Search results for: Golay coded sequences

Authors: Ihor Trots, Yuriy Tasinkevych, Andrzej Nowicki, Marcin Lewandowski

Abstract:

The paper presents the study of synthetic transmit aperture method applying the Golay coded transmission for medical ultrasound imaging. Longer coded excitation allows to increase the total energy of the transmitted signal without increasing the peak pressure. Signal-to-noise ratio and penetration depth are improved maintaining high ultrasound image resolution. In the work the 128-element linear transducer array with 0.3 mm inter-element spacing excited by one cycle and the 8 and 16-bit Golay coded sequences at nominal frequencies 4 MHz was used. Single element transmission aperture was used to generate a spherical wave covering the full image region and all the elements received the echo signals. The comparison of 2D ultrasound images of the wire phantom as well as of the tissue mimicking phantom is presented to demonstrate the benefits of the coded transmission. The results were obtained using the synthetic aperture algorithm with transmit and receive signals correction based on a single element directivity function.

Keywords: Golay coded sequences, radiation pattern, synthetic aperture, ultrasound imaging.

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Authors: Ihor Trots, Yuriy Tasinkevych, Andrzej Nowicki, Marcin Lewandowski

Abstract:

In the paper the study of synthetic transmit aperture method applying the Golay coded transmission for medical ultrasound imaging is presented. Longer coded excitation allows to increase the total energy of the transmitted signal without increasing the peak pressure. Moreover signal-to-noise ratio and penetration depth are improved while maintaining high ultrasound image resolution. In the work the 128-element linear transducer array with 0.3 mm inter-element spacing excited by one cycle and the 8 and 16- bit Golay coded sequences at nominal frequency 4 MHz was used. To generate a spherical wave covering the full image region a single element transmission aperture was used and all the elements received the echo signals. The comparison of 2D ultrasound images of the tissue mimicking phantom and in vitro measurements of the beef liver is presented to illustrate the benefits of the coded transmission. The results were obtained using the synthetic aperture algorithm with transmit and receive signals correction based on a single element directivity function.

Keywords: Golay coded sequences, radiation pattern, signal processing, synthetic aperture, ultrasound imaging.

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Authors: Y. Kumru, K. Enhos, H. Köymen

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In this paper, we report the experimental results on using complementary Golay coded signals at 7.5 MHz to detect breast microcalcifications of 50 µm size. Simulations using complementary Golay coded signals show perfect consistence with the experimental results, confirming the improved signal to noise ratio for complementary Golay coded signals. For improving the success on detecting the microcalcifications, orthogonal complementary Golay sequences having cross-correlation for minimum interference are used as coded signals and compared to tone burst pulse of equal energy in terms of resolution under weak signal conditions. The measurements are conducted using an experimental ultrasound research scanner, Digital Phased Array System (DiPhAS) having 256 channels, a phased array transducer with 7.5 MHz center frequency and the results obtained through experiments are validated by Field-II simulation software. In addition, to investigate the superiority of coded signals in terms of resolution, multipurpose tissue equivalent phantom containing series of monofilament nylon targets, 240 µm in diameter, and cyst-like objects with attenuation of 0.5 dB/[MHz x cm] is used in the experiments. We obtained ultrasound images of monofilament nylon targets for the evaluation of resolution. Simulation and experimental results show that it is possible to differentiate closely positioned small targets with increased success by using coded excitation in very weak signal conditions.

Keywords: Coded excitation, complementary Golay codes, DiPhAS, medical ultrasound.

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Authors: Sanjay Singh, M Sathish Kumar, H. S Mruthyunjaya

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Multicarrier transmission system such as Orthogonal Frequency Division Multiplexing (OFDM) is a promising technique for high bit rate transmission in wireless communication systems. OFDM is a spectrally efficient modulation technique that can achieve high speed data transmission over multipath fading channels without the need for powerful equalization techniques. A major drawback of OFDM is the high Peak-to-Average Power Ratio (PAPR) of the transmit signal which can significantly impact the performance of the power amplifier. In this paper we have compared the PAPR reduction performance of Golay and Reed-Muller coded OFDM signal. From our simulation it has been found that the PAPR reduction performance of Golay coded OFDM is better than the Reed-Muller coded OFDM signal. Moreover, for the optimum PAPR reduction performance, code configuration for Golay and Reed-Muller codes has been identified.

