Addressing health disparities in Hispanic breast cancer: accurate and inexpensive sequencing of BRCA1 and BRCA2 Background: Germline mutations in the BRCA1 and BRCA2 genes account for 20-25 % of inherited breast cancers and about 10 % of all breast cancer cases. Detection of BRCA mutation carriers can lead to therapeutic interventions such as mastectomy, oophorectomy, hormonal prevention therapy, improved screening, and targeted therapies such as PARP-inhibition. We estimate that African Americans and Hispanics are 4-5 times less likely to receive BRCA screening, despite having similar mutation frequencies as non-Jewish Caucasians, who have higher breast cancer mortality. To begin addressing this health disparity, we initiated a nationwide trial of BRCA testing of Latin American women with breast cancer. Patients were recruited through community organizations, clinics, public events, and by mail and Internet. Subjects completed the consent process and questionnaire, and provided a saliva sample by mail or in person. DNA from 120 subjects was used to sequence the entirety of BRCA1 and BRCA2 coding regions and splice sites, and validate pathogenic mutations, with a total material cost of $85/subject. Subjects ranged in age from 23 to 81 years (mean age, 51 years), 6 % had bilateral disease, 57 % were ER/PR+, 23 % HER2+, and 17 % had triple-negative disease.Results: A total of seven different predicted deleterious mutations were identified, one newly described and the rest rare. In addition, four variants of unknown effect were found. Conclusions: Application of this strategy on a larger scale could lead to improved cancer care of minority and underserved populations. Rates of mortality, triple-negative disease, and BRCA1 and BRCA2 mutational and allelic diversity are all higher in African American and Hispanic populations. Although these populations could benefit significantly from genetic testing and screening, the combination of lower average income; lower insurance coverage; reduced knowledge of the benefits of testing; and mistrust of medical and government agencies, have led to a large disparity in participation [42] [43] [44] . From 64,717 women in the Myriad database, this under-participation is 3.9-4.8 times lower in these two populations, which together account for 29 % of the US population [35] . A similarly low rate of participation from the first 10,000 women tested at Myriad was noted by Forman and Hall [43] .. To begin to address these issues in Hispanic populations, we designed a study with a number of potential advantages: a fully de-linked sample not requiring extensive counseling regarding BRCA testing; collection of saliva that can be completed in the home, community clinics or public events; bilingual study materials; and full protection of confidentiality.. Our recruitment success was very modest from online publicity (Facebook, clinicaltrials.gov), and few minority patients participate in public fund-raising events, such Fig. 2 Selected BRCA2 mutations. The Ion Torrent data displayed in IGV [51] is shown for the newly described 6005delT mutation in the left panel, a. The display shows individual forward (F) sequence reads in red and reverse (R) reads in blue. The 6005delT mutation can be seen as a gap in the sequence (arrow) in approximately half of the F and R readsthis is consistent with a heterozygous mutation. Sanger sequencing (not shown) confirmed this mutation. b. Both the Ion Torrent (above) and Sanger sequence (displayed in Mutation Explorer, SoftGenetics, below) for the C1787S and G1788D mutations are displayed in the right panel. The co-occurrence of the C1787S and G1788D variants on the same allele can be clearly seen in the Ion Torrent reads, whereas phase cannot be determined from the Sanger traces. Note: BRCA1 is in reverse orientation in the genome, and so IGV display is of the reverse complement as Avon fundraising walks. However, partnerships with community groups such as Nueva Vida (Baltimore, Richmond) and the Latino Community Development Agency (Oklahoma City) were successful in recruiting a number of Hispanic women of diverse backgrounds. The remainder of the population samples were collected at the Texas Tech University Health Science Hospitals in Lubbock and El Paso, Texas. By sending and receiving saliva kits through the US mail we were able to keep the cost of the collection/shipping and DNA preparation materials to under $20 per subject. Targeted sequencing, performed in batch sizes of 90 samples, has a materials cost of approximately $50, making the total reagent cost under $100, including Sanger validation but excluding labor. This is an important factor if sample sizes in the order of thousands of subjects are to be eventually attained.. We did identify amplicons in BRCA2 that performed poorly in most samples, having <100X average coverage, comprising 261 bp of coding region and 4 splice sites, and 1 splice site of BRCA1 poorly covered. The initial run of 92 samples had three that underperformed and required repetition (3 %); however, these samples performed well on a second run. Our second run of 46 samples allowed the average coverage to increase from 313-361X to 466X. Running 46 samples on a single chip would raise the cost/sample by $5, and may be advisable for clinical testing.. The BRCA1 gene contains multiple mononucleotide repeats, for which it is challenging to accurately detect 1 bp indels; these regions are the most problematic to detect for all current methods [36, 40, 41] . Early versions of the TVC demonstrated relatively higher error rates on homopolymer sequences [40, 41] . This performance has improved with subsequent version of TVC and three studies demonstrate that 70-130X coverage across homopolymer regions is sufficient to get accurate mutation calls in the BRCA1 and BRCA2 genes ( Table 5 , Additional file 1) [42, 43] . Using the 70X standard of Dacheva et al., besides the poor performing exons mentioned above, there are only 2 A5 homopolymer repeats in coding regions (BRCA2, exon 12, 65X average coverage) that are below this threshold in our data. In a small sample set, we show here that the Hi-Q formulation and current TVC analysis settings result in a substantial reduction in 1 bp indel calls, especially in false positive mononucleotide regions. Manual analysis of BAM files in IGV allows most of these variants to be excluded from consideration, although the difference in background between the two enzymes visible in IGV displays are not dramatic. The addition of overlapping amplicons in the most difficult regions could improve this result. Although we chose an amplicon-based method on Ion Torrent, the samples could also be run on multiple platforms or used in a capture-based method [29] . Color Genomics (https://getcolor.com/) now offers a clinical test of 19 breast cancer related genes for $249. While this initial phase of the project was designed to maximize participation and diversity at a modest cost, it has the disadvantage that subjects with mutations could not be retrospectively identified in order to benefit from the testing. A second phase, in which