. A number of strategies was proposed [CLY92,CYW92, HoS9 1,HCY94,SCD90] and their performance was evaluated via simulation. However, no comparative experimental performance evaluation is available. This paper describes the proposed strategies in a common framework. Four strategies 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 of Computing Machinery.To copy otherwke, or to republish, requires a fee and/or specific permission, SIGMOD'95,San Jose, CA USA @ 1995 ACM 0-89791-731 -6/95/0005..$3.50 are implemented on PRISMA/DB and a comparative performance evaluation is done.. The results yield clear guidelines for the choice of a strategy. For a larger number of processors, FP still suffers from the delay over the pipeline, but the negative effect of startup and coordination overhead for SP is stronger. Also, for a small number of processors, FP suffers from load imbalance due to discretization errors in the distribution of processors over operations. Therefore, FP performs better for a large number of processors. As said before, in our experiments, we vary the parallelization strategy, the number ofprocessors used, the shape of the The cost function may seem overly simple, however, it does not seem to make sense to try and estimate the costs more precisely.. As for example indicated in [SrE93] , the parallelization of a query tree influences the total costs of the operations in the query tree. If a strategy allocates two operations (partially) together on one node, the transmission costs are lower than estimated.. Also, parallelization may influence the need to redistribute operands between two Joins. Therefore, it is in principle impossible to make a real accurate estimate of the costs of the individual join operations in the join tree. Our experiments will show, however, that the cost estimate used generates execution plans with good parallel behavior. FP execution of this query tree does show performance gain from parallelism. However, for the 40K experiment, its performance for a low degree of parallelism is not as good as SP. This is caused by the fact that FP suffers from the constant delay over a long linear pipeline.

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Motion-aware temporal coherence for video resizing : Overview of our automatic content-aware video resizing framework. We align the original frames of a video clip to a common coordinate system by estimating interframe camera motion, so that corresponding components have roughly the same spatial coordinates. We achieve spatially and temporally coherent resizing of the aligned frames by preserving the relative positions of corresponding components within a grid-based optimization framework. The final resized video is reconstructed by transforming every video frame back to the original coordinate system.Temporal coherence is crucial in content-aware video retargeting. To date, this problem has been addressed by constraining temporally adjacent pixels to be transformed coherently. However, due to the motion-oblivious nature of this simple constraint, the retargeted videos often exhibit flickering or waving artifacts, especially when significant camera or object motions are involved. Since the feature correspondence across frames varies spatially with both camera and object motion, motion-aware treatment of features is required for video resizing. This motivated us to align consecutive frames by estimating interframe camera motion and to constrain relative positions in the aligned frames. To preserve object motion, we detect distinct moving areas of objects across multiple frames and constrain each of them to be resized consistently. We build a complete video resizing framework by incorporating our motion-aware constraints with an adaptation of the scale-and-stretch optimization recently proposed by Wang and colleagues. Our streaming implementation of the framework allows efficient resizing of long video sequences with low memory cost. Experiments demonstrate that our method produces spatiotemporally coherent retargeting results even for challenging examples with complex camera and object motion, which are difficult to handle with previous techniques. In recent years, content-aware video resizing has been an active research topic. The goal is to change the aspect ratio and the resolution of video data to fit target display devices, while retaining as much important content as possible and avoiding visible artifacts. To achieve this, the recent techniques largely operate at the pixel level, e.g., by removing the least important rows/columns of pixels iteratively through seam carving [Rubinstein et al. 2008] or by distributing the errors from important pixels to less important ones through non-uniform warping [Wolf et al. 2007; Zhang et al. 2008] .. Naïvely resizing individual frames in a content-aware manner easily leads to temporal incoherence, causing flickering or waving artifacts. To address the problem, most previous work considers videos as spatiotemporal cubes and constrains temporally adjacent pixels to transform coherently (by "temporally adjacent pixels", we mean pixels in consecutive frames that have the same spatial location, up to 1-ring neighborhood). However, this approach often fails to guarantee temporal coherence, since it is motion-oblivious: it assumes that features remain in the same spatial location or 1-ring neighborhood between consecutive frames, and this assumption breaks down when large camera or object motion is present. For example, camera zooming makes object features occupy regions of different sizes even between consecutive frames, possibly causing seam