오차 교정 K차 골드스미트 부동소수점 나눗셈

Error correction is important in classical and quantum computation. Decoherence caused by the inevitable interaction of quantum bits with their environment leads to dephasing or even relaxation. Correction of the concomitant errors is therefore a fundamental requirement for scalable quantum computation. Although algorithms for error correction have been known for some time, experimental realizations are scarce. Here we show quantum error correction in a heterogeneous, solid-state spin system. We demonstrate that joint initialization, projective readout and fast local and non-local gate operations can all be achieved in diamond spin systems, even under ambient conditions. High-fidelity initialization of a whole spin register (99 per cent) and single-shot readout of multiple individual nuclear spins are achieved by using the ancillary electron spin of a nitrogen-vacancy defect. Implementation of a novel non-local gate generic to our electron-nuclear quantum register allows the preparation of entangled states of three nuclear spins, with fidelities exceeding 85 per cent. With these techniques, we demonstrate three-qubit phase-flip error correction. Using optimal control, all of the above operations achieve fidelities approaching those needed for fault-tolerant quantum operation, thus paving the way to large-scale quantum computation. Besides their use with diamond spin systems, our techniques can be used to improve scaling of quantum networks relying on phosphorus in silicon, quantum dots, silicon carbide or rare-earth ions in solids.

In the modern age of IOT and Robotics, different intelligent entities like robots, drones, IOT nodes or smart vehicles need fast and error-free communication of data, which is predominantly in the form of images. The medium used for communication of this data is mainly wireless and it can be short distance, medium distance, long haul or even satellite links crossing the ionosphere layers. Different wireless mediums incorporate different types of noises in the images being transmitted by Drones, Robots or IOT Nodes. For better analysis and then performing subsequent action on the basis of these received images using artificial intelligence, machine learning or machine vision, it is imperative that the images transmitted are encoded and recovered as fast and as error-free as possible. Normal conventional methods use different image correction algorithms for detection and correction of errors in images. Reed Solomon codes, which are normally used for error detection and correction at data link layer in TCP/IP protocol stack, have a high probability of signal correction and are highly efficient due to their burst error detection and correction capabilities. The RS codes can be implemented where there is a large number of input symbols and noise duration is relatively small as compared to the code word. Sometimes at the receiver end, we get images which are partially corrupted and only half or some part of them is visible. Most of the filters used for image reconstruction insert the approximated bits in place of the corrupted bits by using some algorithms but if only partial part of the image is corrupted, no filter will be able to recover the images properly as it will also change the bits in the non-corrupted part of the image. We have proposed a novel approach of using RS codes for the detection and correction of errors in the images. This novel technique can be used over a variety of applications including robotics, drones, IOT nodes, smart vehicles using wireless and satellite communication, which include the transfer of images and decision making on the basis of the content of the images.

Reversible logic preserves information and provides low power computing. Floating point multiplier is an important part of arithmetic in DSP applications. IEEE754 provide two basic and widely used formats for representing floating point numbers namely Single Precision Floating point (SPFP) and Double Precision Floating Point (DPFP). In this paper, we have proposed designs for Reversible SPFP and DPFP point multiplier which requires optimum design of 24X24 and 53X53 multiplying circuitry with reversible gates respectively. Also we presented sign bit calculation and exponent bit calculation circuits by reversible logic. Reversible Mantissa bits calculation circuitry requires consumes more area as it has large value of quantum cost and garbage outputs as compare to reversible sign bit and exponent bits calculation circuitry. So, we mainly focused our work on to minimize the area consumed by the reversible mantissa bits calculation circuit by minimizing the value of quantum cost and garbage outputs of it. In this paper, we presented two ways for partial products generation with reversible gates. We propose a new design of reversible 12X12 reversible Wallace tree multiplier for single precision and double precision mantissa multiplier circuit. Also 5X5 and 5X12 reversible Wallace tree multiplier for double precision multiplier. Here we use the optimized designs of reversible half adder, Full adder and 4:2 compressors. In the final summation stage, we carefully shifted the product terms and add them. For this stage we have carefully chosen the adders and compressor in such way to get the optimized results in terms of quantum cost and Garbage output. We have also shown the improvement in single precision floating point multiplier in terms of Quantum cost and Garbage output.