identifiers will be retained and patients counseled about testing, will now be initiated. We expect recruitment to increase as several individuals and groups declined to participate in the unlinked arm of the study. Population growth; advancement in age of the US Hispanic populations; and large family size make it imperative that innovative means be employed to increase participation in clinical and genetic studies. The increasingly recognized involvement of germline mutations in BRCA1 and BRCA2 in diverse cancers, as well as the active design of targeted therapies, further adds to the need to recruit minority subjects.. To date there have been no large nationwide surveys of Latin American with breast cancer. In the report by Hall et al., only the identities of mutations reaching 4 % or greater were made available [35] . The Clinical Cancer Genetics Community Research Network collected samples and data from 746 patients from 14 clinics concentrated in Southwestern USA, and individual data from centers in Texas, California, and Puerto Rico [46] . Our study adds to the diversity of Hispanic BRCA mutations, andinterestinglywe did not find the most common allele in all mainland US Hispanic studies to date, the BRCA1 185delAG mutation. Of the six mutations we identified, only one, BRCA2 E1308X, has been reported in multiple studies. A much larger study, incorporating all the regional and ethnic diversities of Hispanic populations, will have to be carried out to fully understand mutational diversity, and to aid in the classification of VUS. Clearly, a comprehensive characterization of our samples will require copy number analysis to identify large insertion/deletion mutations. Recurrent large deletions in BRCA1 have been found in both Mexican and Puerto Rican breast cancer patients [19, 20] . Rare germline mutations in other genes have been identified in familial breast cancer, and our samples could be used to scan these genes [32] or complete exomes or genomes.. While we and others have documented that the major next-generation sequencers do an excellent job in identifying single nucleotide variants, they can be deficient in the prediction of insertion and deletion variants, especially in mononucleotide repeats [41] . The BRCA1 and BRCA2 genes have numerous mononucleotide repeat regions, and these areas are rich in known mutations. Thus, a method to increase accuracy of sequencing in repeats would be welcome. We documented that the Hi-Q enzyme can achieve a significantly higher accuracy in sequencing through mononucleotide repeats. When combined with methods or specific assays for the most prevalent large deletions, a high percentage of germline mutations can be identified. A recent study with the same BRCA1/2 panel was tested in a diagnostics laboratory with high accuracy [47] . All known publications using Ion Torrent sequencing instruments to sequence known BRCA1 and BRCA2 mutations are displayed. The number of insertion/ deletion variants (indels), those of 1 base pair (1bp) and those in homopolymer regions (homopol.) are tabulated. In summary, we have succeeded in recruiting and anonymously testing diverse groups of Latin American women with breast cancer in the US, all at a materials cost of less than $100 for samples collection, shipment and sequencing, and confirmation. Using DNA sequencing, we found almost exclusively rare mutations, most of which have been observed in other studies. Expansion of this approach could be a component of a larger effort to improve the application of the benefits of genetic testing to Hispanic American women. Mutations in the BRCA1 and BRCA2 genes result in predisposition to breast and ovarian cancers [1, 2] . In addition, there is increasing evidence that BRCA mutations confer risk for cancers of the prostate, pancreas, stomach and skin [3] [4] [5] ; there is also suggestive evidence for their involvement in esophageal and gastric cancers [6] . In Caucasian and Asian ethnicities, BRCA mutations are associated with basal-type and/or -triple-negative disease (in which the estrogen, progesterone, and HER2 receptors are absent from the tumor); however, the nature of this relationship in other ethnicities is understudied [7] [8] [9] [10] .. The identification of BRCA1/2 carriers is a critical component of breast and ovarian cancer prevention as there are multiple screening, surgical, and chemoprevention strategies that can be employed. Magnetic resonance imaging (MRI) screening is effective in detecting early cancers in BRCA1/2 carriers; mastectomy and oophorectomy can reduce ovarian cancers; and estrogen inhibition can reduce both type of malignancy [11] . However, relatively few minorities have participated in these prevention studies.. Although African American and Hispanic women have a lower incidence of breast cancer, they have a higher mortality. Triple-negative breast cancer is more common in African Americans and Hispanic women, accounting, in part, for this health disparity [12] [13] [14] [15] [16] . A study of over 45,000 women referred for BRCA1 and BRCA2 mutation screening from 2006 to 2008, found that 13-16 % of African Americans, Native Americans and Hispanics possess disease-causing mutations and a high rate of variants of unknown significance [17] . An independent study of 389 African Americans and 425 Hispanic women with incomplete gene sequencing, found that 8-10 % of high-risk subjects have a BRCA1 or BRCA2 gene mutation, and a small Puerto Rican study reported a 52 % mutation rate [18, 19] . Common recurrent mutations, including large deletions in BRCA1 and BRCA2, exist in Hispanic/Latin American communities, which accounted for 35-45 % of the mutation carriers [17] [18] [19] [20] .. The BRCA1 and BRCA2 proteins play a role in the repair of double-stranded breaks in DNA. A synthetic lethal strategy for cancer therapy has been developed using DNA damaging chemotherapy agents to cause single-stranded breaks, combined with poly-ADP ribose polymerase (PARP) inhibitors, to inhibit single-stranded DNA repair. This approach may be particularly effective in BRCA mutation carriers, as the tumor will be unable to repair the double-stranded breaks [21, 22] . Clinical trials of PARP inhibitors demonstrate partial response or stable disease in breast, ovarian and prostate cancer subjects [23] [24] [25] [26] [27] .. Mutations in BRCA1 and BRCA2 have been detected with a variety of techniques including multiple mutation scanning methods and Sanger sequencing (reviewed in [28] ). Next-generation sequencing (NGS) has the benefit of high-throughput, automated sequence analysis, and single strand reads. DNA capture, droplet PCR and multiplex PCR methods of template preparation, and sequencing on 454, Illumina and Ion Torrent platforms have all been employed [29] [30] [31] [32] . A clinical diagnostic laboratory validation of the Ion Torrent platform demonstrated an absence of false negatives and a 10 % false positive rate [33] . With the availability of a three-tube multiplex for the complete BRCA1 and BRCA2 genes we sought to apply this approach to a cohort of Hispanic/Latin American breast cancer patients.

