Predicting microRNA modulation in human prostate cancer using a simple String IDentifier (SID1.0) Computational methods Prostate cancer (CaP) SID1.0 PicTar DIANA-MicroT 3.0 microRNA prediction Exhaustive search algorithm Fortran language a b s t r a c tTo make faster and efficient the identification of mRNA targets common to more than one miRNA, and to identify new miRNAs modulated in specific pathways, a computer program identified as SID1.0 (simple String IDentifier) was developed and successfully applied in the identification of deregulated miRNAs in prostate cancer cells. This computationally inexpensive Fortran program is based on the strategy of exhaustive search and specifically designed to screen shared data (target genes, miRNAs and pathways) available from PicTar and DIANA-MicroT 3.0 databases. As far as we know this is the first software designed to filter data retrieved from available miRNA databases. SID1.0 takes advantage of the standard Fortran intrinsic functions for manipulating text strings and requires ASCII input files. In order to demonstrate SID1.0 applicability, some miRNAs expected from the literature to associate with cancerogenesis (miR-125b, miR-148a and miR-141), were randomly identified as main entries for SID1.0 to explore matching sequences of mRNA targets and also to explore KEGG pathways for the presence of ID codes of targeted genes. Besides genes and pathways already described in the literature, SID1.0 has proven to useful for predicting other genes involved in prostate carcinoma. These latter were used to identify new deregulated miRNAs: miR-141, miR-148a, miR-19a and miR-19b. Prediction data were preliminary confirmed by expression analysis of the identified miRNAs in androgen-dependent (LNCaP) and independent (PC3) prostate carcinoma cell lines and in normal prostatic epithelial cells (PrEC). MicroRNAs (miRNAs) are small non-coding RNAs that take part in post-transcriptional regulation either by arresting the translation or by cleavage (degradation) of mRNA targets [1] . MicroRNA regulation is performed through pairing of the miRNA to sites in the messenger RNA of protein coding genes. MicroRNAs have been thought to be involved in many biological processes (i.e. cell proliferation, death and differentiation) and are believed to regulate the expression of approximately one-third of all human genes [2] . Mature miRNAs bind to their target mRNAs by complete or incomplete complementation of their 5 0 -end nucleotides 1-8 (seed sequences) with a binding site in the 3 0 -or 5 0 -untranslated regions (UTRs) of target transcripts or in the coding sequences [3] . This process results in direct cleavage of the targeted mRNAs or inhibition of translation. Currently, nearly 800 human miRNAs have been identified. Target-prediction computer programs often predict that a miRNA could target tens to hundreds of genes, and that a gene can be targeted by many miRNAs. Thus, the expectation that miRNAs play important roles in coordinating many cellular processes, particularly those involved in development and disease, and even in various cancers [4, 5] . Prediction servers such as TargetScan [6] , miRanda [7] , RNAhybrid [8] , PicTar [9] and the recent DIANAMicroT 3.0 [10] provide information about the miRNA-target interactions. This latter, in particular, has been designed to cover a quick and easy interpretation of the involvement of a series of genes in biological processes. DIANA-MicroT 3.0 actually measures the enrichment of genes involved in pathways within a given list [10] .. It has already been demonstrated that miRNAs are aberrantly expressed in prostate cancer (CaP) [11] . In androgen-dependent (AD) and androgen-independent (AI) CaP cell lines differential expression of miR-148a was found [11] . MiR-125b expression was reported to be increased in benign prostate lines compared with CaP lines and androgen receptor positive (AR-positive) cell lines expressed more miR-125b than androgen receptor negative (AR-negative) cell lines [5] . It has been recently reported that even miR-148a expression levels are increased in AR-positive cell lines (PrEC and LNCaP) in comparison to AR-negative cell lines (PC3 and DU145) [11] . Furthermore, in humans, a member of the miR-NA-200 family (miR-141) has been reported to distinguish patients with prostate cancer from healthy controls [12] . Down-regulation of miRNA-200 family members has been identified to be involved in tumor metastasis [13] . These studies showed that miR-125b, miR-148a and miR-141 may have a key role in prostate tumorigenesis.. We developed a simple String IDentifier (SID1.0) to identify common mRNA targets of miR-125b, miR-148a and miR-141 and the associated pathways. In order to identify common strings, SID1.0 performs an exhaustive search within each individual input file and reports the result (i.e. the number of common targets) on an ASCII output file. More sophisticated search strategies have not been explored to date, since the size of the input files (hence the number of IDs to be scrutinized) is, in the experiments performed so far, limited to a few hundreds or thousands. This makes the whole procedure computationally inexpensive. SID1.0 has been developed in a Mac OSX environment and compiled with the Intel Fortran compiler. As far as we know this is the first software designed to filter data retrieved from available databases (e.g.: TargetScan, miRanda, RNAhybrid, PicTar, DIANA-MicroT 3.0), allowing us for retrieving new information that is not directly available from them. The analysis performed by SID1.0, i.e. the identification of common strings, is not directly available through the user interface of the databases above. It is difficult to evaluate the strengths or the limitations of alternative computational approaches because similar tools, possibly developed by other investigators, have not been described or made available to date. Moreover, despite its simplicity, this technique can allow to predict new miRNAs targeting genes modulated in these pathways. To validate the reliability of predictions made by SID1.0, we ascertained that SID1.0 predicted miRNAs were modulated in CaP (LNCaP androgen-dependent and PC3 androgen-independent) cells that were compared with normal prostatic epithelial (PrEC) cells. In view of the relatively large number of data involved in the analyses described in this study, we conclude that even a simple program of string identification as SID1.0 has proven to be a very useful system to predict miRNAs involved in tumor progression thereby representing a potential tool in diagnostics and clinical monitoring of cancer. From a general stand point SID1.0 is simply an implementation of a classical and well known search strategy in computer science. Its merit relies upon the biological application that is described in this paper.. Comparison of human cancers with the corresponding normal tissues revealed that some miRNAs are consistently deregulated in cancer, which may also suggest a direct role of miRNAs in tumourigenesis. Beside to deregulated miRNAs, because of its broad applicability, the proposed prediction tool can help to identify gene targets and biological pathways relevant to cancer development and treatment. Animals encode miRNAs in their genomes which attack protein coding genes altering protein expression by cleavage or translational repression. In human malignancies, including prostate cancer, miRNAs have shown a capability of distinguishing the different tissue developmental and differentiation states. In this study, using miRNAs and related target predictions documented in PicTar and DIANA-MicroT 3.0 databases, we identified the miRNAs and target genes that potentially cause differences in prostate cancer. Taking advantage of the above prediction servers we obtained the information for the miRNA-target interactions desired. By our bioinformatic strategy based on SID1.0, a computationally inexpensive Fortran 90 program, we identified shared data (target genes, miRNA and pathways). SID1.0 performs an exhaustive search based on the manipulation of characters strings in Fortran. Given its versatility, SID1.0 can manage different IDs associated with gene expression, miRNA and pathways (even in large number and from any available databases). SID1.0 software has been designed to filter data retrieved from available databases, thus allowing us for retrieving new information that is not directly available from those databases. Our proposed approach has successfully identified some deregulated miRNA in LNCaP androgen-dependent and PC3 androgen-independent compared to normal prostatic epithelial (PrEC) cells.. By identifying from literature modulated miRNAs in cancerogenesis and in particular in prostate cancer, we extracted the genes modulated by miR-125b, miR-148a and miR-141 in PicTar database. The predicted genes were the following: ATXN1 (ataxin variant 1); RNF44 (ring finger protein 44); AKAP1 (A kinase anchor protein 1); TRPS1 (trichorhinophalangeal syndrome 1); E2F3 (E2F transcription factor 3); CPEB4 (cytoplasmic polyadenylation element binding protein 4) and ESRRG (estrogen-related receptor gamma transcript variant 1, 2 and 3) ( Table 1) .. From the literature it has already been shown that E2F3, ESRRG and TRPS1 are modulated in prostate cancer: E2F3 controls cell cycle, acts on tumor suppressor proteins and increases with the down-regulation of miR-125b in human prostate cancer tissues [17] ; ESRRG functions as antiproliferative or tumor-suppressor in prostate cancer cell lines [18] ; TRPS1 is involved in oxidative stress, and possibly in apoptosis in androgen-independent DU145 prostate cancer cells [19] . The remaining target genes have not been described in prostate cancerogenesis but seem to be involved in other pathogenesis mechanisms, ATXN1 expression can be modulated by miR-19a affecting neuropathology [20] . Table 2 Common pathways (KEGG Pathway IDs) of hsa-miR-125b (92 elements), hsa-miR-141 (111 elements) and hsa-miR-148a (5 elements). We found five common pathways (to the 3 miRNAs) on a total of 74 total possible combinations (common pathways to either to 2 or all of the 3 miRNAs). In the table are reported only the pathways common to the 3 miRNAs. We indicated the KEGG Pathway name (first column), the gene names involved in each pathway (second column) and the identification ID of the pathway used by the KEGG database (third column). The database used for this analysis was DIANA-MicroT 3.0.

