Search results for: DNA copy number

Authors: Kang Zijian, Zhang Tingyu, Burra Venkata Durga Kumar

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This article investigates the challenges in memory migration during the live migration of virtual machines. We found three challenges probably existing in pre-copy technology. One of the main challenges is the challenge of downtime migration. Decrease the downtime could promise the normal work for a virtual machine. Although pre-copy technology is greatly decreasing the downtime, we still need to shut down the machine in order to finish the last round of data transfer. This paper provides an optimization scheme for the problems existing in pro-copy technology, mainly the optimization of the dirty page migration mechanism. The typical pre-copy technology copy n-1th’s dirty pages in nth turn. However, our idea is to create a double iteration method to solve this problem.

Keywords: virtual machine, pre-copy technology, memory migration process, downtime, dirty pages migration method

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Authors: Maria Lopez-Ibarra, Ana Velazquez-Wong, Lucelli Yañez-Gutierrez, Maria Araujo-Solis, Fabio Salamanca-Gomez, Alfonso Mendez-Tenorio, Haydeé Rosas-Vargas

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Congenital heart diseases (CHD) are the most common congenital abnormalities. These conditions can occur as both an element of distinct chromosomal malformation syndromes or as non-syndromic forms. Their etiology is not fully understood. Genetic variants such copy number variants have been associated with CHD. The aim of our study was to analyze these genomic variants in peripheral blood from Mexican children diagnosed with non-syndromic CHD. We included 16 children with atrial and ventricular septal defects and 5 healthy subjects without heart malformations as controls. To exclude the most common heart disease-associated syndrome alteration, we performed a fluorescence in situ hybridization test to identify the 22q11.2, responsible for congenital heart abnormalities associated with Di-George Syndrome. Then, a microarray based comparative genomic hybridization was used to identify global copy number variants. The identification of copy number variants resulted from the comparison and analysis between our results and data from main genetic variation databases. We identified copy number variants gain in three chromosomes regions from pediatric patients, 4q13.2 (31.25%), 9q34.3 (25%) and 20q13.33 (50%), where several genes associated with cellular, biosynthetic, and metabolic processes are located, UGT2B15, UGT2B17, SNAPC4, SDCCAG3, PMPCA, INPP6E, C9orf163, NOTCH1, C20orf166, and SLCO4A1. In addition, after a hierarchical cluster analysis based on the fluorescence intensity ratios from the comparative genomic hybridization, two congenital heart disease groups were generated corresponding to children with atrial or ventricular septal defects. Further analysis with a larger sample size is needed to corroborate these copy number variants as possible biomarkers to differentiate between heart abnormalities. Interestingly, the 20q13.33 gain was present in 50% of children with these CHD which could suggest that alterations in both coding and non-coding elements within this chromosomal region may play an important role in distinct heart conditions.

Keywords: aCGH, bioinformatics, congenital heart diseases, copy number variants, fluorescence in situ hybridization

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Authors: Habtamu Abera Goshu, Ping Yan

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Copy number variation (CNV) is a significant marker of the genetic and phenotypic diversity among individuals that accounts for complex quantitative traits of phenotype and diseases via modulating gene dosage, position effects, alteration of downstream pathways, modification of chromosome structure, and position within the nucleus and disrupting coding regions in the genome. Associating copy number variations (CNVs) with growth and gene expression are a powerful approach for identifying genomic characteristics that contribute to phenotypic and genotypic variation. A previous study using next-generation sequencing illustrated that the choline kinase beta (CHKB), Krüpple-like factor 6 (KLF6), glypican 1(GPC1), and cholinergic receptor muscarinic 3 (CHRM3) genes reside within copy number variable regions (CNVRs) of yak populations that overlap with quantitative trait loci (QTLs) of meat quality and growth. As a result, this research aimed to determine the association of CNVs of the KLF6, CHKB, GPC1, and CHRM3 genes with growth traits in the Datong yak breed. The association between the CNV types of the KLF6, CHKB, GPC1, and CHRM3 genes and the growth traits in the Datong yak breed was determined by one-way analysis of variance (ANOVA) using SPSS software. The CNV types were classified as a loss (a copy number of 0 or 1), gain (a copy number >2), and normal (a copy number of 2) relative to the reference gene, BTF3 in the 387 individuals of Datong yak. These results indicated that the normal CNV types of the CHKB and GPC1 genes were significantly (P<0.05) associated with high body length, height and weight, and chest girth in six-month-old and five-year-old Datong yaks. On the other hand, the loss CNV types of the KLF6 gene is significantly (P<0.05) associated with body weight and length and chest girth at six-month-old and five-year-old Datong yaks. In the contrary, the gain CNV type of the CHRM3 gene is highly (P<0.05) associated with body weight, length, height, and chest girth in six-month-old and five-year-old. This work provides the first observation of the biological role of CNVs of the CHKB, KLF6, GPC1, and CHRM3 genes in the Datong yak breed and might, therefore, provide a novel opportunity to utilize data on CNVs in designing molecular markers for the selection of animal breeding programs for larger populations of various yak breeds. Therefore, we hypothesized that this study provided inclusive information on the application of CNVs of the CHKB, KLF6, GPC1, and CHRM3 genes in growth traits in Datong yaks and its possible function in bovine species.

Keywords: Copy number variation, growth traits, yak, genes

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Authors: Khaled M. Alqahtani

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Copy number alterations (CNA) are structural variations in the genome in which some regions exhibit more or less than the normal two chromosomal copies. This genomic CNA profile provides critical information in tumor progression and is, therefore, informative for patients' survival. It is currently a statistical challenge to model patients' survival using their genomic CNA profiles while at the same time identifying regions in the genome that are associated with patients' survival. Some methods have been proposed, including the Cox proportional hazard (PH) model with ridge, lasso, or elastic net penalties. However, these methods do not take the general dependencies between genomic regions into account and produce results that are difficult to interpret. In this paper, we extend the elastic net penalty by introducing an additional penalty that takes into account general dependencies between genomic regions. This model produces smooth parameter estimates while simultaneously performing variable selection via sparse solution. The results indicate that the proposed method shows a better prediction performance than other models in our simulation study while enabling us to investigate regions in the genome that are associated with the patient's survival with sensible interpretation. We illustrate the method using a real dataset from a lung cancer cohort and simulated data.