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


Evolutionary Search for Faces from Line Drawings Abstract-Single 2D line drawing is a straightforward method to illustrate 3D objects. The faces of an object depicted by a line drawing give very useful information for the reconstruction of its 3D geometry. Two recently proposed methods for face identification from line drawings are based on two steps: finding a set of circuits that may be faces and searching for real faces from the set according to some criteria. The two steps, however, involve two combinatorial problems. The number of the circuits generated in the first step grows exponentially with the number of edges of a line drawing. These circuits are then used as the input to the second combinatorial search step. When dealing with objects having more faces, the combinatorial explosion prevents these methods from finding solutions within feasible time. This paper proposes a new method to tackle the face identification problem by a variable-length genetic algorithm with a novel heuristic and geometric constraints incorporated for local search. The hybrid GA solves the two combinatorial problems simultaneously. Experimental results show that our algorithm can find the faces of a line drawing having more than 30 faces much more efficiently. In addition, simulated annealing for solving the face identification problem is also implemented for comparison. I N computer vision, an important research area is to develop algorithms that can understand a single 2D line drawing representing an object and reconstruct the 3D geometry of the object. This area belongs to the topics shape from line drawings and shape from contours. One application of this research is in CAD, where tools are highly desirable that can convert a design sketch into a 3D model directly. An object consists of faces. If the face configuration of an object is known, the complexity of the 3D reconstruction will be reduced significantly. Roughly speaking, the conversion problem can be divided into two subproblems: face identification and 3D geometry reconstruction. In this paper, we study the face identification problem only. For the 3D geometry reconstruction, the reader is referred to references [1] , [2] , [3] , [4] , [5] , [6] , [7] .. A 2D line drawing in this paper is defined as the projection of a wireframe object where all the edges (including silhouettes) and vertices of the object are visible and the drawing can be represented by a single connected edgevertex graph. A line drawing with hidden lines visible makes it possible to reconstruct its complete 3D model. Fig. 1 shows a line drawing of a solid stair model together with its 10 individual faces. Note that crossing points of two or more edges are not vertices and cannot be used to form faces. If the three edges e 1 , e 2 , and e 3 (hidden lines) are not shown, the stair model is considered as a sheet object with seven faces.. Great effort has been made in the interpretation of line drawings for the past two decades (see Section 3) . The recent work presented in [8] and [9] can handle a larger range of objects than others in face identification. Both methods include two steps: finding a set of circuits that may be potential faces and searching for real faces from this set. Given a set of circuits, Shpitalni and Lipson used a tree search scheme for finding the real faces [8] , while Liu and Lee developed a maximum weight clique finding algorithm for the same goal [9] . It needs to be emphasized that the two steps in each of the two methods correspond to two combinatorial problems. It is well-known that there have been no efficient algorithms for general tree search and maximum weight clique problems. The problems become even more difficult owing to the fact that their inputs are circuits of a line drawing, the number of which is generally exponential in the number of edges of the drawing [10] . In Section 5, it can be seen that the combinatorial explosion prevents the two methods from handling a line drawing having many faces (> 35) within feasible time.. Genetic algorithms (GAs) are a class of probabilistic search algorithms that emulate natural evolutionary process. GAs, if well designed, can often outperform traditional optimization methods. Many successful applications of GAs to various problems have been published in the literature [11] , [12] , [13] , [14] . In this paper, we design an efficient GA with variable-length chromosomes to solve the face identification problem. Geometric constraints on circuits of a line drawing and a heuristic called minimal edge face phenomenon are developed and incorporated into the operations of the GA. The proposed hybrid GA simultaneously tackles the two combinatorial problems involved in the previous methods [8] , [9] . Our experiments show that the new algorithm reduces the computational complexity of face identification from exponential to linear with respect to the number of edges in line drawings.. The rest of this paper is organized as follows: In Section 2, we briefly describe the technical terms that will be used in this paper. The related work on line drawing interpretation is described in Section 3. The proposed hybrid GA for the face identification is presented in Section 4. Section 5 shows experimental results and comparisons of computational times and memory requirements between the new algorithm and the previous ones. In Section 6, we implement a simulated annealing algorithm and compare it with the GA. Finally, the conclusions are given in Section 7. A hybrid GA for finding faces from single 2D line drawings has been presented. The faces identified from a line drawing provide important information for the reconstruction of its 3D geometry. From the experiments, it can be seen that the HGA finds the same faces as the previous two algorithms do, but exhibits significantly better performance for objects with faces > 30, both in computational time and memory requirement. The obstacle for the two previous methods to handle such objects is that each of them involves two combinatorial problems: searching for all MPFs from a line drawing and then searching for faces from the MPFs. This combinatorial explosion makes it difficult, if not impossible, for the two algorithms to handle objects with faces > 30.. Our strategy to conquer the combinatorial explosion is to combine the standard GA with a novel local search scheme. The former is well-known for its good global search ability; the latter has a high likelihood of finding faces directly from a line drawing based on the maximum edge ranks, face adjacency theorem, and minimal edge face phenomenon. The amount of memory allocated in our HGA depends on the size of the population, the maximum length of a chromosome, and the maximum length of a circuit. These quantities do not increase much with the increase of edges in a line drawing. For all the line drawings in the experiments, the HGA takes less than one second to deal with each of them on a 1 GHz Pentium III PC. From the two sets of objects given in Figs. 8 and 10, we can see that the computational time of the HGA grows approximately linearly with the number of edges of the drawings, presenting excellent computational performance. The experiments also demonstrate that the HGA is robust in finding optimal solutions.. We have also implemented a simulated annealing algorithm for face identification based on the local search scheme. Similarly to the HGA, the SSA is designed without the need to search for all the MPFs from a line drawing. The HGA works slightly better than the SSA. We may divide the related work on interpretation of line drawings into three areas: line labeling, 3D reconstruction from multiple views of wireframe models, and face identification and 3D reconstruction from single line drawings with hidden lines visible. Methods for line labeling focus on finding a set of consistent labels from a line drawing without hidden lines in order to test if it is legal and/or on 3D reconstruction based on such a labeled line drawing [17] , [18] , [19] , [20] , [21] , [22] , [23] . Approaches in the second area try to reconstruct a 3D CAD model from its multiple (three, in general) orthographic projections [24] , [25] , [26] . More information can be found from three orthographic views for the reconstruction task than from a single projected view, which is the premise of the third area. Our work belongs to the third area. We especially focus on face identification from single line drawings with hidden lines visible. The earliest work in face identification was done by Markowsky and Wesley [27] . Their topologically-driven algorithm can handle only wireframes with straight lines and planar faces and requires the 3D coordinates of vertices to calculate the normals of planes.. Hanrahan [28] and Dutton and Brigham [29] used purely topological methods to find the faces of a drawing. A drawing (graph) is embedded in the plane with a planar embedding algorithm [15] . The resulting regions represent the faces of the corresponding object. Their methods are suitable only for objects of genus 0 whose drawings are 3-connected, due to the requirement of a unique planar embedding for a drawing. Another approach presented by Ganter and Uicker [30] also uses concepts from graph theory. It is based on the spanning tree of the graph of a drawing. The problem with this approach is that it cannot handle objects with holes. Hojnicki and White [31] improved Ganter and Uicker's algorithm by employing better cycle reduction schemes. However, if the number of faces of an object of genus > 0 is unknown in advance, their algorithms still fail when dealing with it.. Agarwal and Waggenspack's method [32] employs a divide-and-conquer strategy to remove stars (tetrahedra, N-sided pyramids, or multiply connected stars) from a drawing. The faces of the drawing are obtained by combining triangles that are created from the stars. Based on a number of properties implied in line drawings representing manifold objects, Liu et al. [33] used a tree search scheme to find the faces of manifolds.. The abovementioned methods for face identification were designed basically for dealing with solid objects, compared with which the following two methods can handle a larger range of objects (e.g., the manifold shown in Fig. 1 and the nonmanifold in Fig. 2a ). Because these two methods are most related to the work in this paper, we give more detailed descriptions of them in the following sections.