carving to remove features inconsistently across frames due to its strategy of one seam removal per frame. Camera or object sliding also easily leads to deviation from correspondence between temporally adjacent pixels (Figure 2 ). Similar temporal incoherence problems happen with the methods based on non-uniform warping [Wolf et al. 2007; Zhang et al. 2008] (see examples in the accompanying videos).. We introduce motion-aware constraints for temporally coherent resizing of videos, which, to the best of our knowledge, have not been studied before. We observe that temporal coherence can be achieved by preserving the motion information of the input video, usually consisting of camera and object motion, and we thus design separate constraints to preserve camera motion and object motion.. Specifically, we align every pair of consecutive frames using their interframe camera motion and constrain their relative positions to retain camera motion. We preserve object motion by detecting distinct moving areas of objects across multiple aligned frames and constraining each of them to be resized consistently.. The concept of motion-aware temporal coherence constraints is largely orthogonal to the building blocks of the existing video retargeting methods and thus can be used to improve the existing methods. However, in this work we chose to build a new video resizing framework which relies on the scale-and-stretch optimization proposed by Wang et al. [2008b] , originally designed for image retargeting. Unlike other recent image resizing methods [Avidan and Shamir 2007; Wolf et al. 2007; Zhang et al. 2008] , where the optimization is restricted to one spatial direction (horizontal or vertical), the method of Wang et al. distributes the distortion due to aspect ratio change in all spatial directions, and thus generally achieves better results in many resizing scenarios. The nature of this omnidirectional warping poses a more interesting and challenging problem for achieving temporal coherence. We show how to strike a balance between spatial content preservation and temporal coherence using a bounded number of aligned neighboring frames to define a blended importance map for each frame. Since our method is heavily based on frame alignment, our final resizing optimization is naturally formulated over all video frames aligned in a common camera coordinate system, where the resizing effect of individual frames is driven by content-aware deformation of per-frame uniform grids (Figure 1 ). To improve performance and scalability, we break long video sequences into short overlapping clips and resize the individual clips in a streaming manner while constraining their in-between temporal coherence over the overlapping frames.. We apply our method to a variety of videos that contain large object motion and/or camera motion. Experiments show that our method produces consistent, visually pleasing results and tends to preserve salient content and temporal coherence better than the previous techniques. An ideal solution to temporally coherent video resizing is to first recognize compatible objects across different video frames and then resize them within individual frames in a consistent manner. However, this involves object recognition and tracking, which are challenging tasks on their own. Observing that achieving temporal co-. herence largely means avoiding motion artifacts, such as flickering and waving, we aim to preserve the motion information in an input video, usually consisting of camera motion and object motion.. Camera motion and object motion have very different nature, demanding separate strategies to preserve them. Camera motion is of low degree of freedom and brings a global visual effect to whole scene, usually containing both static and dynamic objects. Assuming that input videos always contain static objects (e.g., static background) whose visual movement is completely due to camera movement, we use a feature-based method to estimate the camera motion between every pair of consecutive frames (Section 4.1). By "object motion", we refer to the intrinsic motion of dynamic objects, independent of camera movement. Object motion can often be of high degree of freedom and simultaneously caused by multiple objects at different locations. Precise estimation of object motion is a challenging task. Fortunately, by the smooth warping nature of the core technique, it is sufficient to use the remaining motion subtracted from the camera motion to roughly estimate object motion, avoiding the necessity for precise alpha-masks of the dynamic objects.. Since the importance map of each frame largely determines how each image is non-uniformly deformed during resizing, we require importance maps that change smoothly across adjacent frames. To achieve this, we compute the importance map of each frame by considering a bounded number of neighboring frames aligned in a common camera coordinate system of the current frame, instead of only the frame itself (Section 4.2). Each importance map takes into account salient information in both spatial and temporal context, but excludes motion purely caused by camera movement, since it is almost homogeneous within individual frames and thus of little importance.. We build a new video resizing framework by designing motionaware temporal coherence constraints (Section 5.2) and applying the importance maps to guide content-aware resizing of individual frames (Section 5.1), for which we adopt the image resizing method proposed by Wang et al. [2008b] . We embed each frame into a uniform grid mesh. Our system simultaneously deforms all the meshes with spatial and