Keywords: copy number alterations, cox proportional hazard, lung cancer, regression, sparse solution

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Authors: Cheng-Yang Lee, Petrus Tang, Tzu-Hao Chang

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Copy number variations (CNVs) have played an important role in many kinds of human diseases, such as Autism, Schizophrenia and a number of cancers. Many diseases are found in genome coding regions and whole exome sequencing (WES) is a cost-effective and powerful technology in detecting variants that are enriched in exons and have potential applications in clinical setting. Although several algorithms have been developed to detect CNVs using WES and compared with other algorithms for finding the most suitable methods using their own samples, there were not consistent datasets across most of algorithms to evaluate the ability of CNV detection. On the other hand, most of algorithms is using command line interface that may greatly limit the analysis capability of many laboratories. We create a series of simulated WES datasets from UCSC hg19 chromosome 22, and then evaluate the CNV detective ability of 19 algorithms from OMICtools database using our simulated WES datasets. We compute the sensitivity, specificity and accuracy in each algorithm for validation of the exome-derived CNVs. After comparison of 19 algorithms from OMICtools database, we construct a platform to install all of the algorithms in a virtual machine like VirtualBox which can be established conveniently in local computers, and then create a simple script that can be easily to use for detecting CNVs using algorithms selected by users. We also build a table to elaborate on many kinds of events, such as input requirement, CNV detective ability, for all of the algorithms that can provide users a specification to choose optimum algorithms.

Keywords: whole exome sequencing, copy number variations, omictools, pipeline

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Authors: A. Delimitsou, C. Gouedard, E. Konstanta, A. Koletis, S. Patera, E. Manou, K. Spaho, S. Murray

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Background: There remains a lack of International Standard Control Reference materials for Next Generation Sequencing-based approaches or device calibration. We have designed and validated dsDNA biomimetic reference materials for targeted such approaches incorporating proprietary motifs (patent pending) for device/test calibration. They enable internal single-sample calibration, alleviating sample comparisons to pooled historical population-based data assembly or statistical modelling approaches. We have validated such an approach for BRCA Copy Number Variation analytics using iQRS™-CNVSUITE versus Mixed Ligation-dependent Probe Amplification. Methods: Standard BRCA Copy Number Variation analysis was compared between mixed ligation-dependent probe amplification and next generation sequencing using a cohort of 198 breast/ovarian cancer patients. Next generation sequencing based copy number variation analysis of samples spiked with iQRS™ dsDNA biomimetics were analysed using proprietary CNVSUITE software. Mixed ligation-dependent probe amplification analyses were performed on an ABI-3130 Sequencer and analysed with Coffalyser software. Results: Concordance of BRCA – copy number variation events for mixed ligation-dependent probe amplification and CNVSUITE indicated an overall sensitivity of 99.88% and specificity of 100% for iQRS™-CNVSUITE. The negative predictive value of iQRS-CNVSUITE™ for BRCA was 100%, allowing for accurate exclusion of any event. The positive predictive value was 99.88%, with no discrepancy between mixed ligation-dependent probe amplification and iQRS™-CNVSUITE. For device calibration purposes, precision was 100%, spiking of patient DNA demonstrated linearity to 1% (±2.5%) and range from 100 copies. Traditional training was supplemented by predefining the calibrator to sample cut-off (lock-down) for amplicon gain or loss based upon a relative ratio threshold, following training of iQRS™-CNVSUITE using spiked iQRS™ calibrator and control mocks. BRCA copy number variation analysis using iQRS™-CNVSUITE™ was successfully validated and ISO15189 accredited and now enters CE-IVD performance evaluation. Conclusions: The inclusion of a reference control competitor (iQRS™ dsDNA mimetic) to next generation sequencing-based sequencing offers a more robust sample-independent approach for the assessment of copy number variation events compared to mixed ligation-dependent probe amplification. The approach simplifies data analyses, improves independent sample data analyses, and allows for direct comparison to an internal reference control for sample-specific quantification. Our iQRS™ biomimetic reference materials allow for single sample copy number variation analytics and further decentralisation of diagnostics to single patient sample assessment.

Keywords: validation, diagnostics, oncology, copy number variation, reference material, calibration

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Authors: Grishma D. Solanki, Karshan Kandoriya

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In modern era of information age, digitalization has revolutionized like never before. Powerful computers, advanced photo editing software packages and high resolution capturing devices have made manipulation of digital images incredibly easy. As per as image forensics concerns, one of the most actively researched area are detection of copy move forgeries. Higher computational complexity is one of the major component of existing techniques to detect such tampering. Moreover, copy move forgery is usually performed in three steps. First, copying of a region in an image then pasting the same one in the same respective image and finally doing some post-processing like rotation, scaling, shift, noise, etc. Consequently, pseudo Zernike moment is used as a features extraction method for matching image blocks and as a primary factor on which performance of detection algorithms depends.

Keywords: copy-move image forgery, digital forensics, image forensics, image forgery

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Authors: Chen Wang, Jared Evans, Yan Asmann

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With the quick evolvement of next-generation sequencing techniques, whole-exome or exome-panel data have become a cost-effective way for detection of small exonic mutations, but there has been a growing desire to accurately detect copy number variations (CNVs) as well. In order to address this research and clinical needs, we developed a sequencing coverage pattern-based method not only for copy number detections, data integrity checks, CNV calling, and visualization reports. The developed methodologies include complete automation to increase usability, genome content-coverage bias correction, CNV segmentation, data quality reports, and publication quality images. Automatic identification and removal of poor quality outlier samples were made automatically. Multiple experimental batches were routinely detected and further reduced for a clean subset of samples before analysis. Algorithm improvements were also made to improve somatic CNV detection as well as germline CNV detection in trio family. Additionally, a set of utilities was included to facilitate users for producing CNV plots in focused genes of interest. We demonstrate the somatic CNV enhancements by accurately detecting CNVs in whole exome-wide data from the cancer genome atlas cancer samples and a lymphoma case study with paired tumor and normal samples. We also showed our efficient reuses of existing exome sequencing data, for improved germline CNV calling in a family of the trio from the phase-III study of 1000 Genome to detect CNVs with various modes of inheritance. The performance of the developed method is evaluated by comparing CNV calling results with results from other orthogonal copy number platforms. Through our case studies, reuses of exome sequencing data for calling CNVs have several noticeable functionalities, including a better quality control for exome sequencing data, improved joint analysis with single nucleotide variant calls, and novel genomic discovery of under-utilized existing whole exome and custom exome panel data.