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


Sensitivity and uncertainty analysis for river quality modelling Uncertainty analysis for model simulation is of growing importance in the field of water quality management. The importance of this concern is provided by recent public awareness over health risks from improper disposal of toxic wastes as well as by the continuing emphasis on risk assessment. The first step in the chain of risk assessment is the quantification of the error in predicting water quality.In each mathematical modelling application, different uncertainties are involved. The uncertainty sources can be classified into different categories (in this study, as model-input uncertainty, model-structure uncertainty, model-parameter uncertainty and measurement errors). These different types of uncertainty sources determine collectively the total uncertainty in the model results. In this paper, the relative contributions of uncertainties associated with each source are studied for the physico-chemical water quality modelling of a river in Belgium. This provides information as to where available modelling resources should be focused. Mechanistic modelling of physical systems is often complicated by the presence of uncertainties. River water quality modelling, for example, entails uncertainties in the estimates of pollutant emissions, transformation and transport parameters, etc., that impact on estimates of the water quality status of the river and of the related risks.. The implications of these uncertainties are particularly important in the assessment of several potential regulatory options, for example, with respect to the selection of a strategy for the control of pollution levels. Even though significant effort may be needed to incorporate uncertainties into the modelling process, this could potentially result in providing useful information that can aid in decision-making.. A systematic uncertainty analysis provides insight into the level of confidence in model estimates and can aid in assessing how various possible model estimates should be weighed. Further, it can lead to the identification of the key sources of uncertainty (such as data gaps) which merit further research, as well as the sources of uncertainty that are not important with respect to a given response.. The purpose of quantitative uncertainty analysis is to use currently available information in order to quantify the degree of confidence in the existing data and models.. The purpose is not to somehow 'reduce' uncertainty.. Reduction in uncertainty can only come from gathering additional information and filling 'data gaps'. Even though the applicability of a model is limited by the model assumptions, the input data and the uncertainties in the evaluation data, understanding the judgements associated with the modelling process is more valuable than sidestepping the uncertainty analysis. In fact, it is precisely for problems where data are limited and where simplifying assumptions have been used that a quantitative uncertainty analysis can provide an illuminating role, to help identify how robust the conclusions about model results are, and to help target data gathering efforts (Frey 1992) .. For each mathematical modelling application, different uncertainties are involved. In this study, the uncertainty sources have been classified into the following categories: The primary objective of the sensitivity and uncertainty analysis presented in this paper is to study the uncertainties associated with each of the above-mentioned uncertainty sources. Further, this can be used to identify the relative contributions of uncertainties associated with each source. This provides information as to where available resources should be focused, for example, increasing the amount of input data to calibrate the model parameters, filling data gaps, through more detailed measurement campaigns or by model-structure refinement. Uncertainty analysis for model simulations is assuming a growing importance in the field of water quality management. The importance of this concern is provided by recent public awareness over health risks from the improper disposal of pollutants as well as by the continuing emphasis on risk assessment. The first step in the chain of risk assessment is quantification of the error in predicting water quality.. In water quality models for water resources management and planning, the model output depends on the modelled processes (model structure), the input data and a number of parameters, which are essentially not known perfectly. The task of the uncertainty analysis is to estimate the different uncertainty contributions to the model output in terms of the uncertainties in the input, the model parameters and the model structure. Also, the measurement errors have to be taken into account. To be able to do this analysis for the water quality model results, the uncertainty due to the hydrological and hydrodynamic modelling has to be excluded in a first step. Then the remaining uncertainty can be explained by the water quality modelling. To split this uncertainty into the different components, the model structure uncertainty was first calcu- (Rauch 1998) .