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


Reconstruction of 3D genome architecture via a two-stage algorithm AbstractThe three-dimensional (3D) configuration of chromosomes within the eukaryote nucleus is an important factor for several cellular functions, including gene expression regulation, and has also been linked with cancer-causing translocation events. While visualization of such architecture remains limited to low resolutions, the ability to infer structures at increasing resolutions has been enabled by recently-devised chromosome conformation capture techniques. In particular, when coupled with next generation sequencing, such methods yield an inventory of genome-wide chromatin contacts or interactions. Various algorithms have been advanced to operate on such contact data to produce reconstructed 3D configurations. Studies have shown that these reconstructions can provide added value over raw interaction data with respect to downstream biological insights. However, only limited, low-resolution reconstructions have been realized for mammals due to computational bottlenecks. Results: Here we propose a two-stage algorithm to partially overcome these computational barriers. The central idea is to initially utilize existing reconstruction techniques on an individual chromosome basis, using intra-chromosomal contacts, and then to relatively position these chromosome-level reconstructions using inter-chromosomal contacts. This two-stage strategy represents a natural approach in view of the within-versus between-chromosome distribution of contacts. It can increase resolution ≈20 fold for mouse and human. After describing the algorithm we present 3D architectures for mouse embryonic stem cells and human lymphoblastoid cells. We evaluate the impact of several factors on reconstruction reproducibility and explore a variety of sampling schemes. We further analyze replicate data at differing resolutions obtained from recently devised in situ Hi-C assays. In all instances we demonstrate insensitivity of the whole-genome 3D reconstruction obtained by the two-stage algorithm to the sampling strategy used. Conclusions: Our two-stage algorithm has the potential to significantly increase the resolution of 3D genome reconstructions. The improvements are such that we can progress from 1 Mb resolution to 100 kb resolution, notable since this latter value has been identified as critical to inferring topological domains in analyses performed on the contact (rather than 3D) level. The proposed two-stage algorithm offers a promising technique for obtaining whole genome 3D reconstructions from Hi-C assays. By sampling 3D coordinates from individual chromosome solutions (obtained using any existing method), and deploying inter-chromosomal contacts to relatively position these solutions, it efficiently leverages contact data enabling substantial improvements in resolution. The purpose of this article was to demonstrate proofof-principle for a two-stage approach to obtaining whole genome 3D reconstructions from Hi-C assays. The advantages of such a strategy include (i) effective use of both within chromosome (majority of interaction counts) and between chromosome (majority of interaction pairs) contacts; (ii) the ability to use existent reconstruction tools, especially for the first stage generation of individual chromosome solutions; and (iii) the potential to obtain higher resolution whole genome reconstructions. As noted, this latter point is consequential with respect to eliciting topological and contact domains in mammalian genomes [11, 12] . The two-stage reconstruction method could potentially be improved by employing more sophisticated sampling schemes. These could make recourse to targeting loci with large inter-chromosomal counts or be based on curvature summary measures for the individual chromosome solutions. Moreover, a variety of sampling schemes could be deployed and a consensus (averaged) structure reported after performing Procrustes alignment. The regression-based testing of between versus within sample variation, as utilized for the comparisons presented in the 'Results' , could be used as a precursor determinant as to whether such averaging was justified, analogous to the consensus index [7] . For demonstration purposes we have, in part, used ChromSDE for stage one reconstructions of individual chromosomes because of its desirable characteristics. Two recent papers purportedly show relatively poor performance of ChromSDE; accordingly we make some brief comments on these assessments. Varoquaux et al. [8] use MDS to provide an initial 3D reconstruction then refine this configuration using Poisson regression. In making comparisons between differing reconstruction approaches, they comment that "ChromSDE does not infer the relative position of chromosomes. " Our twostage algorithm provides such relative positioning thereby expanding the scope and utility of ChromSDE. Moreover, based on simulation studies, [8] contend that ChromSDE performs relatively poorly in low signal-to-noise settings. However, the simulations were based on data generated according to their Poisson model and employed a fixed α value conforming to this model. Such a framework deprives ChromSDE from demonstrating putative advantages associated with estimating α. A more complete comparison would result from applying the Poisson model to data generated with a misspecified α value.. In evaluating ShRec3D, Lesne et al. [24] also make comparisons with ChromSDE, again based on simulation. While the methods are comparable with respect to accuracy, ChromSDE is deemed worse with respect to both problem size capability and computational time. Again, these are aspects wherein our proposed two-stage algorithm can extend applicability of ChromSDE. Further, contrary to [7] , Lesne et al. contend that the choice of α is not critical. As they note, weak or vanishing contact frequencies do not contribute to inferred distances, since shortest path constructions will avoid corresponding links (of large or infinite lengths). Accordingly, ShRec3D involves an implicit filtering. Since 3D solutions are also obtained via MDS it is presumably the degree of this filtering that is responsible for its improved problem size and compute time characteristics.. Recent work by Diament and Tuller [26] also employs sampling as a precursor to 3D genome reconstruction. For S. cerevisiae they demonstrate that even under sparse samplings, down to the 5 % level, the resultant reconstructions are concordant with the original reconstruction in terms of co-localization of various genomic landmarks and functional groups. This concordance is used to suggest the possibility of reducing the scale of Hi-C experimentation, if 3D reconstruction is used to analyze the data. As such, their findings are consistent with our results that show that sampling, also down to the 5 % level, does not impact the 3D reconstruction itself. Accordingly, our two-stage approach is able to realize 20-fold improvements in resolution.. The mouse and human data analyzed herein are diploid. To date, 3D whole-genome reconstructions based on Hi-C data from diploid organisms implicitly treat homologous chromosome pairs as coincident (i.e. as occupying roughly the same position, relative to inter-chromosomal positioning) [7, 8, 24] . The reasonableness of such an assumption is unclear. The emergence of high resolution in situ Hi-C assays [12] has enabled phasing of Hi-C maps. This derives from having sufficient reads overlap SNPs so that contacts can be assigned to specific chromosomal homologs. At present, the resolutions needed for such phasing are such that computational bottlenecks, even with our twostage algorithm, preclude 3D genome reconstruction on a diploid level. Even though the disambiguation provided by phasing shows that, for autosomes, maternal and paternal homologs exhibit very similar inter-and intra-chromosomal contact profiles (Pearson's R > 0.998) and, accordingly, very similar between loci distances, this does not in itself imply that are homologous pairs are roughly coincident in view of results from computational geometry [39] . We note that for a near-haploid chronic leukemia cell line (KBM7) Ay et al., [27] provide a diploid reconstruction.. Contact data at 1 kb resolution from in situ Hi-C assays will challenge existing 3D reconstruction algorithms on both memory and computational complexity grounds. For example, 10 % downsampling of