temporal constraints. We preserve camera motion by constraining relative positions of every two consecutive meshes, aligned using the estimated interframe camera motion. We achieve temporally coherent resizing of dynamic objects by detecting their moving areas and deforming each distinct moving area in a consistent manner. As our temporal constraints and importance maps are all dependent on the frame alignment, we found it more intuitive to formulate the optimization in a common camera coordinate system. Once we obtain the deformed meshes, we transform them back to the original coordinate system of each frame and warp the corresponding images to produce the final resized video. Figure 1 gives an overview of our resizing framework. Note that we show every twentieth frame for better visualization.. It is unnecessary to retain temporal coherence at scene/shot boundaries of videos. Therefore we manually segment input videos into individual scenes and leave the implementation of an automatic scene boundary detection algorithm (e.g., [Rasheed and Shah 2003] ) for future work. The performance of our optimization depends on both the resolution of the video and the number of frames involved. To make our method scalable to long video sequences of single scenes, we break the input into short clips with a small set of overlapping frames and resize the individual clips sequentially. We constrain the temporal coherence in the overlapping areas in order to achieve coherent resizing of the entire sequence. Since we trade speed for coherence quality, our current implementation is interactive (around 5 fps) but not realtime. In the following sections, we first present our algorithm for resizing a single video clip and then discuss our solution to the scalability problem in Section 5.4.. c MAMMOTH HD Figure 3 : We blend the information of a bounded number of aligned neighboring frames to define an importance map at each frame. Pixels with high and low importance are visualized in green and blue, respectively. Our model produces time-smoothing maps that capture salient information in both spatial and temporal context. We have presented a practical video resizing framework which can handle videos of complex dynamic scenes. We observed that camera and object motion cause feature correspondences to deviate from temporally adjacent pixels, easily causing flickering or waving artifacts. We found that minimizing motion artifacts during resizing can be achieved by preserving both camera and object moMotion-Aware Temporal Coherence for Video Resizing • 127:9 tion and introduced motion-aware temporal coherence constraints to preserve them. Our streaming implementation leads to a scalable video resizing system that consistently produces spatiotemporally coherent resizing results. We believe that by introducing the concept of motion-aware constraints, we have taken a significant step towards a more practical video resizing system. Different content-aware image/video resizing methods each have their own strengths. It would be interesting to combine our ideas of motion-aware constraints with the other image resizing methods or with the existing video retargeting methods to achieve better temporal coherence. In addition, the preservation of global structures, such as straight lines and different types of symmetries, is as well important, requiring explicit structure detection and extra structural constraints. Image Retargeting. Many content-aware image retargeting techniques have been proposed to adapt images to target displays with different resolutions and aspect ratios. They often share the same common structure: first, define an importance map of the image, followed by content-aware operations which try to retain important visual information as much as possible. Those methods mainly vary by the specific content-aware operations. For example, cropping methods [Chen et al. 2003; Liu et al. 2003; Suh et al. 2003; Santella et al. 2006 ] search for a single window covering important content and retain it while completely discarding the rest. Unlike a homogeneous resizing, which is simply a linear mapping, recent works, such as non-photorealistic retargeting [Setlur et al. 2005] , seam carving [Avidan and Shamir 2007; Rubinstein et al. 2008] , one-directional image warping [Gal et al. 2006; Wolf et al. 2007; Zhang et al. 2008] and omnidirectional image warping [Wang et al. 2008b ] allow nonlinear retargeting of images. They strive to redistribute the pixels of the entire image according to their importance values. The method of [Wang et al. 2008b ] allows local content drifting/rescaling in both the horizontal and vertical dimensions even if the user changes only the width or height of the image.. Redistribution of pixels under patch-based coherence and completeness constraints is studied in [Cho et al. 2008; Simakov et al. 2008] . These methods afford more flexibility for image editing operations, including image resizing, though at much higher computational cost. The concepts from image retargeting have also been transferred to content-aware shape resizing [Kraevoy et al. 2008] and focus+context visualization of 3D models [Wang et al. 2008a ].. c Mammoth HD Figure 2 : Object or camera motion diverts feature correspondence from temporally adjacent pixels. In this example, due to camera movement, features within the quad in red should be constrained to those within the yellow quad instead of the temporally adjacent quad in blue.. Video Retargeting. Almost all the image retargeting methods can be adapted to resize videos by addressing two problems: augmenting image importance models with motion