Managing Misspelled Queries in IR Applications Our work concerns the design of robust information retrieval environments that can successfully handle queries containing misspelled words. Our aim is to perform a comparative analysis of the efficacy of two possible strategies that can be adopted.A first strategy involves those approaches based on correcting the misspelled query, thus requiring the integration of linguistic information in the system. This solution has been studied from complementary standpoints, according to whether contextual information of a linguistic nature is integrated in the process or not, the former implying a higher degree of complexity.A second strategy involves the use of character n-grams as the basic indexing unit, which guarantees the robustness of the information retrieval process whilst at the same time eliminating the need for a specific query correction stage. This is a knowledgelight and language-independent solution which requires no linguistic information for its application.Both strategies have been subjected to experimental testing, with Spanish being used as the case in point. This is a language which, unlike English, has a great variety of morphological processes, making it particularly sensitive to spelling errors.The results obtained demonstrate that stemming-based approaches are highly sensitive to misspelled queries, particularly with short queries. However, such a negative impact can be effectively reduced by the use of correction mechanisms during querying, particularly in the case of context-based correction, since more classical approaches introduce too much noise when query length is increased. On the other hand, our n-gram based strategy shows a remarkable robustness, with average performance losses appreciably smaller than those for stemming. Many information retrieval (IR) applications such as information extraction, question answering and dialog systems require user queries to be congruent with the documentary databases we are exploiting. In this sense, although formal IR models are designed for well-spelled corpora and queries, useful querying should be robust against spelling errors. We include in this category (Kukich, 1992) errors resulting from a lack of knowledge of orthography; typographical errors caused by a lack of accuracy in typing; and errors resulting from noisy generation tasks, usually deriving from texts written and published before the computer age 1 . Regardless of their cause, we shall refer to this kind of phenomena as misspelling errors, whose presence can substantially hinder the performance of IR applications.. The design of error-tolerant solutions able to mitigate or limit the effects of misspellings has become a priority in the design of query languages. Nowadays, there is a redoubled interest (Guo et al., 2008) in the management of misspelled queries arising from the phenomenon of globalization, led by increased access to information and the widespread popularity of its use. Within this context, there is a need to tackle aspects that have a decisive effect on the complexity of the problem, such as content heterogeneity (Huang and Efthimiadis, 2009; Kwon et al., 2009; Li et al., 2006) and the increasing size of the databases on which the search is performed (Celikik and Bast, 2009 ). This has led to the appearance of specific proposals both with regard to language (Hagiwara and Suzuki, 2009; Magdy and Darwish, 2008; Suzuki et al., 2009) and the area of knowledge under consideration (Wilbur et al., 2006) , making it advisable to foresee the inclusion of mechanisms for managing misspelled queries of this nature during the design stage of IR tools (Konchady, 2008) .. From a practical point of view, most significant experimental examination seems to be limited to texts written in English (Kukich, 1992; Croft et al., 2009 ), a language with a very simple lexical structure. Practical results suggest that while baseline IR can remain relatively unaffected by misspellings, relevance feedback via query expansion becomes highly unstable under these conditions (Lam-Adesina and Jones, 2006 ). This constitutes a major drawback in the design of IR systems, since query expansion is a major issue in the production of improved query formulations (Guo and Ramakrishnan, 2009; Lu et al., 2009a,b; Stokes et al., 2009 ). This fact in itself justifies efforts made in dealing with misspelled queries.. The operational basis for the treatment of misspelled queries consists of replacing the original string matching algorithm with a more flexible approximate method. It is interesting to note that practical constraints for solving misspellings in IR systems are different from those present in Text Processing systems. In the latter, the usual solution consists in presenting the user with a set of candidate corrections and lower first-guess accuracy is usually tolerated (Mitton, 2009 ). However, in IR systems, this kind of interaction is impractical. Therefore, the strategies considered for IR systems should assure fully automatic treatment (Agirre et al., 1998; Kukich, 1992) , with no need for the user to intervene after inputting the initial query.. In this article we consider two different strategies for managing misspelled queries (Manning et al., 2008) . The first of these is based on correcting the query before it is sent to the search engine, which necessarily implies the need for a dictionary. We can here distinguish two forms of spelling correction problems:. • Isolated-word error correction (Mitton, 2009; Savary, 2001; Vilares et al., 2004) , which tries to correct a single query term at a time, limiting the possibility of correction to non-word errors. In this sense, this kind of technique could fail to detect real-word errors, i.e. errors that produce another word that is also valid. An example would be the query "word swimming championships", which contains a misspelling of "world"; this would not be detected because each individual term in the sentence is correctly spelled in isolation.. • Context-dependent word correction (Otero et al., 2007; Reynaert, 2004) , which is able to address the real-word error case and the correction of non-word errors that have more than one potential correction.. The second strategy is to consider a technique based on the use of character ngrams (McNamee and Mayfield, 2004a; Robertson and Willett, 1998) . This technique is applicable to the case of isolated-word error correction and is independent of the extent of linguistic knowledge. In this case n-grams are used as the basis for generating indexes, thereby eliminating the need for dictionaries.. In order to study the validity of these strategies and make the relevant comparisons, a testing framework has been formally designed. To the best of our knowledge, no relevant in-depth work of this kind has been previously documented. This testing framework allows us to study the influence, if any, of whether or not linguistic information is taken into account. We consider three incremental levels: the total exclusion of linguistic information, the use of dictionaries alone and the additional integration of contextual information. This cline is paralleled in the sphere of computational complexity, thus enabling us to also evaluate the real impact of each strategy in terms of its cost. The consideration of Spanish as a case in point will allow us to estimate the validity of these strategies outside standard working frames for English.. The structure of the rest of this article is as follows. Firstly, Section 2 describes the state-of-the-art in this domain. Next, Section 3 deals with the spelling correction techniques to be used in the correction-based strategy. After justifying in Section 4 the use of Spanish because of its challenging nature (from a spelling correction point of view), we introduce in the following sections the experiments we have performed for testing the proposed strategies. First, Section 5 states the research objectives pursued, while Section 6 describes the methodology we have used for designing our experiments. Next, the results obtained in these tests are presented in Section 7 and then discussed in Sections 8 and 9. Finally, Section 10 presents our conclusions and proposals for future work. This work introduces a proposal in the design of robust search on IR systems, intended to be used in a generic, non-specialized, domain of application. Our main goal is to add flexibility to the process, allowing misspelled query execution to continue while avoiding complex implementation, not only from the computational point of view but also from the linguistic one.. For this task two different strategies have been described throughout this work. Firstly, a correction-based strategy has been proposed. This way, the input misspelled query is corrected before being submitted to the IR system, which employs a classical stemming-based approach, i.e. the misspelled words of the query are replaced by their candidate corrections proposed by the correction algorithm. Two different correction techniques have been studied. On the one hand, a global correction algorithm which retrieves the forms closest to the input (misspelled) word is used. However, this implies that in case of a tie, i.e. when two or more equally close correction candidates exist, the input misspelled word is replaced by the whole set of candidates, thus introducing a large amount of noise into the system. On the other hand, a contextual spelling corrector is employed. This algorithm is an extension of the former which makes use of contextual information obtained through part-of-speech tagging, thus providing a solution for ties and returning a single correction.. The second strategy we have proposed consists of using character n-grams instead of classical stems as the processing unit. This allows us to work directly with the misspelled topics without further processing, since the matching process is no longer performed at word-level, but at subword-level, thus increasing robustness since partial matchings between a word and its misspelled form are now allowed.. Moreover, in this work we also introduce two methodologies for the design of experiments in this field by introducing, respectively, artificial errors (easy to generate and to control their variables) and human errors (more realistic) in the input topic set in order to analyze their impact on the performance of the system. These methodologies provide three major contributions. Firstly, their simplicity, both in their use and their understanding. Secondly, the fact that input error rate can be set at will, even in the case of human errors. Finally, the fact that through their application we are able to study the effect of the progressive introduction of misspellings in a homogeneous way, since the misspelled forms which are present for a given error rate continue to be present for a higher rate, thereby avoiding any distortion in the results.. Once performed, our experiments demonstrate that classic stemming-based approaches are highly sensitive to misspelled queries, particularly with short queries, since the information lost when a term no longer matches because of a misspelling may not be recovered from the rest of the topic. Such a negative impact can be appreciably reduced by the use of correction mechanisms during querying. Moreover, our contextual correction approach has been proved to outperform classical global correction in a consistent way, particularly in the case of mid-size queries containing human errors (a not uncommon situation in practical environments). In this case classical global correction has shown to be of little help, while contextual correction proved to be far superior by remarkably reducing the impact of misspellings on performance. This is because of the high level of noise introduced by the global corrector in such a context.. On the other hand, our n-gram based strategy has shown a remarkable robustness, with average performance losses appreciably smaller than those for classical stemming. It must be noted that in the presence of no misspellings classical stemming-based approaches obtain a better performance than n-grams. However, in the case of very short queries such as those of practical systems, n-grams have been able to outperform stemming when misspellings are introduced. In the case of longer queries, n-grams are also able to do this, but only for high error rates. Moreover, since such a subword-based approach does not rely on language-specific processing, it can be used with languages of very different natures, even in the face of the lack of linguistic information and resources available; in contrast, previous correction-based approaches needed languagespecific resources for their application, such as stemmers, stop-word lists, lexicons, tagged corpora, etc.. With regard to future work, in the case of our contextual corrector we plan to extend it for dealing with tokenization errors. In the case of our n-gram based proposal, we intend to extend the concept of stop-word to the case of n-grams in order to both increase the performance of the system and reduce processing and storage resources. Such stop-n-grams should be generated automatically from the input texts (Lo et al., 2005) in order to preserve the language-independent nature of this approach.