Keywords: OFDM, PAPR, Perfect Codes, Golay Codes, Reed-Muller Codes

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Authors: Peter Drotar, Juraj Gazda, Pavol Galajda, Dusan Kocur

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The study in this paper underlines the importance of correct joint selection of the spreading codes for uplink of multicarrier code division multiple access (MC-CDMA) at the transmitter side and detector at the receiver side in the presence of nonlinear distortion due to high power amplifier (HPA). The bit error rate (BER) of system for different spreading sequences (Walsh code, Gold code, orthogonal Gold code, Golay code and Zadoff-Chu code) and different kinds of receivers (minimum mean-square error receiver (MMSE-MUD) and microstatistic multi-user receiver (MSF-MUD)) is compared by means of simulations for MC-CDMA transmission system. Finally, the results of analysis will show, that the application of MSF-MUD in combination with Golay codes can outperform significantly the other tested spreading codes and receivers for all mostly used models of HPA.

Keywords: HPA, MC-CDMA, microstatistic filter, multi-user receivers, PAPR.

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Authors: Osman Bizim

Abstract:

In this work we study elliptic divisibility sequences over finite fields. MorganWard in [11, 12] gave arithmetic theory of elliptic divisibility sequences. We study elliptic divisibility sequences, equivalence of these sequences and singular elliptic divisibility sequences over finite fields Fp, p > 3 is a prime.

Keywords: Elliptic divisibility sequences, equivalent sequences, singular sequences.

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Authors: Mai S. Mabrouk, Nahed H. Solouma, Abou-Bakr M. Youssef, Yasser M. Kadah

Abstract:

Many digital signal processing, techniques have been used to automatically distinguish protein coding regions (exons) from non-coding regions (introns) in DNA sequences. In this work, we have characterized these sequences according to their nonlinear dynamical features such as moment invariants, correlation dimension, and largest Lyapunov exponent estimates. We have applied our model to a number of real sequences encoded into a time series using EIIP sequence indicators. In order to discriminate between coding and non coding DNA regions, the phase space trajectory was first reconstructed for coding and non-coding regions. Nonlinear dynamical features are extracted from those regions and used to investigate a difference between them. Our results indicate that the nonlinear dynamical characteristics have yielded significant differences between coding (CR) and non-coding regions (NCR) in DNA sequences. Finally, the classifier is tested on real genes where coding and non-coding regions are well known.

Keywords: Gene prediction, nonlinear dynamics, correlation dimension, Lyapunov exponent.

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Authors: Abhijit Mitra

Abstract:

Maximal length sequences (m-sequences) are also known as pseudo random sequences or pseudo noise sequences for closely following Golomb-s popular randomness properties: (P1) balance, (P2) run, and (P3) ideal autocorrelation. Apart from these, there also exist certain other less known properties of such sequences all of which are discussed in this tutorial paper. Comprehensive proofs to each of these properties are provided towards better understanding of such sequences. A simple test is also proposed at the end of the paper in order to distinguish pseudo noise sequences from truly random sequences such as Bernoulli sequences.

Keywords: Maximal length sequence, pseudo noise sequence, punctured de Bruijn sequence, auto-correlation, Bernoulli sequence, randomness tests.

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Authors: Betül Gezer, Ahmet Tekcan, Osman Bizim

Abstract:

In this work, we study elliptic divisibility sequences over finite fields. Morgan Ward in [14], [15] gave arithmetic theory of elliptic divisibility sequences and formulas for elliptic divisibility sequences with rank two over finite field Fp. We study elliptic divisibility sequences with rank three, four and five over a finite field Fp, where p > 3 is a prime and give general terms of these sequences and then we determine elliptic and singular curves associated with these sequences.

Keywords: Elliptic divisibility sequences, singular elliptic divisibilitysequences, elliptic curves, singular curves.

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Authors: Paul O'Leary, Matthew Harker

Abstract:

This paper presents unified theory for local (Savitzky- Golay) and global polynomial smoothing. The algebraic framework can represent any polynomial approximation and is seamless from low degree local, to high degree global approximations. The representation of the smoothing operator as a projection onto orthonormal basis functions enables the computation of: the covariance matrix for noise propagation through the filter; the noise gain and; the frequency response of the polynomial filters. A virtually perfect Gram polynomial basis is synthesized, whereby polynomials of degree d = 1000 can be synthesized without significant errors. The perfect basis ensures that the filters are strictly polynomial preserving. Given n points and a support length ls = 2m + 1 then the smoothing operator is strictly linear phase for the points xi, i = m+1. . . n-m. The method is demonstrated on geometric surfaces data lying on an invariant 2D lattice.

