Genome data classification based on fuzzy matching Abstract Genomic data mining and knowledge extraction is an important problem in bioinformatics. Some research work has been done on unknown genome identification and is based on exact pattern matching of n-grams. In most of the real world biological problems exact matching may not give desired results and the problem in using n-grams is exponential explosion. In this paper we propose a method for genome data classification based on approximate matching. The algorithm works by selecting random samples from the genome database. Tolerance is allowed by generating candidates of varied length to query from these sample sequences. The Levenshtein distance is then checked for each candidate and whether they are k-fuzzily equal. The total number of fuzzy matches for each sequence is then calculated. This is then classified using the data mining techniques namely, naive Bayes, support vector machine, back propagation and also by nearest neighbor. Experiment results are provided for different tolerance levels and they show that accuracy increases as tolerance does. We also show the effect of sampling size on the classification accuracy and it was observed that classification accuracy increases with sampling size. Genome data of two species namely Yeast and E. coli are used to verify proposed method. Bioinformatics [1] [2] [3] , has emerged as a forefront research area in the recent past since biological data is accumulating at an accelerated rate. In particular, the number and sizes of genome databases have grown rapidly over the last few years. One of the most important problems is automatically determining the group to which a previously unseen genome sequence belongs [4] .. Classifying organisms from its genomic database into groups within a taxonomical hierarchy has several applications which include specific identification of any unknown organism, study of evolutionary characteristics, and study of mutual relationship existing between organisms [5] . Currently more than a million organisms have been discovered, but a large number are yet to be discovered. Any systematic study on an organism can be done only when it is identified to be in a particular group. Thus genome identification finds wide application in evolutionary studies of organisms. Classification and species identification have also been associated with practical applications such as bio-diversity studies [6] , forensic investigations [7] and food and meat authentication [8] , to name a few.. Pattern matching can be considered as either exact matching or approximate matching for sequential data [9] . In exact sequence pattern matching problems, we aim to find a substring in text T that is exactly the same as the searching pattern P. In real world biological applications, most of the sequences are ''similar'' instead of exactly the same. Most fundamental operations like repeat pattern mining, similarity between two sequences, sequence alignment, etc., can be modeled as searching for given ''patterns'' in a ''text.'' However, exact searching is of little use for this application, since the patterns rarely match the text exactly. Thus searching in sequence repositories often requires going beyond exact matching to determine the sequences which are similar [10, 11] . This gave a motivation to ''search allowing errors'' or approximate match. Approximate matching/fuzzy matching is the finding of the most similar match of a particular pattern within a sequence.. The existing approaches extract dinucleotide composition or trinucleotide composition from the sequences using exact pattern matching method and are used as features for classifier. In most of the real world biological problems exact matching may not give desired results because sequences are similar and the patterns rarely match the sequences. The problem which can appear in using n-grams is exponential explosion. It is clear that many of algorithms with n-grams are computationally too expensive [4] .. In this paper identification of organism from its genomic database is considered. In the present work, we propose an approach for genome identification based on approximate pattern matching. Since genome data is very huge, we sample the data into different sizes. Given a database of randomly selected samples of genomic sequences, our proposed work includes two algorithms viz. algorithm for finding fuzzy occurrences based on Levenshtein distance and algorithm for finding total number of fuzzy matching patterns by varying candidate length so as to allow both positive and negative tolerance from the genome data sequences. These fuzzy matching patterns are used as features for a classifier. Since, candidate length is varied so as to allow both positive and negative tolerance, the length of subsequences and number of subsequences that are used as feature for classifier also changes. Classification has been done using data mining techniques namely, Naïve Bayes, support vector machine, backpropagation and also by nearest neighbor. Experimental results are reported for 100 randomly selected samples (size varying from 2,000 to 10,000 bp) from each of complete genome data of Yeast and E. coli. To extract fuzzy matching patterns from genome sequences, we used query of length 10 and allowed tolerance from 10 to 70 %. The proposed model is tested separately for fuzzy matching patterns extracted with each of the fault tolerance and the classification accuracies are monitored. The experimental results vary according to the tolerance allowed as well as according to sampling/ sequence size.. The article is arranged as follows. In Sect. 2 we give some background information. Related work is explained in Sect. 3. In Sect. 4, proposed approach is explained. The experimental results obtained by using genome data of two species namely Yeast and E. coli are explained in Sect. 5 . Conclusion section summarizes the results. Genomic data mining and knowledge extraction is an important problem in bioinformatics. Only a few attempts are seen in literature focusing on unknown genome identification by using either dinucleotide or trinucleotide composition. Existing approaches are based on exact pattern matching. In most of the real world biological problems exact matching may not give desired results because, biological sequences are ''similar'' instead of exactly same. In this paper, a novel approach for identification of species based on fuzzy patterns is proposed. Genome data of two species namely, Yeast and E. coli is sampled into different sizes and then fuzzy patterns with given tolerance are extracted by using Levenshtein distance. Candidate length is varied so as to allow both positive and negative tolerance. Fuzzy matches/approximate matches for these candidates/subsequences are used as feature values for the classifiers. Classification has been done by using data mining techniques namely, Naïve Bayes and support vector machine, backpropagation and nearest neighbor. To extract fuzzy matching patterns from genome sequences, we used query of length 10 and allowed tolerance from 10 to 70 %. The proposed model is tested separately for fuzzy matching patterns extracted with each of the fault tolerance and the classification accuracies are monitored. The experimental results vary according to the tolerance allowed as well as according to sampling/sequence size. Total 200 samples are used to test the model (100 samples are from E. coli and 100 samples are from Yeast). Our experimental results show that, the classification accuracy achieved is 98.5 % by BP, 96.5 % by other classifiers, i.e., by NB, SVM and KNN for sampling/ sequence size of 10,000 bp and with allowed tolerance of 50 % and at 70 % all classifiers achieved 99 % accuracy. It can be observed from the obtained results that classification accuracy increases with increase in tolerance and sampling size. We used a query of length 10 in our experiment, in future experimental results are to be verified with different query length and a relationship between query length and tolerance values is to be established. Patil et al. [14] proposed a method for species identification based on approximate pattern matching. The novelty in the work was feature extraction technique for genome data. The existing n-gram based methods extract frequencies of 4 n features from genome data. In [14] authors extracted all candidate/subsequences that satisfy: length grater or equal to given minimum length, given number of mismatches and support grater or equal to user threshold. These frequent subsequences are used as features to construct a binary table where the presence or absence of an attribute/feature in a sequence is represented by 1 or 0 respectively. Classification of genome sequences has been done using data mining techniques namely, naive Bayes, support vector machine and k-nearest neighbor. Based on experimentation, data mining techniques with approximate patterns showed better results. In this work very short sequences were analyzed and all the frequent subsequences represented in binary form are used as features for classifier.. In [16] , a set of 16 kinds of dinucleotide compositions was used to analyze the protein-encoding nucleotide sequences in nine complete genomes: Escherichia coli, Haemophilus influenzae, Helicobacter pylori, Mycoplasma genitalium, Mycoplasma pneumoniae, Synechocystis sp., Methanococcus jannaschii, Archaeoglobus fulgidus, and Saccharomyces cerevisiae. The dinucleotide composition was significantly different between the organisms. The distribution of genes from an organism was clustered around its center in the dinucleotide composition space. The genes from closely related organisms such as Gramnegative bacteria, mycoplasma species and eukaryotes showed some overlap in the space. The genes from nine complete genomes together with those from humans were discriminated into respective clusters with 80 % accuracy using the dinucleotide composition alone. Classification of organisms into 2 classes-Bacteria and Archea, based on their di-nucleotide frequencies in DNA sequence using naive Bayesian approach was discussed by [23] . The methodology is based on scanning all genomes for the occurrences of all possible overlapping motifs with a length of n nucleotides. Then a genomic sequence is chosen at random from anywhere inside a genome. From this genomic sequence, all overlapping motifs are extracted. The naive Bayesian classifier uses the extracted motifs to predict