whole genome human 1 kb resolution data will still yield a distance matrix requiring ∼670 GB of RAM. Accordingly, even obtaining individual chromosome solutions will require downsampling and/or algorithmic refinements (cf. [40, 41] ). However, once these are generated, the two-stage approach developed here will again be valuable in eliciting whole genome 3D architecture. The result of a Hi-C experiment, following important preprocessing and normalization steps [13, [16] [17] [18] [19] , is the contact map, a symmetric n × n matrix F = [ F ij ] of contact counts between n (generally binned) genomic loci i, j on a genome-wide basis. This matrix can be exceedingly sparse with many zero entries even after binning. The 3D genome reconstruction problem is then to obtain a 3D point configuration, with a one-to-one correspondence between points and genomic loci, such that the resulting pairwise inter-point distances best recapitulate the corresponding frequencies. We operationalize "best recapitulate" below. Many approaches have been proposed to tackle this problem, with broad distinction [8, 20] between optimization/consensus and probabilistic/ensemble methods, although these can overlap. Our focus here is on the former. A common first step in these reconstruction algorithms (e.g. [6, 8, 9, 14, [24] [25] [26] [27] ) is conversion of the frequency matrix into a distance matrix D = [ D ij ]. This is often followed by a second step which solves the graph realization [28] or multi-dimensional scaling (MDS, [29] ) problem: position points (corresponding to genomic loci) in 3D so that the resultant interpoint distances best conform to the distance matrix. We briefly describe aspects of each of these components in order to position our two-stage algorithm.

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


A Monte Carlo study of old and new frontier methods for efficiency measurement Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte.This study presents the results of an extensive Monte Carlo experiment to compare dierent methods of eciency analysis. In addition to traditional parametric-stochastic and nonparametric-deterministic methods recently developed robust nonparametric-stochastic methods are considered. The experimental design comprises a wide variety of situations with dierent returns-to-scale regimes, substitution elasticities and outlying observations. As the results show, the new robust nonparametricstochastic methods should not be used without cross-checking by other methods like stochastic frontier analysis or data envelopment analysis. These latter methods appear quite robust in the experiments. JEL classication: C14, D24, C15 Until recently estimation methods for frontier production and cost functions widely in use could be divided in two broad groups: parametric-stochastic and nonparametric-deterministic. Both groups have their own advantages and disadvantages. Parametric-stochastic methods such as stochastic frontier analysis (SFA) require the functional specication of the production or cost function as well as the distributions of the stochastic parts but are considered robust against measurement errors. Nonparametric-deterministic methods such as data envelopment analysis (DEA) and free disposal hull (FDH) do not require functional form assumptions or distributional assumptions but are more sensitive to measurement errors.. There is a long history of attempts to combine nonparametric and stochastic methods for eciency analysis. Grosskopf (1996) gives an early overview of those attempts. Most of these methods remained in an experimental state. Recently two approaches, the so-called order-m and order-α approaches which are explained below, appeared which have the potential of combining the advantages of the parametricstochastic and the nonparametric-deterministic approaches. These nonparametric-stochastic approaches not require functional form or distributional assumptions and are robust with respect to measurement errors. This paper reports the results of an extensive Monte Carlo study with scenarios containing dierent production functions, returns-to-scale regimes and the introduction of outliers in addition to the general presence of measurement errors. Considered are a wide range of eciency measurement methods, including SFA, DEA and FDH as well as the recently developed order-m and order-α approaches which are not considered in such comparisons so far. It is not clear a priori that the conceptual advantages of the nonparametric-stochastic methods also materialize in small-sample situations with dierent extents of measurement errors and outliers. Including these methods in a unied Monte Carlo experiment is thus important for evaluating their properties in a direct comparison to the more traditional methods.. Indeed, the simulation results reveal that the traditional methods such as SFA and DEA are not as bad as frequently posited on theoretical grounds, at least in the setting chosen in this paper. Moreover, it is shown the robust nonparametric-stochastic order-m and order-α approaches can be much worse than the more traditional approaches when measurement errors are not excessively large and outliers are absent.. Thus, these methods should not be employed as a standard procedure without cross-checking by other methods.. The plan of the analysis is as follows. The following section 2 presents the methods of eciency measurement which are considered in the Monte Carlo study of this paper. Section 3 gives a brief survey of previous Monte Carlo studies and points out their deciencies. Section 4 describes the design of the Monte Carlo experiment conducted in this paper and section 5 discusses the results of various scenarios.. Finally, section 6 draws conclusions for the choice of appropriate methods of eciency analysis. Which general guidelines for the application of eciency analysis methods can be derived from the results discussed above? Since we are faced here with results from a Monte Carlo experiment it is dicult to derive general guidelines. All Monte Carlo experiments are faced with the problem of specicity (Hendry 1984, p. 941 ) meaning that those experiments can cover only a small part of the space of possible parameters and functional forms. Thus we have generated only selective results pertaining to a limited set of points of the parameter space.. Keeping this caveat in mind we can summarize a few general patterns. SFA shows a good performance also in the CES scenarios and even in the presence of outliers. Although we have to be cautious with this statement since the experimental design is quite favorable for SFA, we can say that the criticism raised against this method (i.e. that it is not able to separate ineciency and measurement error) can not be conrmed by the present study. The performance of DEA and FDH is also quite remarkable even for larger measurement error variances and in the presence of outliers. Some changes can be observed when increasing or decreasing returns to scale are induced. The results are, however, not much aected by the CES scenarios even in the case of the larger elasticity of substitution.. Overall, we have the ranking of SFA dominating DEA, which itself is dominating FDH and order-m and order-α are dominated in general. Nevertheless, order-m becomes better at larger measurement error variances and for larger extents of outliers. When outliers are induced, order-m and order-α are rather stable and sometimes even slightly better compared to their performance in the baseline scenario.. Moreover, order-m performs better than the theoretically more robust order-α approach. This conclusion is, however, somewhat tentative. Maybe dierently designed Monte Carlo experiments with less well behaved environments change this conclusion.. Compared to that the performance of the robust nonparametric-stochastic methods, the order-m and order-α approaches, appears not to be very advantageous in well behaved settings. At the bottom line it can be said that it is not appropriate to use order-m and order-α routinely in situations which are characterized by a smooth well behaved production environment with no outliers or limited extents of outliers. Even with the induction of additional outliers it depends much on the values of the other parameters whether these methods become better than more traditional methods of eciency analysis.. Thus, it is always wise to cross-check the results with other methods to asses their validity.