Keywords: bioinformatics, computational genetics, copy number variations, data reuse, exome sequencing, next generation sequencing

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Authors: N. Chaitawittanun, M. Munlin

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Due to rapid advancement of powerful image processing software, digital images are easy to manipulate and modify by ordinary people. Lots of digital images are edited for a specific purpose and more difficult to distinguish form their original ones. We propose a clustering method to detect a copy-move image forgery of JPEG, BMP, TIFF, and PNG. The process starts with reducing the color of the photos. Then, we use the clustering technique to divide information of measuring data by Hausdorff Distance. The result shows that the purposed methods is capable of inspecting the image file and correctly identify the forgery.

Keywords: image detection, forgery image, copy-paste, attack detection

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Authors: Michael Zimba

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A novel set of features for copy-move image forgery, CMIF, detection method is proposed. The proposed set presents a new approach which relies on electrostatic field theory, EFT. Solely for the purpose of reducing the dimension of a suspicious image, firstly performs discrete wavelet transform, DWT, of the suspicious image and extracts only the approximation subband. The extracted subband is then bijectively mapped onto a virtual electrostatic field where concepts of EFT are utilised to extract robust features. The extracted features are shown to be invariant to additive noise, JPEG compression, and affine transformation. The proposed features can also be used in general object matching.

Keywords: virtual electrostatic field, features, affine transformation, copy-move image forgery

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Authors: Jaco Oosthuizen, Nerina C. Van Der Merwe

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The National Health Laboratory Services in Bloemfontien has been the diagnostic testing facility for 1830 patients for familial breast cancer since 1997. From the cohort, 540 were comprehensively screened using High-Resolution Melting Analysis or Next Generation Sequencing for the presence of point mutations and/or indels. Approximately 90% of these patients stil remain undiagnosed as they are BRCA1/2 negative. Multiplex ligation-dependent probe amplification was initially added to screen for copy number variation detection, but with the introduction of next generation sequencing in 2017, was substituted and is currently used as a confirmation assay. The aim was to investigate the viability of utilizing internationally designed copy number variation detection assays based on mostly European/Caucasian genomic data for use within a South African context. The multiplex ligation-dependent probe amplification technique is based on the hybridization and subsequent ligation of multiple probes to a targeted exon. The ligated probes are amplified using conventional polymerase chain reaction, followed by fragment analysis by means of capillary electrophoresis. The experimental design of the assay was performed according to the guidelines of MRC-Holland. For BRCA1 (P002-D1) and BRCA2 (P045-B3), both multiplex assays were validated, and results were confirmed using a secondary probe set for each gene. The next generation sequencing technique is based on target amplification via multiplex polymerase chain reaction, where after the amplicons are sequenced parallel on a semiconductor chip. Amplified read counts are visualized as relative copy numbers to determine the median of the absolute values of all pairwise differences. Various experimental parameters such as DNA quality, quantity, and signal intensity or read depth were verified using positive and negative patients previously tested internationally. DNA quality and quantity proved to be the critical factors during the verification of both assays. The quantity influenced the relative copy number frequency directly whereas the quality of the DNA and its salt concentration influenced denaturation consistency in both assays. Multiplex ligation-dependent probe amplification produced false positives due to ligation failure when ligation was inhibited due to a variant present within the ligation site. Next generation sequencing produced false positives due to read dropout when primer sequences did not meet optimal multiplex binding kinetics due to population variants in the primer binding site. The analytical sensitivity and specificity for the South African population have been proven. Verification resulted in repeatable reactions with regards to the detection of relative copy number differences. Both multiplex ligation-dependent probe amplification and next generation sequencing multiplex panels need to be optimized to accommodate South African polymorphisms present within the genetically diverse ethnic groups to reduce the false copy number variation positive rate and increase performance efficiency.

Keywords: familial breast cancer, multiplex ligation-dependent probe amplification, next generation sequencing, South Africa

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Authors: S. Fahiminiya, J. Nadaf, F. Rauch, L. Jerome-Majewska, J. Majewski

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Background: Sequencing of protein coding regions of human genome (Whole Exome Sequencing; WES), has demonstrated a great success in the identification of causal mutations for several rare genetic disorders in human. Generally, most of WES studies have focused on rare variants in coding exons and splicing-sites where missense substitutions lead to the alternation of protein product. Although focusing on this category of variants has revealed the mystery behind many inherited genetic diseases in recent years, a subset of them remained still inconclusive. Here, we present the result of our WES studies where analyzing only rare variants in coding regions was not conclusive but further investigation revealed the involvement of non-coding variants and copy number variations (CNV) in etiology of the diseases. Methods: Whole exome sequencing was performed using our standard protocols at Genome Quebec Innovation Center, Montreal, Canada. All bioinformatics analyses were done using in-house WES pipeline. Results: To date, we successfully identified several disease causing mutations within gene coding regions (e.g. SCARF2: Van den Ende-Gupta syndrome and SNAP29: 22q11.2 deletion syndrome) by using WES. In addition, we showed that variants in non-coding regions and CNV have also important value and should not be ignored and/or filtered out along the way of bioinformatics analysis on WES data. For instance, in patients with osteogenesis imperfecta type V and in patients with glucocorticoid deficiency, we identified variants in 5'UTR, resulting in the production of longer or truncating non-functional proteins. Furthermore, CNVs were identified as the main cause of the diseases in patients with metaphyseal dysplasia with maxillary hypoplasia and brachydactyly and in patients with osteogenesis imperfecta type VII. Conclusions: Our study highlights the importance of considering non-coding variants and CNVs during interpretation of WES data, as they can be the only cause of disease under investigation.