In this work we present a flexible, probabilistic and reference-free method of error correction for high throughput DNA sequencing data. The key is to exploit the high coverage of sequencing data and model short sequence outputs as independent realizations of a Hidden Markov Model (HMM). We pose the problem of error correction of reads as one of maximum likelihood sequence detection over this HMM. While time and memory considerations rule out an implementation of the optimal Baum-Welch algorithm (for parameter estimation) and the optimal Viterbi algorithm (for error correction), we propose low-complexity approximate versions of both. Specifically, we propose an approximate Viterbi and a sequential decoding based algorithm for the error correction. Our results show that when compared with Reptile, a state-of-the-art error correction method, our methods consistently achieve superior performances on both simulated and real data sets.

The relevance of the research is due to the growing need to automate the processes of text analysis and correction, in particular for Ukrainian-language content, which is characterized by a wealth of morphological and syntactic structure. Due to the wide range of errors that can occur in texts, from spelling to contextual, there is an urgent need to create systems that can accurately identify errors and offer their correct corrections. The specificity of the Ukrainian language, including its grammatical complexity and multifacetedness, requires the adaptation of machine learning models to local features. The purpose of the research is to develop a mathematical model of a decision support system for identifying and correcting errors in Ukrainian-language texts. The task includes both the formalization and mathematical description of the text processing process, and the construction of a model with an orientation to the tasks of classification and text generation. Special attention is paid to the effective consideration of structural features specific to the Ukrainian language in order to increase the accuracy and productivity of the system. The research method is based on the construction of a mathematical model of error correction, which is presented as a context-aware text generation problem. The study used statistical methods and machine learning approaches. Special attention is paid to the formation of a training sample, which combines texts with real and artificial errors to ensure a balanced learning process. The correction module includes generation mechanisms based on contextual models capable of predicting the correct correction for erroneous tokens. Approaches to text vectorization are mathe- matically substantiated, taking into account the peculiarities of the morphology and syntax of the Ukrainian language. The constructed model is a universal basis for creating intelligent systems for automatic editing of Ukrainian-language text. As a result of the research, approaches to building an error correction model in Ukrainian-language texts are formulated and mathematically substantiated. The main result was the creation of an integrated system that uses contextual information to ensure high accuracy of error recognition and correction. The applied mathematical methods include probabilistic approaches and vector representation of tokens, which allows adapting the system to the peculiarities of the Ukrainian language with its high morphological and syntactic complexity. The formed basis of the model creates opportunities for scaling and further use in practical tasks, such as automatic text editing or improving the quality of content in the Ukrainian-speaking environment.

Recent advancements in next-generation sequencing have rapidly improved our ability to study genomic material at an unprecedented scale. Despite substantial improvements in sequencing technologies, errors present in the data still risk confounding downstream analysis and limiting the applicability of sequencing technologies in clinical tools. Computational error-correction promises to eliminate sequencing errors, but the relative accuracy of error correction algorithms remains unknown. In this paper, we evaluate errorcorrection algorithms' ability to fix errors across different types of datasets that contain various levels of heterogeneity. We perform a realistic evaluation of several error correction tools. To measure the efficacy of these techniques, we apply the UMI-based high-fidelity sequencing protocol to eliminate sequencing errors from both simulated data and the raw reads. In terms of accuracy, we find that method performance varies substantially across different types of datasets with no single method performing best on all types of examined data. We also identify the techniques that offer a good balance between precision and sensitivity. This highlight showcases our paper's main findings [1], showing the advantages and limitations of computational error correction techniques across different domains of biology, including immunogenomics and virology.

Automatic detection and correction of errors in the residue number system involves the conversion of residue representations to integers and base extension. The residue number system is generally restricted to moduli that are pairwise relatively prime. In this paper we consider error detection and correction using a moduli set with common factors. A method to construct a moduli set that leads to simplified error detection and correction is presented. Error detection can now be performed by computing residues in parallel. Error correction does not involve base extension any more. It is also shown that, removing all restrictions on the moduli set, leads to more complex error detection/correction algorithms.