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


Seeking Multi-Thresholds Directly From Support Vectors for Image Segmentation Threshold selection is an important topic and also a critical preprocessing step for image analysis, pattern recognition and computer vision. In this letter, a novel automatic image thresholding approach only from the support vectors is proposed. It first fits the 1D histogram of a given image by support vector regression (SVR) to obtain all boundary support vectors and then sifts automatically soneeded (multi-)threshold values directly from the support vectors rather than the optimized extrema of the fitted histogram in which finding the extrema is in general difficult. The proposed approach is not only computationally efficient but also does not require a priori assumptions whatsoever are made about the image (type, features, contents, stochastic model, etc.). Such an algorithm is most useful for applications that are supposed to work with different (and possibly initially unknown) types of images. The experimental results demonstrate that the proposed approach can select the thresholds automatically and effectively, and the resulting images can preserve the main features of the components of the original images very well. In many applications of image processing, abstractions of objects or features, which are used in high level tasks, are derived from images. For the purpose of abstraction, the pixels in an image have to be grouped into meaningful regions by a process called image segmentation.. In many cases, the gray levels of pixels belonging to the object are substantially different from the gray levels of the pixels belonging to the background. Thresholding then becomes a simple but effective tool to separate objects from the background. Its applications include document image analysis, where the goal is to extract printed characters [1, 2] , logos, graphical content, or musical scores; map processing, where lines, legends, and characters are to be found [3] ; scene processing, where a target is to be detected [4] ; and quality inspection of materials [5, 6] , where defective parts must be delineated.. Thresholding in its simplest form involves mapping all pixels above a threshold value to one gray value, say white, and the rest to another, say black. Since the result is an image with two gray vales, the process is called bilevel segmentation. When multiple threshold values are used, the result is a multilevel image, and the process is called multilevel segmentation. Bilevel segmentation is appropriate for some of the "classical" image processing applications such as the automatic image analysis of documents or industrial parts. But for the applications dealing with more complex scenes, automatic multilevel image segmentation methods have to be adopted.. Many automatic thresholding techniques use the histogram of a given image to select a good threshold.. An image histogram is a frequency distribution of its gray levels. If, in an image, the objects have distinctly different gray values from the background, the histogram will exhibit two different peaks with a valley between them. The determination of a suitable threshold value, usually selected at the bottom of the valley between these two peaks, is a relatively simple. However, in many real-world images, this assumption is unrealistic. There have been a number of methods for threshold selection discussed in the literature, including those based on entropy [7] [8] [9] , moment preservation [10] , error minimization [11] and maximum likelihood [12] . One common characteristic of these existing methods is that the histogram is viewed as a mixture density function, and usually the problem of threshold determination is treated as a case of classification. In this paper, we propose a new threshold selection technique different from the existing approaches mentioned above. It first fits the 1D histogram of a given image by support vector regression (SVR) to obtain all boundary support vectors (BSV) and then sifts or selects automatically soneeded (multi-) threshold values directly from the BSVs rather than the extrema of the fitted histogram.. Since there are more than one support vectors, this approach can consequently lead to multilevel thresholding. This paper organizes as follows. In Section 2, the automatic threshold determination approach based on the functional regression of the histogram is described. Experimental results for the proposed approach and comparison with two other approaches are presented in Section 3. We compare the performance of our approach with two other approaches from the literature, namely Belkasim et al's phase-based optimal image thresholding [13] and Chung et al's fast adaptive PNN-based thresholding algorithm 1 [14] . Finally, Section 4 ends the paper with some future work. In this section, two types of experiments are carried out to evaluate the performance of the proposed algorithm. The first experiment is used to evaluate the bi-thresholded images by using our approach. The second one is used to justify the performance of multi-thresholding.