their most probable genomic origin by comparing the frequencies of the extracted motifs with the motif frequencies of the different genomes. The average accuracy obtained was 85 %.. Protein classification into domains of life was attempted and the test protein was predicted to be of bacterial or eukaryotic origin with 85 % accuracy using a Markov model for compositional bias analysis [24] .. Norashikin et al. [25] , used 2-g encoding, which is the frequency of occurrence of two consecutive amino acids from a protein sequence to investigate the effect of the spread factor value towards cluster separation in the growing self-organizing map GSOM. They used simple k-means algorithm as a method to identify clusters in the GSOM. By using Davies-Bouldin index, clusters formed by different values of spread factor were obtained and the resulting clusters of protein sequences were analyzed.. Andrija et al. [4] have addressed the problem of automated classification of isolates, i.e., the problem of determining the family of genomes to which a given genome belongs and also the problem of automated unsupervised hierarchical clustering of isolates, according only to their statistical substring properties. For both of these problems, they presented novel algorithms based on nucleotide ngrams, with no required preprocessing steps such as sequence alignment.. In [26] an approach for genome data clustering based on approximate matching is proposed. The proposed work includes finding total number of approximate matches to a query with specified fault tolerance from the genome data sequences. The number of matches is used as a feature value for clustering. Clustering has been done using soft computing technique namely, Fuzzy C-means (FCM), Possibilistic C-means (PCM) and results are compared to hard clustering technique, i.e., K-means. Experimental results are reported for 100 randomly selected samples (size 10,000 bp) from two different complete genome data sets namely, Yeast, E. coli and Drosophila, Mouse. It is also verified that proposed method outperforms existing ngram frequency based method for both the data sets.. Overall performance comparison of different clustering techniques shows that FCM has performed better compared to K-means and PCM for both the data sets. PCM is also a good clustering technique to genome data clustering except the undesirable effect of coincident centroids formed at lower tolerances.. Narasimhan et al. [17] designed a scheme for automatic identification of a species from its genome sequence. A set of 64 3-tuple keywords was first generated using the 4 types of bases A (for Adenine), T (for Thymine), C (for Cytosine) and G (for Guanine). These keywords were searched on randomly sampled genome sequence of a given length (10,000 elements) and frequency count for each of the 4 3 = 64 keywords was determined to obtain a DNA-descriptor. The process was repeated for N such sampled genome sequences and then Principal Component Analysis was employed on the frequency counts for N sampled instances to obtain a unique feature descriptor which identifies the species from its genome sequence. It was shown that the feature descriptors were effective representatives of the structural signature of the species. No quantitative measures of accuracy are seen reported.. Narasimhan and coworkers [18] also proposed an alternative approach to automatic classification and identification of species using self-organizing feature map. The computational map was trained by using the DNAdescriptors (frequency count for each of the 4 3 = 64 keywords from N number of sampled genome sequences of given length 10,000) of different species as the training inputs. The maps for different dimensions were constructed and analyzed for optimum performance. The scheme presented a novel method for identifying a species from its genome sequence with the help of a two dimensional map of neuron clusters, where each cluster represents a particular species. The map has been shown to provide an easier technique for recognition and classification of a species based on its genomic data. But once again no quantitative measures of accuracy are seen reported.. Wei et al. [27] attempted classification of several DNA sequences of bacteria using the artificial neural network model. The ''dinucleotides compositions'' method was used to characterize the DNA sequences which transform every DNA sequence to a 16-dimension vector. A backpropagation artificial neural network was developed and trained using ''leave-one-out'' method. Results showed that the accuracy of classification was 84.3 %, which proved that the model was satisfactory in summary. However, the author stated that the applicability of the characterization strategy needs to be improved to reflect the features of the DNA sequences.. All the work mentioned above take DNA sequence for classification. The possibility of species classification using CGR images of DNA sequences, by using different distance metrics [28] and by using neural networks [29] has been investigated. In both these works, only species identification is done taking a few different species. A detailed classification problem, addressing 6 categories in the taxonomical hierarchy of eukaryotic organisms, using a combination of FCGR and naive Bayesian approach is also attempted [30] . The average classification accuracy is reported as 85.63 %.. Thus, the drawbacks of existing approaches for genome identification are as follows:. 1. Existing methods extract dinucleotide composition or trinucleotide composition from the sequences using exact pattern matching. In most real world biological problems, exact matching may not give desired results because the sequences are similar. Thus searching in sequence repositories often requires going beyond exact matching [11] . 2. In the n-gram frequency based classification, the number of features (4 n for DNA sequence and 20 n for protein sequence) for classifiers, increases with increase in n and sometimes the classifier performance gets hampered by a lot of redundant features in the dataset [31] . Further, algorithms with n-grams are computationally too expensive [4] . 3. Sequence alignment algorithms and techniques for estimating homologies and mismatches among DNA sequences that are used for comparing sequences of relatively small sizes, are not applicable to sequences with sizes varying between a few thousand base pairs to a few hundred thousand base pairs. Even for comparison of small sequences, the standard alignment and matching algorithms are known to be time consuming. There is a need for procedures that may be somewhat approximate in nature, yet useful in producing quick and significant results. To fill this gap [17, 18] has clustered complete genome data of Yeast and E. coli, by sampling it into size of 10,000 elements and choosing N such random samples. But no quantitative measures of accuracy are reported.. In the present work, we propose a novel approach for genome identification based on approximate pattern matching. Given a database of randomly selected samples of genomic sequences, our proposed work includes extraction of total number of fuzzy matching patterns with given fault tolerance. These total number of fuzzy matches are used as features for classifier. Classification of genome sequences has been done by data mining techniques and the number of subsequences that are used as features for classifier depends on the tolerance allowed. Experimental results are reported for randomly selected samples from complete genome data of Yeast and E. coli. The proposed approach is compared with n-gram sequence encoding method in binary form which resulted in highest accuracy of 53 %. But the proposed approach based on approximate matching resulted in highest accuracy of 99 % with 70 % tolerance and sampling size of 10,000 bp. Our proposed approach used for species identification from genome data is as shown in Fig. 1 . First, we sample the complete genome data of species into 2,000-10,000 bp size and then we choose randomly 200 such samples. In the next step we extract approximate matches for a given query with specified fault tolerance by varying candidate length so as to allow both positive and negative tolerance from the given sequences. These total approximate matches are used as features for classification algorithms and then the results are analyzed. Figure 2 shows extraction of total number of approximate matching patterns from a genome sequence database with query pattern of length p and percentage of fault tolerance allowed k.. In the next section, two algorithms namely, algorithm for finding approximate occurrences based on Levenshtein distance and algorithm for finding total number of approximate matches by varying candidate length so as to allow both positive and negative tolerance from the genome data sequences are explained. Finally, we explain classification techniques used in our method. Given a pattern P, a text string T P j j ¼ m and T j j ¼ n ð Þ and fuzziness factor k, the task is to find all positions j in T such that there exists a suffix of T 1. . .; j ½ that has edit distance of less than k with P. We first define:. D(i, j) will hold the Levenshtein distance between the first i characters of P and the first j characters of T for all i, j.. We then use the following recursion to compute the table D i j ð Þ for all i and j:. The positions of interest are those j's for which D m; j ð Þ\ k:. 4.2 Algorithm for finding total number of approximate matches for a specified fault tolerance from sequence database Given complete genome data of length l, sample size s. Sample the complete genome data into N number of sequences of size s. Now, given a sequence database with N number of sequences, query pattern of length p and percentage of fault tolerance allowed k, we want to find, for every sequence in the database, the total number of candidate patterns that will approximately match the query pattern by varying candidate length, so as to allow both positive and negative tolerance (at most k). The algorithm is given below.. 1 for all sequences in database do step 2.. 2 for all candidate length from (p -p*k/100) to (p ? p*k/100) do steps 3-8. 3 Generate candidates of length in step 2.. 4 Count = 0.. 5 Find the Levenshtein distance between candidate pattern and query pattern. 6 If distance Bk, then increment count.. 7 Repeat steps 3 and 4 for all generated candidates.. 8 Output count as total number of approximate matches.