information and resizing individual frames in a temporally coherent manner. We show that the influence of camera and object motion should be considered in both problems. However, to the best of our knowledge, none of the existing importance models except those used in the croppingbased retargeting methods [Liu and Gleicher 2006; Tao et al. 2007 ] take camera motion into account. Liu and Gleicher [2006] compute motion contrast, i.e., the motion at each pixel subtracted from the background motion, to define motion saliency, which is then incorporated into the importance model together with image saliency and object saliency. Tao et al. [2007] explicitly extract moving foreground objects to solely define important parts.. The cropping-based retargeting methods achieve temporally coherent results by searching for a smooth cropping sequence. The retargeting methods involving local redistribution of pixels demand pixel-level temporal coherence, which is apparently more difficult. The existing methods enforce coherence between temporally adjacent pixels in a spatiotemporal video cube. For example, Wolf et al. [2007] propose to penalize position changes of temporally adjacent pixels in a linear least-squares optimization formulation. Similar temporal coherence is achieved using a 3D random walk model in [Zhang et al. 2008] , which instead focuses on improving the efficiency of [Wolf et al. 2007] . Rubinstein et al. [2008] obtain time-smoothing seams by solving for monotonic 2D connected manifold seams using graph cuts. However, we observed that simply enforcing constraints between temporally adjacent pixels is often insufficient or even invalid, especially when large object movement or large camera motion is involved, causing flickering or waving artifacts.. Note that the above retargeting methods have their own advantages and disadvantages [Rubinstein et al. 2008] . For example, compared to cropping-based methods, which completely discard less important regions, nonlinear retargeting, such as seam carving and nonuniform warping, has better ability to preserve scene context at the cost of allowing some degree of distortion, especially to less important regions. Our resizing framework, as another nonlinear retargeting method, is proposed not to replace any existing resizing tool, but to provide users more options for their specific needs. As recently shown, several types of retargeting methods may need to be used together to produce visually pleasing resizing of a general image or video [Rubinstein et al. 2009 ].

O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O B 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 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 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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 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 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On dynamic signaling congestion mitigation by overlapping tracking area lists Mitigating signaling congestion of tracing user equipments (UEs), adaptively to the changes in UE location and mobility patterns is a challenging issue in mobility management of Long Term Evolution (LTE) networks. Signaling congestion usually occurs due to many UEs behaving in a similar manner, e.g., massive and simultaneous UE mobility in a train movement scenario. LTE networks allow the use of tracking area lists (TALs), each being a list containing multiple tracking areas (TAs). The overlapping TAL scheme has been previously used for signaling congestion mitigation for snapshot scenarios. For maintaining the improved performance over non-list-oriented TA configuration over time, an automatic dynamic configuration framework, which is a key aspect in Self Organizing Network (SON), has been applied in this paper. We develop a linear programming model for optimal TAL configuration. Repetitively solving the model for different time intervals gives an evaluation framework on the performance of SON location management. Comprehensive numerical results are presented in this study, using a large-scale realistic network scenario. The experiments demonstrate the effectiveness of the SON dynamic framework in reducing the total signaling overhead of the network compared to the static TA. Moreover, the overlapping TAL scheme significantly improves the performance of the network in the tracking area update congested scenarios over the conventional TA Location management, which is sometimes called reachability, aims to track and page user equipments (UEs) in cellular network. Tracking Area (TA) in Long Term Evolution (LTE) is a logical area-partition of the network, that each partition is a subset of cells [1] . In the idle state, a UE is in power-conservation mode and does not inform the network of each cell change. Hence, the location of idle UEs is known to the network to the granularity of TA. In the conventional TA scheme, when a UE passes a TA boundary, it sends an uplink signaling message to the Mobility Management Entity (MME). This procedure is called tracking area update (TAU). On the other hand, for placing a call to a UE, the MME sends downlink paging signaling messages to the cells inside the UE's current TA, in order to find the cell from which the UE can receive the call.. UEs in active mode also perform TAUs as part of the handover (HO) procedure.. However, while UEs are in active mode the corresponding signaling due to TAU is a small portion compared to the whole signaling including HO procedure.. Therefore, the topic of this research becomes interesting while focusing on idle UEs, due to the fact that the