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


On Tests for Global Maximum of the Log-Likelihood Function Abstract-Given the location of a relative maximum of the loglikelihood function, how to assess whether it is the global maximum? This paper investigates an existing statistical tool, which, based on asymptotic analysis, answers this question by posing it as a hypothesis testing problem. A general framework for constructing tests for global maximum is given. The characteristics of the tests are investigated for two cases: correctly specified model and model mismatch. A finite sample approximation to the power is given, which gives a tool for performance prediction and a measure for comparison between tests. The sensitivity of the tests to model mismatch is analyzed in terms of the Renyi divergence and the Kullback-Leibler divergence between the true underlying distribution and the assumed parametric class and tests that are insensitive to small deviations from the model are derived thereby overcoming a fundamental weakness of existing tests. The tests are illustrated for three applications: passive localization or direction finding using an array of sensors, estimating the parameters of a Gaussian mixture model, and estimation of superimposed exponentials in noise-problems that are known to suffer from local maxima.Index Terms-Array processing, Gaussian mixtures, global optimization, local maxima, maximum likelihood (ML), parameter estimation, superimposed exponentials in noise. T HE maximum-likelihood (ML) estimation method is one of the standard tools for parameter estimation. Among its appealing properties are consistency and asymptotic efficiency [1] - [3] . However, a major drawback of this method when applied to nonlinear estimation problems is the fact that the associated likelihood equations required for the derivation of the estimator rarely have a closed-form analytic solution. This shortcoming poses a global optimization problem. Solving this problem by applying numerical methods is usually computationally prohibitive. To date, there have been few global optimization methods applied to ML estimation (e.g., [4]- [8] ) because of the computational complexity involved. More commonly, initiate and converge methods are applied. These methods are based on an initial guess (often found by a simpler method) which is followed by a local, often iterative, optimization procedure (e.g., the expectation maximization algorithm [9] and its variations [10] , Fisher scoring [10] , the Gauss-Newton method [11] , and majorizing or minorizing algorithms [12] , [13] ). As a consequence, the performance of these methods highly depends on the starting point. In particular, if the log-likelihood function is not strictly convex and there is no available method that is guaranteed to provide an initial guess within the attraction region of the global maximum, then there is a risk that a local search will stagnate at a local maximum. This phenomenon leads to large-scale estimation errors. The ML framework would benefit from an answer to the following question: Given a location of a relative maximum of the log-likelihood function, how to assess whether this is the global maximum? One approach to this question is the Kronecker-Picard integral framework [6] . However, the computation of this multidimensional integral is difficult, indeed, equivalent to the complexity involved in finding the global maximum, rendering this approach impractical. Instead, in this paper we take a statistical approach to answering this question.. The first statistical solutions for discriminating between local and global maxima were based on sampling the domain of the log-likelihood function. Given a sequence of random starting points and the corresponding set of relative maxima found by a local search method, Finch et al. [14] proposed a statistical method to assess the probability that the global maximum has not yet been found based on an asymptotic (in the number of starting points) result on the total probability of unobserved outcomes due to Bickel and Yahav [15] . Veall [16] used an order statistic result due to de Haan [17] that characterizes the distribution of the ordered values of a smooth function, sampled at random points. Given a relative maximum, the log-likelihood function is evaluated at a large number of randomly selected points. If a point with a value larger than the value of the candidate maximum is found, then clearly it is not the global maximum. If no such point is found, de Haan's result is used to assess the probability that the relative maximum is the global one. Since these methods are based on sampling the domain of the log-likelihood function, they suffer from the curse of dimensionality and do not generalize well to high-dimensional problems. Yet high-dimensional problems are exactly those in which global optimization methods are computationally demanding.. As an alternative, several authors applied results from asymptotic statistics that, instead of relying on sampling the domain of the log-likelihood function, require a large sample size. Dorsey and Mayer [18] reported poor performance of Veall's method and, as an alternative, proposed to use the available methods for testing parametric models to answer the question at hand. They observed that a local maximum of the log-likelihood function is in fact a global maximum of a particular misspecified model-a model in which the parameters are restricted to a region that does not contain the true parameter. For scenarios in which the model is known to be correctly specified, these authors tested whether a relative maximum is the global one by applying a test that detects model mismatch. If the result of the test leads to the conclusion that a model mismatch is likely, the hypothesis that the relative maximum is the global one is rejected. Otherwise, the relative maximum is declared the final estimate. Independently, Gan and Jiang [19] made the same observation and proposed White's information matrix test [20] as a test for global maximum. More recently, Biernacki [21] , [22] proposed a new test, which is closely related to Cox's tests for separate families of hypotheses [23] , [24] , and showed through simulations that his new test outperforms White's information matrix test.. A drawback of the methods of [18] , [19] , and [22] is that they are sensitive to model mismatch. In particular, when the model is not specified correctly, the tests lose their power to distinguish between local and global maxima. In some engineering applications, the statistical model is derived from the underlying physical phenomenon and deviations from this model are unlikely. In these cases, the methods can be directly applied. However, when there are uncertainties about the model, the methods [18] , [19] , and [22] need to be modified so as to not classify a global maximum of a misspecified model as a local maximum.. In this paper, the asymptotic statistics regime is also adopted, but the tests are derived under possible model mismatch. The sensitivity of the tests to model mismatch is analyzed in terms of the Renyi divergence and the Kullback-Leibler divergence between the true underlying distribution and the assumed parametric class. The analysis leads to a simple threshold correction method that accounts for possible deviations from the model as long as these deviations are bounded in terms of the mentioned divergences. When deviations from the model are defined in terms of an embedding in a larger parametric class, insensitivity to a Pitman drift is established by constructing tests based on a vector valued validation function that is orthogonal to the elements of the gradient of the log-likelihood function of the larger class. This construction leads to tests that are locally robust to deviations from the assumed model.. An exhaustive catalogue of all the available methods for model specification testing that might be considered as candidates for tests for global maximum is beyond the scope of this paper. Rather, this paper focuses on the class of M-tests, which includes the tests of [19] and [22] as special cases, and investigates their performance as tests for global maximum.. The problem of testing a relative maximum is related to the problem of eliminating spurious maxima in scenarios in which the ML estimator (MLE) is not necessarily consistent or may not even exist (see [25] and references therein). Although some of the results apply to that problem as well, we do not pursue this connection here.. The contributions in this paper are as follows. First, an analytical approximation to the power function of the test is given, which gives a tool for performance prediction and a measure for comparison between tests. Second, the effect of model mismatch on the tests' performance is analyzed and two methods for constructing robust tests are given, thereby overcoming a fundamental weakness of existing tests. Finally, the tests' performance is illustrated via three applications that are known to suffer from local maxima.. In Section II, we review the properties of the MLE under a possible model mismatch and pose the problem of discriminating between local and global maxima as a statistical hypothesis testing problem. The general framework for constructing M-tests [26] - [28] is presented, and it is shown that two of the available tests in the literature are special cases of M-tests. In Section III, the consistency of the tests is established and an approximation of the finite sample power of the tests is derived, which is useful for predicting performance and provides a measure for comparing between tests. The problem of model mismatch is treated in Section IV. The effect of model mismatch is characterized in terms of the Renyi divergence and the Kullback-Leibler divergence and two methods for making the tests robust to small deviations from the underlying model are given. Finally, to show the applicability of this framework, in Section V a Monte Carlo evaluation of the performance of the tests is presented in terms of level and power under both correct and mismatched models. While the analysis in the paper is carried under the assumption that the measurements are independent and identically distributed (i.i.d.), in section Section V-C a case in which the measurements are not identically distributed is considered to show the potential application of the results beyond the i.i.d. case.. II. PRELIMINARIES Let be a collection of independent observations drawn from an unknown distribution with density , . The information we want to extract from the data is encoded in a parameter vector , through which we define a parametric family of densities that are twice continuously differentiable in for all . For scalar functions denote by and the column vector of partial derivatives and the Hessian matrix with respect to , respectively. For vector valued functions, let be the matrix whose element is the partial derivative of the th element of the function with respect to the th element of . Assume that the elements of the matrices and are dominated by functions integrable with respect to , for all , a compact subspace of . The parameter space is compact whenever the optimization discussed below is carried out on a computer. In Section IV, we will impose additional assumptions on and . Denote by the normalized log-likelihood function of the measurements, where . The MLE 1 is defined as. Denote by the expectation with respect to the true underlying distribution , and by the minimizer of the Kullback-Leibler divergence, i.e., where is the ambiguity function, defined as (2) and assume that is a well defined unique interior point of .. Define the matrices. assume that and are nonsingular. Under these assumptions, Theorems 2.1, 2.2, and 3.2 of White [20] assert that (4) as , and is asymptotically Gaussian in the sense that. When almost everywhere for some unique , we say that the model is correctly specified and this result becomes the standard consistency, and asymptotic Normality result for the MLE. More specifically, if the elements of the matrix are dominated by functions integrable with respect to , for all , where is the dominating measure such that , and the support of does not depend on , then is the inverse of the Fisher information matrix (FIM) [3, p. 80] .. Denote by one of the relative maxima of the log-likelihood function. Then the problem addressed in this paper can be formulated as a hypothesis testing problem. Given , decide between (6) statistical test which gives a solution to this problem is called a test for global maximum.