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Robust and automated three-dimensional segmentation of densely packed cell nuclei in different biological specimens with Lines-of-Sight decomposition Background: Due to the large amount of data produced by advanced microscopy, automated image analysis is crucial in modern biology. Most applications require reliable cell nuclei segmentation. However, in many biological specimens cell nuclei are densely packed and appear to touch one another in the images. Therefore, a major difficulty of three-dimensional cell nuclei segmentation is the decomposition of cell nuclei that apparently touch each other. Current methods are highly adapted to a certain biological specimen or a specific microscope. They do not ensure similarly accurate segmentation performance, i.e. their robustness for different datasets is not guaranteed. Hence, these methods require elaborate adjustments to each dataset. Results: We present an advanced three-dimensional cell nuclei segmentation algorithm that is accurate and robust. Our approach combines local adaptive pre-processing with decomposition based on Lines-of-Sight (LoS) to separate apparently touching cell nuclei into approximately convex parts. We demonstrate the superior performance of our algorithm using data from different specimens recorded with different microscopes. The three-dimensional images were recorded with confocal and light sheet-based fluorescence microscopes. The specimens are an early mouse embryo and two different cellular spheroids. We compared the segmentation accuracy of our algorithm with ground truth data for the test images and results from state-of-the-art methods. The analysis shows that our method is accurate throughout all test datasets (mean F-measure: 91 %) whereas the other methods each failed for at least one dataset (F-measure ≤ 69 %). Furthermore, nuclei volume measurements are improved for LoS decomposition. The state-of-the-art methods required laborious adjustments of parameter values to achieve these results. Our LoS algorithm did not require parameter value adjustments. The accurate performance was achieved with one fixed set of parameter values. Conclusion: We developed a novel and fully automated three-dimensional cell nuclei segmentation method incorporating LoS decomposition. LoS are easily accessible features that ensure correct splitting of apparently touching cell nuclei independent of their shape, size or intensity. Our method showed superior performance compared to state-of-the-art methods, performing accurately for a variety of test images. Hence, our LoS approach can be readily applied to quantitative evaluation in drug testing, developmental and cell biology. The automated, robust and accurate detection of a single cell nucleus is a crucial and challenging step for a precise quantification in many biological applications. Up to now, several three-dimensional cell nuclei segmentation methods exist but in most cases they need further adjustments to the considered image data and biological specimen. We introduce a three-dimensional segmentation method that incorporates separating apparently touching cell nuclei. It combines local adaptive pre-processing with a Lines-of-Sight approach for approximately convex decomposition. Our method is readily applicable to threedimensional microscopy images of different biological specimens acquired by diverse imaging techniques.. The segmentation quality is largely independent of cell type, size, intensity, cell density, and image quality. A comparison with state-of-the-art algorithms revealed an overall better performance of our method in terms of identification of individual cell nuclei and extraction of relevant features such as the nuclear volume.. Three-dimensional cell nuclei segmentation with our LoS method provides the crucial starting point for many applications. Cellular spheroids e.g. serve as in vitro tissue models, especially in tumur biology. They show an improved resemblance of the spatial arrangements compared to two-dimensional cell cultures [48] . Therefore, they have become increasingly important for drug testing assays. Volume changes of cell nuclei within such spheroids upon drug treatment might provide insights into drug efficacy. Developmental systems such as mouse embryos serve as a good model for exploring the coordination of cell linage specification and morphogenesis [49] . Thereby, a reliable identification of cell nuclei positions facilitates accurate tracking and lineaging of cell nuclei during different processes and hence opens up a variety of possibilities for investigating cellular dynamics. In general, the wide applicability of our proposed segmentation method enables a reliable and robust quantification of cell nuclei in fluorescence images that will contribute to our knowledge in many biological applications. We developed a segmentation pipeline for cell nuclei in three-dimensional fluorescence images. The algorithm consists of local adaptive pre-processing followed by decomposition into approximately convex objects. Our detailed analysis revealed the contributions of the two parts to the robustness of the algorithm with respect to differences in image properties like the biological specimen, imaging technique, signal quality, intensity distribution and size of the cell nuclei. These major parts are discussed in the following sections. Biological processes rely on spatial cell-cell and cellmatrix interactions and are highly influenced by the microenvironment of the cells [1] [2] [3] . A large number of biomarkers and dyes are available to label distinct cellular structures. Well-defined protocols enable the observation and quantification of dynamic processes of cells within intrinsically three-dimensional structures. Several techniques have been explored to track cells in vivo or in vitro. The classical method is fluorescent labelling of cell nuclei [4, 5] and visualization by advanced threedimensional fluorescence microscopy. This method enables the localization of cell nuclei and is also utilized to assess cell viability.. Optical imaging has experienced a significant progress during the past 20 years [6] . The most widely applied advanced three-dimensional fluorescence imaging technique is confocal microscopy [7, 8] . Light sheet-based fluorescence microscopy (LSFM) such as single plane illumination microscopy (SPIM) [9, 10] and digital scanned laser light sheet-based fluorescence microscopy (DSLM) ( [11] ) are becoming increasingly popular. They have demonstrated their applicability for imaging biological specimens ranging from a single cell to entire animals ( [12, 13] ). However, fluorescence images produced by all microscopes are affected by their optical properties. The brightness as well as the signal-to-noise ratio in images of large, thick and light-scattering multicellular specimens decreases with the penetration depth [14] . Furthermore, the axial resolution is at least three times worse than the lateral resolution, which often causes objects in the image to apparently touch one another.. The availability of three-dimensional microscopes for three-dimensional biological specimens has pushed the development of three-dimensional