Keywords: Gram polynomials, Savitzky-Golay Smoothing, Discrete Polynomial Moments

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Authors: J.S. Ubhi, M.S. Patterh, T.S. Kamal

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Exact expressions for bit-error probability (BEP) for coherent square detection of uncoded and coded M-ary quadrature amplitude modulation (MQAM) using an array of antennas with maximal ratio combining (MRC) in a flat fading channel interference limited system in a Nakagami-m fading environment is derived. The analysis assumes an arbitrary number of independent and identically distributed Nakagami interferers. The results for coded MQAM are computed numerically for the case of (24,12) extended Golay code and compared with uncoded MQAM by plotting error probabilities versus average signal-to-interference ratio (SIR) for various values of order of diversity N, number of distinct symbols M, in order to examine the effect of cochannel interferers on the performance of the digital communication system. The diversity gains and net gains are also presented in tabular form in order to examine the performance of digital communication system in the presence of interferers, as the order of diversity increases. The analytical results presented in this paper are expected to provide useful information needed for design and analysis of digital communication systems with space diversity in wireless fading channels.

Keywords: Cochannel interference, maximal ratio combining, Nakagami-m fading, wireless digital communications.

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Authors: G. Lavanya Devi, Allam Appa Rao, A. Damodaram, GR Sridhar, G. Jaya Suma

Abstract:

Cluster analysis divides data into groups that are meaningful, useful, or both. Analysis of biological data is creating a new generation of epidemiologic, prognostic, diagnostic and treatment modalities. Clustering of protein sequences is one of the current research topics in the field of computer science. Linear relation is valuable in rule discovery for a given data, such as if value X goes up 1, value Y will go down 3", etc. The classical linear regression models the linear relation of two sequences perfectly. However, if we need to cluster a large repository of protein sequences into groups where sequences have strong linear relationship with each other, it is prohibitively expensive to compare sequences one by one. In this paper, we propose a new technique named General Regression Model Technique Clustering Algorithm (GRMTCA) to benignly handle the problem of linear sequences clustering. GRMT gives a measure, GR*, to tell the degree of linearity of multiple sequences without having to compare each pair of them.

Keywords: Clustering, General Regression Model, Protein Sequences, Similarity Measure.

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Authors: M. Kulkarni, R. K. Sinha, D. R. Bhaskar

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In this paper, we have compared the performance of a Turbo and Trellis coded optical code division multiple access (OCDMA) system. The comparison of the two codes has been accomplished by employing optical orthogonal codes (OOCs). The Bit Error Rate (BER) performances have been compared by varying the code weights of address codes employed by the system. We have considered the effects of optical multiple access interference (OMAI), thermal noise and avalanche photodiode (APD) detector noise. Analysis has been carried out for the system with and without double optical hard limiter (DHL). From the simulation results it is observed that a better and distinct comparison can be drawn between the performance of Trellis and Turbo coded systems, at lower code weights of optical orthogonal codes for a fixed number of users. The BER performance of the Turbo coded system is found to be better than the Trellis coded system for all code weights that have been considered for the simulation. Nevertheless, the Trellis coded OCDMA system is found to be better than the uncoded OCDMA system. Trellis coded OCDMA can be used in systems where decoding time has to be kept low, bandwidth is limited and high reliability is not a crucial factor as in local area networks. Also the system hardware is less complex in comparison to the Turbo coded system. Trellis coded OCDMA system can be used without significant modification of the existing chipsets. Turbo-coded OCDMA can however be employed in systems where high reliability is needed and bandwidth is not a limiting factor.

Keywords: avalanche photodiode, optical code division multipleaccess, optical multiple access interference, Trellis codedmodulation, Turbo code

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Authors: V. Anil Kumar, Abhijit Mitra, S. R. Mahadeva Prasanna

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We analyze the effectivity of different pseudo noise (PN) and orthogonal sequences for encrypting speech signals in terms of perceptual intelligence. Speech signal can be viewed as sequence of correlated samples and each sample as sequence of bits. The residual intelligibility of the speech signal can be reduced by removing the correlation among the speech samples. PN sequences have random like properties that help in reducing the correlation among speech samples. The mean square aperiodic auto-correlation (MSAAC) and the mean square aperiodic cross-correlation (MSACC) measures are used to test the randomness of the PN sequences. Results of the investigation show the effectivity of large Kasami sequences for this purpose among many PN sequences.

Keywords: Speech encryption, pseudo-noise codes, maximallength, Gold, Barker, Kasami, Walsh-Hadamard, autocorrelation, crosscorrelation, figure of merit.