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


Good Recognition is Non-Metric Abstract-Recognition is the fundamental task of visual cognition, yet how to formalize the general recognition problem for computer vision remains an open issue. The problem is sometimes reduced to the simplest case of recognizing matching pairs, often structured to allow for metric constraints. However, visual recognition is broader than just pair matching -especially when we consider multi-class training data and large sets of features in a learning context. What we learn and how we learn it has important implications for effective algorithms. In this paper, we reconsider the assumption of recognition as a pair matching test, and introduce a new formal definition that captures the broader context of the problem. Through a metaanalysis and an experimental assessment of the top algorithms on popular data sets, we gain a sense of how often metric properties are violated by good recognition algorithms. By studying these violations, useful insights come to light: we make the case that locally metric algorithms should leverage outside information to solve the general recognition problem. Recognition is a term everyone in computer vision and machine learning understands -or at least we think we do. Despite multiple decades of research, it may be somewhat surprising to learn that a very basic question remains unresolved: is recognition metric? Familiar distance metrics used in vision include Euclidean distance and Mahalanobis distance, both computed in feature space. Given one of these metrics, the task of recognizing an unknown object can be approached by finding the class label of its nearest neighbor under that distance metric in a set of training samples. Clearly such an approach provides a recognition function, so some level of recognition can be accomplished with a metric. However, at a more fundamental level, we would like to know if distance truly captures all that is meant by the term recognition, and if metrics are good approaches to solving complex recognition tasks in computer vision. In this paper, we adopt the convention that a problem is metric if the best solutions to that problem can be achieved by directly applying a distance metric to compute the answer.. An important observation with implications for recognition is that in separable metric space, using a distance metric and the nearest neighbor (NN) algorithm provides useful consistency. As the number of i.i.d. samples from the classes approaches infinity, the NN algorithm will converge to an error rate no worse than twice the Bayes error rate, i.e. no worse than twice the minimum achievable error rate given the distribution of the data [11] . To many, this convergence theorem suggests that A common constraint placed upon recognition algorithms is that they must be metric, meaning their distance scores adhere to the properties of non-negativity, identity, symmetry and the triangle inequality. At first glance, the scores from many recognition algorithms appear to satisfy these constraints. However, violations can be subtle. For example, the distance scores produced by the top-performing Tom-vsPete algorithm [1] for these images from LFW [18] violate the triangle inequality. recognition can always be formulated as NN matching with an appropriate distance metric. However, having to double the error of the optimal algorithm over the same data often does not lead to a particularly good algorithm. This becomes apparent when actual error rates are considered during experimentation.. With the recent popularity of metric learning [8] , [13] , [20] , [25] , [37] , [58] , [60] for various recognition tasks, where a metric is learned over given pairs of images that are similar or dissimilar, one might infer that recognition is always a metric process. We note that the NN convergence theorem [11] is true for any metric -hence any improvements from the choice of metric, or metric learning, are not about the asymptotic error, but something else such as the error for finite samples and/or the rate of convergence. This paper will show that while metric learning can produce reasonable results, enforcing metric properties leaves out information, often limiting the quality of recognition with finite data.. If the convergence theorem itself is about recognition, then the recognition problem is assumed to be formulated in an arXiv:1302.4673v1 [cs.CV] 19 Feb 2013 asymptotic sense with infinite i.i.d. samples. We argue that visual recognition does not rely on either of those assumptions, but rather focuses on maximizing the accuracy for finite, and, unfortunately, opportunistic and hence potentially biased sampling.. Recall that a function d : X × X → R is metric over a set X if it satisfies four properties for {x, y, z} ⊆ X:. Metric functions have useful properties that allow one to show that a particular problem leads to a convex minimization problem, or that various types of sequences converge in the limit. There are also several cases where one of the properties is excluded. Functions that do not satisfy the triangle inequality are called semimetrics, those that violate symmetry are called quasimetrics, and those missing one or both halves of the identity requirement are called pseudometrics 1 . While the term "distance measure" is sometimes used to mean a distance metric, it is more appropriate to use this term to mean a measurement that provides information about dissimilarity, but may be formally non-metric (our use of the term follows this convention).. A natural place to begin examining if recognition is metric is to consider its formulation. Is it reasonable to assume that a distance metric d maps pairs of elements from X into R during recognition? When a person recognizes an object, do they refer to an actual image of the object of interest? A more likely alternative is a comparison to a stored model with a more complex internal representation, not a direct copy of some prior trained input. This view is consistent with prototype theory [40] in cognitive psychology. Thus, at a structural level, recognition in this mode takes an input x ∈ X, and a model M, and hence cannot be metric because it is not even of the proper functional form. It is possible to build a model using just x, and then consider the distance between models. However, for many commonly used recognition algorithms, e.g. support vector machines, one cannot induce a proper model from a single input. Thus, the general problem of recognition cannot be restricted to just metrics, even though it must include them.. To structure the recognition problem in a form consistent with directly using a distance metric, various approaches formulate it as a pair matching task. This is a specific case of recognition: given a pair of images, an algorithm must indicate whether or not they match (the popular face recognition challenge problem Labeled Faces in the Wild [18] is of this form). While it is convenient to build a binary classifier for this type of problem and easier to evaluate this type of data, pair matching itself cannot be considered the general recognition problem, where n number of known classes might be candidates during matching, represented by complex models incorporating information from potentially thousands of training images.. It is also natural to ask if the human mind, a most successful recognition system, operates in a way that satisfies the key metric properties of symmetry and the triangle inequality. The consensus in the cognitive psychology community is a definitive no. In seminal work, Tversky [47] showed that human analysis of "similarity" is non-symmetric and is context dependent. One of the visual experiments conducted by Tversky was a simple pair matching task, where subjects were asked if two block letters were the same or not. A similarity function S(p, q) indicated the frequency at which subjects noted letter p to be the same as q. The experiment showed that the order of presentation of the letters mattered in a statistically significant way: S(p, q) S(q, p). This result, along with others for matching faces, abstract symbols, and the names of countries led Tversky to conclude that "similarity is not necessarily a symmetric relation.". In subsequent work, Tversky and Gati [48] examined if the triangle inequality is satisfied by humans when assessing similarity. Because the triangle inequality can always be satisfied by adding a large constant to the distances between individual points when measuring dissimilarity on an ordinal scale, Tversky and Gati proposed a test that assumes segmental additivity:. Over numerous pair matching trials across stimuli, human similarity judgments were found to violate the triangle inequality in a statistically significant manner. Even without the triangle inequality for additive functions, it is still possible to induce metric models with subadditive metrics. However, in experiments where subjects provided subjective probability estimates, Tversky and Koehler [49] showed that the reported scores are, in general, not subaddative 2 . If humans are employing non-metric, non-symmetric similarity measures, do we really want to constrain our recognition algorithms in computer vision to be metric? Addressing this notion, we present the following contributions:. • A new general definition of recognition that is not restricted to pair matching, and which includes provisions for complex models trained over sets of images and assumptions.. • An extensive meta-analysis of metric learning on vision problems, along with experiments that give an indication of how often metric constraints are violated for top performing algorithms and common data sets.. • A series of useful recommendations, based on our results, for recognition algorithm designs in metric and non-metric spaces. Our meta-analysis, which often required digging very deeply into papers that at first glance had titles and terminology suggesting a metric algorithm, revealed that many such cases are in fact non-metric in their final scoring. Def. 1 and a clear specification of where to test for metric properties should help resolve such ambiguity going forward. In some of the truly metric cases, we cannot actually tell if enforcing metric properties helped or hurt performance. When approaching recognition, it is important that we understand what leads to improvement, and what is tangential.. During the course of this work, we found that some problems and their corresponding solutions do not even have the structural form necessary to be metric -they compare input features to more complex models. Similar observations have been made. In [4] it is proved "that under the Naive-Bayes assumption, the optimal distance to use in image classification is the KL "Image-to-Class" distance, and not the commonly used "Image-to-Image" distribution distances." Moreover, even for the restricted recognition problem of matched pairs, which at least initially looks as if it is metric, the best performing algorithms have a model for "matched pairs" that is nonmetric. Metric properties allow some powerful mathematical machinery to be employed and, with effort, any recognition problem's solution can be "made" metric -the real question is if employing metric constraints improves recognition performance. Our meta-analysis and experimental analysis of top-performing algorithms show violations of symmetry for some and violations of the triangle inequality for others. With so many cases where performance improves as metric conditions are relaxed, we conclude that, in general, good recognition is non-metric.. However, this paper should not be interpreted as suggesting that metrics have no role in computer vision or that metric learning is not useful for recognition. On the contrary, our analysis has shown that metric learning has provided interesting first cut solutions. Furthermore, many good recognition algorithms use local metrics as the core of an overall nonmetric algorithm. Learning metrics, at least locally, appears to be an effective way to incorporate various type of constraints. In many cases, the original feature space (Eq. 1) is transformed into another locally normalized/metric feature space, before combining data, yielding a non-metric but effective scoring process.. One observation, which can be exploited in other vision work, is why we believe the problem is inherently non-metric. General recognition problems need to capture and model the uncertainty in the data and in the class definitions. They must handle local variations in features, in sample density and in labeling. If, as is true in the general setting, the data is not uniformly sampled with uniform error, good recognition algorithms develop local distance measures in a way that may result in asymmetric measures and/or measures that violate the triangle inequality. Thus, even if one chooses to use local metric learning to help normalize the data, one should also look for models that integrate multiple sources of information (including sideinformation and other assumptions) and use them to model the regional variations and errors.. A good metric-based recognition algorithm would need to have approximately uniform error. If its "learning" could transform an inherently non-uniform biased sampling and errors into a single representation with uniform errors, it would provide a near perfect "whitening" filter correcting the per-class biases and errors. While it is true that in the limit, assuming i.i.d. samples, a metric + nearest neighbor classification has an error rate no more than twice the Bayes error rate, we note that "in the limit' the infinite i.i.d. sampling requirement is effectively removing any sampling bias and providing uniform error. Most recognition problems do not have the luxury of i.i.d. sampling nor can they wait for the limit of infinite samples. Thus we believe it is important that computer vision researchers develop robust features and models of uncertainty/error to design more effective recognition algorithms. Finally, we should not stray far from the observations of Tversky, who states that metrics, "which enhance the interpretability and appeal of spacial representations, cannot always be accepted as valid principles of psychological similarity" [48] .