image segmentation methods. Three-dimensional cell nuclei segmentation methods commonly rely on pre-processing steps (e.g. filtering, initial thresholding or seed detection) combined with watershed ( [15] [16] [17] ), graph cut ( [18, 19] ), machine learning ( [20, 21] ), gradient flow tracking [22] , active surface models [23] , level set [24] , or concavity-based segmentation ( [25, 26] ). But despite the continual progress in three-dimensional cell nuclei segmentation, there is still a need to improve accuracy, level of automation and adaptability.. A major challenge for segmentation is the separation of densely packed or apparently touching cell nuclei. Another difficulty arises from the diversity in terms of the imaged biological specimens or the imaging techniques used for acquisition. In general, segmentation methods are adopted to either a specific specimen (e.g. mouse embryo [8] , C. elegans [27] or zebra fish [28] ) or a specific imaging technique (e.g. DSLM or confocal microscope [29] [30] [31] ); or their accuracy has only been tested for one particular application ( [32, 33] ). To achieve a satisfactory performance of such a method for images that contain another specimen or were obtained by a different imaging technique, sets of parameter values need to be optimized.. To tackle these problems and establish a method that does not rely on signal intensity, heavy parameterization or effective initialization of an algorithm, we chose approximate convex decomposition as the basis of our cell nuclei segmentation method. In the literature, several approaches exist for separating objects into approximately convex parts. However, none of them have been applied to biological images. In Lien's and Amato's approach [34] , first the most concave regions are identified, and then they are partitioned such that the concavity is reduced below a specified threshold -resulting in approximately convex parts. Another approach is based on greedy region growing of a surface part until the distance to its convex hull decreases below a given threshold [27] . This again yields approximately convex parts. In Attene et al. [35] , a shape is represented by a tetrahedral mesh. Decomposition is achieved by calculating a hierarchy of convex polyhedra that tightly enclose the shape. In a bottom-up manner, a single polyhedron is clustered into approximately convex parts.. In the work of Asafi et al. [36] , approximate convex decomposition is achieved by analyzing pairs of surface points of a shape that are visible to each other. Lines between such mutually visible pairs of points are called "Lines-of-Sight" [36] . Neither a tetrahedralization nor the convex hull have to be calculated for an object. Therefore, Lines-of-Sight are easily accessible features for which neither shape and size information nor intensity distributions have to be considered. We apply this segmentation method to biological images for the very first time.. We combine the Lines-of-Sight (LoS) concept with a local adaptive pre-processing to separate apparently touching cell nuclei into approximately convex parts representing single cell nuclei. We show that our LoS implementation accurately segments three-dimensional cell nuclei due to effective separation of apparently touching cell nuclei. The accuracy of our proposed method exceeded 86 %. Furthermore, volumes of split cell nuclei were well represented. In a direct comparison with methods that are based on a graph cut algorithm (FARsight), seeded watershed transformation (ImageJ 3D Watershed) or machine learning (ilastik) -commonly used techniques for three-dimensional cell nuclei segmentation -we demonstrate overall superior segmentation performance and volume measurements. Thereby, our automated LoS approach is applied with the same set of parameter values for real test images that differ in terms of biological specimen, size, imaging technique, and quality. Together, this demonstrates the high accuracy, adaptability and applicability of the proposed method. Approximately convex decomposition with Lines-of-Sight. In many biological specimens cell nuclei are naturally densely packed. In three-dimensional fluorescence microscopy images, they even seem to touch each other, e.g. due to a lower axial than lateral resolution of the microscope. The differences in intensity are often not sufficient to distinguish single cell nuclei within a clump. Therefore, basic segmentation by intensity thresholding fails to identify individual nuclei (Fig. 1) .. We developed an automated and robust threedimensional cell nuclei segmentation. The idea is that a single nucleus is expected to be convex, whereas clumps of apparently touching cell nuclei are in general not convex. However, object decomposition into exact convex parts can be costly and too strict for segmentation due to the generation of an incontrollable number of components [34] . Hence, the concept of approximate convex decomposition was implemented to decompose apparently touching cell nuclei. The definition of approximately convex and the concept of Lines-of-Sight (LoS) was taken from the work of Asafi et al. [36] and was adapted to cell nuclei. Two surface points of a shape are said to be in line-of-sight if the connecting line between those two points does not leave the inner volume of the shape. Such mutually visible points are in a convex position. Hence, an object is convex if all surface points are in a convex position. If few surface points are not in a convex position, an object is approximately convex. Fig. 2 illustrates Lines-of-Sight for a given surface point. As evident, not all pairs of points that are in line-of-sight belong to a connected part of the shape surface. Thus, this object is not convex.. Using this definition, we cluster surface points that are in line-of-sight. To ensure robust clustering we determine an initial guess of the number of clusters. For a number of k clusters, each cluster represents a first approximation of an individual cell nucleus. Subsequently, this rough estimation is optimized such that we obtain clearly separated cell nuclei. The method was implemented as a processing pipeline for three-dimensional gray level images. The raw images pass through four main stages: (1) local adaptive binarization, (2) collecting connected components, (3) determining the number of divisible parts and (4) decomposition of components into approximately convex parts with LoS.. The details of the algorithm are described in the next section and illustrated in Fig. 3 . Thereby, all parameter values described in the following section were determined by a parameter scan. We chose one common parameter set that showed equally good performance of our algorithm for all test datasets. The method is implemented in Mathematica language (Version 9) and uses the ImageJ plugin for automatic local thresholding [38] . The source code is freely downloadable from [39] . Data processing using the complete pipeline with the test datasets took 8916 s for the mouse embryo, 3408 s for the breast cancer spheroid and 26487 s for the pancreatic cancer spheroid on a 2.67 GHz 12-core Intel Xeon E5650 with 96 GB of RAM. We expect to continue improving the performance of the LoS pipeline.