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Authors: Paula Verdugo-Hernández, Patricio Cumsille

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We analyze a first-class on the convergence of real number sequences, named hereafter sequences, to foster exploration and discovery of concepts through graphical representations before engaging students in proving. The main goal was to differentiate between sequences and continuous functions-of-a-real-variable and better understand concepts at an initial stage. We applied the analytic frame of Mathematical Working Spaces, which we expect to contribute to extending to sequences since, as far as we know, it has only developed for other objects, and which is relevant to analyze how mathematical work is built systematically by connecting the epistemological and cognitive perspectives, and involving the semiotic, instrumental, and discursive dimensions.

Keywords: Convergence, graphical representations, Mathematical Working Spaces, paradigms of real analysis, real number sequences.

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Authors: Abhijit Mitra

Abstract:

The paper provides an in-depth tutorial of mathematical construction of maximal length sequences (m-sequences) via primitive polynomials and how to map the same when implemented in shift registers. It is equally important to check whether a polynomial is primitive or not so as to get proper m-sequences. A fast method to identify primitive polynomials over binary fields is proposed where the complexity is considerably less in comparison with the standard procedures for the same purpose.

Keywords: Finite field, irreducible polynomial, primitive polynomial, maximal length sequence, additive shift register, multiplicative shift register.

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Authors: Yan-zhao Yang

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In this paper, some limit properties for mixing random variables sequences were studied and some results on weak law of large number for mixing random variables sequences were presented. Some complete convergence theorems were also obtained. The results extended and improved the corresponding theorems in i.i.d random variables sequences.

Keywords: Complete convergence, mixing random variables, weak law of large numbers.

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Authors: Ali Akbar Attari, Ali Asghar Beheshti Shirazi

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In this paper, we propose a blind and robust audio watermarking scheme based on spread spectrum in Discrete Wavelet Transform (DWT) domain. Watermarks are embedded in the low-frequency coefficients, which is less audible. The key idea is dividing the audio signal into small frames, and magnitude of the 6^th level of DWT approximation coefficients is modifying based upon the Direct Sequence Spread Spectrum (DSSS) technique. Also, the psychoacoustic model for enhancing in imperceptibility, as well as Savitsky-Golay filter for increasing accuracy in extraction, is used. The experimental results illustrate high robustness against most common attacks, i.e. Gaussian noise addition, Low pass filter, Resampling, Requantizing, MP3 compression, without significant perceptual distortion (ODG is higher than -1). The proposed scheme has about 83 bps data payload.

Keywords: Audio watermarking, spread spectrum, discrete wavelet transform, psychoacoustic, Savitsky-Golay filter.

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Authors: Ruigang Zhang, Wuyungaowa, Xingchen Ma

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In this paper, we present some formulas of symbolic operator summation, which involving Generalization well-know number sequences or polynomial sequences, and mean while we obtain some identities about the sequences by employing M-R‘s substitution rule.

Keywords: Generating functions, operators sequence group, Riordan arrays, R. G operator group, combinatorial identities.

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Authors: Sidhartha Panda, C. Ardil

Abstract:

Power system stabilizers (PSS) are now routinely used in the industry to damp out power system oscillations. In this paper, real-coded genetic algorithm (RCGA) optimization technique is applied to design robust power system stabilizer for both singlemachine infinite-bus (SMIB) and multi-machine power system. The design problem of the proposed controller is formulated as an optimization problem and RCGA is employed to search for optimal controller parameters. By minimizing the time-domain based objective function, in which the deviation in the oscillatory rotor speed of the generator is involved; stability performance of the system is improved. The non-linear simulation results are presented under wide range of operating conditions; disturbances at different locations as well as for various fault clearing sequences to show the effectiveness and robustness of the proposed controller and their ability to provide efficient damping of low frequency oscillations.

Keywords: Particle swarm optimization, power system stabilizer, low frequency oscillations, power system stability.

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Authors: Oluseye Adeniyi Adeleke, Mohd Fadzli Salleh

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Cooperative communication provides transmit diversity, even when, due to size constraints, mobile units cannot accommodate multiple antennas. A versatile cooperation method called coded cooperation has been developed, in which cooperation is implemented through channel coding with a view to controlling the errors inherent in wireless communication. In this work we evaluate the performance of coded cooperation in flat Rayleigh fading environment using a concept known as the pair wise error probability (PEP). We derive the PEP for a flat fading scenario in coded cooperation and then compare with the signal-to-noise ratio of the users in the network. Results show that an increase in the SNR leads to a decrease in the PEP. We also carried out simulations to validate the result.