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


Coalgebraic Characterizations of Context-Free Languages Abstract. In this article, we provide three coalgebraic characterizations of the class of context-free languages, each based on the idea of adding coalgebraic structure to an existing algebraic structure by specifying output-derivative pairs. Final coalgebra semantics then gives an interpretation function into the final coalgebra of all languages with the usual output and derivative operations. The first characterization is based on systems, where each derivative is given as a finite language over the set of nonterminals; the second characterization on systems where derivatives are given as elements of a term-algebra; and the third characterization is based on adding coalgebraic structure to a class of closed (unique) fixed point expressions. We prove equivalences between these characterizations, discuss the generalization from languages to formal power series, as well as the relationship to the generalized powerset construction. The set P(A * ) of all formal languages over an alphabet A is a final coalgebra of the functor B × (−) A , where B is the Boolean semiring with carrier {0, 1}, uniquely defined by the defining equation 1 ∨ 1 = 1. Deterministic automata are B × (−) A -coalgebras and their behaviour, in terms of language acceptance, is given by the final homomorphism into P(A * ). A language is regular if it is in the image of the final homomorphism from a finite B × (−) Acoalgebra to P(A * ). Or, equivalently by Kleene's theorem, if it is in the image of the final homomorphism from the set of regular expressions, which constitute a B × (−) A -coalgebra by means of so-called Brzozowski derivatives.. Thus the coalgebraic picture of regular languages and regular expressions is wellunderstood (cf. [Rut98] for details). Moreover the picture is so elementary that it has recently been possible [Sil10] to generalize it to a large class of other systems, including Mealy machines, labelled transition systems, and various probabilistic automata.. In this article, we develop a similar coalgebraic picture for context-free languages, which form another well-known class, extending regular languages. Our focus is on context-free grammars, one of the common definition schemes for context-free languages. (Another well-known characterization is through pushdown automata, which are treated here.). Because the set of all languages is a final coalgebra of the functor B × (−) A , we model context-free languages using coalgebras for this functor. We do so in three different but ultimately equivalent ways:. (1) In Section 3, we view context-free grammars in Greibach normal form as coalgebras for the functor B × P ω ((−) * ) A , or equivalently, as systems of behavioural differential equations, where each derivative is given as a set of words of nonterminals. These coalgebras can then be canonically extended to B×(−) A -coalgebras, yielding a mapping to the final coalgebra of all languages that coincides with the classical denotational semantics of context-free grammars. For example, in the system o(x) = 1 x a = {xy} x b = ∅ o(y) = 0 y a = ∅ y b = { } x is mapped onto the language {a n b n | n ∈ N}.. (2) In Section 4, we will represent context-free languages using coalgebras for the functor B × T(−) A , where T(X) is the free term algebra containing all terminals in A and nonterminals in X, constants0 and1, and closed under binary operations + and ×. These coalgebras can be seen as syntactic systems of behavioural differential equations, again can be extended to B×(−) A -coalgebras, and thus be assigned a semantics through the final coalgebra mapping. (3) In Section 6, we will define context-free languages and power series by means of generalized regular expressions, in which the Kleene star operation is replaced by a unique fixed point operator. The set of closed expressions again can be given a B × (−) A -coalgebra structure, again yielding an operational semantics through the final homomorphism into the coalgebra of all languages. We show that the three coalgebraic characterizations above are equivalent in the following sense: a language is context-free if and only if it is in the image of the final homomorphism of an extension of a B × P ω ((−) * ) A -coalgebra; if and only if it is in the image of the final homomorphism of an extension of a B × T(−) A -coalgebra; if and only if it occurs as the image under the final homomorphism of some context-free expression.. In Section 5, we will moreover generalize the picture to a wider class of systems, namely to Moore automata where the output alphabet possesses a commutative semiring structure. Here, we obtain a coalgebraic characterization of classes of formal power series, which can be called context-free or (constructively) algebraic.. In Section 7, we will cast the results from this article in a categorical framework, by showing that the constructions from Sections 3 and 4 can be seen as instances of the generalized powerset construction presented in [SBBR10] , and highlight some of the subtleties that arise when this is attempted.. This article is an extended and revised version of [WBR11] , which has been presented at the CALCO conference in 2011. Some newer results from [BRW12] have been incorporated as well. The main new contributions of the present version include a more precise and formal presentation of the results, a more comprehensive treatment of the connection to the 2.2. Category theory. Although for the most part (with the major exception of Section 7), this article only has a light dependence on category theory, we will occasionally make use of the language of category theory. When we do this, we will assume familiar the notions of categories, (endo)functors, and natural transformations. Furthermore recall that a monad on a category C consists of an endofunctor T on C, together with two natural transformations η : 1 C → T , called the unit of the monad, and µ : T 2 → T , called the multiplication of the monad, such that µ • µ T = µ • T µ, and µ • η T = 1 = µ • T η.. In general, given a category C and endofunctor T , a T -algebra consists of an object X of C, together with a mapping α : T X → X. Given a monad T over a category C, an algebra for the monad T is a T -algebra α such that α • η X = 1 X , and α • T (α) = α • µ X . We note that, given any X, µ X : T 2 X → T X is the free T -algebra over X.. For a more comprehensive background view on monads, algebras, and category theory in general, we refer to e.g. [Awo10] . Our coalgebraic account of context-free languages in terms of grammar coalgebras and automata, syntactic systems of behavioural equations, and closed µ-expressions can be taken as a starting point for a generalization in at least two different and orthogonal directions. In one direction (in which the first steps have already been taken, see Section 5 and [BRW12]), we can generalize from languages towards power series in commutative semirings. Here, a good deal of work remains to be done in order to see how existing results from the literature on formal power series and languages can be cast into the coalgebraic framework, and to find uses of coalgebraic and coinductive techniques in this area.. In another direction, we can consider other languages of expressions for the functor B × (−) A to obtain different classes of languages. As an interesting example of this type, one could consider syntactic systems of behavioural differential equations for which the term at the right of each equation stems from the language of expressions:. The semantic solution of such a system is given by regular languages, while the syntactic one is given by a language of expressions as studied in [SBR10] . The corresponding notion of grammars for regular languages is then given by considering productions of the form p : X → B × P ω (A * × X) A , i.e. right-linear grammars [HMU06] . When we generalize this language of expressions to the specification. over an arbitrary semiring K, we obtain the rational power series over K. In both cases, it is also possible to give a corresponding notion of µ-expressions.. It might also be worthwhile to look at systems of equations in which other coinductively specified operators than sum and concatenation (or, in the general case, the convolution product) are involved: we can for example investigate systems of equations where, on the right-hand side, the operator for language intersection (or, more generally, the Hadamard product) is allowed. Because the class of context-free languages is not closed under intersection, it is directly clear that adding this operator to the language of terms will yield a larger class of languages.. Further research directions include a coalgebraic characterization of context-free languages in terms of pushdown automata [HMU06] , and the study of coinductive decision procedures for bisimilarity of subclasses of the context-free languages of which equivalence is decidable, such as deterministic pushdown automata [Sti01] and visibly pushdown automata [AM04] .