Keywords: whole exome sequencing data, non-coding variants, copy number variations, rare diseases

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Authors: Eirini Konstanta, Cedric Gouedard, Aggeliki Delimitsou, Stefania Patera, Samuel Murray

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Introduction: Quality reference DNA standards (QRS) for molecular testing by next-generation sequencing (NGS) are essential for accurate quantitation of copy number variations (CNV) for germline and variant allelic frequencies (VAF) for somatic analyses. Objectives: Presently, several molecular analytics for oncology patients are reliant upon quantitative metrics. Test validation and standardisation are also reliant upon the availability of surrogate control materials allowing for understanding test LOD (limit of detection), sensitivity, specificity. We have developed a dual calibration platform allowing for QRS pairs to be included in analysed DNA samples, allowing for accurate quantitation of CNV and VAF metrics within and between patient samples. Methods: QRS™ blocks up to 500nt were designed for common NGS panel targets incorporating ≥ 2 identification tags (IDTDNA.com). These were analysed upon spiking into gDNA, somatic, and ctDNA using a proprietary CalSuite™ platform adaptable to common LIMS. Results: We demonstrate QRS™ calibration reproducibility spiked to 5–25% at ± 2.5% in gDNA and ctDNA. Furthermore, we demonstrate CNV and VAF within and between samples (gDNA and ctDNA) with the same reproducibility (± 2.5%) in a clinical sample of lung cancer and HBOC (EGFR and BRCA1, respectively). CNV analytics was performed with similar accuracy using a single pair of QRS calibrators when using multiple single targeted sequencing controls. Conclusion: Dual paired QRS™ calibrators allow for accurate and reproducible quantitative analyses of CNV, VAF, intrinsic sample allele measurement, inter and intra-sample measure not only simplifying NGS analytics but allowing for monitoring clinically relevant biomarker VAF across patient ctDNA samples with improved accuracy.

Keywords: calibrator, CNV, gene copy number, VAF

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Authors: Ghada Al-Kafaji, Mohamed Sabry

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Mitochondria are the site of cellular respiration and produce energy in the form of adenosine triphosphate (ATP) via oxidative phosphorylation. They are the major source of intracellular reactive oxygen species (ROS) and are also direct target to ROS attack. Oxidative stress and ROS-mediated disruptions of mitochondrial function are major components involved in the pathogenicity of diabetic complications. In this work, the changes in mitochondrial DNA (mtDNA) copy number, biogenesis, gene expression of mtDNA-encoded subunits of electron transport chain (ETC) complexes, and mitochondrial function in response to hyperglycemia-induced ROS and the effect of direct inhibition of ROS on mitochondria were investigated in an in vitro model of diabetic nephropathy using human renal mesangial cells. The cells were exposed to normoglycemic and hyperglycemic conditions in the presence and absence of Mn(III)tetrakis(4-benzoic acid) porphyrin chloride (MnTBAP) or catalase for 1, 4 and 7 days. ROS production was assessed by the confocal microscope and flow cytometry. mtDNA copy number and PGC-1a, NRF-1, and TFAM, as well as ND2, CYTB, COI, and ATPase 6 transcripts, were all analyzed by real-time PCR. PGC-1a, NRF-1, and TFAM, as well as ND2, CYTB, COI, and ATPase 6 proteins, were analyzed by Western blotting. Mitochondrial function was determined by assessing mitochondrial membrane potential and adenosine triphosphate (ATP) levels. Hyperglycemia-induced a significant increase in the production of mitochondrial superoxide and hydrogen peroxide at day 1 (P < 0.05), and this increase remained significantly elevated at days 4 and 7 (P < 0.05). The copy number of mtDNA and expression of PGC-1a, NRF-1, and TFAM as well as ND2, CYTB, CO1 and ATPase 6 increased after one day of hyperglycemia (P < 0.05), with a significant reduction in all those parameters at 4 and 7 days (P < 0.05). The mitochondrial membrane potential decreased progressively at 1 to 7 days of hyperglycemia with the parallel progressive reduction in ATP levels over time (P < 0.05). MnTBAP and catalase treatment of cells cultured under hyperglycemic conditions attenuated ROS production reversed renal mitochondrial oxidative stress and improved mtDNA, mitochondrial biogenesis, and function. These results show that hyperglycemia-induced ROS caused an early increase in mtDNA copy number, mitochondrial biogenesis and mtDNA-encoded gene expression of the ETC subunits in human mesangial cells as a compensatory response to the decline in mitochondrial function, which precede the mtDNA defect and mitochondrial dysfunction with a progressive oxidative response. Protection from ROS-mediated damage to renal mitochondria induced by hyperglycemia may be a novel therapeutic approach for the prevention/treatment of DN.

Keywords: diabetic nephropathy, hyperglycemia, reactive oxygen species, oxidative stress, mtDNA, mitochondrial dysfunction, manganese superoxide dismutase, catalase

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Authors: Aishwarya Shekhar, Himanshu Sharma

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Data deduplication is one of important data compression techniques for eliminating duplicate copies of repeating data, and has been widely used in cloud storage to reduce the amount of storage space and save bandwidth. In this process, duplicate data is expunged, leaving only one copy means single instance of the data to be accumulated. Though, indexing of each and every data is still maintained. Data deduplication is an approach for minimizing the part of storage space an organization required to retain its data. In most of the company, the storage systems carry identical copies of numerous pieces of data. Deduplication terminates these additional copies by saving just one copy of the data and exchanging the other copies with pointers that assist back to the primary copy. To ignore this duplication of the data and to preserve the confidentiality in the cloud here we are applying the concept of hybrid nature of cloud. A hybrid cloud is a fusion of minimally one public and private cloud. As a proof of concept, we implement a java code which provides security as well as removes all types of duplicated data from the cloud.

Keywords: confidentiality, deduplication, data compression, hybridity of cloud

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Authors: Ashrafosadat Mousavi Lar, Elahe Moravej

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To investigate and explain the history of each copy, we must refer to its past because it highlights parts of the civilization of people among which this copy has been codified. In this paper, eight Ferdowsi’s Shahnameh of Safavid era of Tabriz doctrine available in Iranian libraries and museums are studied. Undoubtedly, it can be said that Ferdowsi’s Shahnameh is one of the most important books that has been transcribed many times in different eras because it explains the Iranian champions’ prowess and it includes the history of Iran from Pishdadian to Sasanian dynasty. In addition, it has been attractive for governors and artists. The research methodology of this article is based on the analytical-descriptive arguments. The research hypothesis is based on papers used in Shahnameh writing in Safavid era of Tabriz doctrine were mostly Isfahanian papers existed. At that time, Isfahanian paper was unique in terms of quality, clarity, flatness of the sheets, volume, shape, softness and elegance, strength, and smoothness. This paper was mostly used to prepare the courtier and exquisite copies. This shows that the prepared copies in Safavid era of Tabriz doctrine were very important because the artists and people who ordered and were out of the court have ordered Isfahanian paper for writing their books.