As communication technologies such as e-mail have becoming indispensable for business communication, the study of the use and effects of technologies is increasingly relevant. This study is aimed at analyzing the correlation between personality traits and the choice of communication media. Research data from 22 studies published in the journals and the articles posted in the internet in the years of 1999 – 2006 were analyzed using meta analysis technique. The total of 4267 participants were involved in the research. Analysis was focused only on the correlation between three personality traits: extraversion, neuroticism, openness to experience, and the use of email. Two statis¬tical technique error corrections were applied in analyzing the data, namely sampling error correction and measurement error correction. It was found that after sampling error correction was calculated the correlation between extraversion and email usage was (ř) = 0,33. Further, when measurement error was also calculated, the correlation between those two variables increased to (ρ) = 0,38. When sampling error corection was applied, the correlation between neuroticism and email usage was (ř) = 0,13. Similar to extra¬version when measurement error was cor¬rect¬ed, the correlation between these two variables increased to (ρ) = 0,14. The corre¬la¬tion between openness to experience with email usage was (ř) = 0,30 when sampling error correction was calculated. Further when the measurement error correction was applied the coeficient correlation was increas¬ed to (ρ) = 0,33. These findings indi¬cated that personality traits correlate with email usage. Keywords: meta analisis, extraversion, neu¬ro-ticism, openness to experience, email

Older adults often correct errors in existing knowledge as effectively as younger adults despite the fact that inaccurate knowledge has the potential to cause interference with memory for a correct response. In the current experiments, we sought to explore whether error corrections are maintained across a delay and identify mechanisms that may support this process. In Experiment 1, younger and older adults answered general knowledge questions, rated confidence in their responses, were shown feedback, and rated their prior knowledge of the question and answer. Half of the participants took a final test after a 6-min delay and half returned 1 week later. Across a 1-week delay, older adults maintained a greater proportion of corrected responses than did younger adults. In Experiment 2, we examined whether participants use their memory for errors on the initial test to mediate retrieval of the correct answer on the final test (i.e., the mediator hypothesis). Participants were more likely to answer questions correctly on a final test when they recalled their initial error, but memory for the initial error was a stronger predictor of final test accuracy for younger adults than for older adults. Additionally, older adults, in comparison with younger adults, corrected a higher proportion of errors when the initial error was forgotten. Overall, inaccurate knowledge did not interfere with older adults' ability to maintain revisions in memory. In addition, we found support for the mediator hypothesis; however, other mechanisms also contribute to older adults' error correction. (PsycINFO Database Record (c) 2020 APA, all rights reserved).

In Residue Number System (RNS), a large integer is represented as a set of smaller integers called residues. Redundant Residue Number System (RRNS) is obtained by adding some redundant residues which brings in error detection and error correction capability. This capability makes RRNS a promising way to provide a very fast arithmetic in the field of digital computers. At the receiver, RRNS codes are decoded using Chinese Remainder theorem (CRT). An alternative scheme called Mixed Radix Conversion (MRC) is also used which results in low decoding complexity when compared to CRT. This paper presents a single bit error correction algorithm using RRNS. This algorithm doesn't require table lookup which helps to save memory during implementation. Representative examples are given.

The most important features of error correction tools for sequencing data are accuracy, memory efficiency and fast runtime. The previous version of BLESS was highly memory-efficient and accurate, but it was too slow to handle reads from large genomes. We have developed a new version of BLESS to improve runtime and accuracy while maintaining a small memory usage. The new version, called BLESS 2, has an error correction algorithm that is more accurate than BLESS, and the algorithm has been parallelized using hybrid MPI and OpenMP programming. BLESS 2 was compared with five top-performing tools, and it was found to be the fastest when it was executed on two computing nodes using MPI, with each node containing twelve cores. Also, BLESS 2 showed at least 11% higher gain while retaining the memory efficiency of the previous version for large genomes. Freely available at https://sourceforge.net/projects/bless-ec dchen@illinois.edu Supplementary data are available at Bioinformatics online.