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


Evaluating measures of nonclassical correlation in a multipartite quantum system We introduce and compare several measures of nonclassical correlation defined on the basis of a widely-recognized paradigm claiming that a multipartite system represented by a density matrix having no product eigenbasis possesses nonclassical correlation. Classical/nonclassical separation is a controversial subject. There have been debates on the definition of nonclassical correlation of a multipartite system. It is well-known that the separability paradigm 1,2,3 is widely-accepted to define entanglement as a quantum correlation that cannot be generated from scratch using only local operations and classical communication (LOCC) (See, e.g., Ref. 4) . There are different paradigms to define nonclassical correlation of a multipartite system from operational viewpoints. Bennett et al. 5 discussed a certain nonlocality about locally nonmeasurable separable states. Ollivier and Zurek 6 introduced a measure called quantum discord defined as a discrepancy of two expressions of a mutual information that should be equivalent to each other in a classical information theory. A simple classical/nonclassical separation was given by Oppenheim et al. 7, 8 which is also widely recognized. They defined the class of (properly) classically correlated states that are the states with a product eigenbasis. Its complement is the class of nonclassically correlated states that are the states without product eigenbasis. This definition is in accord with their measure called quantum deficit defined as a discrepancy between the information that can be localized by applying closed LOCC (CLOCC) operations and the total information of the system. The CLOCC protocol allows only local unitary operations, attaching ancillas in separable pure states, and operations to send subsystems through a complete dephasing channel. Thus classically correlated states have vanishing quantum deficit. Other measures 9,10 were later proposed on the basis of the same definition of classical/nonclassical correlation.. We aim to evaluate measures based on the following separation of classical/nonclassical correlations.. Definition 1 (Oppenheim-Horodecki) . A quantum bipartite system consisting of subsystems A and B is (properly) classically correlated if and only if it is described by a density matrix having a biproduct eigenbasis.. A straightforward extension gives the definition: Definition 2. A quantum multipartite system consisting of subsystems 1, ..., m is nonclassically correlated if and only if it is described by a density matrix having no m-product eigenbasis.. The set of classically correlated states is a nonconvex subset of the set of separable states. Thus a convexity cannot be a property of a measure of nonclassical correlation. The natural statement is that a measure M of nonclassical correlation should satisfy the following conditions: (i) M = 0 if a system is described by a density matrix having a product eigenbasis.. (ii) M is invariant under local unitary operations. These conditions are considered to be prerequisite hereafter.. In addition, the additivity property should be satisfied if one needs to compare systems with different dimensions. There are two ways to define additivity for a measure. One is defined as follows, which is valid for any measure of bipartite correlation.. Definition 3. Let F (ρ AB ) A|B be a measure of correlation between subsystems A and B of a bipartite system AB, where A|B denotes splitting between A and B. Then, F (ρ AB ) A|B is called an additive measure if and only if the equality. Another definition of additivity may be introduced for a multipartite measure when we focus on scaling. . with σ 1 the density matrix of an m 1 -partite system and σ 2 the density matrix of an m 2 -partite system. Second, the measure possesses weak additivity if and only if M m n (σ ⊗n ) = nM m (σ). Third, the measure possesses subadditivity if and only if. In this contribution, we first compare the definitions and properties of measures of nonclassical correlation in Sec. 2. Then we compare these measures numerically in simple examples in Sec. 3. The paper concludes with several remarks. There are many different ways to define a measure of nonclassical correlation. We have seen four of them. The measures D and D G look stable and faithful against changes of parameters among tested measures as far as we could see in the three simple examples. Further investigation is required to find desirable properties in addition to additivity properties. Computational cost should be another factor to choose a measure. A seemingly natural measure D cannot be used for a system with a large dimension due to the cost of searching over all possible local bases. Thus the measures other than D are good candidates in this sense.. We have found that a more general framework to detect and quantify nonclassical correlation can be constructed with EnCE, in analogy with the PnCP map theory, in the process of defining the measure K. Consider a map Λ such that Λ preserves the eigenvalues of a density matrix while I ⊗ Λ in general does not. It is obvious that I ⊗ Λ preserves eigenvalues of a density matrix if it has a biproduct eigenbasis. Thus such Λ can be used to detect and quantify nonclassical correlation. Further investigation in this approach will be reported elsewhere 12 . for Private Universities: matching fund subsidy from MEXT. He is also supported by the Grant-in-Aid for Scientific Research from JSPS (Grant No. 19540422 ).

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


IPO: a tool for automated optimization of XCMS parameters Background: Untargeted metabolomics generates a huge amount of data. Software packages for automated data processing are crucial to successfully process these data. A variety of such software packages exist, but the outcome of data processing strongly depends on algorithm parameter settings. If they are not carefully chosen, suboptimal parameter settings can easily lead to biased results. Therefore, parameter settings also require optimization. Several parameter optimization approaches have already been proposed, but a software package for parameter optimization which is free of intricate experimental labeling steps, fast and widely applicable is still missing. Results: We implemented the software package IPO ('Isotopologue Parameter Optimization') which is fast and free of labeling steps, and applicable to data from different kinds of samples and data from different methods of liquid chromatography -high resolution mass spectrometry and data from different instruments. IPO optimizes XCMS peak picking parameters by using natural, stable 13 C isotopic peaks to calculate a peak picking score. Retention time correction is optimized by minimizing relative retention time differences within peak groups. Grouping parameters are optimized by maximizing the number of peak groups that show one peak from each injection of a pooled sample. The different parameter settings are achieved by design of experiments, and the resulting scores are evaluated using response surface models. IPO was tested on three different data sets, each consisting of a training set and test set. IPO resulted in an increase of reliable groups (146% -361%), a decrease of non-reliable groups (3% -8%) and a decrease of the retention time deviation to one third. We introduced the software package IPO, 'Isotopologue Parameter Optimization' , performing parameter optimization for the open source R-package XCMS. IPO exploits the existence of natural, stable 13 C isotopes that are ubiquitous in all biological samples. IPO was applied to LC-HRMS data from tissue, serum and yeast samples and the results showed that it is applicable to data from different types of samples as well as from different LC-MS devices and (See figure on previous page.) Figure 2 Selected chromatograms showing the different peak types at well-defined masses obtained from the different data sets. Chromatograms derive from a) metabolite fingerprinting data set; b) lipidomics data set; c) central carbon metabolism data set. Peaks derived from default parameters are presented in the left chromatograms and peaks coming from optimized parameters are shown in the chromatograms on the right side, respectively. The peak area integrated by XCMS is colored red. The m/z range for the chromatogram was chosen from the respective minimum and maximum m/z values of the particular peak. Comparison of chromatograms a) clearly demonstrate that default peak width parameters were too small for the broad peaks, b) shows an example where the mass range used in the default settings was too wide and c) illustrate peaks where the default peak width parameters were too wide. methods. The optimization time has been remarkable reduced by separating optimization for peak picking parameters from optimization for retention time correction and grouping parameters. IPO is also suitable for XCMS beginners, because the default settings are the start values of the optimization process. We recommend a powerful workstation with multiple processors and cores, which costs only a fraction of the enormous costs of a modern LC-MS instrument and will enable the user to exploit the full potential of the LC-MS.. IPO is continuously improved, optimization of additional XCMS methods will be implemented, other DoE evaluation techniques will be tested and additional identification of isotopic peaks with the R-package CAMERA [23] will be made available to further increase the power of IPO. Untargeted metabolomics screens biological samples with the aim to reveal new compounds and to understand biological mechanisms. Untargeted metabolomics by using liquid chromatography (LC) generates a huge amount of data when coupled to mass spectrometry (MS). Software packages for automated data processing are needed to successfully process large data sets. Recently, a tool MetExtract has been presented which uses carbon labeling with stable isotopes to find reliable peaks [1, 2] . This tool increases the selectivity of compounds with biological origin, performs feature reduction and assesses molecular structures of measured substances. Disadvantages of MetExtract are the time and the cost intensive labeling step and its feasibility which is limited to samples that can be labeled.. A number of software packages for processing LC-MS data have already been developed for data sets of samples that do not rely on labeling [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] . They provide methods for peak detection, peak picking, retention time correction and grouping and offer a variety of adjustable parameters to provide reasonable results. But even though these parameters are intended to optimize the results, wrong parameter selection can lead to distorted outcomes. Parameter optimization is necessary to counter wrong selection. Up to now, several parameter optimization approaches have been proposed to increase the reliability of the results [13] [14] [15] .. One parameter optimization approach uses design of experiments (DoE) [13] . A designed experiment is a series of tests in which specific modifications are made to the input variables of a process. DoE aims to optimize the response to modifications or to either explain changes of the response variable. . For metabolomics data a dilution series of a pooled sample is measured and a reliability index for each experiment of the DoE is calculated. This reliability index is based on the assumption that peaks which correlate with the dilution series are reliable ones, and those which do not correlate are unreliable peaks. The DoE optimization approach provides quality evaluation of the resulting optimization, but is very time intensive. To accelerate the DoE optimization approach, Zheng, H et al. [14] refined the workflow by first applying a screening step prior to the optimization. Screening steps are usually performed in the first stage of an optimization process with the purpose of identifying the parameters that have large effects on the target variable. For the screening step Zhen et al. used a Plackett-Burman design. Such a fractional factorial design defines only two levels for each parameter and thus requires relatively few experiments. Two levels stand for two different tested values for each parameter. Second, only parameters with a significant positive influence on the target value are optimized and thus the overall optimization time is considerably decreases. However, potential important parameters may be lost because they may fall into a range where they do not significantly influence the target value and hence they may not be further optimized. A software package for parameter optimization which is even faster, widely applicable and free of intricate labeling steps is still missing.. To close this gap we implemented the R-package IPO ('Isotopologue Parameter Optimization') that exploits natural, stable 13 C isotope peaks which are ubiquitously present in biological samples. The use of these 13 C isotope peaks makes all labeling steps expendable and leads to the calculation of a target value to assess the optimization quality. IPO increases the reliability of peak picking, retention time correction and grouping results and starts the optimization process for the parameters to be optimized at the respective default settings of the XCMS methods and is thus also well suited for inexperienced XCMS users. We developed the R-package IPO to optimize parameters of the open-source package XCMS [3, 4] . The process for the parameter optimization by IPO is described in the following subsections ( Figure 1 ).