O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I 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 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 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 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-means: An Optimized Clustering Method for Analyzing Spam Based Attacks In recent years, the number of spam emails has been dramatically increasing and spam is recognized as a serious internet threat. Most recent spam emails are being sent by bots which often operate with others in the form of a botnet, and skillful spammers try to conceal their activities from spam analyzers and spam detection technology. In addition, most spam messages contain URLs that lure spam receivers to malicious Web servers for the purpose of carrying out various cyber attacks such as malware infection, phishing attacks, etc. In order to cope with spam based attacks, there have been many efforts made towards the clustering of spam emails based on similarities between them. The spam clusters obtained from the clustering of spam emails can be used to identify the infrastructure of spam sending systems and malicious Web servers, and how they are grouped and correlate with each other, and to minimize the time needed for analyzing Web pages. Therefore, it is very important to improve the accuracy of the spam clustering as much as possible so as to analyze spam based attacks more accurately. In this paper, we present an optimized spam clustering method, called O-means, based on the K-means clustering method, which is one of the most widely used clustering methods. By examining three weeks of spam gathered in our SMTP server, we observed that the accuracy of the O-means clustering method is about 87% which is superior to the previous clustering methods. In addition, we define 12 statistical features to compare similarity between spam emails, and we determined a set of optimized features which makes the O-means clustering method more effective.

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


Performance Analysis of CSMA/CA Protocols with Multi-packet Transmission Wireless objects equipped with multiple antennas are able to simultaneously transmit multiple packets by exploiting the channel's spatial dimensions. In this paper, we study the benefits of such Multiple Packet Transmission (MPT) approach, when it is used in combination with a Carrier Sense Multiple Access with Collision Avoidance (CSMA/CA) protocol for fully interconnected networks, addressing the interactions between the two mechanisms and showing the performance gains that can be achieved. To this end, a very simple Media Access Control (MAC) protocol that captures the fundamental properties and tradeoffs of a CSMA/CA channel access protocol supporting MPT is introduced. Using this protocol as a reference, a new analytical model is presented for the case of non-saturated traffic sources with finite buffer space. Simulation results show that the analytical model is able to accurately characterize the steady-state behavior of the reference protocol for different number of antennas and different traffic loads, providing a useful tool for understanding the performance gains achieved by MAC protocols supporting MPT. MIMO techniques allow for a more efficient use of transmission resources by making the channel's spatial dimension available, using simple and effective signal processing techniques [1] . This new spatial dimension can be used to enhance coverage and reliability (spatial diversity) or to boost the system throughput (spatial multiplexing) [2] . In this paper, we will focus on the spatial multiplexing feature, which can be used to transmit multiple packets at the same time, referred to as Multi-Packet Transmission (MPT). MPT by using Spatial Multiplexing can be seen as a packet-based extension of the Space Division Multiple Access (SDMA) or Multi-user MIMO concepts [3] .. Although the benefits and drawbacks of MPT in point to point links are well-known, there is still a lack of results focusing on the new challenges and benefits that can arise by combining MPT capabilities with random-access MAC protocols. On the one hand, using MPT will reduce the number of transmission attempts and therefore decrease the collision probability in a contention scenario. On the other hand, in order to make the MPT work properly, the MAC protocol needs to be modified, at the expense of some extra temporal overhead, e.g., to include the necessary procedures for estimating the channel state between the transmitter and each receiver, required for isolating the different spatial streams, or to feed the CSI (Channel State Information) back to the transmitter when necessary. There will also be a need for extra acknowledgments to confirm the reception of all spatial streams. The negative impact of the extra temporal overhead imposed by these modifications on the system performance needs to be quantified and contrasted with the performance boost gained by enabling the simultaneous transmission of multiple packets.. This paper intends to provide insight on the interactions between CSMA/CA random access MAC protocols and the MPT scheme. We study and characterize these interactions by introducing a basic MAC protocol that combines these mechanisms and includes all the required features to make it work properly. The performance of the overall system is evaluated using an analytical model, whose accuracy is validated using simulations. The applied analysis strategy and the resulting model are general enough to provide deep insight into the analysis of any CSMA/CA MAC protocol with MPT capabilities.. In this context, the main contribution of this paper is to present a queueing model for wireless objects with MPT capabilities using a CSMA/CA protocol for channel access. We show that the considered approach provides a suitable path to modeling packet-based, multiple-antenna access protocols in non-saturation conditions. The presented results confirm the accuracy of the presented model and show the performance benefits of such protocols, as well as providing insights on how the system parameters have to be configured in order to achieve better performance gains.. CSMA/CA-based MAC protocols with MPT capability have been recently considered for WLANs due to their ability to improve the network performance, while keeping both the simplicity and the efficiency that random access MAC protocols possess [4, 5] . In addition, the upcoming appearance of the IEEE 802.11ac amendment for WLANs [6] , which only enhances the Access Points with the MPT capability, is also pushing in that direction.. In [4] , a MAC protocol for WLANs supporting MPT at the Access Point (AP) is presented. The RTS/CTS handshake procedure is extended to both coordinate the transmission of multiple packets from the AP to different STAs, and to provide the AP with the required CSI. An analytical model of the presented protocol in non-saturation conditions is introduced, although the authors only focus on the MAC performance, as queueing is not included in the model, hence not allowing for metrics such as average waiting delay per packet or the packet-loss probability due to buffer overflow to be computed. In [5] , the performance of MPT in the downlink for the upcoming IEEE 802.11ac standard is evaluated. An accurate physical-layer and channel model is provided when a zero-forcing precoding scheme [3] is used to create the multiple spatial streams. To evaluate the system performance, an analytical model in saturation conditions is presented, where it is assumed that the AP can always transmit as many packets as the number of antennas it has, thus also not considering the queueing dynamics. However, MPT can be also applied to a wider set of scenarios in which the use of CSMA/CA MAC protocols is common, such as in Wireless Multimedia Sensor Networks that may have high bandwidth demands to transmit audio and video signals [7] , in clusterbased Wireless Networks [8] , to enhance the cluster-head capabilities to transmit to multiple nodes simultaneously, or in vehicular networks [9] , to improve the car-to-car communication, among others. As these scenarios usually include a large number of nodes contending for the channel, they are more interesting from the point of view of the interactions between the MPT and CSMA/CA protocols, and for that reason we focus on them in this paper.. The rest of the paper is structured as follows. Section 2 presents the considered reference scenario, i.e., a single-hop network where N nodes compete for the channel. Section 3 details the reference protocol. In Section 4, the analytical model is presented. The analytical model validation and performance results are discussed in Section 5. Finally, the main conclusions of the paper are summarized in Section 6. In this paper, an analytical model for a CSMA/CA MAC protocol with MPT capabilities has been presented. Simulation results show that the presented model is able to capture the fundamental interactions between the CSMA/CA channel access mechanism and the MPT capabilities of the reference protocol, as well as providing a good approximation of the system performance.. As observed, the required extra overheads to support multiple packet transmission are compensated by the larger amount of data that can be sent at each transmission, as well as by the reduction in the number of transmissions, which in turn results in lower collision probabilities for a given number of contending nodes and a given traffic load, thus providing a higher throughput and lower delay.. Moreover, given a node equipped with multiple antennas, two new parameters called s min and s max , which control the number of packets that are scheduled at each transmission, were introduced and their impact on the system performance was evaluated, drawing several conclusions. Mainly, it