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


Large Scale Multikernel Relevance Vector Machine for Object Detection The Relevance Vector Machine(RVM) is a widely accepted Bayesian model commonly used for regression and classification tasks. In this paper we propose a multikernel version of the RVM and present an alternative inference algorithm based on Fourier domain computation to solve this model for large scale problems, e.g. images. We then apply the proposed method to the object detection problem with promising results. The Relevance Vector Machine (RVM). 1 is a Bayesian treatment of the linear model given by:. where. is a set of basis functions. Learning on such a model, is the process of estimating the weights {w i } M i=1 , using a training set {( x n , t n )} N n=1 . The weights are typically assigned those values that maximize the likelihood of the training set, however the training examples must be significantly more than the parameters in order to achieve good generalization performance. The RVM overcomes this limitation by following Bayesian principles and assuming prior knowledge for the model. Specifically, a suitable hierarchical prior distribution is assumed for the weights of the model, which has most probability mass concentrated in sparse solutions, meaning that it forces most of the weights to be assigned to zero values 1 . This results in prunning basis functions that are not sufficiently supported by the training data. There are several reasons to seek sparse solutions:. • Sparseness automatically adjusts the complexity of the model, thus very complex models may be considered.. • The basis functions that remain on the model provide information about which basis functions are relevant with the data. This may be usefull in many applications.. • The output of sparse models is computed very efficiently, since only few basis functions are considered.. In a typical RVM there is one basis function centered at each training example, resulting in the following model:. As in most Bayesian models, inference in RVM is analytically intractable. The most well-known approximations are based on the expectation maximization (EM) algorithm 1 and the variational approximation 2 . Both approaches seem to provide similar results, but the first is generally preferred because it is computationally more efficient. However, time complexity is of order O(N 3 ) and memory complexity of order O(N 2 ), making inference on large training sets extremely difficult. The method based on the EM algorithm can be accelerated by considering incrementally adding basis function to an initially empty model 3 , improving time complexity to order O(M 3 ), where M is the number of the basis functions that are included in the model. Since the model is sparse, M could be only a small fraction of the total number of basis functions N .. In this paper we use the RVM for modeling images. Unfortunately, the standard RVM training algorithms are too computationally demanding, even for small images. We notice that if the training points x i lie on a uniform grid, the RVM model given in Eq. (2) can be rewritten as the convolution of the weight vector w = (. T , which consists of the basis function φ( x) evaluated at the training points x i . The RVM output can then be written as:. where y = (y( x 1 ), . . . , y( x N )) T is the output of the model evaluated at the training points. In section 2 we present in detail the RVM model and propose an alternative implementation of the EM-based algorithm 1 . Our implementation computes convolutions in the DFT domain, improving both time and memory requirements and allows to train RVM models on high resolution images, with reasonable computational costs. In addition we propose a multikernel RVM model, where more than one types of basis functions is allowed to be simultaneously used. The proposed implementation is evaluated in subsection 2.4.. We then use the proposed algorithm to solve the object detection problem, which is the problem of finding the location of an unknown number of occurrences of a given 'target' image in another given 'observed' image, under the presence of noise. The 'target' may appear significantly different in the observed image, as a result of being scaled, rotated, occluded by other objects, different illumination conditions and other effects.. The most common approaches to solve the object detection problem are variants of the matched filter, such as the phase-only 7 and the symmetric phase-only 8 matched filters. These are based on computing the correlation image between the 'observed' and 'target' images and then using a threshold to determine the locations where the 'target' object is present. Alternatively, the problem can be formulated as an image restoration problem, where the image to restore is considered as an impulse function at the location of the 'target' object. This technique allows many interesting background models to be considered, such as autoregressive models 9 . A different object detection approach, which has been succesfully appllied on face detection 10 , is to split the observed image in several regions and train a classifier with some features of the target 'object' in order to decide which regions contain the 'target' object.. In section 3 we propose a method for object detection, which is based on training a multikernel RVM model on the 'observed' image. The RVM model consists of two sets of basis functions: basis functions that are used to model the 'target' image and basis functions that are used to model the background. After training the model each 'target' basis function, whose corresponding weight is larger than a specified threshold, is considered as a detected 'target' object. Examples of the RVM based object detection algorithm and a comparison with the autoregressive impulse restoration 9 method are provided in section 4. We have proposed an approximate but accelerated inference method for training the RVM model on large scale images, based on fast computation of the posterior statistics in the Fourier domain. Experiments on images demonstrate that the proposed approximation allows inference on large scale images, where the typical RVM argorithm is too computationally demanding to run. We then presented an application of the method to the object detection problem. Experimental results indicate that this approach is more robust than existing methods. Furthermore, the proposed technique can be extended to solve the rotation and scaling invariant object detection problem, by optimizing the model with respect to rotation and scaling of the basis functions.