Keywords: paper, Shahnameh, Safavid era, Tabriz doctrine

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Authors: L. M. Al-Harbi, A. M. Shokry, J. S. M. Sabir, A. Chaudhary, J. Manikandan, K. S. Saini

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Breast cancer is the second most common cause of cancer death worldwide and is the most common malignancy among Saudi females. During breast carcinogenesis, a wide-array of cytogenetic changes involving deletions, or amplification, or translocations, of part or whole of chromosome regions have been observed. Because of the limitations of various earlier technologies, newer tools are developed to scan for changes at the genomic level. Recently, Array Comparative Genomic Hybridization (aCGH) technique has been applied for detecting segmental genomic alterations at molecular level. In this study, aCGH was performed on twenty breast cancer tumors and their matching non-tumor (normal) counterparts using the Agilent 2x400K. Several regions were identified to be either amplified or deleted in a tumor-specific manner. Most frequent alterations were amplification of chromosome 1q, chromosome 8q, 20q, and deletions at 16q were also detected. The amplification of genetic events at 1q and 8q were further validated using FISH analysis using probes targeting 1q25 and 8q (MYC gene). The copy number changes at these loci can potentially cause a significant change in the tumor behavior, as deletions in the E-Cadherin (CDH1)-tumor suppressor gene as well as amplification of the oncogenes-Aurora Kinase A. (AURKA) and MYC could make these tumors highly metastatic. This study validates the use of aCGH in Saudi breast cancer patients and sets the foundations necessary for performing larger cohort studies searching for ethnicity-specific biomarkers and gene copy number variations.

Keywords: breast cancer, molecular biology, ecology, environment

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Authors: Doaa Hashad, Amany Elyamany, Perihan Salem

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Introduction: Hepatitis C virus infection (HCV) constitutes a serious dilemma that has an impact on the health of millions of Egyptians. Hepatitis C virus related hepatocellular carcinoma (HCV-HCC) is a crucial consequence of HCV that represents the third cause of cancer-related deaths worldwide. Aim of the study: assess the use of mitochondrial DNA (mtDNA) content as a non-invasive molecular biomarker in hepatitis c virus related hepatocellular carcinoma (HCV-HCC). Methods: A total of 135 participants were enrolled in the study. Volunteers were assigned to one of three groups equally; a group of HCV related cirrhosis (HCV-cirrhosis), a group of HCV-HCC and a control group of age- and sex- matched healthy volunteers with no evidence of liver disease. mtDNA was determined using a quantitative real-time PCR technique. Results: mtDNA content was lowest in HCV-HCC cases. No statistically significant difference was observed between the group of HCV-cirrhosis and the control group as regards mtDNA level. HCC patients with multi-centric hepatic lesions had significantly lower mtDNA content. On using receiver operating characteristic curve analysis, a cutoff of 34 was assigned for mtDNA content to distinguish between HCV-HCC and HCV-cirrhosis patients who are not yet complicated by malignancy. Lower mtDNA was associated with greater HCC risk on using healthy controls, HCV-cirrhosis, or combining both groups as a reference group. Conclusions: mtDNA content might constitute a non-invasive molecular biomarker that reflects tumor burden in HCV-HCC cases and could be used as a predictor of HCC risk in patients of HCV-cirrhosis. In addition, the non significant difference of mtDNA level between HCV-cirrhosis patients and healthy controls could eliminate the grey zone created by the use of AFP in some cirrhotic patients.

Keywords: DNA copy number, HCC, HCV, mitochondrial

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Authors: Fatma Sümer

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Introduction: This case report aims to report myopic anisometropia with copy-image in monozygotic twins. Methods: In February 2021, a 6-year-old identical twin was seen, who was referred to us with the diagnosis of amblyopia in their left eye from an external center. Both twins had a full ophthalmic examination, which included visual acuity testing, ocular motility testing, cycloplegic refraction, and fundus examination. Results: On examination, “copy image” myopic anisometropia was discovered. Twin 1 had anisometropia with myopic astigmatism in the left eye. His cycloplegic refraction was +1.00 (-0.75x 75) in the right eye and -8.0 (-1.50x175) in the left eye. Similarly, twin 2 had anisometropia with myopic astigmatism in the left eye. His cycloplegic refraction was -7.75 (-1.50x180) in the left eye and +1.25 (-0.75x90 ) in the right eye. The best-corrected visual acuity was 20/60 in the amblyopic eyes and 20/20 in the unaffected eyes. There was no ocular deviation. In either patient, a slit-lamp microscopic examination revealed no abnormalities in the anterior parts of either eye. Fundoscopic examination revealed no abnormalities. No abnormal ocular movements were demonstrated. Conclusion: As far as we have reviewed in the literature, previous studies with twins were mostly concerned with mirror-effect myopic anisometropia and myopic anisometropia, whereas ipsilateral amblyopia and anisometropia were not reported in monozygotic twins. This case underscores the possible genetic basis of myopic anisometropia.

Keywords: amblyopia, anisometropia, myopia, twins

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Authors: Salma M. Wakil

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Advances in the field of genetics overwhelmed detecting large number of inherited disorders at the molecular level and directed to the development of innovative technologies. These innovations have led to gene sequencing, prenatal mutation detection, pre-implantation genetic diagnosis; population based carrier screening and genome wide analyses using microarrays. Microarrays are widely used in establishing clinical and diagnostic setup for genetic anomalies at a massive level, with the advent of cytoscan molecular karyotyping as a clinical utility card for detecting chromosomal aberrations with high coverage across the entire human genome. Unlike a regular karyotype that relies on the microscopic inspection of chromosomes, molecular karyotyping with cytoscan constructs virtual chromosomes based on the copy number analysis of DNA which improves its resolution by 100-fold. We have been investigating a large number of patients with Developmental Delay and Intellectual disability with this platform for establishing micro syndrome deletions and have detected number of novel CNV’s in the Arabian population with the clinical relevance.

Keywords: microarrays, molecular karyotyping, developmental delay, genetics

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Authors: R. Rama Kishore, Sunesh

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Nowadays, robust and secure watermarking algorithm and its optimization have been need of the hour. A watermarking algorithm is presented to achieve the copy right protection of the owner based on visual cryptography, histogram shape property and entropy. In this, both host image and watermark are preprocessed. Host image is preprocessed by using Butterworth filter, and watermark is with visual cryptography. Applying visual cryptography on water mark generates two shares. One share is used for embedding the watermark, and the other one is used for solving any dispute with the aid of trusted authority. Usage of histogram shape makes the process more robust against geometric and signal processing attacks. The combination of visual cryptography, Butterworth filter, histogram, and entropy can make the algorithm more robust, imperceptible, and copy right protection of the owner.