was observed that, although the number of packets that can be included in a space-batch increases when s max increases, the PER also increases. Therefore, the value of s max has to be set to the highest possible value that still guarantees a reasonably low PER (i.e., based on the observed SNR and available number of antennas in each node). It was also observed that adapting s min to the traffic load and the number of active nodes, the system performance can be optimized in terms of delay and throughput. Additionally, although not analyzed in this paper, the impact of both parameters also depends on the backoff algorithm and its parameters (i.e., CW and number of stages), thus opening a new opportunity to search optimal configurations for all those parameters simultaneously. Figures 7(a) and 7(b) show the aggregate throughput and expected delay, respectively, each for two different arrival rates (5 and 15 packets/second) when ξ 0 = 20 dB, s min = 1, s max = 2, and M = 2 or 4 antennas 2 , as indicated by [M, s min , s max ] in the legend. For both metrics, the best performance is observed when the nodes are equipped with M = 4 antennas and s max is set to 2, showing that in some cases the lower PER that the Zero Forcing receiver is able to provide by using the channel's extra degrees of freedom for diversity, compensates the transmission of less packets at each channel attempt. A similar result is observed in both the aggregate throughput (Figure 7(c) ) and the expected delay (Figure 7(d) ) when the number of nodes is fixed to N = 4 and 8 nodes, and the packet arrival rate at each node is increased.. The impact of different s min values is evaluated when multiple nodes contend for the channel. The results are plotted in Figure 8 . The considered parameters are M = 4 antennas, ξ 0 = 40 dBs, s max = 4, and s min = 1 or 4 packets. In this case, in order to highlight the effect of increasing s min on network performance, the average SNR has been set to 40 dBs, as opposed to 20dBs in Figure 7 where transmissions containing 4 packets resulted in high error probability. By increasing the SNR to 40 dBs in Figure 8 , the transmission of large space-batches becomes beneficial and setting s min = 4 can be advantageous. As can be observed, setting s min = 4 improves the performance of the MAC protocol for larger networks when the traffic load of each node is low (for instance, between 22 and 36 nodes for λ = 5 packets/second), compared to the case with s min = 1 (Figure 8(a) ). Additionally, an interesting issue here, already known from the analysis of the DCF with single-antenna nodes [22] , is that in some specific circumstances (i.e., when the collision probability just before saturation remains very low), the non-saturated throughput just before the saturation point is higher than the saturation throughput, as it is also observed here. Setting s min = 4 results in fewer channel attempts as the queue remains inactive, i.e., with less than s min packets, for longer periods of time (Figure 8(b) ), which results in a lower collision probability until the saturation point is reached (Figure 8(c) ). However, values of s min larger than 1 have a negative impact on the delay (Figure 8(d) ), due to the extra time required to have s min In all of the plots, the model and the simulation curves show a very good match, with the model always slightly above the simulation curve. This may be justified by the higher randomness of the exponential distribution, as well as by the assumption that the transmission probability at each slot is constant and does not depend on the instantaneous number of nodes that are contending for the channel access, which has been used to obtain the expected service time. However, from the results we can conclude that the model is accurate enough to be useful as a tool for understanding the effect of different scenarios and parameter configurations, as well as for finding robust parameter values that yield to a close-to-optimum performance if the model is embedded in optimization algorithms.

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


Null subspace-based damage detection of structures using vibration measurements A damage detection method of mechanical system based on subspace identification concepts and statistical process techniques is presented. The aim is to propose a method that is sensitive to small-sized structural damages and suitable for on-line monitoring. Measured time-responses of structures subjected to artificial or environmental vibrations are assembled to form the Hankel matrix, which is further factorised by performing singular-value decomposition to obtain characteristic subspaces. It may be demonstrated that the structural responses are mainly located in the active subspace defined by the first principal components, which is orthonormal to the null subspace defined by the remaining principal components. If no structural damage occurs, the orthonormality relation between the subspaces remains valid with small residues when consecutive data sets are compared, and these residues may be evaluated by the proposed damage indicators. The method is validated using an experimental mock-up of an airplane subjected to different levels of damages simulated. It is also applied in environmental vibration testing of a street lighting device to monitor structural fatigue evolution. r Early diagnosis of structural damages or machinery malfunctions allows to reduce the maintenance cost of systems and to increase their reliability and safety. Visual and systematic inspections may be periodically performed, sometimes requiring shutdown and disassembly of the system. In many practical situations, it is of interest to use condition-based inspections by continuous or periodical vibration measurements. The combined application of these two kinds of inspections allows to make an optimal maintenance decision. In developing an on-line monitoring tool, both efficiency and simplicity are pursued.. The aim of this paper is to address the damage detection problem by statistical analysis on output-only measurements of structures. The method requires neither an identification of modal parameters nor a construction of a finite element model. Several techniques exist to satisfy partially or completely this objective. For instance, Basseville et al. [1] proposed a subspace identification-based fault detection algorithm using a w 2 -type test; Worden et al. [2] developed a novelty analysis for damage detection, which was also used by Sohn and Farrar [3] with a twostage (AR-ARX) prediction model; principal component analysis (PCA) was applied by Friswell and Inman [4] for the sensor validation; this technique has also been used in [5, 6] for detection and localisation of structural damage, and the method has been further enhanced in [7] to improve its efficiency. A novelty analysis based on the Kalman model was recently proposed in [8] . The basic assumption is that there is a significant increase in the residual errors when a Kalman model identified from the undamaged system is used to predict responses of the damaged system. Besides, special effort has been paid to eliminate the effect of varying environmental conditions (e.g. temperature variations) on damage detection during a long-term monitoring [9, 10] .. The present work provides an alternative method to the above developments. It concerns mainly the damage detection problem, which is basically important in some practical situations. Further, damage localisation may be realised by assessing structural matrix information when using enough measuring sensors, see [11, 12] as example. The severity of damage may also be approximately assessed by relating the damage indicators with simulated damage cases. The key idea of the proposed method relies on the concepts of subspace identification and null subspace. The response data (such as displacements, velocities, accelerations, stresses, etc.) periodically collected from the monitored structure are used to construct the Hankel matrices. If no structural damage occurs, the orthonormality assumption between the subspaces of the Hankel matrices corresponding to different data sets remains approximately valid according to small residues, which in turn may serve as damage-sensitive features. The threshold level of the residues may be determined by monitoring the healthy structure in various excitation conditions. Several damage indicators are proposed to assess the residues for the damage detection. This null-subspace-based damage detection method is expected to be sensitive to small and local damages of structures and suitable for on-line monitoring in controlled environmental conditions. The efficiency of the proposed method will be illustrated on several experimental applications. The damage detection method proposed in this paper is based on subspace analysis of the Hankel matrices constructed from output-only vibration measurements. It is demonstrated that the column active subspace of the Hankel matrix defined by the first principal components is orthonormal to the column null subspace defined by the remaining principal components. The residues in the orthonormality relation obtained from different data sets (i.e. between the null subspace of the reference data and the active subspace of the current data) may be used to detect possible damage in the structure. Several damage indicators are proposed to characterise the residue matrices, which are expected to be sensitive to small and local structural damages. Experimental applications with two kinds of excitation, one is random excitation and the other one following the first resonance mode of the structure, have been used to illustrate the efficiency of the method. Because of its simplicity, the method is expected to be suitable for on-line monitoring of structures in service or vibration fatigue testing.