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


An object-oriented parallel programming language for distributed-memory parallel computing platforms In object-oriented programming (OOP) languages, the ability to encapsulate software concerns of the dominant decomposition in objects is the key to reaching high modularity and loss of complexity in large scale designs. However, distributed-memory parallelism tends to break modularity, encapsulation, and the functional independence of objects, since parallel computations cannot be encapsulated in individual objects, which reside in a single address space. For reconciling object-orientation and distributed-memory parallelism, this paper introduces OOPP (Object-Oriented Parallel Programming), a style of OOP where objects are distributed by default. As an extension of C++, a widespread language in HPC, the PObC++ language has been designed and prototyped, incorporating the ideas of OOPP. The better cost-benefit of parallel computing platforms for High Performance Computing (HPC). 1 , due to the success of off-the-shelf distributed-memory parallel computing platforms, such as Clusters [1] and Grids [2] , has motivated the emergence of new classes of applications from computational sciences and engineering. Besides high performance requirements, these applications introduce stronger requirements of modularity, abstraction, safety and productivity for the existing parallel programming tools [3] . Unfortunately, parallel programming is still hard to incorporate into the usual large scale software development platforms that may be developed to deal with such kinds of requirements [4] . Also, automatic parallelization is useful only in restricted contexts, such as in scientific computing libraries [5] . Skeletal programming [6] , a promising alternative for high-level parallel programming, has not achieved the acceptance expected [7] . These days, libraries of message-passing subroutines that conform to the MPI (Message Passing Interface) standard [8] are widely adopted by parallel programmers, offering expressiveness, portability and efficiency across a wide range of parallel computing platforms. However, they still present a low level of abstraction and modularity in dealing with the requirements of the emerging large scale applications in HPC domains.. In the context of corporative applications, object-oriented programming (OOP) has been consolidated as the main programming paradigm to promote development productivity and software quality. Objectorientation is the result of two decades of research in programming tools and techniques motivated by the need to deal with the increasing levels of software complexity since the software crisis context of the 1960's [9] . Many programming languages have been designed to support OOP, such as: C++, Java, C#, SmallTalk, Ruby, Objective-C, and so on. Despite their success in the software industry, object-oriented languages are not popular in HPC, dominated by Fortran and C, as a consequence of the high level of abstraction and modularity offered by these languages. When parallelism comes onto the scene, the situation is worse, due to. • Object-Orientation (OO), intended for large-scale applications, which have stronger productivity requirements for development and maintenance, generally found in corporative domains.. The following sections review concepts of the two above programming techniques that are important in the context of this work, also providing a discussion about the strategies that have been applied for their integration (related works). PObC++ is an open source project hosted at http://pobcpp.googlecode.com, released under the BSD license. It is composed of a compiler and a standard library.

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


Multimodal augmented reality tangible gaming Abstract This paper presents tangible augmented reality gaming environment that can be used to enhance entertainment using a multimodal tracking interface. Players can interact using different combinations between a pinch glove, a Wiimote, a six-degrees-of-freedom tracker, through tangible ways as well as through I/O controls. Two tabletop augmented reality games have been designed and implemented including a racing game and a pile game. The goal of the augmented reality racing game is to start the car and move around the track without colliding with either the wall or the objects that exist in the gaming arena. Initial evaluation results showed that multimodal-based interaction games can be beneficial in gaming. Based on these results, an augmented reality pile game was implemented with goal of completing a circuit of pipes (from a starting point to an end point on a grid). Initial evaluation showed that tangible interaction is preferred to keyboard interaction and that tangible games are much more enjoyable. Computerized games which have learning or training purposes demonstrate a popular trend in training due to the wide availability and ease of use of virtual worlds. The use of serious games in virtual worlds not only opens up the possibility of defining learning game-based scenarios but also of enabling collaborative or mediated learning activities that could lead to better learning [1] . An added benefit of using serious games in combination with virtual worlds is that learners engage with these in a multimodal fashion (i.e. using different senses) helping learners to fully immerse in a learning situation [2] which might lead to learning gains [3] . The multimodal nature of virtual worlds [4] and the facilities they offer to share resources, spaces and ideas greatly support the development and employment of serious games and virtual worlds for learning and training. The use of games as learning devices is not new. The popularity of video games among younger people led to the idea of using them with educational purposes [5] . As a result, there has been a tendency to develop more complex serious games which are informed by both pedagogical and game-like, fun elements. One common example of these combinations is the use of agents [6] : The idea behind agents is to provide pedagogical support [7] while providing motivating environments in the form of agents [8] . However, the use of agents is not the only motivating element in serious games as the use metaphors [9] and narratives [10] have been used to support learning and training in game-like scenarios.. Tangible games can sometimes have an educational aspect. The whole idea of playability in tangible games is the player's interaction with the physical reality. In addition, the accessibility space that is the key to the oscillation between embedded and tangible information [11] . On the contrary, augmented reality (AR) has existed for quite a few years and numerous prototypes have been proposed mainly from universities and research institutes. AR refers to the seamless integration of virtual information with the real environment in real-time performance. AR interfaces have the potential of enhancing ubiquitous environments by allowing necessary information to be visualized in a number of different ways, depending on the user needs. However, only a few gaming applications combined them together to offer a very enjoyable and easy to use interface. This paper presents tangible augmented reality gaming environment that can be used to enhance entertainment using a multimodal tracking interface. The main objective of the research is to design and implement generic tangible augmented reality interfaces that are user-friendly in terms of interaction and can be used by a wide range of players including the elderly or people with disabilities. Players can interact using different combinations between a pinch glove, a Wiimote, a six-degrees-of-freedom tracker, through tangible ways as well as through I/O controls. Two tabletop augmented reality games have been designed and implemented including a racing game and a pile game. The goal of the augmented reality racing game is to start the car and move around the track without colliding with either the wall or the objects that exist in the gaming arena. Initial evaluation results showed that multimodal-based interaction games can be beneficial in gaming. Based on these results, an augmented reality pile game was implemented with goal of completing a circuit of pipes (from a starting point to an end point on a grid). Initial evaluation showed that tangible interaction is preferred to keyboard interaction and that tangible games are much more enjoyable. Tangible AR gaming has the potential to change a number of applications that we perform in our day-to-day activities. This paper has presented a generic tangible augmented reality gaming environment that can be used to enhance entertainment using a multimodal tracking interface. The main objective of the research is to design and implement generic tangible interfaces that are user-friendly in terms of interaction and can be used by a wide range of players, including the elderly or people with disabilities. Players can interact using different combinations between a pinch glove, a Wiimote, a six-degrees-of-freedom tracker, through tangible ways as well as through I/O controls. Two tabletop augmented reality games have been designed and implemented, including a racing game and a pile game. The goal of the augmented reality racing game is to start the car and move around the track without colliding with either the wall or the objects that exist in the gaming arena. Initial evaluation results showed that multimodal-based interaction games can be beneficial in gaming. Based on these results, an augmented reality pile game was implemented with goal of completing a circuit of pipes (from a starting point to an end point on a grid). Initial evaluation showed that tangible interaction is preferred to keyboard interaction and that tangible games are much more enjoyable. From the research proposed many potential gaming applications could be produced such as strategy, puzzles and action games.. Future development will include more work on the graphical user interface to make it more user-friendly, and speech recognition is considered as an alternative option to enhance the usability of interactions. A potentially better solution that will be tested for the glove in the future on this system is to use a model for the hand that has separate sections for each finger, the position of which would be determined by the current readings on each of the finger sensors on the glove. This model could then use an alpha color value of 1.0, meaning that it is entirely transparent in the scene. As a result the model would become an alpha mask for the live video of the user's hand; the real-world hand would then appear to be above any virtual objects that the depth testing determined were further away from the camera. Finally, a formal evaluation with 30 users is currently under way and results will be used to refine the architecture. In the past, a number of AR games have been designed in different areas including education, learning, enhanced entertainment and training [12] . A good survey of tracking sensors used in ubiquitous AR environments [13] , as well a taxonomy of mobile and ubiquitous applications, was previously documented [14] . This section presents an overview of the most characteristic applications and prototypes that integrate tracking sensors into AR tabletop and gaming environments. One of the earliest examples of educational AR was the MagicBook [15] . This is a real book which shows how AR can be used in schools for educational purposes and is an interesting method of teaching. MagicBook was also used as a template for a number of serious applications in numerous AR games.. One of the earliest pervasive AR prototypes is NaviCam [16] , which has the ability to recognize the user's situation by detecting color-code IDs in real-world environments by displaying situation-sensitive information by superimposing messages on its video see-through screen. Another early important work refers to the Remembrance Agent [17] , a textbased AR wearable system which allows users to explore over a long period of time augmented representations and provide better ways of managing such information. EMMIE [18] is a hybrid user interface to a collaborative augmented environment which combines a variety of different technologies and techniques, including virtual elements such as 3D widgets, and physical objects such as tracked displays and input devices. Users share a 3D virtual space and manipulate virtual objects that can be moved among displays (including across dimensionalities) through drag-and-drop. A more recent prototype is DWARF [19] which includes user interface concepts, such as multimedia, multimodal, wearable, ubiquitous, tangible, or augmented reality-based interfaces. DWARF covers different approaches that are all needed to support complex human-computer interactions. Higher level functionality can be achieved allowing users to manage any complex, interrelated processes, using a number of physical objects in their surroundings. The framework can be used for single-user as well as multi-user applications. In another prototype, the combination of AR and ubiquitous computing can lead to more complex requirements for geometric models that are appearing [20] . For such models a number of new requirements appear concerning cost, ease of reuse, inter-operability between providers of data, and finally use in the individual application.. In terms of enhanced entertainment, outdoor AR gaming plays a significant role. A characteristic example is the Human Pacman project [21] that is built upon position and perspective sensing via GPS, inertia sensors and tangible human-computer interfacing with the use of Bluetooth and capacitive sensors. The game brings the computer gaming experience to a new level of emotional and sensory gratification by embedding the natural physical world ubiquitously and seamlessly with a fantasy virtual playground. AR Tennis [22] is the first example of a face-to-face collaborative AR application developed for mobile phones. Two players sit across the table from each other, while computer vision techniques are used to track the phone position relative to the tracking markers. When the player points the phone camera at the markers, they see a virtual tennis court overlaid on live video of the real world.. Another interesting project is STARS [23] which focused on the nature of state representation in augmented game designs and developed several games based on these principles. Moreover, Mixed Fantasy [24] presents a MR experience that applies basic research to the media industries of entertainment, training and informal education. As far as training is concerned, the US Army paid more than $5 million to design an educational game based on the Xbox platform to train troops in urban combat [25] . Another example is the MR OUT project [26] which uses extreme and complex layered representation of combat reality, using all the simulation domains such as live, virtual, and constructive by applying advanced video see-through mixed reality (MR) technologies. MR OUT is installed at the US Army's Research Development and Engineering Command and focuses on a layered representation of combat reality.