number of idle UEs is significantly more than the active ones.. In designing the TA layouts of a network, the overheads resulted by TAU and paging signaling messages are the key parameters to be taken into account.. Planning and optimization of TAs (or Location Areas (LAs) and Routing Areas (RA) for the previous generations of cellular networks) by considering signaling overhead have been dealt with in a large amount of literature [8, 10, 12, 20, 33, 34] . There are two new concepts in LTE networks, that need to be more explored and investigated with the objective of improving the network performance: One is the concept of self-organizing networks (SON) [4, 5] , and two is the concept of TA list (TAL) [2] . Both of these concepts are standardized by 3rd Generation Partnership Project (3GPP), Release 8, for LTE. In this paper, we aim to reduce the operating expenditure (OPEX) cost and improve the overall performance of LTE's location management by deploying these two concepts in the network.. Conventionally, TAs are manually configured and the configuration is static.. As UE distribution and mobility patterns change over time, the TA configuration of the network does not perform optimally for all time intervals. In the conventional TA scheme, reconfiguring TAs, such as moving a cell from one TA to another, requires temporarily tearing down the cell causing service interruption [19] . Due to the excessive cost caused for the operator, it is not feasible to make small time interval reconfigurations in the conventional TA scheme. However in SON, an automated and efficient deployment of updated configurations is possible. For a stable optimization, a global view of the UEs' movements and call arrival rate statistics is a requirement. In a static TA, the average of this statistic is used for the TA design. However, in a dynamic framework, we incorporate time of day and day of week data patterns into our design, which can further strengthen the performance of the network over the static TA.. During signaling congestion, there is resource exhaustion for tracking UEs.. Therefore, mitigating signaling congestion is to ensure no significant degradation in the quality of service (QoS) of a network. Normally, the TAU congestion occur in densely populated cities, where there is a huge number of UEs moving concurrently during specific times of day and night (rush-hours) [3] . Paging signaling congestion may also occur in scenarios where close-to-static UEs are simultaneously gathered at some hotspots. The focus in this paper is only on TAU congestion mitigation, with the assumption that it is a more critical issue in real-life deployments. The optimization framework used in this paper for mitigating TAU signaling congestion has been introduced in [24] and is based on the use of TA lists (TALs), which may contain overlapping TAs. Instead of updating the UE with one TA, the UE can be assigned a list of TAs, referred as a TAL. The UE performs a TAU, when it moves to a TA not being in its TAL. Hence, the location of a UE is known in the MME to the granularity of its allocated TAL. In the overlapping TAL scheme used in this paper, all cells in one TA use the same collection of TALs, and they update their UEs with the same proportional use of each TAL. The standard TA design is considered as the underlying structure. The optimal proportional use of the TALs for congestion mitigation is obtained via a linear program (LP).. One difficulty in evaluating the performance of TAL is the existence of UEs in a same location with different TALs, and thus calculating the total number of TAUs depend on the specific mobility pattern of each individual UE. This information is not available, and therefore the performance of TAL configuration rely heavily on the validity of the assumptions made in the models [11, 21, 22] .. The main advantage of applying overlapping TAL is that no mobility information is required for the calculation of the signaling overhead. Moreover, as all cells in the same area will assign TAL consistently based on their proportional usage, the performance evaluation can be effectively assessed.. The creation and reconfiguration of TALs are supported in SON architecture, therefore our dynamic optimization framework is cost efficient in implementation. One main advantage of using overlapping TAL scheme for SON is the possibility of entering the TAs with high number of TAUs at their boundaries and their neighboring TAs to the optimization formulation and hence applying it only to the congested area and not to the whole network. This will significantly reduce the problem size, which makes it practically useful to implement.. However, we should consider that as TAs are geographically connected to each other, solving the congestion problems for subsets of TAs may omit the optimum solutions of TAL proportions for the overall network. Hence in this paper, we apply the model to the whole network and solve the problem of exponentially higher size. Numerical evaluations for mitigating massive number of TAUs demonstrates the effectiveness of applying overlapping TAL on a dynamic framework compatible to SON.. The remainder of the paper is constructed as follows. In Section 2, we review some works which are relevant to our study. Section 3 is devoted to description of the dynamic framework, basic notation and an illustrative example of the overlapping TAL scheme. The optimization formulation for using the over-lapping TAL scheme for congestion avoidance of TAU is given in Section 4.. In Section 5, we explain a mechanism to apply the proposed overlapping TAL scheme on a SON dynamic framework. In