Keywords: Channel state information, coded cooperation, cooperative systems, pairwise-error-probability, Reed-Solomon codes.

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Authors: Achraf El Allali, John R. Rose

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A number of competing methodologies have been developed to identify genes and classify DNA sequences into coding and non-coding sequences. This classification process is fundamental in gene finding and gene annotation tools and is one of the most challenging tasks in bioinformatics and computational biology. An information theory measure based on mutual information has shown good accuracy in classifying DNA sequences into coding and noncoding. In this paper we describe a species independent iterative approach that distinguishes coding from non-coding sequences using the mutual information measure (MIM). A set of sixty prokaryotes is used to extract universal training data. To facilitate comparisons with the published results of other researchers, a test set of 51 bacterial and archaeal genomes was used to evaluate MIM. These results demonstrate that MIM produces superior results while remaining species independent.

Keywords: Coding Non-coding Classification, Entropy, GeneRecognition, Mutual Information.

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Authors: Libin Wu, Bainian Li

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In This Article We establish moment inequality of dependent random variables,furthermore some theorems of strong law of large numbers and complete convergence for sequences of dependent random variables. In particular, independent and identically distributed Marcinkiewicz Law of large numbers are generalized to the case of m0-dependent sequences.

Keywords: Lacunary System, Generalized Gaussian, NA sequences, strong law of large numbers.

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Authors: Adam Roman

Abstract:

Finding synchronizing sequences for the finite automata is a very important problem in many practical applications (part orienters in industry, reset problem in biocomputing theory, network issues etc). Problem of finding the shortest synchronizing sequence is NP-hard, so polynomial algorithms probably can work only as heuristic ones. In this paper we propose two versions of polynomial algorithms which work better than well-known Eppstein-s Greedy and Cycle algorithms.

Keywords: Synchronizing words, reset sequences, Černý Conjecture

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Authors: Abdellali Kelil, Shengrui Wang, Ryszard Brzezinski

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The literature reports a large number of approaches for measuring the similarity between protein sequences. Most of these approaches estimate this similarity using alignment-based techniques that do not necessarily yield biologically plausible results, for two reasons. First, for the case of non-alignable (i.e., not yet definitively aligned and biologically approved) sequences such as multi-domain, circular permutation and tandem repeat protein sequences, alignment-based approaches do not succeed in producing biologically plausible results. This is due to the nature of the alignment, which is based on the matching of subsequences in equivalent positions, while non-alignable proteins often have similar and conserved domains in non-equivalent positions. Second, the alignment-based approaches lead to similarity measures that depend heavily on the parameters set by the user for the alignment (e.g., gap penalties and substitution matrices). For easily alignable protein sequences, it's possible to supply a suitable combination of input parameters that allows such an approach to yield biologically plausible results. However, for difficult-to-align protein sequences, supplying different combinations of input parameters yields different results. Such variable results create ambiguities and complicate the similarity measurement task. To overcome these drawbacks, this paper describes a novel and effective approach for measuring the similarity between protein sequences, called SAF for Substitution and Alignment Free. Without resorting either to the alignment of protein sequences or to substitution relations between amino acids, SAF is able to efficiently detect the significant subsequences that best represent the intrinsic properties of protein sequences, those underlying the chronological dependencies of structural features and biochemical activities of protein sequences. Moreover, by using a new efficient subsequence matching scheme, SAF more efficiently handles protein sequences that contain similar structural features with significant meaning in chronologically non-equivalent positions. To show the effectiveness of SAF, extensive experiments were performed on protein datasets from different databases, and the results were compared with those obtained by several mainstream algorithms.

Keywords: Protein, Similarity, Substitution, Alignment.

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Authors: N. Hussain, G. Jaffery, A.N. Sabri, S. Hasnain

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The main aim is to perform mutational analysis of CTLA4 gene Exon 1 in SLE patients. A total of 61 SLE patients fulfilling “American College of Rheumatology (ACR) criteria" and 61 controls were enrolled in this study. The region of CTLA4 gene exon 1 was amplified by using Step-down PCR technique. Extracted DNA of band 354 bp was sequenced to analyze mutations in the exon-1 of CTLA-4 gene. Further, protein sequences were identified from nucleotide sequences of CTLA4 Exon 1 by using Expasy software and through Blast P software it was found that CTLA4 protein sequences of Pakistani SLE patients were similar to that of Chinese SLE population. No variations were found after patients sequences were compared with that of the control sequence. Furthermore it was found that CTLA4 protein sequences of Pakistani SLE patients were similar to that of Chinese SLE population. Thus CTLA4 gene may not be responsible for an autoimmune disease SLE.