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


Alignment of Optical Maps We introduce a new scoring method for calculation of alignments of optical maps. Missing cuts, false cuts, and sizing errors present in optical maps are addressed by our alignment score through calculation of corresponding likelihoods. The size error model is derived through the application of Central Limit Theorem and validated by residual plots collected from real data. Missing cuts and false cuts are modeled as Bernoulli and Poisson events, respectively, as suggested by previous studies. Likelihoods are used to derive an alignment score through calculation of likelihood ratios for a certain hypothesis test. This allows us to achieve maximal descriminative power for the alignment score. Our scoring method is naturally embedded within a well known DP framework for finding optimal alignments. O ptical mapping is a powerful technology that allows construction of ordered restriction maps. Each optical map is a single DNA molecule digested by the restriction enzyme and imaged by the optical system. The map is comprised of estimates of fragment sizes in the order they appear on the imaged molecule. Hence, there are two types of information associated with each optical map: sizes of restriction fragments on the molecule and their relative order.. A broad spectrum of problems can be effectively addressed by means of optical mapping. Among the most important are analysis of genomic variation (deletions, insertions, and rearrangements on a scale of thousands of base pairs), construction of genomewide restriction maps without knowledge of the original DNA sequence, validation and finishing of sequence contigs, and genomic placement during sequencing projects. Despite the fact that optical mapping lacks single nucleotide resolution, it is capable of quickly In this paper, we formulated a novel statistical model for the measurements of fragment sizes that arise in optical maps. We also proposed a novel model to address false cuts in optical maps. These two models, along with previously known models, such as distribution of restriction sites and observation of cuts in optical maps, are combined to derive a likelihood ratio based alignment score that we report in this paper. We also show how this score can be used within an existing DP framework for finding optimal alignments. Our alignment score improves existing methods because it (1) does not require guessing of alignment parameters as is the case for heuristic scores (all distribution parameters are derived once from the mapping system) and (2) provides maximum discrimination power for scores of true alignments compared to spurious ones. We have tested our likelihood ratio based score on a variety of organisms and sets of optical maps. Our scoring method is highly capable of producing accurate alignments. 1 Figure 2 illustrates one such alignment along with the scoring pattern. Overall, spurious alignments have low scores, usually close to or less than zero (natural logs), while correct ones usually produce very high scores, usually in the neighborhood of 100 (natural logs) depending on the map size. Naturally, longer maps are easier to align correctly because they contain more information in the form of fragment sizes.. Next we demonstrate the advantage of our new likelihood based alignment score over the heuristic alignment score for restriction maps proposed by Waterman et al. (1984) . Hereafter, "likelihood score" refers to the score described in this paper, and "heuristic score" refers to the heuristic alignment score due to Waterman et al. (1984) . Table 1 demonstrates some comparative results between these two alignment scores. We have synthetically generated 1,000 maps from a region of human chromosome 13. For generation of maps, we have used our model assumptions for sizing errors, missing cuts, and false cuts. This made it possible to infer exact positions from where maps were generated, as well as the exact positions of all true cut sites, together with information concerning which cuts are spurious. We then aligned these maps to the reference genomic restriction map of the human chromosome 13. By comparing original and fit positions, we were able to infer whether the fits were correct. For correct fits, we have collected information about correctly and incorrectly aligned sites and summarized them in Table 1 .. As is evident, both alignment methods produce similar results for synthetic maps with our new method, likelihood having a slight advantage. However, the most important feature of the score is its discriminative power for distinguishing true and spurious alignments. It turns out to be significantly different for the two scoring schemes (refer to Table 2 ). For each synthetic map that fits into the correct reference location (using both likelihood and heuristic scores), we have collected its 20 best alignment scores (10 in each orientation, including the score for the true fit) by declumping dependent alignments. The idea is that if the discriminative power of the score is high, no other independent alignments will have scores in the proximity of the score of the true alignment (corresponding to the correct fit). To measure this, we counted the number of other alignment scores (from the 19) within k standard deviations of the true alignment score. Standard deviation of that score was estimated based on fit scores from 10,000 random maps with the same number of fragments as the map of interest. The results for both methods are summarized in Table 2 .. As now becomes apparent, the likelihood score possesses significantly more discriminative power since even within three standard deviations of the true fit score, on average 0.17 spurious fit scores are observed, while the same number for the heuristic score is 6.28 (≈ 37 times more). Not surprisingly, our likelihood score, when compared to the heuristic score, shows even more discriminative power for real optical maps when compared to the same result based on synthetic maps. Hence, our alignment score produces significantly more confident alignments for real optical map data compared to the heuristic score.. We used a Kim strain of Y. Pestis commonly known as plague to study the performance of the alignment score on real data. The data set was comprised of 251 optical maps. The reference restriction map was inferred from the NCBI sequence database. This bacterial genome consists of 4.6 Mb and 267 restriction a Maps are being fitted into the reference. False positives and false negatives rates are calculated for the maps fitted into correct reference location using both methods. False positives represent the percentage of false cuts incorrectly matched to the reference, false negatives represent percentages of unmatched true restriction sites. The corresponding alignment parameters are chosen to be µ = 0.2, ν = 1, λ = 2 for the heuristic score and σ 2 = 0.306, λ = 32, p = 0.8, ζ = 0.005, η 2 = 5 for likelihood score. a Scoring parameters for likelihood and heuristic scores are taken to be the same as in Table 1 . Of the 20 top scores of independent alignments (10 in each orientation), the table gives the average number of scores (other than optimal) within k standard deviations (k = 1, 2, . . . , 9) of the optimal score. Hence, table entries never exceed 19. Likelihood score refers to likelihood ratio scoring scheme (σ 2 = 0.306, λ = 17, p = 0.8, ζ = 0.005, η 2 = 5) and heuristic score refers to a score suggested by Waterman et al. (1984) (µ = 0.2, λ = 2, ν = 1). Optimal score corresponds to the top alignment score for the given map. Optimal p-value corresponds to the p-value of the optimal score. Total of 251 different maps were fitted. For likelihood, 174 passed 0.002 p-value threshold; for heuristic, 119 passed 0.002 p-value threshold.. sites specific to the XhoI endonuclease that was used for digestion of its DNA during collection of optical maps.. For real optical maps, we have calculated alignments using both likelihood and heuristic scores. Furthermore, a p-value threshold of 0.002 was used to select confident fits. As a result, the likelihood score allowed 174 maps to pass the p-value threshold, while only 119 maps passed the same threshold using the heuristic score. Notably, our alignment score allowed us to confidently align 47% more maps than did the heuristic score, which is significantly larger than the result for synthetic maps. Selected comparisons are shown in the Table 3. P-values were computed based on simulation. For an optical map of n fragments, 10,000 random maps (each composed of n fragments) are generated by sampling from the fragment size distribution for optical maps in the current mapping project. Then, each random map is fitted into the reference, and its optimal score is stored. For the optimal alignment score of an optical map, the p-value is based on the number of optimal scores in simulation (out of 10,000) exceeding the given alignment score. It took 10,000 random maps in order to achieve the p-value accuracy of 10 −4 in Table 3 . Thus, we need to show results only for optical maps with one p-value larger than 10 −4 and at least one significant score (p − value < 0.002). Nine maps satisfying these conditions were selected to illustrate the significance of the results.