Keywords: digital watermarking, visual cryptography, histogram, butter worth filter

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Authors: Welder A. Baldassini, Jon J. Ramsey, Marcos R. Chiaratti, Amália S. Chaves, Renata H. Branco, Sarah F. M. Bonilha, Dante P. D. Lanna

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With increased production costs there is a need for animals that are more efficient in terms of meat production. In this context, the role of mitochondrial DNA (mtDNA) on physiological processes in liver, muscle and adipose tissues may account for inter-animal variation in energy expenditures and heat production. The purpose this study was to investigate if the amounts of mtDNA in liver, muscle and adipose tissue (subcutaneous and visceral depots) of Nellore bulls are associated with residual feed intake (RFI) and estimated heat production (EHP). Eighteen animals were individually fed in a feedlot for 90 days. RFI values were obtained by regression of dry matter intake (DMI) in relation to average daily gain (ADG) and mid-test metabolic body weight (BW). The animals were classified into low (more efficient) and high (less efficient) RFI groups. The bulls were then randomly distributed in individual pens where they were given excess feed twice daily to result in 5 to 10% orts for 90 d with diet containing 15% crude protein and 2.7 Mcal ME/kg DM. The heart rate (HR) of bulls was monitored for 4 consecutive days and used for calculation of EHP. Electrodes were fitted to bulls with stretch belts (POLAR RS400; Kempele, Finland). To calculate oxygen pulse (O2P), oxygen consumption was obtained using a facemask connected to the gas analyzer (EXHALYZER, ECOMedics, Zurich, Switzerland) and HR were simultaneously measured for 15 minutes period. Daily oxygen (O2) consumption was calculated by multiplying the volume of O2 per beat by total daily beats. EHP was calculated multiplying O2P by the average HR obtained during the 4 days, assuming 4.89 kcal/L of O2 to measure daily EHP that was expressed in kilocalories/day/kilogram metabolic BW (kcal/day/kg BW0.75). Blood samples were collected between days 45 and 90th after the beginning of the trial period in order to measure the concentration of hemoglobin and hematocrit. The bulls were slaughtered in an experimental slaughter house in accordance with current guidelines. Immediately after slaughter, a section of liver, a portion of longissimus thoracis (LT) muscle, plus a portion of subcutaneous fat (surrounding LT muscle) and portions of visceral fat (kidney, pelvis and inguinal fat) were collected. Samples of liver, muscle and adipose tissues were used to quantify mtDNA copy number per cell. The number of mtDNA copies was determined by normalization of mtDNA amount against a single copy nuclear gene (B2M). Mean of EHP, hemoglobin and hematocrit of high and low RFI bulls were compared using two-sample t-tests. Additionally, the one-way ANOVA was used to compare mtDNA quantification considering the mains effects of RFI groups. We found lower EHP (83.047 vs. 97.590 kcal/day/kgBW0.75; P < 0.10), hemoglobin concentration (13.533 vs. 15.108 g/dL; P < 0.10) and hematocrit percentage (39.3 vs. 43.6 %; P < 0.05) in low compared to high RFI bulls, respectively, which may be useful traits to identify efficient animals. However, no differences were observed between the mtDNA content in liver, muscle and adipose tissue of Nellore bulls with high and low RFI.

Keywords: bioenergetics, Bos indicus, feed efficiency, mitochondria

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Authors: Mevlüt Burak Dalmış, Kemal Yaman

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In this study, flutter characteristics of cantilever rectangular plate structure under incompressible flow regime are investigated by comparing the results of commercial flutter analysis program ZAERO^© with wind tunnel tests conducted in Ankara Wind Tunnel (ART). A rectangular polycarbonate (PC) plate, 5x125x1000 mm in dimensions, is used for both numerical and experimental investigations. Analysis and test results are very compatible with each other. A comparison between two different solution methods (g and k-method) of ZAERO^© is also done. It is seen that, k-method gives closer result than the other one. However, g-method results are on conservative side and it is better to use conservative results namely g-method results. Even if the modal analysis results are used for the flutter analysis for this simple structure, a modal test should be conducted in order to validate the modal analysis results to have accurate flutter analysis results for more complicated structures.

Keywords: flutter, plate, subsonic flow, wind tunnel

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Authors: Akterono Budiyati, Gita Kusumo, Teguh Putra, Fritzie Rexana, Antonius Kurniawan, Aru Sudoyo, Ahmad Utomo, Andi Utama

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The presence of the programmed death ligand-1 (PD-L1) has been used in multiple clinical trials and approved as biomarker for selecting patients more likely to respond to immune checkpoint inhibitors. However, the expression of PD-L1 is regulated in different ways, which leads to a different significance of its presence. Positive PD-L1 within tumors may result from two mechanisms, induced PD-L1 expression by T-cell presence or genetic mechanism that lead to constitutive PD-L1 expression. Amplification of PD-L1 genes was found as one of genetic mechanism which causes an increase in PD-L1 expression. In case of colorectal cancer (CRC), targeting immune checkpoint inhibitor has been recommended for patients with microsatellite instable (MSI). Although the correlation between PD-L1 expression and MSI status has been widely studied, so far the precise mechanism of PD-L1 gene activation in CRC patients, particularly in MSI population have yet to be clarified. In this present study we have profiled 61 archived formalin fixed paraffin embedded CRC specimens of patients from Medistra Hospital, Jakarta admitted in 2010 - 2016. Immunohistochemistry was performed to measure expression of PD-L1 in tumor cells as well as MSI status using antibodies against PD-L1 and MMR (MLH1, MSH2, PMS2 and MSH6), respectively. PD-L1 expression was measured on tumor cells with cut off of 1% whereas loss of nuclear MMR protein expressions in tumor cells but not in normal or stromal cells indicated presence of MSI. Subset of PD-L1 positive patients was then assessed for copy number variations (CNVs) using single Tube TaqMan Copy Number Assays Gene CD247PD-L1. We also observed KRAS mutation to profile possible genetic mechanism leading to the presence or absence of PD-L1 expression. Analysis of 61 CRC patients revealed 15 patients (24%) expressed PD-L1 on their tumor cell membranes. The prevalence of surface membrane PD-L1 was significantly higher in patients with MSI (87%; 7/8) compared to patients with microsatellite stable (MSS) (15%; 8/53) (P=0.001). Although amplification of PD-L1 gene was not found among PD-L1 positive patients, low-level amplification of PD-L1 gene was commonly observed in MSS patients (75%; 6/8) than in MSI patients (43%; 3/7). Additionally, we found 26% of CRC patients harbored KRAS mutations (16/61), so far the distribution of KRAS status did not correlate with PD-L1 expression. Our data suggest genetic mechanism through amplification of PD-L1 seems not to be the mechanism underlying upregulation of PD-L1 expression in CRC patients. However, further studies are warranted to confirm the results.

