Error-free matrix symmetrizers and equivalent symmetric matrices

A symmetrizer of the matrix A is a symmetric solution X that satisfies the matrix equation XA=AprimeX. An exact matrix symmetrizer is computed by obtaining a general algorithm and superimposing a modified multiple modulus residue arithmetic on this algorithm. A procedure based on computing a symmetrizer to obtain a symmetric matrix, called here an equivalent symmetric matrix, whose eigenvalues are the same as those of a given real nonsymmetric matrix is presented.

Hardware implementation of 4x4 DCT/Quantization block using multiplication and error-free algorithm

The 4ÃÂ4 discrete cosine transform is one of the most important building blocks for the emerging video coding standard, viz. H.264. The conventional implementation does some approximation to the transform matrix elements to facilitate integer arithmetic, for which hardware is suitably prepared. Though the transform coding does not involve any multiplications, quantization process requires sixteen 16-bit multiplications. The algorithm used here eliminates the process of approximation in transform coding and multiplication in the quantization process, by usage of algebraic integer coding. We propose an area-efficient implementation of the transform and quantization blocks based on the algebraic integer coding. The designs were synthesized with 90 nm TSMC CMOS technology and were also implemented on a Xilinx FPGA. The gate counts and throughput achievable in this case are 7000 and 125 Msamples/sec.

An error free passive UHF RFID system using a new form of wireless signal distribution

A wide area and error free ultra high frequency (UHF) radio frequency identification (RFID) interrogation system based on the use of multiple antennas used in cooperation to provide high quality ubiquitous coverage, is presented. The system uses an intelligent distributed antenna system (DAS) whereby two or more spatially separated transmit and receive antenna pairs are used to allow greatly improved multiple tag identification performance over wide areas. The system is shown to increase the read accuracy of 115 passive UHF RFID tags to 100% from <60% over a 10m × 8m open plan office area. The returned signal strength of the tag backscatter signals is also increased by an average of 10dB and 17dB over an area of 10m 8m and 10m × 4m respectively. Furthermore, it is shown that the DAS RFID system has improved immunity to tag orientation. Finally, the new system is also shown to increase the tag read speed/rate of a population of tags compared with a conventional RFID system. © 2012 IEEE.

An Error Free Passive UHF RFID System using a New Form of Wireless Signal Distribution

A wide area and error free ultra high frequency (UHF) radio frequency identification (RFID) interrogation system based on the use of multiple antennas used in cooperation to provide high quality ubiquitous coverage, is presented. The system uses an intelligent distributed antenna system (DAS) whereby two or more spatially separated transmit and receive antenna pairs are used to allow greatly improved multiple tag identification performance over wide areas. The system is shown to increase the read accuracy of 115 passive UHF RFID tags to 100% from <60% over a 10m x 8m open plan office area. The returned signal strength of the tag backscatter signals is also increased by an average of 10dB and 17dB over an area of 10m x 8m and 10m x 4m respectively. Furthermore, it is shown that the DAS RFID system has improved immunity to tag orientation. Finally, the new system is also shown to increase the tag read speed/rate of a population of tags compared with a conventional RFID system.

Roles of DNA polymerases V and II in SOS-induced error-prone and error-free repair in Escherichia coli

DNA polymerase V, composed of a heterotrimer of the DNA damage-inducible UmuC and UmuD\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} \begin{equation*}{\mathrm{_{2}^{^{\prime}}}}\end{equation*}\end{document} proteins, working in conjunction with RecA, single-stranded DNA (ssDNA)-binding protein (SSB), β sliding clamp, and γ clamp loading complex, are responsible for most SOS lesion-targeted mutations in Escherichia coli, by catalyzing translesion synthesis (TLS). DNA polymerase II, the product of the damage-inducible polB (dinA ) gene plays a pivotal role in replication-restart, a process that bypasses DNA damage in an error-free manner. Replication-restart takes place almost immediately after the DNA is damaged (≈2 min post-UV irradiation), whereas TLS occurs after pol V is induced ≈50 min later. We discuss recent data for pol V-catalyzed TLS and pol II-catalyzed replication-restart. Specific roles during TLS for pol V and each of its accessory factors have been recently determined. Although the precise molecular mechanism of pol II-dependent replication-restart remains to be elucidated, it has recently been shown to operate in conjunction with RecFOR and PriA proteins.

Finite-size effects and error-free communication in Gaussian channels

The efficacy of a specially constructed Gallager-type error-correcting code to communication in a Gaussian channel is examined. The construction is based on the introduction of complex matrices, used in both encoding and decoding, which comprise sub-matrices of cascading connection values. The finite-size effects are estimated for comparing the results with the bounds set by Shannon. The critical noise level achieved for certain code rates and infinitely large systems nearly saturates the bounds set by Shannon even when the connectivity used is low.

On the Error-Free Computation of Fast Cosine Transform

We extend our previous work into error-free representations of transform basis functions by presenting a novel error-free encoding scheme for the fast implementation of a Linzer-Feig Fast Cosine Transform (FCT) and its inverse. We discuss an 8x8 L-F scaled Discrete Cosine Transform where the architecture uses a new algebraic integer quantization of the 1-D radix-8 DCT that allows the separable computation of a 2-D DCT without any intermediate number representation conversions. The resulting architecture is very regular and reduces latency by 50% compared to a previous error-free design, with virtually the same hardware cost.