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Measuring Efficiency in Imperfectly Competitive Markets: An Example of Rational Inefficiency The standard assumption in the efficiency literature, that firms attempt to produce on the production frontier, may not hold in markets that are not perfectly competitive, where the production decisions of all firms will determine the market price, i.e., an increase in a firm's output level leads to a lower market clearing price and potentially lower profits. This paper models both the production possibility set and the inverse demand function, and identifies a Nash equilibrium and improvement targets which may not be on the production frontier when some inputs or outputs are fixed. This behavior is referred to as rational inefficiency because the firm reduces its productivity levels in order to increase profits. For a general short-run multiple input/output production process, which allows a firm to adjust its output levels and variable input J Optim Theory Appl levels, the existence and the uniqueness of the Nash equilibrium is proven. The estimation of a production frontier extends standard market analysis by allowing benchmark performance to be identified. On-line supplementary materials include all proofs and two additional results; when changes in quantity have a significant influence on price and all input and outputs are adjustable, we observe more benchmark production plans on the increasing returns to scale portion of the frontier. Additionally, a direction for improvement toward the economic efficient production plan is estimated, thus providing a solution to the direction selection issue in a directional distance analysis. Standard productivity and efficiency analysis assumes perfectly competitive markets and exogenous prices [1] . Basic microeconomic theory states that firms operating in less than perfectly competitive markets can reduce production levels and increase a product's market price when they face a downward sloping demand curve. Thus, the standard assumption in the efficiency literature that all firms attempt to produce on the production frontier 1 may not hold in an imperfectly competitive market. In this paper, we combine efficiency analysis with standard Nash imperfectly competitive market equilibrium analysis by bounding the production strategies using the production possibility set. For the efficiency literature, this provides an example of rational inefficiency. 2 For imperfectly competitive market analysis, this provides methods for measuring scale, technical, and allocative inefficiency separately, which provides guidance in selecting improvement strategies.. Most of the efficiency and productivity literature adapts the work developed by [3] and articulated by [4] as the concept of X-efficiency, which assumes that deviations from a production frontier are due to managerial inefficiency, lack of motivation, and lack of knowledge [5] . Alternatively, Stigler [6] argues that firms and individuals are rational, meaning that what is observed as inefficiency is actually the difference between individual employees of the firm maximizing their individual value functions and the firm's value function. However, recent results in the economics literature show large and persistent variations in productivity levels across narrowly defined industries [7] , and significant variation in managerial practices [8] . Bogetoft and Hougaard [9] suggest that, while some portion of these deviations can be attributed to inefficient managerial practices, a significant portion can be called "rational inefficiency", meaning the firm intentionally operates at lower productivity because the coordination or policy would be too costly in order to assure workers' behavior is consistent with firm objectives.. In this paper, we explore another source of rational inefficiency, specifically a firm may choice to lower productivity and, due endogenous prices, may thus increase price and profits. This concept is not new. Cournot [10] , the first to consider endogenous prices, assumes a homogeneous product with an inverse demand function known to all firms, which then independently select output levels; in this market characterized by imperfect competition, price is treated as an endogenous parameter. Nash [11, 12] considers a general non-cooperative game and estimates an equilibrium point in n-person game in which no firm can increase its objective function by unilaterally changing the quantity or price to any other feasible point. These games are consistent with the oligopolies described by Cournot, where each firm maximizes its own profits and the output decisions affect the price faced by all firms. Rosen [13] proves that a finite non-cooperative game always has at least one equilibrium point when the strategy space of each player is restricted, and the payoff functions are a bilinear function of the strategies. Furthermore, for a constrained n-person game, he proves the existence and uniqueness of an equilibrium point with a strictly concave payoff function. A systematic discussion applying equilibrium concepts to economic systems is developed in Arrow and Debreu [14] .. While the relationship between oligopolies and Nash-equilibriums is well established in the literature, the connection to production theory and measures of managerial, allocative, and economic efficiency is lacking. This paper models the production of multiple outputs and a variable rate of substitution using convex output sets. This approach allows production trade-offs and the feasibility of the production bundles to be considered in the Nash-equilibrium analysis. Furthermore, a technical inefficiency measure can be used to estimate the reduced utilization levels at which a firm may strategically operate in order to have excess capacity to deter market entry for future potential entrants. In addition, allocative efficiency and scale efficiency can be measure relative to the Nash-equilibrium benchmark.. The remainder of this paper is organized as follows. Section 2 shows the equivalence between a Nash equilibrium and the two approaches, variational inequalities and the complementarity problem, when production is restricted to the production possibility set. Section 3 examines revenue maximization. Both a single output case and a multiple output case are presented. Section 4 introduces a generalized profit model with fixed input levels, in which a firm maximizes profits by adjusting both input and output levels. The existence and uniqueness of a Nash equilibrium identified through the complementarity problem is proven. Section 5 presents our conclusions. An on-line electronic supplementary material includes all proofs, a discussion of instrumental variables and dominance properties, and the relationship between the benchmark frontier and scale properties is discussed. Furthermore, the direction for improvement used in the directional distance function is identified using the results of the Nash equilibrium analysis. This paper analyzes endogenous prices in productivity analysis. Given inverse demand and supply functions, a Nash equilibrium solution corresponding to profit Table 3 Nash equilibrium in two-output two-variable-input production C a s e maximization production plan within the production possibility set is identified using a MiCP. When the inverse demand and supply functions are constant functions, the standard analysis of efficiency assuming perfect competition and exogenous prices follows. For markets in which demand is heavily influence by the total supply quantity, firms seek to decrease their output levels and maintain higher product prices to maximize profits. The proposed MiCP model integrates imperfectly competitive market equilibrium and productivity analysis. We find that the resulting Nash equilibrium is an example of rational inefficiency.. Deviating from standard economic analysis, we consider the production limitations estimated from observed data and interpret the Nash equilibrium as the benchmark, or the production plans each of the firms should work toward for more profitable production. Our work extends the efficiency literature on demand functions by considering multiple output production and allowing both outputs and variable inputs to be adjusted by the firm. Prior work primarily focused on individual firms decisions without consideration for the other firms in the market.. The identification of a unique Nash equilibrium allows further insights to operational improvement strategies. We show the relationship between price sensitivity and returns to scale in the Nash equilibrium. Based on the concept of allocative efficiency, we conclude that the Nash equilibrium is a useful guide for determining direction in the directional distance function.. We note that this paper only considers the case of the linear inverse demand function. In fact, the inverse demand function can be nonlinear and estimated by piecewise linear approximation. Future development of an empirical nonlinear inverse demand function would be a valuable contribution to capture the precise Nash equilibrium. Moreover, the panel data and a time-rolling dynamic analysis will be useful for supporting a sequential control of firm's behavior.