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


On fractional Gaussian random fields simulations To simulate Gaussian fields poses serious numerical problems: storage and computing time. The midpoint displacement method is often used for simulating the fractional Brownian fields because it is fast. We propose an effective and fast method, valid not only for fractional Brownian fields, but for any Gaussian fields. First, our method is compared with midpoint for fractional Brownian fields. Second, the performance of our method is illustrated by simulating several Gaussian fields. The software FieldSim is an R package developed in R and C and that implements the procedures on which this paper focuses. Rough phenomena arise in various fields (Frisch and Parisi 1985; Leland, Taqqu, Willinger, and Wilson 1994; Mandelbrot 1975; Peitgen and Saupe 1988; Pentland 1984) : texture simulations and image processing, natural scenes (clouds, mountains) simulations, fluid mechanics, financial mathematics, ethernet traffic . . . From a mathematical point of view, roughness is often measured by the Hölder index H. The lower H, the more rough the phenomenon, whereas H greater than 1 corresponds to smooth phenomenon. There is a real need to have models for rough phenomena. The fractional Brownian motions, in short FBM, introduced by Kolmogorov (1940) and further developed by Mandelbrot and Ness (1968) , play a key role. FBM have then be extended in many directions: higher dimensions, anisotropy, multifractionality (Ayache, Léger, and Pontier 2002; Ayache and Lévy-Vehel 2000; Benassi, Bertrand, Cohen, and Istas 2000; Benassi, Cohen, and Istas 1998; Benassi, Jaffard, and Roux 1997; Bonami and Estrade 2004; Herbin 2006; Kamont 1996; Peltier and Levy-Véhel 1996) .. The simulation of fractional Gaussian processes is not difficult in one dimension (e.g., the surveys of Bardet, Lang, Oppenheim, Philippe, and Taqqu 2003; Coeurjolly 2000) . Let us recall the numerical complexity of some classical methods : the Cholesky method has a complexity of O(N 3 ), where N is the size of the simulated sample path, Levinson's a complexity of O(N 2 log N ) and Wood and Chan's a complexity of O(N log N ). These complexities do not pose problems in dimension one, but become problematic in higher dimensions. These methods are indeed no longer tractable: these algorithms are time and memory expensive. Since its introduction by Lévy (1965) for Brownian motion, the random midpoint displacement method has been intensively used for generating fractional Brownian field (Fournier, Fussel, and Carpenter 1982; Peitgen and Saupe 1988; Voss 1985) . This method is a rough approximation and is very fast.. Our approach is based on exact simulation plus a fast step, that is an improvement of the midpoint method. Let us be more precise. The aim is to simulate a Gaussian field over a fine grid. We first simulate the field in an exact way on a rough grid via the Cholesky method. We then propose a refinement of the midpoint method. The field is simulated, using a set of neighbors, and not only the nearest neighbors. This requires a computation of local weighting coefficients. This is a major difference with the midpoint method. For midpoint, these local coefficients are fixed to 1/4. For our method, these local coefficients are exactly determined from the second-order structure. Contrary to the midpoint method, this allows us to simulate fields with arbitrary covariance as well rough as smooth.. One then needs to compare our methods called fieldsim with the midpoint method. Since the real aim is to simulate rough phenomenon, we estimate the Hölder index H of the simulation. The closer the estimation of H is, the better the simulation is. Our conclusion is the following. First, on fractional Brownian fields, fieldsim is slightly better than midpoint. Since the midpoint method is faster, this means that midpoint simulator is nevertheless relevant for fractional Brownian fields. Note that the Hölder index is only one criterion that can be used to assess the accuracy of the simulation. The procedure fieldsim produces fields with the desired Hölder index. But we do not focus on the difference between the simulated field covariance and the specified one. Second, we illustrate the good performances of our method by simulating several Gaussian fields, for which midpoint is no longer applicable.. The paper proceeds as follows. In the second section, we present our procedure fieldsim. Then we compare with the midpoint method. In the third section, we present our method on many examples. We recall in the appendix some classical results on the estimation of the Hölder index and details about our package in R (R Development Core Team 2007). After introducing some notations, we present the both steps of the procedure fieldsim: accurate and refined steps. Then we recall the random midpoint displacement method which is comparable with the procedure proposed here. We underline the drawbacks of this approach compared with ours.