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


On a parallel multilevel preconditioned Maxwell eigensolver We report on a parallel implementation of the Jacobi-Davidson algorithm to compute a few eigenvalues and corresponding eigenvectors of a large real symmetric generalized matrix eigenvalue problemThe eigenvalue problem stems from the design of cavities of particle accelerators. It is obtained by the finite element discretization of the time-harmonic Maxwell equation in weak form by a combination of Nédélec (edge) and Lagrange (node) elements.We found the Jacobi-Davidson (JD) method to be a very effective solver provided that a good preconditioner is available for the correction equations that have to be solved in each step of the JD iteration. The preconditioner of our choice is a combination of a hierarchical basis preconditioner and the ML smoothed aggregation AMG preconditioner. It is close to optimal regarding iteration count.The parallel code makes extensive use of the Trilinos software framework. In our examples from accelerator physics we observe satisfactory speedups and efficiencies. Many applications in electromagnetics require the computation of some of the eigenpairs of the curl-curl operator, curl µ −1 r curl e(x) − k 2 0 ε r e(x) = 0, div e(x) = 0, x ∈ Ω, (1.1). in a bounded simply-connected, three-dimensional domain Ω with homogeneous boundary conditions e × n = 0 posed on the connected boundary ∂Ω. ε r and µ r are the relative permittivity and permeability. Equations (1.1) are obtained from the Maxwell equations after separation of the time and space variables and after elimination of the magnetic field intensity. While ε r and µ r are complex numbers in problems from waveguide or laser design [8] , in simulations of accelerator cavities the materials can be assumed to be loss-free, thus admitting real ε r and µ r , whence all eigenvalues are real. Here, we will assume ε r = µ r = 1. Thus, the discretization of (1.1) by finite elements leads to a real symmetric generalized matrix eigenvalue problem. where A is positive semidefinite and M is positive definite. In order to avoid spurious modes we approximate the electric field e by Nédélec (or edge) elements [20] . The Lagrange multiplier (a function) introduced to treat properly the divergence free condition is approximated by Lagrange (or nodal) finite elements [3] .. In this paper we consider a parallel eigensolver for computing a few of the smallest eigenvalues and corresponding eigenvectors of (1.2) as efficiently as possible with regard to execution time and memory cost. In earlier studies [3] we found the Jacobi-Davidson algorithm [21, 12] a very effective solver for this task. We have parallelized this solver in the framework of the Trilinos parallel solver environment [13] .. In section 2 we review the symmetric Jacobi-Davidson eigensolver and the preconditioner that is needed for its efficient application. In section 3 we discuss data distribution and issues involving the use of Trilinos.. In section 4 we report on experiments that we conducted by means of problems originating in the design of the RF cavity of the 590 MeV ring cyclotron installed at the Paul Scherrer Institute (PSI) in Villigen, Switzerland. These experiments indicate that the implemented solution procedure is almost optimal in that the number of iteration steps until convergence only slightly depends on the problem size. In conclusion, the parallel algorithm shows a very satisfactory behavior. The efficiency of the parallelized code does not get below 65 percent for 16 processors. We usually have a big efficiency loss initially. Then efficiency decreases slowly as the number of processors increases. This is natural due to the growing communication-to-computation ratio.. The accuracy of the results are satisfactory. The computed eigenvectors were M -orthogonal and orthogonal to C to machine precision. The 2-norm of the residuals of the computed eigenpairs were below 10 −9 .. Our next goals in this project are the reduction of the memory costs and the overhead of the redistribution of our matrices. The memory costs are still so high that we are not capable to solve the very large problems that really interest the engineers. The reason for this lies not primarily in the size of these problems, but in a lack of memory scalability of the code. The cost of the redistribution may be reduced by working with a smaller than our artificial graph G. We may, e.g., just determine a good parallel distribution for the vertices and then adjust the edges and faces.