Keywords: colorectal cancer, gene amplification, microsatellite instable, programmed death ligand-1

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Authors: Pavlina Capkova, Josef Srovnal, Vera Becvarova, Marie Trkova, Zuzana Capkova, Andrea Stefekova, Vaclava Curtisova, Alena Santava, Sarka Vejvalkova, Katerina Adamova, Radek Vodicka

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ASDs are heterogeneous and complex developmental diseases with a significant genetic background. Recurrent CNVs are known to be a frequent cause of ASD. These CNVs can have, however, a variable expressivity which results in a spectrum of phenotypes from asymptomatic to ID/DD/ASD. ASD is associated with ID in ~75% individuals. Various platforms are used to detect pathogenic mutations in the genome of these patients. The performed study is focused on a determination of the frequency of pathogenic mutations in a group of ASD patients and a group of ID/DD patients using various strategies along with a comparison of their detection rate. The possible role of the origin of these mutations in aetiology of ASD was assessed. The study included 35 individuals with ASD and 68 individuals with ID/DD (64 males and 39 females in total), who underwent rigorous genetic, neurological and psychological examinations. Screening for pathogenic mutations involved karyotyping, screening for FMR1 mutations and for metabolic disorders, a targeted MLPA test with probe mixes Telomeres 3 and 5, Microdeletion 1 and 2, Autism 1, MRX and a chromosomal microarray analysis (CMA) (Illumina or Affymetrix). Chromosomal aberrations were revealed in 7 (1 in the ASD group) individuals by karyotyping. FMR1 mutations were discovered in 3 (1 in the ASD group) individuals. The detection rate of pathogenic mutations in ASD patients with a normal karyotype was 15.15% by MLPA and CMA. The frequencies of the pathogenic mutations were 25.0% by MLPA and 35.0% by CMA in ID/DD patients with a normal karyotype. CNVs inherited from asymptomatic parents were more abundant than de novo changes in ASD patients (11.43% vs. 5.71%) in contrast to the ID/DD group where de novo mutations prevailed over inherited ones (26.47% vs. 16.18%). ASD patients shared more frequently their mutations with their fathers than patients from ID/DD group (8.57% vs. 1.47%). Maternally inherited mutations predominated in the ID/DD group in comparison with the ASD group (14.7% vs. 2.86 %). CNVs of an unknown significance were found in 10 patients by CMA and in 3 patients by MLPA. Although the detection rate is the highest when using CMA, recurrent CNVs can be easily detected by MLPA. CMA proved to be more efficient in the ID/DD group where a larger spectrum of rare pathogenic CNVs was revealed. This study determined that maternally inherited highly penetrant mutations and de novo mutations more often resulted in ID/DD without ASD in patients. The paternally inherited mutations could be, however, a source of the greater variability in the genome of the ASD patients and contribute to the polygenic character of the inheritance of ASD. As the number of the subjects in the group is limited, a larger cohort is needed to confirm this conclusion. Inherited CNVs have a role in aetiology of ASD possibly in combination with additional genetic factors - the mutations elsewhere in the genome. The identification of these interactions constitutes a challenge for the future. Supported by MH CZ – DRO (FNOl, 00098892), IGA UP LF_2016_010, TACR TE02000058 and NPU LO1304.

Keywords: autistic spectrum disorders, copy number variant, chromosomal microarray, intellectual disability, karyotyping, MLPA, multiplex ligation-dependent probe amplification

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Authors: Mohammed Abdullah Alshahrani

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This research focuses on the investigation of partial least squares (PLS) methodology to deal with high-dimensional correlated data. Current developments in technology have enabled experiments to produce data that are characterized by, first, the number of variables that far exceeds the number of observations and, second, variables that are substantially correlated between them. These types of data are commonly found in, first, chemometrics, where absorbance levels of chemical samples are recorded across hundreds of wavelengths in a calibration of a near-infrared (NIR) spectrometer. Second, they are also common to be found in genomics where copy number alterations (CNA) are recorded across thousands of genomic regions from cancer patients. In our study, we investigated key areas to address these challenges. Firstly, we tackled the issue of three main PLS algorithms having potentially different interpretations of relevant quantities. We unified these interpretations by identifying scenarios where all three algorithms yield the same estimates. Secondly, we explored the phenomenon of unusual negative shrinkage factors encountered during PLS model fitting. Unlike ridge regression or principal component regression, where shrinkage factors range between zero and one, PLS can exhibit factors greater than one or even negative, hence more aptly termed ‘filter factors’ rather than ‘shrinkage factors’. This characteristic allows PLS to effectively handle high-dimensional data by applying shrinkage to estimates. To our knowledge, there has been no previous meaningful investigation on the negative filter factors (NFF) in PLS. In this research we present a novel result whereby we identify the condition for NFF to happen and investigate characteristics of the data that are associated with NFF to get an insight. Lastly, the main challenge of the application of PLS is in the interpretation of weights associated with the predictors. With hundreds and thousands of predictors, each and every predictor variable has non-zero weight. However, we expect that only some predictor variables are contributing to the association with the outcome variable. We, therefore, resort to the sparse estimation of predictor weights where some weights are zero estimated and the other weights are non-zero. A (standard) lasso estimation has a weakness in dealing with correlated variables as it picks up one variable within a correlation block without knowing the reason. A novel approach is needed to consider the dependencies between predictor variables in estimating the weights. We propose a new method where a new penalty function is introduced in the likelihood function associated with the estimation of weights. The penalty function is a combination of a lasso penalty that imposes sparsity and a penalty based on Cauchy distribution with a smoother matrix to take into account dependencies between genomic regions. The results show that the estimates of the weights are sparse: many weights are zero estimated, and those non-zero estimates are grouped and exhibit smoothness within them. The interpretation of genomic regions becomes easy, and the identification of important regions for each component can be done simultaneously with prediction in a single modeling framework. We investigate the relation between PLS and graphical modeling using the information in the weights to construct the graph with unsuccessful results. High-dimensional data where the number of predictors (p) exceeds the number of observations (n) are widely used in many applications of regression analysis. Ordinary least squares regression (OLS), which is the most well-known method for regression problems, has less performance with high-dimensional and highly- correlated data. Previous studies have shown that there is an association between copy number alterations (CNA) in some key genes and disease phenotypes. Moreover, it is very important in high-dimensional data to classify the samples into groups, such as tumor types, of gene expression data in bioinformatics and biology. However, the standard regression of classification methods will fail in these cases because the predictors matrix is singular and so, cannot be inverted. Hence, regularised methods are needed such as shrinkage methods and dimension reduction methods. One of the most suggested methods in the literature is partial least squares regression (PLS) for linear regression and classification.