Keywords: American College of Rheumatology criteria, autoimmune disease, Cytotoxic T Lymphocyte Antigen-4, Polymerase Chain Reaction, Systemic Lupus Erythematosus

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Authors: Robles F, Chevez J, Angulo R, Díaz E, González C.

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These All pig-producing countries from around the world report the presence of Postweaning multisystemic wasting syndrome (PMWS.) In America, PCV2 has been recognized in Canada, United States and Brazil. Knowledge concerning the genetic sequences of PMWS has been very important. In Mexico, there is no report describing the genetic sequences and variations of the PCV2 virus present around the country. For this reason, the main objective was to describe the homology and genetic sequences of the PCV2 virus obtained from different regions of Mexico. The results show that in Mexico are present both subgenotypes \"a\" and \"b\" of this virus and the homologies are from 89 to 99%. Regarding with the aminoacid sequence, three major heterogenic regions were present in the position 59-91, 123–136 and 185–210. This study presents the results of the first genetic characterization of PCV2 in production herds from Mexico.

Keywords: PCV-2, sequencing analysis, Mexico

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Authors: Xu Huang, Jing Fan, Maonian Wu, Yonggen Gu

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This paper discusses the design of an indoor mobile robot positioning system. The problem of indoor positioning is solved through Wi-Fi fingerprint positioning to implement a low cost deployment. A wireless fingerprint matching algorithm based on the similarity of unequal length sequences is presented. Candidate sequences selection is defined as a set of mappings, and detection errors caused by wireless hotspot stability and the change of interior pattern can be corrected by transforming the unequal length sequences into equal length sequences. The presented scheme was verified experimentally to achieve the accuracy requirements for an indoor positioning system with low deployment cost.

Keywords: Fingerprint match, indoor positioning, mobile robot positioning system, Wi-Fi, wireless fingerprint.

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Authors: Naveed Ur Rehman, Rehan Jamil, Irfan Jamil

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In this paper, we regard as a coded transmission over a frequency-selective channel. We plan to study analytically the convergence of the turbo-detector using a maximum a posteriori (MAP) equalizer and a MAP decoder. We demonstrate that the densities of the maximum likelihood (ML) exchanged during the iterations are e-symmetric and output-symmetric. Under the Gaussian approximation, this property allows to execute a one-dimensional scrutiny of the turbo-detector. By deriving the analytical terminology of the ML distributions under the Gaussian approximation, we confirm that the bit error rate (BER) performance of the turbo-detector converges to the BER performance of the coded additive white Gaussian noise (AWGN) channel at high signal to noise ratio (SNR), for any frequency selective channel.

Keywords: MAP, ML, SNR, Decoder, BER, Coded transmission.

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Authors: M. Senthil Arumugam, M.V.C. Rao

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This paper presents a novel two-phase hybrid optimization algorithm with hybrid genetic operators to solve the optimal control problem of a single stage hybrid manufacturing system. The proposed hybrid real coded genetic algorithm (HRCGA) is developed in such a way that a simple real coded GA acts as a base level search, which makes a quick decision to direct the search towards the optimal region, and a local search method is next employed to do fine tuning. The hybrid genetic operators involved in the proposed algorithm improve both the quality of the solution and convergence speed. The phase–1 uses conventional real coded genetic algorithm (RCGA), while optimisation by direct search and systematic reduction of the size of search region is employed in the phase – 2. A typical numerical example of an optimal control problem with the number of jobs varying from 10 to 50 is included to illustrate the efficacy of the proposed algorithm. Several statistical analyses are done to compare the validity of the proposed algorithm with the conventional RCGA and PSO techniques. Hypothesis t – test and analysis of variance (ANOVA) test are also carried out to validate the effectiveness of the proposed algorithm. The results clearly demonstrate that the proposed algorithm not only improves the quality but also is more efficient in converging to the optimal value faster. They can outperform the conventional real coded GA (RCGA) and the efficient particle swarm optimisation (PSO) algorithm in quality of the optimal solution and also in terms of convergence to the actual optimum value.

Keywords: Hybrid systems, optimal control, real coded genetic algorithm (RCGA), Particle swarm optimization (PSO), Hybrid real coded GA (HRCGA), and Hybrid genetic operators.

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