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


Distances based on neighbourhood sequences in non-standard three-dimensional grids Properties for distances based on neighbourhood sequences on the face-centred cubic (fcc) and the body-centred cubic (bcc) grids are presented. Formulas to both compute the distances and assure that the distances satisfy the conditions for being metrics are presented and proved to be correct. The formulas are used to calculate the neighbourhood sequences that generates distances with lowest deviation from the Euclidean distance. When acquiring three-dimensional images using projections with techniques such as X-ray CT scans, magnetic resonance imaging (MRI), and positron emission tomography (PET), the image is obtained by two-dimensional projections of a three-dimensional object. Traditionally, the intensity values are computed for grid points in the cubic grid. There are, however, reasons for considering other grids such as the face-centred cubic (fcc) and body-centred cubic (bcc) grids. First of all, there are many similarities with the cubic grid; all three grids are lattices and have integer grid point coordinates. Also, it is very easy to construct efficient data-structures for the fcc and bcc grids. One important difference is that less samples are needed on the fcc and bcc grids to obtain the same image representation/reconstruction quality compared to the cubic grid [16, 10] . An image processing package for electron microscopy with support for the fcc and bcc grids has recently been developed [26] . The literature is, however, still lacking in image analysis and image processing algorithms developed for the fcc and bcc grids.. There are several reasons for using the fcc and bcc grids. For example, since these grids are reciprocal and both have higher packing density than the cubic grid (the fcc grid is a densest packing lattice in 3D), less samples can be used without affecting the image representation/reconstruction quality [16] . The high number of neighbours at approximately the same distance on these grids (12 neighbours at distance √ 2 for the fcc grid and 14 neighbours at distance √ 3 and 2 for the bcc grid) implies that the rotational dependency for these grids is lower than for the cubic grid. In [17] , this difference is quantified using surface area estimates and it is shown that the fcc and bcc grids produce more accurate surface area estimates for random planes than the cubic grid.. Each grid is equipped with some neighbourhood relations. For example, the usual two-dimensional square grid is equipped with the 4-and 8-neighbourhoods. A more flexible distance is obtained by alternating these neighbourhoods using a sequence of neighbourhood relations, a neighbourhood sequence. Distances based on neighbourhood sequences approximate the Euclidean distance better. This was first noted in [25] ; the authors state that the approximation obtained when the ratio between the number of steps using the different neighbourhood relations in Z 2 is equal to 1 : √ 2 is optimal. The literature on distances based on neighbourhood sequences is rich; a theory for periodic neighbourhood sequences not connected to any specific neighbourhood relations in Z n is presented in [29, 30] and further developed for the natural neighbourhood structure, by the so-called octagonal neighbourhood sequences in [7, 6] . Results for general (not necessarily periodic) neighbourhood sequences are presented in [9, 21] .. There is another very common way of modifying the city block and chessboard distances in order to obtain a less rotational dependent distance, the weighted distances, [1] . With these distances, each local step is given a weight, which is considered when computing the distance, i.e., when finding the shortest path. The calculation of optimal local weights have been the subject of many papers, see for example [1, 28] . For optimal weights on the fcc and bcc grids, see [27] . Note that the computation of the Euclidean distance as in e.g. [3] is not included here, since we consider only rational values in the discrete spaces in this paper.. Many approaches where the deviation from the Euclidean distance is minimized in order to find the optimal neighbourhood sequence have been proposed for Z 2 and Z 3 . Several error functions minimizing the asymptotic maximum difference of two balls of equal radius using a distance based on periodic neighbourhood sequences and a Euclidean sphere, respectively, is presented in [5, 8, 30] (Z 2 ), [18] (Z 3 ). An investigation of optimal non-periodic neighbourhood sequences in Z 2 with optimal sequences also for finite distances is found in [12] . In [4] , an optimization for Z 3 is carried out using a geometric approach. All the above approaches are based on the difference between a Euclidean ball and a ball generated by distances based on neighbourhood sequences of the same radius. Such error functions are natural to use in Z n , because a ball generated by a distance obtained by only considering first-order/nth order neighbours will always be an underestimation/overestimation of the Euclidean ball of the same radius. Using non-standard grids as in this paper, there is in general no order of neighbours generating a distance that is an overestimation of the Euclidean one. Instead, an error function that is independent of the radius of the Euclidean ball is used in the optimization. It should be mentioned that such error function has been applied on Z 3 in [11] . Distances based on neighbourhood sequences have been applied, e.g., for shading of three-dimensional objects [19] using a medial axis representation for distances based on neighbourhood sequences [15] . Also, distances based on neighbourhood sequences have been used for indexing and segmenting colour images [13] .. In this paper, the theory of distances based on neighbourhood sequences is developed for the fcc and bcc grids. Formulas for computing the distance generated by given neighbourhood sequences are presented and proved to be correct in Section 3. Note the difference between such formulas, which are very important for theoretical considerations, and the more application-oriented chamfer algorithm presented for weighted distances in e.g. [1, 27] and for distances based on neighbourhood sequences in [3, 4] . In applications, it is often desirable that the resulting distances are metrics. Necessary and sufficient conditions for a distance generated by a neighbourhood sequence to be a metric are presented in Section 4. Also, a computationally efficient formula for deciding whether a neighbourhood sequence generates a metric or not is presented. Using these results, neighbourhood sequences generating distances with minimal deviation from the Euclidean distance is presented in Section 5. Several important contributions concerning distances based on neighbourhood sequences on the fcc and bcc grids have been presented. Since there are only two direct neighbours to each grid point in these grids, the theory becomes somewhat easier to handle compared to the cubic grid. For example, the condition for a distance being a metric presented in Theorem 11 is less complicated than in the cubic grid.. Furthermore formulas for computing the distances have been presented. These formulas have been used to define a compactness measure which then was used to calculate the theoretical optimal ratio between the number of 2-steps and 1-steps in a neighbourhood sequence. The compactness measure has also been used to evaluate which periodic neighbourhood sequences give the best results. Since the performance of the periodic neighbourhood sequences approaches the optimal limit resonably fast, a periodic neighbourhood sequence of length five seems to be a good choice if it is preferable to have a short neighbourhood sequence.

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


Theoretical

justification

of

the

central

area

indices

and

the

central

interval

indices

Abstract

The

central

area

indices

and

the

central

interval

indices,

as

introduced

in

DortaGonzález

and

Dorta-González

(Scientometrics

[729][730][731][732][733][734][735][736][737][738][739][740][741][742][743][744][745]

are

studied

from

a

theoretical

point

of

view.

They

are

defined

in

order

to

yield

higher

impact

values

of

''selective''

authors

(i.e.,

authors

with

concentrated

number

of

citations

over

their

publications).

We

show

that

this

property

is

not

valid

for

every

citation

distribution.

However,

if

Zipf's

law

is

adopted

for

the

citation

distribution,

we

can

show

that

the

central

area

indices

and

the

central

interval

indices

have

indeed

higher

values

for

more

selective

authors.

The

Hirsch

index

(or

h-index)

was

introduced

in

Hirsch

to

measure

the

impact

of

a

researcher's

papers

by

means

of

their

received

citations.

If

we

rank

the

papers

of

this

researcher

in

decreasing

order

of

their

received

citations

then

this

researcher

has

h-index

h

if

r

h

is

the

highest

rank

such

that

all

the

papers

on

ranks

h

have

at

least

h

citations.