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


The plausibility of computing the h-index of scholarly productivity and impact using reference-enhanced databases Purpose -This paper aims to provide a general overview, to be followed by a series of papers focusing on the analysis of pros and cons of the three largest, cited-reference-enhanced, multidisciplinary databases (Google Scholar, Scopus, and Web of Science) for determining the h-index. Design/methodology/approach -The paper focuses on the analysis of pros and cons of the three largest, cited-reference-enhanced, multidisciplinary databases (Google Scholar, Scopus and Web of Science). Findings -The h-index, developed by Jorge E. Hirsch to quantify the scientific output of researchers, has immediately received well-deserved attention in academia. The theoretical part of his idea was widely embraced, and even enhanced, by several researchers. Many of them also recommended derivative metrics based on Hirsch's idea to compensate for potential distortion factors, such as high self-citation rates. The practical aspects of determining the h-index also need scrutiny, because some content and software characteristics of reference-enhanced databases can strongly influence the h-index values. Originality/value -The paper focuses on the analysis of pros and cons of the three largest, cited-reference-enhanced, multidisciplinary databases.Paper type General review The h-index, developed by Jorge E. Hirsch to quantify the scientific output of researchers, has immediately received well-deserved attention in academia. The theoretical part of his idea was widely embraced, and even enhanced, by several researchers. Many of them also recommended derivative metrics based on Hirsch's idea to compensate for potential distortion factors, such as high self-citation rates. The practical aspects of determining the h-index also need scrutiny, because some content and software characteristics of reference-enhanced databases can strongly influence the h-index values. This paper provides a general overview of these issues, to be followed by a series of papers focusing on the analysis of pros and cons of the three largest, cited-reference-enhanced, multidisciplinary databases (Google Scholar, Scopus and Web of Science) for determining the h-index.Bibliometric, informetric and scientometric measures are being increasingly employed as a means of evaluating scientists, researchers, universities, research institutions and their departments at the national and international levels. These measures are employed in making decisions for awarding tenure, grants and allocationThe current issue and full text archive of this journal is available at

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Converting OBR-scolio ontology in OWL DL Abstract. We developed the OBR-Scolio ontology that models scoliosis as pathological state of spine using the method of extracting from the FMA reference ontology in anatomical domain and the principal ontology framework of the OBR reference ontology, which is spread over anatomy, physiology and pathology domains. Following the FMA modeling framework, OBR-Scolio ontology initially is created in Protégé using its frame based representation. In order to enable more powerful reasoning support, ontology visualization, and more precise concepts' definition and description, we converted OBR-Scolio in OWL DL language, due to its higher expressiveness. The paper addresses and discusses the key conversion principles, as well as our experience in such conversion, and the results obtained from Racer reasoner. Significant amount of efforts employed so far in developing reference and application ontologies in the domain of medicine and biology, including anatomy structures, brought essential advances in both deep fundamental understanding of the issue, as well as the application capabilities and power deep fundamental understanding of the issue [1] [2] [3] [4] [5] [6] [7] [8] [9] as well as the application capabilities and power [10] [11] [12] . Widely accepted and applied frame [13] , [14] and semantic network [15] based representations of the global medical concepts and terminology turns to demonstrate the lack of formal semantics for precise definition of ontology's concepts, particularly in the pathology (sub) domain and cannot benefit from the reasoning support provided by description logics (DL) [16] , [17] . This is recognized as the essential need for conversion frame-based ontology representations into more expressive forms that provide more accurate and meaningful reasoning with subtle and delicate anatomical and pathological concepts.. We have developed the OBR-Scolio ontology that models scoliosis as pathological state of spine [18] , [19] . It is extracted (pruned) from the FMA reference ontology [20] using de-novo method [21] . Having the FMA ontology constructed using Protégé frame-based representation 1 OBR-Scolio ontology consequently inherits the same encoding formalism. Although Protégé as frame based representation tool is equipped with complex knowledge capturing and ontology construction capabilities, the knowledge representation formalism it uses lacks in expressiveness [5] , [6] . The key semantic deficiency stems from the fact that medical terminology used in domain knowledge representation, together with very rich relationships between corresponding entities, requires modeling approach and methodology that ensures high precision, which in turn prevents from misclassification, i.e. imprecise or even incorrect reasoning. In that course, OWL DL as the most desirable dialect of OWL for ontology development [16] , [22] [23] [24] [25] lends its description logic mechanisms for more accurate concepts' definition and more reliable reasoning for clinical application.. In order to overcome aforementioned deficiencies, as well as to improve interoperability with other OWL ontologies, we convert original OBR-Scolio frame-based representation into OWL DL. The key objective is to facilitate and empower the scoliosis ontology with the expressivity that supports sound and consistent anatomical and pathological semantics [16] , [23] , [24] . In addition, this conversion also enhances features of reusability, sharing, maintenance and integration with other individual (application) biomedical ontologies.. For the sake of terminological clarification, in our study we use term conversion, in the same sense as used in [16] in particular, as well as in [23] , [26] , adopting the fact that OBR-Scolio originates from the FMA ontology and has been created with the same encoding formalism. In many other works terms migration [26] [27] [28] [29] [30] , translation [23] , [31] and transformation [32] are used interchangeably with the term conversion. Although in deep fundamental meaning each of the terms (may) make the difference, the term conversion applied in our case supports the widely accepted approach of conversion of frame based encoding into OWL DL and does not affect the overall methodology and findings.. Similarly with many others biomedical ontologies (see Section 2 for details) we found that conversion process from frame-based ontology representation into the OWL DL representation is indispensable for our application ontology OBR-Scolio too, due to higher expressiveness of the OWL DL language, possibility to visualize the ontology and to invoke reasoners for subsumption and consistency testing, as well as the capability to integrate it with other OWL ontologies.. The paper is organized as follows: Section 2 briefly overviews the work related to converting frame-based biomedical ontologies with DL formalisms. The next section introduces frame-based representation of OBR-Scolio application ontology in scoliosis domain. Fourth section describes our experience in converting OBR-Scolio Ontology in OWL DL. Finally, we provide the conclusions and directions of future work. OBR-Scolio ontology initially has been developed using frame-based representation framework, since its key cornerstones are the FMA and the OBR reference ontologies that play crucial role in medicine. That is, the OBRScolio's modeling approach extracts from both relevant entities of biomedical reality in the domain of spinal deformities, and consequently inherits the same representation. Its key intention is to bring together and merge essential anatomical and pathological concepts and knowledge that intrinsically supports faithful clinical communication in diagnosis and treatment of spinal disorders, primarily scoliosis. However, frame-based representation demonstrates numerous deficiencies that fundamentally stems from poor or no semantics. Since reliable and faithful clinical communication and decision making assumes high level of precision and relevancy, unambiguous and consistent information and data integration is absolutely indispensable. Therefore, we have chosen OWL DL language as it is based on description logic modeling framework that provides highly expressive capabilities of semantic reasoning.. The Protégé frame-based mode has an "export to OWL" option. However, this option only performs a straightforward translation that ignores all the features that do not have a direct equivalent. This paper presents detailed additional steps needed to transform the OBR-Scolio ontology into OWL DL representation using Protégé ontology editor and knowledge acquisition system that supports both formalisms. Although virtually similar, these two approaches rely on fundamentally different modeling assumptions. The differences between description logics and frames are not only syntactic, but also semantic. Frames' semantics is not as precisely defined as description logics' one. A description logics representation of the OBR-Scolio application ontology in the OWL DL would allow developers to combine it with other OWL ontologies and to employ advanced inference capabilities: satisfiability, subsumption, classification, consistency checking, instantiation, realization and retrieval using generic reasoning tools. All these contribute to maintenance of a consistent terminological system and improve results of queries.. The conversion process from frame-based to OWL DL ontology representation is accomplished using the Export function in Protégé and by applying many additional rules that include: deleting all information of metaclass instantiation, converting Protégé slots into OWL DL properties and converting Protégé classes in OWL DL classes.. The result of conversion process provides ontology specification completeness, semantic consistency, and possibility to employ reasoners for subsumption testing and automatic checking for consistency, ambiguity, and redundancy