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


On the Importance of Transition Regions for Automatic Speaker Recognition This letter describes the importance of transition regions, e.g. at phoneme boundaries, for automatic speaker recognition compared with using steady-state regions. Experimental results of automatic speaker identification tasks confirm that transition regions include the most speaker distinctive features. A possible reason for obtaining such results is described in view of articulation, in particular, the degree of freedom of articulators. These results are expected to provide useful information in designing an efficient automatic speaker recognition system. There have been various research activities on assessing the relative importance of phonetic classes to speaker recognition. Fundamentally, they use the fact that some classes of phonemes, such as vowels and nasals, include more speaker-related information than obstruents such as stops, affricatives, and fricatives [1] . One of the approaches assigns different weights to each phoneme depending on how much each phoneme includes speaker related information [2] . Pelecanos et al. found an optimal feature type and a frame length of each phoneme for speaker identification [3] . Gutman and Bistritz investigated phoneme-adapted Gaussian mixture models (GMM) to enhance overall speaker verification performance [4] .. In addition to using intra-phonetic information, there have been other approaches introducing inter-phonetic information such as coarticulatory effects in recognition [5] . In fact, conventional research in speech has focused on finding invariant cues for uncovering phonetic identity from the acoustic signal, and has traditionally regarded coarticulatory effects as a nuisance. We can then question whether those regions of speech which seem most problematic in yielding phonetic information should be rich in providing other unrelated information, such as speaker identity. In past studies in acoustic phonetics, "steady-state" characteristics corresponding to phonemes in the acoustic signal have been suggested as "targets" for articulatory realization. It has been also shown that speakers enjoy some degree of freedom in the production of a given phoneme [6] , [7] the production process, as articulatory targets are continuously being supplied, the articulatory organs attempt to produce the configurations for the targets; however, they are not constrained by any targets during those intervals in between. These transition regions, which straddle the interval between acoustically steady portions of the speech signal, display much of the coarticulatory effects that occur between phonemes, and are most free to be produced by whatever combination or sequence of mechanisms each speaker wishes to employ, subject only to physical constraints. Thus, it is expected that these regions contain the major part of inter-speaker variability in the signal, which may be exploited in schemes for speaker identification. Actually, in [8] , the authors have shown that the transition frames have more discriminative power than stationary frames. However, they only focused on building efficient speaker recognition system by utilizing difference between steady-state regions and transition regions without in-depth investigation of transition regions. Hence, in this paper, we focus on transition region itself and verification of speaker discriminative capability of transition regions. The motivation of this paper is to re-examine the discriminative capability of each phonetic class, especially transitions. At first, we verify the relevance of our assumption by evaluating the recognition error rates as the number of test frames used in each class varies. To further investigate the impact of transition regions in detail we classify transition regions into four categories depending on the manner types of the preceding and the following phonemes, and compare recognition rates for each type of transition. Experimental results confirm the discriminative power of transition regions, especially in the segment boundary between two vowels. Finally, we describe possible reasons for obtaining the outcomes by linking them to the physical characteristics of voice production mechanism, especially to the degree of freedom while pronouncing sounds. The outcome of the experimental results and the analysis will provide useful information for designing speaker recognition systems. This letter describes the importance of transition regions in speaker identification tasks. We defined the transition frame as a frame straddling two or more phonemes in speech frames obtained from conventional short-time speech analysis processing and performed speaker identification tests for each phoneme class and the transition class. From various experiments, we found that transitions had the best speaker discriminative capability. Moreover, among the transitions, vowel to vowel transitions gave the best improvement.. The outcomes obtained in this letter can be used for designing efficient automatic speaker recognition systems. For example, we may enhance recognition accuracy by increasing the number of features extracted in transition regions and/or by assigning higher weights to the transition region relative to other regions. The analysis we have made in this letter can be further extended if we find a relationship between speaking rate and speaker recognition performance as well as the effects of adopting variable lengths of analysis frames at the feature extraction stage.

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


Biomedical Informatics Research and Education at the EuroMISE Center Objectives: In the paper we described the partial achievements reached by the EuroMISE Center in research and higher education, supporting better healthcare in future information society. Methods: Through the research cooperation, the EuroMISE Centre suggests publicly available tools and methods that allow the application of new technologies for various healthcare organizations and citizens, with a special focus on the national environment of the Czech Republic. It provides a platform for a greater level of research cooperation with the usage of the most up-to-date information and communication technologies and a wide spectrum of clinical and genetic data and knowledge. Results: Results of research and higher education of the EuroMISE Centre in the field of Biomedical Informatics are described in outputs of national and European projects. Further results have been published and/or presented at national and international meetings and incorporated in education and healthcare practice. Conclusions: The long-term effect of postgraduate doctoral education in the field of biomedical informatics consists in the rapid increase of scientists that are needed in the Czech Republic to reach the goals of information society in health care. The multidisciplinary research at the EuroMISE Center moves towards direct usage in the informational support of diagnostics and therapy, mining of the medical databases, and in the customization of healthcare based on the clinical and genetic profile of a patient. The European Centre for Medical Informatics, Statistics and Epidemiology (EuroMISE Centre) was set up in April 1994 as the joint Teaching and Research Centre of Charles University and the Academy of Sciences of the Czech Republic with the support of European projects. In the year 2000, the Euro-MISE Centre was enlarged with three additional institutions (University of Economics in Prague, General University Hospital in Prague and Municipal Hospital in Caslav). Nowadays, the EuroMISE Centre creates an interdisciplinary workplace that continually, and on the European level, focuses on the research and development on information and knowledge technologies for the improvement of healthcare and higher education. Through the research cooperation, the EuroMISE Centre (http:// www.euromise.cz) suggests publicly available tools and methods that allow the application of new technologies for various healthcare organizations and citizens with a special focus on the Czech national environment. It provides a platform for a higher level of research cooperation with the usage of the most up-to-date information and communication technologies and a wide spectrum of clinical and genetic data and knowledge. Some activities in biomedical research, higher education and knowledge dissemination are further described in more details. The ability to manage modern communication tools such as Internet services is one of the most important prerequi-sites for the development and use of eeducation (especially in the area of lifelong education) and e-health applications. Computer literacy and how to prove it is a very important task for today. In medicine and health care, sound education and training plays a very important role in achieving high quality and economy of healthcare. The research in the field of biomedical informatics can strengthen and accelerate the possibility of reaching this goal. Everyone understands that the main source of wealth of any nation is information management and the efficient transformation of information into knowledge. There appear completely new decisive factors for the economics of the near future based on circulation and information exchange. It is clear that modern healthcare cannot be built without information and communication technologies. Telemedicine is largely based on an electronic health record and new methods and tools for how to structure information and extract information from medical free text. Sharing knowledge is the main objective of many research projects. In the paper we described the partial achievements reached by the EuroMISE Center in research and higher education

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Proposition and evaluation of a collision detection method for real time surgery simulation of opening a brain fissure In neurosurgery, opening a brain fissure allows an operator to access to the basis cranii and to treat a disease part safely, but the operator is required highly sophisticated techniques. In order to develop a neurosurgery simulator enabling surgeons to train themselves for opening a brain fissure procedure, it is required to detect collision between a thin instrument model and a deformable brain model and furthermore to compute feasible enforced displacements to deformable object. This paper proposes a new collision detection method which considers to the collision state of objects in previous loop of simulation. And simulation of opening a brain fissure is implemented using the proposed method which is accelerated by GPU (Graphics Processing Unit). Finally the performance of the proposed method is evaluated. This paper proposes a new collision detection method which uses ray-triangle intersection test and history of collision state. Using history information, proposed method can search and cull collision pairs and realize interactive simulation of opening a brain fissure. In order to accelerate computing time of the proposed method, decreasing number of source node is easy and useful, but there is limitation with respect of precision. So it is required to introduce some hierarchical data structures to our algorithm. To develop more realistic brain surgery simulator, it is required to introduce blood veins, nervous tissue and connective tissue into the brain model and collision detection which can handle contact with those complex inner structures. After improvement the physical model of brain, computational speed, interface and so on, a quantitative evaluation by surgeons is desirable whether the proposed method is adoptable for movement of their hands.

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 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 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