Keywords: negative filter factors, partial least square regression, high-dimensional data, biostatistics, bioinformatics

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Authors: Daria Grechishnikova, Maria Poptsova

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Transposable elements play an important role in the evolution of various species from bacteria to human. Long Interspersed Nuclear Elements (LINEs) and Short Interspersed Nuclear Elements (SINEs) are two major classes of retrotransposons that occupy a considerable part of any genome and their copy numbers can range form several hundreds to a million. Both LINEs and SINEs multiply through a copy-and-paste mechanism. LINEs encode proteins, which make them capable of self-propagation while SINEs are parasitic and require the machinery of LINEs to multiply. The mechanisms how LINE and SINE RNA is recognized by the LINE-encoded reverse transcriptase (RT) remain unclear. For some SINE-LINE pairs, it was shown that they share a common 3’-end with a stem-loop structure. Majority of the SINE-LINE pairs do not have a common 3’-end. Recently we have shown that in the human genome Alu-L1 pairs have structurally similar stem-loop structure at the 3’-end. Here we extended our analysis to a wide range of species and analyzed LINEs from 161 different species from Repbase and 217 SINE sequences from SINEBase. It appeared that all of the analyzed sequences contained stem-loop structures at the 3’-end. Here we conclude that it is very likely that a common evolutionary mechanism of transposon RNA recognition requires the presence of stem-loop structures at their 3’-end.

Keywords: LINE, SINE, mechanisms of retrotransposition, retrotransposons, stem-loop, stem-loop structures, transposons

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Authors: Gurkirat Kaur, Manoj Kumar, Manju Bala

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Ethernet is the most influential and widely used technology in the world. With the growing demand of low latency and high throughput technologies like InfiniBand and RoCE, unique features viz. RDMA (Remote Direct Memory Access) have evolved. RDMA is an effective technology which is used for reducing system load and improving performance. InfiniBand is a well known technology which provides high-bandwidth and low-latency and makes optimal use of in-built features like RDMA. With the rapid evolution of InfiniBand technology and Ethernet lacking the RDMA and zero copy protocol, the Ethernet community has came out with a new enhancements that bridges the gap between InfiniBand and Ethernet. By adding the RDMA and zero copy protocol to the Ethernet a new networking technology is evolved, called RDMA over Converged Ethernet (RoCE). RoCE is a standard released by the IBTA standardization body to define RDMA protocol over Ethernet. With the emergence of lossless Ethernet, RoCE uses InfiniBand’s efficient transport to provide the platform for deploying RDMA technology in mainstream data centres over 10GigE, 40GigE and beyond. RoCE provide all of the InfiniBand benefits transport benefits and well established RDMA ecosystem combined with converged Ethernet. In this paper, we evaluate the heterogeneous Linux cluster, having multi nodes with fast interconnects i.e. gigabit Ethernet and Soft RoCE. This paper presents the heterogeneous Linux cluster configuration and evaluates its performance using Intel’s MPI Benchmarks. Our result shows that Soft RoCE is performing better than Ethernet in various performance metrics like bandwidth, latency and throughput.

Keywords: ethernet, InfiniBand, RoCE, RDMA, MPI, Soft RoCE

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Authors: Zeeshan Khan, Faisal Nouroz, Shumaila Noureen

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European or common rabbit (Oryctolagus cuniculus) belongs to class Mammalia, order Lagomorpha of family Leporidae. They are distributed worldwide and are native to Europe (France, Spain and Portugal) and Africa (Morocco and Algeria). LTR retrotransposons are major Class I mobile genetic elements of eukaryotic genomes and play a crucial role in genome expansion, evolution and diversification. They were mostly annotated in various genomes by conventional approaches of homology searches, which restricted the annotation of novel elements. Present work involved de novo identification of LTR retrotransposons by LTR_FINDER in haploid genome of rabbit (2247.74 Mb) distributed in 22 chromosomes, of which 7,933 putative full-length or partial copies were identified containing 69.38 Mb of elements, accounting 3.08% of the genome. Highest copy numbers (731) were found on chromosome 7, followed by chromosome 12 (705), while the lowest copy numbers (27) were detected in chromosome 19 with no elements identified from chromosome 21 due to partially sequenced chromosome, unidentified nucleotides (N) and repeated simple sequence repeats (SSRs). The identified elements ranged in sizes from 1.2 - 25.8 Kb with average sizes between 2-10 Kb. Highest percentage (4.77%) of elements was found in chromosome 15, while lowest (0.55%) in chromosome 19. The most frequent tRNA type was Arginine present in majority of the elements. Based on gained results, it was estimated that rabbit exhibits 15,866 copies having 137.73 Mb of elements accounting 6.16% of diploid genome (44 chromosomes). Further molecular analyses will be helpful in chromosomal localization and distribution of these elements on chromosomes.

Keywords: rabbit, LTR retrotransposons, genome, chromosome

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Authors: Iryna Shevchenko

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The science of mathematics was originated at the order of count of objects and subsequently for the measurement of size and quality of objects using the logical or abstract means. The laws of mathematics are based on the study of absolute values. The number 0 or "nothing" is the purely logical (as the opposite to absolute) value as the "nothing" should always assume the space for the something that had existed there; otherwise the "something" would never come to existence. In this work we are going to prove that the number "0" is the abstract (logical) and not an absolute number and it has the absolute value of “∞” (infinity). Therefore, the number "0" might not stand in the row of numbers that symbolically represents the absolute values, as it would be the mathematically incorrect. The symbolical value of number "0" in the row of numbers could be represented with symbol "∞" (infinity). As a result, we have the mathematical row of numbers: epsilon, ...4, 3, 2, 1, ∞. As the conclusions of the theory of number “0” we presented the statements: multiplication and division by fractions of numbers is illegal operation and the mathematical division by number “0” is allowed.

Keywords: illegal operation of division and multiplication by fractions of number, infinity, mathematical row of numbers, theory of number “0”

Procedia PDF Downloads 508