in classes' hierarchy and specification. For the reasoning purpose over OBR-Scolio ontology we have used the Racer, a DIG compliant reasoner. The Racer was launched from Protégé-OWL, but the classification processing has failed because Racer could not handle the entire OBR-Scolio OWL ontology. Due to the presence of complex restrictions on inverse pairs of properties such as: part, part_of and systemic_part, systemic_part_of checking the consistency and computing inferred classes hierarchy were successful only without these properties.. The OBR-Scolio ontology is aimed as guide for scoliosis professionals and for other medical staff in health institutions and also for educating orthopedic students. OBR-Scolio ontology is due to its OWL-DL representation currently employed in ScolioMedIS, a web-based information system for visualization and monitoring of idiopathic scoliosis [19] . The system provides innovative programming access to orthopedics and physicians for convenient and reliably diagnose, treat and monitor patients with idiopathic scoliosis. Goran Devedžić is professor at Faculty of Engineering, University of Kragujevac, Serbia. His research interests focus on the advanced product and process development, industrial and medical application of soft computing techniques, and bioengineering. He has authored/co-authored more than 100 research papers, published in international and national journals or presented at international and national conferences, as well as three books on CAD/CAM technology and 3D product modeling. Numerous researchers and developing teams used Protége [33] , modeling environment and knowledge representation tool for building frame-based medical ontologies [34], due to its powerful functionalities and capabilities. On the other side, this is not the only platform and tool in the field of medical ontology development that employs frame-based representations for modeling the domain's concepts and associated properties and relationships. Ontolingua Server [35] , Onto Edit Professional [36] , WebODE [37] and WebOnto [38] ontology development tools allow representing knowledge following a hybrid approach, based on frames and first order logic. However, these all demonstrate the same kind of deficiency -the lack of expressiveness required for derivation of the new facts resulting from reasoning over a single or multiple representations. The same holds for checking consistency and hierarchical organization of the classes in the ontology, in the sense of existence of classes' instances and classes' hierarchy. This is of the crucial importance for proper inferring process of the reasoner.. Description Logic (DL) adds a formal, logic-based semantics to structured knowledge representation paradigm, which is employed in frame and semantic network knowledge representation [15] and provides the theoretical foundation forontology web languges (OWL). A DL knowledge base can be divided conceptually into three components: the Tbox, the Rbox and the Abox. The Tbox contains assertions about concepts (such as subsumption and equivalence axioms). The Rbox contains role inclusion axioms and constraints on the roles. The Abox contains role assertions between individuals and membership assertions. Beside formal, logic-based paradigm in knowledge representation another advantage of description logic is expressed in possibility to provide reasoning services. Main reasoning tasks concern: satisfiability, subsumption and instance checking. Subsumption and satisfiability reasoning tasks are description logic reasoning services which are typical for a terminology (TBox). Subsumption DLs reasoning service that supports the classification of the ontology is intended to indicate whether one concept is more general than another one, that is, whether the first subsumes the second [39] . At the other hand, a concept makes sense and is said to be satisfiable if there is some interpretation (meaning) that satisfies the axioms of the terminology of the domain such that the concept denotes a nonempty set in that interpretation (for more formal definitions of satisfiability refer to [39] ). A class is deemed to be unsatisfiable (inconsistent) if it cannot possibly have any instances [39] , [40] . The basic reasoning task in an ABox is instance checking, which verifies whether a given individual is an instance of (belongs to) a specified concept. Instance checking reasoning support also realization, which finds the most specific concept an individual object is an instance of; and retrieval, which finds the individuals in the knowledge base that are instances of a given concept.. There are many description logic based languages like: DAML (DARPA Agent Markup Language), OIL (Ontology Inference Layer), DAML+OIL [41] and OWL [42, 43] , which is based on DAML+OIL language. Description logics-based languages have a precisely and formally defined semantics. Some generic reasoning tools have been developed to leverage this semantics. Thus, an application can reason about an ontology represented in description logics without having to implement any inference function.. The most popular description logic formalism is currently the OWL (Web Ontology Language) that provides three increasingly expressive sublanguages: OWL Lite, OWL DL and OWL Full. Particularly, OWL-Lite and OWL-DL belong to description logics. OWL Lite possesses minimum and limited expressivity, without losing computational completeness and decidability (all computations will finish in finite time). OWL DL sublanguage is high expressive and decidable. OWL Full is maximally expressive but undecidable, with no computational guarantees (reasoning support is unsure). For the purpose of converting our application ontology we chose OWL DL sublanguage, because it offers a trade-off between expressivity and decidability.. There are many description logic based ontology development tools such as: OILEd [44] and OntoSaurus [45] . Although the new Protége releases provide Protégé-OWL editor for representing ontologies using DL based formalisms, the need for conversion previously built frame-based Protégé ontologies into highly expressive OWL (W3C's Web Ontology Language) continually attracts the attention.. Biomedical ontologies are increasingly taking advantage of Description Logic (DL) based formalisms in representing knowledge. GALEN [46] and SNOMED CT (SNOMED Clinical Terms) [3] ontologies are two important examples of ontologies which were both developed in a native DL formalism. Other terminologies have been converted into DL formalism.. In [16] and [23] the conversion process of the FMA reference ontology from its frame-based representation in Protégé into OWL DL is described in detail. The conversion relies on translation and enrichment rules, implemented with flexible options. In [26] authors propose the conversion of the FMA reference ontology into OWL Full language, in other to directly represent metaclasses and to form application independent representation of the ontology. For the applications specific needs, OWL Full model of the FMA ontology needs to be further restricted to the fragment that consist only application relevant concepts, which is then simplified into OWL DL. This is achieved by deleting all the OWL Full constructs (typically metaclasses and some relationships) that are not used in OWL DL representation of the application.. Unlike methods which are proposed in [16] , [23] and [26] in [31] authors suggest complete OWL transformation of the Protégé frame based canonical representation of the FMA reference ontology. This is achieved by representing only the information that is explicitly present in the frames representation of the FMA or that can be directly inferred from the semantics of Protégé frames and by representing all the information that is present in the frames representation of the FMA. Complete representation of the FMA in OWL consists of two components: an OWL DL component that contains the FMA constructs that are compatible with OWL DL; and an OWL Full component that imports the OWL DL component and adds the FMA constructs that OWL DL does not allow.. Another approach assumes the FMA transformation into a description logic-based representation different than OWL based [47] . The special emphasis is given to the representation of partitive relations using special modeling technique, called ePI (extended part/include), which is an extension of the SEP (Structure Entity Part) triplet [48] and the PI modeling scheme [49] .. The ontology migration process has been conducted for other OWL DL sublanguages, as well. Namely, in [27] the authors present migration and enhancement process of the existing Catalogue and Index of Frenchspeaking Medical Sites (CISMeF) terminology into OWL DL sublanguage. CISMeF "encapsulates" the MeSH (Medical Subject Headings) ontology, which is a component of the UMLS (Unified Medical Language System) Metathesaurus [50] in French version. The CISMeF terminology is automatically transformed from the previous relational database into OWL ontology, using Java and SQL queries.. Gene Ontology (GO) [17] migrated into DAML+OIL ontology language from XML version using five well defined staged approaches [28] . The key intention is to take the advantage of the richer formal expressiveness and the reasoning capabilities of DAML+OIL description logic language. The conversion capability is achieved using OilEd ontology development tool for editing DAML+OIL ontologies. Consistency checking and automatic concept classification is performed using FaCT description logic reasoner [51] .. In order to provide more formal representation of the previously framebased ontology intended for the use in intensive care units DICE (Diagnosis in Intensive Care Evaluation) [4] developed in Protégé, Cornet and Abu-Hanna proposed migration to DL formalism [29] . Their work stress that the DL formalization process of the ontology representation revealed implicit ambiguities and deficiencies in concepts' definitions and that the result of the process is the representation that can support automatic inference.. In [30] authors describe the conversion process of Semantic Network component of the UMLS Metathesaurus ontology [7] , [52] in OWL language. National Cancer Institute Thesaurus ontology (NCI Thésaurus) [1] is public domain description logic-based terminology firstly developed in XML format.. Afterwards the ontology is converted from XML format to computationally complete and decidable OWL Lite language.. In this paper we describe our own experience in converting the OBR-Scolio ontology from the frame-based representation into the OWL DL representation.

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