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Introduction to the Fractality Principle of Consciousness and the Sentyon Postulate Abstract Recently, consciousness research has gained much attention. Indeed, the question at stake is significant: Why is the brain not just a computing device, but generates a perception from within? Ambitious endeavors trying to simulate the entire human brain assume that the algorithm will do the trick: as soon as we assemble the brain in a computer and increase the number of operations per time, consciousness will emerge by itself. I disagree with this simplistic representation. My argument emerges from the ''atomism paradox'': the irreducible space of the consciously perceived world, the endospace is incompatible with the reducible and decomposable architecture of the brain or a computer. I will first discuss the fundamental challenges in current consciousness models and then propose a new model based on the fractality principle: ''the whole is in each of its parts.'' This new model copes with the atomism paradox by implementing an iterative mapping of information from higher-order brain structures to smaller scales on the cellular and molecular level, which I will refer to as ''fractalization.'' This information fractalization gives rise to a new form of matter that is conscious (''bright matter''). Bright matter is composed of conscious particles or units named ''sentyons.'' The internal fractality of these sentyons will close a loop (the ''psychic loop'') in a recurrent fractal neural network (RFNN) that allows for continuous and complete information transformation and sharing between higher-order brain structures and the endpoint substrate of consciousness at the molecular level.

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Approximation of a Variable Density Cloud of Points by Shrinking a Discrete Membrane Abstract Scattered data points obtained from real objects with optical, ultrasonic, tactile or other sensors are frequently used as data sources. Geometric modeling applications must process these scattered data points to obtain a surface that approximates the data point set. In this way,. • The generated surface will be more compact than the initial data point set.. • A more realistic visualization can be obtained from the surface.. • Standard geometric modeling operations (surface evaluation and editing, surface-surface intersection, etc.) will be feasible.. A large diversity of algorithms that approximate scattered data points have been published. There are many valid solutions approximating a cloud of points and each algorithm provides a solution with its own "aesthetic".. It is not possible to detail all published papers dealing with this problem here. The reader can consult some of the existing State-of-the-Art reports 1, 2 . Some papers are mentioned below. They are classified in four blocks according to the taxonomy used in the Mencl and Müller report 1 :. • Spatial subdivision. The space is decomposed in cells, then the cells that are stabbed by the final surface (surface oriented algorithms) or the cells that do not belong to the volume bounded by the surface (oriented to volume) are determined and, from them, the final surface is computed. Some surface oriented algorithms use a regular voxelization (Algorri et al. 3 and Hoppe et al. 4 ), others decompose the space in tetrahedrals (Bajaj et al. 5 , α-shapes of Edelsbrunner et al. 6 , Amenta et al. 7 and the Cocone algorithm of Amenta et al. 8 ). Examples of volume oriented algorithms are Veltkamp 9 , Boissonnat 10 and Isselhard et al. 11 (their strategy is based on computing a Delaunay tetrahedrization of the convex-hull of the data point set and eliminating successively the tetrahedrals carrying out some properties).. • Distance function. The distance function calculates the minimum distance from any point of the space to the final surface. The distance function can give positive or negative values if the surface is closed. The final surface is implicitly determined by the distance function. Examples of algorithms using a distance function are Hoppe et al. 4 , Roth et al. 12 , Bajaj et al. 5 , Boissonnat et al. 13 and the level set method of Zhao et al. 14 .. • Deformation techniques or Warping. An initial surface is deformed progressively to obtain a better approximation to the initial data points. In this kind of algorithm it is convenient to start with a surface that is a coarse approximation of the data point set. Examples are the "blobby model" of Muraki 15 , the mass and spring model built from a triangular mesh of Algorri et al. 3 and the variational level set method applied to implicit surfaces 14 . Also the algorithms based on 3D snakes (energy-minimizing spline which is attracted toward the initial point set) can be classified in this category (Takanashi et al. 16 and Kass et al. 17 ).. • Incremental construction. The surface is constructed in an incremental way from the properties of the initial data points. Normally, from an initial element (edge, triangle), the algorithm works by successively adding new elements (typically triangles) in its neighborhood enlarging the surface. This is the idea of the surface oriented algorithm of Boissonnat 10 and the ball-pivoting algorithm of Bernardini et al. 18 .. This taxonomy has several drawbacks. Some algorithms can be included in more than one category. For example, some spatial subdivision algorithms use a distance function to find out which cells are stabbed by the surface 4, 5 . As we will see later, our algorithm can be classified in two different categories. Notice that this taxonomy classifies the algorithms by the method being used, not by the obtained result. For example, spatial subdivision algorithms can get a mesh of triangles 3, 4 , tri-variate implicit Bernstein-Bezier patches 5 or polytopes (sets of points, edges, triangles and tetrahedrals not necessarily defining a closed and regular surface) in the α-shapes algorithm 6 .. The problem framework is defined in next section. Section 3 introduces an overview of the algorithm. In Section 4 the main part of the algorithm is discussed: the voxelization of the space and the membrane shrinking. Section 5 describes the relaxation of the membrane and section 6 the construction of the final surface. The results are explained in section 7 and the final conclusions are pointed out in section 8. An algorithm that obtains one or more closed surfaces approximating a data point set in the 3D space has been presented. The algorithm does not require to know the topological relations among the points or other additional information. The obtained surface approximates and does not stab exactly the points: The approximation error has a certain tolerance d in relation to the initial data point set. By using a shrinking plate of diminishing size, the algorithm allows to reconstruct surfaces from initial data points not having a uniform density. Surfaces with genus ≥ 1 and/or surfaces with disconnected shells can be reconstructed due to the way of detecting the incursions to the interior of the surface. The algorithm is robust and efficient since it works only with discrete values (voxels) and does not need to calculate distances among points or find the neighbour points (as normally done by most of the existing algorithms).. The algorithm could be improved with the employment of hierarchical structures like octrees. But it is important to remark that the success of the algorithm is based on displacing the plate one voxel every time.. A post process to relax the final membranes has been introduced to get better results in zones where the initial data point density was low. Different types of surfaces can be obtained from the final membranes like meshes of triangles or piecewise algebraic surfaces.. The construction of a piecewise algebraic surface stabbing the final discrete membrane includes a constrained fairing algorithm 