Section 6, we present results of performance evaluation of the proposed approach and compare the static TA with the SON framework. Conclusions are provided in Section 7. We proposed an automated process in location management of LTE networks within the paradigm of self-optimization networks. We tackled the problem of mitigating TAU signaling congestion in a dynamic framework by using over- One extension line of this research is to build the overlapping TAL framework compatible for both minimization of the total signaling overhead, and mitigation of the signaling congestion depending on the priority of either problem in the network. Reasonable thresholds must be computed for triggering the overlapping TAL assignments according to the two problems. As mentioned in Section 1, there is an impressive number of surveys on optimization models and algorithms of conventional TA configuration [8, 10, 12, 20, 33, 34] . On the design of unconventional location update and paging schemes, which form another line of research, see for example [6, 28, 35] . For thorough surveys on location management, we refer to [7, 36] .. Recently, the concept of TAL in LTE has received a great attention due to its flexibility over the conventional TA concept [18, 27, 30, 31, 38] . Previous studies of using TAL for minimizing the total signaling overhead, with the assumption that a cell updates one common TAL to all UEs getting registered in that cell, have been previously presented in [11, 21, 22] . TALs, in forms of rings of cells, are used in [11] . In [21, 22] , each cell belongs to a specific TAL. Any UE getting registered in the cell, is updated by that specific TAL. In [25] , the authors prove that the optimum TAL configuration solution for minimizing the sum of TAU and paging signaling overhead is to assign only one TAL to each cell.. In general, to optimize the configuration of TALs, a major challenge is to estimate the signaling overhead. UEs in the same location may be registered to different TALs, thus the resulting overhead, in contrast to the conventional TA case, heavily depends on the forthcoming UE behaviors. Hence, assumptions on UE behavior, ranging from simple rule of thumb to statistical mobility models, are required. Nevertheless, previous works, in particular [21, 22] , show that TAL is promising in extending the capability of the conventional TA scheme.. TAL is promising for solving a couple of issues imposed by the conventional TA scheme. For example, TAL can be used to prevent the ping-pong effect, which is the frequent updates when a UE keeps hopping between two or more adjacent cells [27] . Another example is the train scenario associated with high uplink signaling traffic due to simultaneous updates of massive UEs crossing a boundary along a path [18, 23] . In [24] , the authors generalize the TAL optimization formulation of a line-form train scenario in [23] to an arbitrary network topology. In the current paper, we use the TAL optimization model for congestion mitigation of TAU given in [24] . Hence, the following study is an extension to [24] by introducing a dynamic framework to the model and adapting the TAL optimization formulation to SON. Moreover, the large-scale realistic dynamic scenario used in performance evaluation of this paper not only present the potential of overlapping TAL on a SON paradigm, but also presents a close-to-reality overview of mobility behavior and call arrival rate of UEs in a network for one week time horizon.. The problem of load balancing and signaling congestion mitigation in location management are investigated in [17, 29, 32, 37] . In [17] , the authors use randomized time distribution of cell reselection to avoid the mass mobility signaling congestion. However, their mechanism requires additional network configuration in order to provide the algorithm parameters. The main contributions of [29, 32] are models and algorithms for load balancing of the database servers in location update. However, most of the mechanisms of unconventional update and paging schemes require the use of non-standard system elements and parameters. The authors in [37] present a queuing model for location updates by group mobility, and examine the performance of using an information buffer at base stations to reduce update failures. The TAL scheme for signaling congestion mitigation used in the current paper allows a cell to belong to a collection of potentially overlapping TALs, which can be assigned to its UEs.. As cells are fully consistent in the proportional use of the correlated TALs, the signaling overhead estimation becomes straightforward and there is no need for any UE mobility assumption.. Self-optimization have already been studied in 2G and 3G networks, typically with the objective of improving radio coverage and channel capacity, however in recent years, there has been an increasing interest in the SON paradigm applied to mobility and location management of wireless networks [9] . The authors in [15] present a self-organized TAL mechanism to reduce the signaling overhead of a network of femtocells. The mechanism adapts the size of UE-specific TALs to the mobility speed and the paging arrival rate of each UE. Their performance evaluation is based on a simple hexagonal network topology, and a Markovbased mobility model. Our application focus is signaling congestion mitigation, and our proposed self-organized TAL framework is applied to a real-life largescale network topology, and it is independent of UEs mobility model. Moreover, our study can also be applied to femtocell networks.

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