This

index

was

then

later

applied

to

other

units

such

as

journals,

institutes,

topics,

For

this

see

the

review

paper

Egghe

and

the

many

references

therein..

Also

in

Egghe

(and

references)

the

advantages

and

disadvantages

of

the

h-index

are

described.

One

disadvantage

is

that,

once

a

paper

is

in

the

h-core

(i.e.,

once

a

paper

belongs

to

the

first

h

papers

defining

the

h-index),

it

does

not

matter

anymore

how

many

citations

this

paper

has

received

(as

long

as

it

is

h

or

more).

This

has

led

researchers

to

define

alternatives

for

the

h-index

that

take

more

into

account

the

actual

number

of

citations

to

the

most

cited

papers

(e.g.,

the

g-index

(Egghe

and

the

R-index

(Jin

et

al.

Another

approach

is

to

define

areas

under

the

citation

curve

(e.g.,

of

a

researcher)

so

that,

for

papers

within

this

area,

all

citations

to

these

papers

are

counted.

This

is

the

approach

followed

in

Dorta-González

and

Dorta-González

Their

exact

definitions

are

as

follows.

Order

the

papers

(e.g.,

of

a

researcher)

in

decreasing

order

of

the

number

of

received

citations.

Denote

by

g(r)

the

number

of

citations

to

the

paper

on

rank

r

and

let

h

be

the

h-index

of

this

researcher.

Then

the

''Central

Interval

Index''

(CII)

of

radius

j

h

is

defined

as.

The

''Central

Area

Index''

(CAI)

of

radius

j

is

defined

as.

also

for

j

h

They

are

depicted

in

Figs.

and

for

a

convexly

decreasing

citation

function

g(r),

in

a

continuous

format..

If

we

let

j

…h

in

the

discrete

setting)

increase,

we

include

more

papers

and

more

citations

to

these

papers

than

in

the

calculation

of

the

h-index.

It

is

claimed

in

DortaGonzález

and

Dorta-González

that,

when

comparing

two

researchers

with

the

same

h-index,

the

more

selective

researcher

will

receive

the

larger

I

j

and

A

j

values.

What

does

this

mean?.

First

of

all,

since

they

have

the

same

h-index,

their

citation

curves,

g

(r)

and

g

(r)

intersect

in

the

point

(h,h)

(by

definition

of

the

h-index)-see

Fig.

As

a

consequence

of

this

we

have

that

one

citation

curve

(say

g

(r))

is

above

the

other

one

(say

g

(r))

for

abscissae

smaller

than

h

while

g

(r)

is

below

g

(r)

for

abscissae

larger

than

h.

What

consequences

does

this

have

on

the

calculation

of

the

I

j

and

A

j

indices

for

these

two

researchers?

Denote

by

I

j.

and

I

j

the

''Central

Interval

Indices''

(CII)

of

researcher

and

researcher

respectively

and

similarly

we

denote

by

A

j.

and

A

j

the

Fig.

The

area

under

the

curve

g(r)

for

abscissae

between

h

-j

and

h

j

is

the

''Central

Interval

index''

I

j

of

radius

j

''Central

Area

Indices''

(CAI)

of

researcher

and

researcher

respectively.

Define

(see

Fig.

A

to

be

the

area

between

the

two

citation

curves

g

(r)

and

g

(r)

for

abscissae

r

between

h

and

h

j

(j

h

fixed).

Similarly

define

B

to

be

the

area

between

the

two

citation

curves

g

(r)

and

g

(r)

for

abscissae

r

between

h

-j

and

h.

Finally

define

C

to

be

the

area

of

the

rectangle

where

the

coordinates

are

(x,

y)

where

x

B

h

-j

and

g

(h

-j)

B

y

B

g

(h

-j).

Since

g

(r)

is

above

g

(r)

for

abscissae

smaller

than

h

and

since

g

(r)

is

below

g

(r)

for

abscissae

larger

than

h

we

have

the

following

relations

between

I

j.

and

I

j

and

between

A

j.

and

A

j

Due

to

the

fact

that

one

subtracts

the

value

A

it

is

not

always

so

that

I

j

I

j

and

although

this

is

implicitly

assumed

in

Dorta-González

and

Dorta-González

(see

their

Fig.

p.

and

experimentally

verified

(in

a

heuristic

way).

This

was

exactly

the

reason

for

the

introduction

of

the

indices

I

j

and

A

j

complementing

the

h-index

so

that

higher

impact

is

given

to

more

''selective''

cases,

i.e.,

where

the

citations

are

more

concentrated

in

the

highly

cited

papers.

A

counterexample,

however,

for

is

given

by,

given

a

situation

as

in

Fig.

leaving

g

(r)

and

g

(r)

for

r

h

and

by

moving

g

(r)

close

to

g

(r)

for

r

h.

In

this

way

the

areas

B

and

C

can

be

made

as

small

as

needed

while

letting

the

area

A

constant

so

that

and

Note,

however,

that,

in

the

definition

of

Dorta-González

and

Dorta-González

researcher

is

more

''selective''

than

researcher

since

the

citations

to

papers

of

researcher

are

more

concentrated

in

highly

cited

papers

than

is

the

case

with

researcher

(since

the

citation

curve

g

(r)

is

above

g

(r)

for

r

h

and

g

(r)

is

below

g

(r)

for

r

h)..

By

the

above

counterexample,

the

CIIs

I

j

and

the

CAIs

A

j

do

not

give

higher

impact

values

to

the

more

''selective''

researchers.

In

terms

of

concentration

theory

(see

e.g.,

Egghe

Chapter

III),

the

situation

in

Fig.

yields

a

more

concentrated

situation

for

researcher

in

comparison

with

researcher

citations

are

more

unequally

distributed

for

researcher

in

comparison

with

researcher

This

would

mean

that,

if

we

were

constructing

the

Lorenz

curves

of

these

two

researchers,

the

one

of

researcher

would

be

strictly

above

the

Lorenz

curve

of

researcher

(see

Egghe

Chapter

III)..

Does

this

mean

that

the

indices

I

j

and

A

j

are

bad

impact

measures?

Not

necessarily:

if

we

can

prove

that

the

I

j

s

and

A

j

s

increase

for

more

selective

cases

(e.g.,

g

(r)

is

more

selective

than

g

(r)

in

Fig.

using

citation

curves

that

occur

in

practice

in

informetrics,

then

we

have

proved

that

the

indices

I

j

and

A

j

are

good

impact

measures.

The

most

classical

informetrics

theory

is

Lotkaian

informetrics

(see

Egghe

Chapters

I,

II).

In

this

case

we

assume

that

the

size-frequency

curve

f(j)

is

the

law

of

Lotka

(Lotka

a

decreasing

power

law:

denote

by

f(k)

the

number

of

papers

(of

a

researcher)

with

k

citations,

then.

where

C

and

a

are

parameters

and

k

C

is

the

variable.

This

size-frequency

function

f(k)

is

equivalent

with

the

rank-frequency

function

g(r)

(as

used

above:

the

citation

curve,

i.e.,

the

number

of

citations

to

the

paper

on

rank

r)

by

the

following

wellknown

proposition.

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