24 to achieve smoother surfaces and to approximate better the final surface to the initial data points. The first example is the approximation to the vertices of the Utah teapot. It is the same that has been used to illustrate the explanations in the previous sections.. A voxelization of size 164 × 104 × 82 has been built from a set of 35910 points ( Figure 20 ). There are 19144 hard voxels in the voxelization since 16766 points have coincided in voxels where there were other points. Then the initial DM has been built, a previous silhouette shrinking has been performed and the DM has been contracted with plates of sizes 41, 21, 11, 6, 3, 2 and 1 ( Figure 21 ). The table 1 shows the evolution of the DM shrinking. In the table, for each size of the plate, the number of soft voxels not frozen in the DMS just before beginning the shrinking, the number of initiated contractions with this plate size (number of different locations in the DMS where a recursive sequence of CONTRAC-TION operations has been started to apply) and the number of backtrackings performed (number of times that a recursive sequence of CONTRACTION operations has been canceled and undone), are shown. The final DM is composed of 18817 hard voxels (painted in red) and 25822 frozen voxels (painted in blue). Inside the DM 356639 soft voxels and 327 hard voxels remain. Hence a little percentage of hard voxels stay inside the DM (1.7%). Most of the data points (98.3%) are within the bounded distance to the surface. In all cases a post-process can be performed to connect the remaining inside hard voxels with the DM at the closest locations. Figure 22 shows the final surface obtained from the DM with two different algorithms.. The second example uses a set of 100461 points modeling a toy bird. The voxelization has a size of 153×209×203 with 73156 hard voxels (27305 points are within hard voxels that already contained other data points). The final DM (Figure 23(a) ) is composed of 71386 hard voxels and 61618 soft voxels. Inside the DM 1228510 soft voxels and 1770 hard voxels (a 2.4% of the total of hard voxels) remain. The final surface, a cubic Bspline isosurface displayed with a raycasting algorithm, appears in Figure 23 The third example uses a set of 56306 points modeling a dinosaur. The voxelization has a size of 201 × 170 × 70 with 31089 hard voxels (25217 points are within hard voxels that already contained other data points). The final DM (Figure 24(a) ) is composed of 31067 hard voxels and 11250 soft voxels. Inside the DM 90855 soft voxels and 22 hard voxels (a 0.07% of the total of hard voxels) remain. The final surface displayed with a raycasting algorithm appears in Figure 24 (b). The table 3 shows the evolution of the DM shrinking of the dinosaur.. Finally Figure 25 shows the DM obtained from a cloud of 543652 points modeling a Buddha sculpture. Notice how the algorithm is capable to recover the holes of the model. The All these examples illustrate a correct and robust operation of the gradual DM shrinking algorithm.. The run-times of the whole shrinking process are listed in Table 5 . These times have been obtained on a personal computer with a 1.6GHz AMD-XP CPU and 256Mb of main memory. The reasons for the high run-time of the Buddha model are the big size of the voxelization, the big size the initial plate (50 × 50) and the use of swap memory on hard disk to store the model.. We have compared these results with those achieved by Cocone 8 on the same models. The Cocone algorithm enjoys theoretical guarantees and a faster runtime. However, on For instance, the large hole at the base of the bird model in figure 23 violates the ε-sampling hypothesis. Cocone fails to fill up that hole, but in its attempts to do so, generates several artifact triangles. Algorithm 1 illustrates the main reconstruction algorithm.. The first step builds the voxelization from the initial data point set. This step is immediate if the edge's length of the voxel l is known: We must divide the lengths (lx, ly, lz) of the sides of the rectangular box that contains the data point set by the edge's length of the voxel to obtain the sizes of the voxelization (nx = lx/l, ny = ly/l, nz = lz/l). When we build the voxelization, the voxels that contain one or more points of the initial set are labeled as hard voxels and the others as soft voxels. In Figure 20 If the length l is not known, it can be estimated as. where n points is the number of the initial data points. This. repeat n := (n+1) div 2; FindContractionPlace( DMS, n, placeOk, place ); while placeOk do incursion := FALSE; NewStack( ContractionStack ); RecursiveContraction( DMS, n, place, ContractionStack, incursion ); FindContractionPlace( DMS, n, placeOk, place ); end while until n = 1 heuristics considers that the data point set defines a surface of similar extension as the 6 faces of the rectangular box that contains it. In all examples shown in Section 7 this formula has been used, getting satisfactory results.. When the data point set has a very irregular sampling density, it is convenient to calculate the ratio number of voxels containing two or more points divided by the number of voxels containing one point. If this value is too high we can recalculate the voxelization decreasing the edge's length of the voxel l.. From here on we will use the chosen l as unit length.. The second step constructs the initial discrete membrane with the voxels belonging to the exterior faces of the voxelization. From then on the algorithm applies the 3 defined operations (CONTRACTION, UNDO CONTRAC-TION, FREEZING) to contract gradually the DMS until it is adapted to the hard voxels. Concretely:. • It applies the CONTRACTION operation with a plate of size n Voxelization Size and the plate size is reduced progressively until n = 1. Each reduction of n defines a new generation.. • From a fixed value of n, it searches in all boundary soft voxels the locations where a CONTRACTION operation with a plate of size n can be applied. The locations found are the starting points to apply recursively the CON-TRACTION operation.. To find easily a place where to start a recursive contraction operation (function FindContractionPlace()), the boundary soft voxels are stored in a list. This list is searched for the first voxel that satisfies the required conditions to perform a contraction operation (see section 4.2).. The results of the algorithm depend on the choice of the initial plate size and how it is reduced progressively. The best solution, though with more computational cost, is to start with a plate size equal to the maximum of the three voxelization sizes n := max(nx, ny, nz) and decreasing the plate size 1 by 1. However, with data point sets obtained from 3D scanners, normally it is sufficient to divide the size of the plate by 2 in each iteration n := (n + 1)/2. In this way, the run-time of the algorithm is reduced considerably. The results shown in Section 7 show that this choice is reasonable under widely varying conditions. The algorithm can be sped up even more with a pre-process consisting in shrinking the initial DM to get the exterior silhouette of the hard voxels in the X, Y and Z directions (Figure 21(b) ).. From a fixed value n and a particular location where the CONTRACTION operation can be applied, the CON-TRACTION operation is applied recursively at the front, up, down, left and right directions in relation to the plate orientation (always with a plate of size n). Every time the CON-TRACTION operation is applied, it is checked for incursion in the hard voxels of the front, lateral and lateral front side of the plate. If an incursion is detected (Figure 9(b) ), the UNDO CONTRACTION operation is applied as many times as CONTRACTION operations were performed. Then a FREEZING operation is applied (Figure 9(c) ). This cancels an undesired expansion of the plate inside the solid. Incursion detection

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