Pairwise comparison matrices and the error-free property of the decision maker

Pairwise comparison is a popular assessment method either for deriving criteria-weights or for evaluating alternatives according to a given criterion. In real-world applications consistency of the comparisons rarely happens: intransitivity can occur. The aim of the paper is to discuss the relationship between the consistency of the decision maker—described with the error-free property—and the consistency of the pairwise comparison matrix (PCM). The concept of error-free matrix is used to demonstrate that consistency of the PCM is not a sufficient condition of the error-free property of the decision maker. Informed and uninformed decision makers are defined. In the first stage of an assessment method a consistent or near-consistent matrix should be achieved: detecting, measuring and improving consistency are part of any procedure with both types of decision makers. In the second stage additional information are needed to reveal the decision maker’s real preferences. Interactive questioning procedures are recommended to reach that goal.

Single Events in a COTS Soft-Error Free SRAM at Low Bias Voltage Induced by 15-MeV Neutrons

This paper presents an experimental study of the sensitivity to 15-MeV neutrons of Advanced Low Power SRAMs (A-LPSRAM) at low bias voltage little above the threshold value that allows the retention of data. This family of memories is characterized by a 3D structure to minimize the area penalty and to cope with latchups, as well as by the presence of integrated capacitors to hinder the occurrence of single event upsets. In low voltage static tests, classical single event upsets were a minor source of errors, but other unexpected phenomena such as clusters of bitflips and hard errors turned out to be the origin of hundreds of bitflips. Besides, errors were not observed in dynamic tests at nominal voltage. This behavior is clearly different than that of standard bulk CMOS SRAMs, where thousands of errors have been reported.

Extension of the C-XSC Library with Scalar Products with Selectable Accuracy

The C++ class library C-XSC for scientific computing has been extended with the possibility to compute scalar products with selectable accuracy in version 2.3.0. In previous versions, scalar products have always been computed exactly with the help of the so-called long accumulator. Additionally, optimized floating point computation of matrix and vector operations using BLAS-routines are added in C-XSC version 2.4.0. In this article the algorithms used and their implementations, as well as some potential pitfalls in the compilation, are described in more detail. Additionally, the theoretical background of the employed DotK algorithm and the necessary modifications of the concrete implementation in C-XSC are briefly explained. Run-time tests and numerical examples are presented as well.

Error, Confidence, and Cost in Engineering Computations

The questions that one should answer in engineering computations - deterministic, probabilistic/randomized, as well as heuristic - are (i) how good the computed results/outputs are and (ii) how much the cost in terms of amount of computation and the amount of storage utilized in getting the outputs is. The absolutely errorfree quantities as well as the completely errorless computations done in a natural process can never be captured by any means that we have at our disposal. While the computations including the input real quantities in nature/natural processes are exact, all the computations that we do using a digital computer or are carried out in an embedded form are never exact. The input data for such computations are also never exact because any measuring instrument has inherent error of a fixed order associated with it and this error, as a matter of hypothesis and not as a matter of assumption, is not less than 0.005 per cent. Here by error we imply relative error bounds. The fact that exact error is never known under any circumstances and any context implies that the term error is nothing but error-bounds. Further, in engineering computations, it is the relative error or, equivalently, the relative error-bounds (and not the absolute error) which is supremely important in providing us the information regarding the quality of the results/outputs. Another important fact is that inconsistency and/or near-consistency in nature, i.e., in problems created from nature is completely nonexistent while in our modelling of the natural problems we may introduce inconsistency or near-inconsistency due to human error or due to inherent non-removable error associated with any measuring device or due to assumptions introduced to make the problem solvable or more easily solvable in practice. Thus if we discover any inconsistency or possibly any near-inconsistency in a mathematical model, it is certainly due to any or all of the three foregoing factors. We do, however, go ahead to solve such inconsistent/near-consistent problems and do get results that could be useful in real-world situations. The talk considers several deterministic, probabilistic, and heuristic algorithms in numerical optimisation, other numerical and statistical computations, and in PAC (probably approximately correct) learning models. It highlights the quality of the results/outputs through specifying relative error-bounds along with the associated confidence level, and the cost, viz., amount of computations and that of storage through complexity. It points out the limitation in error-free computations (wherever possible, i.e., where the number of arithmetic operations is finite and is known a priori) as well as in the usage of interval arithmetic. Further, the interdependence among the error, the confidence, and the cost is discussed.

Error exponent analysis of energy-based Bayesian decentralized spectrum sensing under fading

This paper considers decentralized spectrum sensing, i.e., detection of occupancy of the primary users' spectrum by a set of Cognitive Radio (CR) nodes, under a Bayesian set-up. The nodes use energy detection to make their individual decisions, which are combined at a Fusion Center (FC) using the K-out-of-N fusion rule. The channel from the primary transmitter to the CR nodes is assumed to undergo fading, while that from the nodes to the FC is assumed to be error-free. In this scenario, a novel concept termed as the Error Exponent with a Confidence Level (EECL) is introduced to evaluate and compare the performance of different detection schemes. Expressions for the EECL under general fading conditions are derived. As a special case, it is shown that the conventional error exponent both at individual sensors, and at the FC is zero. Further, closed-form lower bounds on the EECL are derived under Rayleigh fading and lognormal shadowing. As an example application, it answers the question of whether to use pilot-signal based narrowband sensing, where the signal undergoes Rayleigh fading, or to sense over the entire bandwidth of a wideband signal, where the signal undergoes lognormal shadowing. Theoretical results are validated using Monte Carlo simulations. (C) 2015 Elsevier B.V. All rights reserved.