The Bose – Chaudhuri – Hocquenghem type of linear cyclic codes (BCH codes) is one of the most popular and widespread error-correcting codes. Their close connection with the theory of Galois fields gave an opportunity to create a theory of the norms of syndromes for BCH codes, namely, syndrome invariants of the G-orbits of errors, and to develop a theory of polynomial invariants of the G-orbits of errors. This theory as a whole served as the basis for the development of effective permutation polynomial-norm methods and error correction algorithms that significantly reduce the influence of the selector problem. To date, these methods represent the only approach to error correction with non-primitive BCH codes, the multiplicity of which goes beyond design boundaries. This work is dedicated to a special error-correcting code class – generic Bose – Chaudhuri – Hocquenghem codes or simply GBCH-codes. Sufficiently accurate evaluation of the quantity of such codes in each length was produced during our work. We have investigated some properties and connections between different GBCH-codes. Special attention was devoted to codes with constructive distances of 3 and 5, as those codes are usual for practical use. Their almost complete description is given in the range of lengths from 7 to 107. The paper contains a fairly clear theoretical classification of GBCH-codes. Special attention is paid to the corrective capabilities of the codes of this class, namely, to the calculation of the minimal distances of these codes with various parameters. The codes are found whose corrective capabilities significantly exceed those of the well-known GBCH-codes with the same design parameters.

Somatic mutations are one of the major factors contributing to oncogenesis and tumor progression. Second generation sequencing allows rapid generation of several giga-bases of sequence, enabling genome-wide mutation discovery in individual samples. This is particularly effective when used with genome partitioning strategies. The biological significance of mutations may be assessed by their prevalence at the gene or pathway level and by their functional implications, requiring larger sample cohorts. Adding sequence barcodes to discriminate individual identity allows pooling of sample sets larger than those described by current Illumina protocols which are relatively complex and currently offer only up to 12 barcodes. We report a novel barcoding protocol for Illumina GA2-x sequencers, which permits multiplexing up to 2048 samples per flow-cell. Reducing hands-on time in the protocol was one major goal in designing the protocol. Throughput has been increased by up to ten-fold compared to Illumina protocols. This improvement was achieved by eliminating several enzymatic steps and gel purification/size selection and replacing those with two consecutive PCR steps. Instead of enzymatically ligating of the bar-code, our protocol incorporates barcode, sequencing and flow cell binding sites into the DNA product through a universal set of oligo primers, independent of target selection. Additionally, the PCR based protocol utilized the Fluidigm Biomark system for parallel processing allowing the processing of 317 amplimers x 48 samples in parallel. “Cross-talk” between samples and loss of usable sequences induced by read-errors in the bar-code is a major concern in multiplexed experiments. In order to minimize such effects, we introduced an error correcting 8nt DNA code using concepts from computer science. The double 8,4 Hamming code utilized guarantees error correction of read errors affecting up to 2nt, thereby boosting the number of usable codes. Additionally, error detection of read errors affecting up to 4nt minimize cross-talk between multiplexed samples. The protocol has been validated in a 48-way multiplexed experiment demonstrating the viability of the more automated, less laborious library preparation. Error detection and correction was highly effective with the number of reads mapped to a valid bar-codes could be increased by15-20% on average. In one particularly difficult barcode, almost 60% of reads were rescued by error correction. In summary, the protocol presented here extends the use of Illumina GA2 sequencers for mutation screening in cohorts of up to 2048 samples per experiment for a small set of target genes. Citation Format: {Authors}. {Abstract title} [abstract]. In: Proceedings of the 101st Annual Meeting of the American Association for Cancer Research; 2010 Apr 17-21; Washington, DC. Philadelphia (PA): AACR; Cancer Res 2010;70(8 Suppl):Abstract nr 2186.

Hard-decision renormalization group (HDRG) decoders are an important class of decoding algorithms for topological quantum error correction. Due to their versatility, they have been used to decode systems with fractal logical operators, color codes, qudit topological codes, and non-Abelian systems. In this work, we develop a method of performing HDRG decoding which combines strengths of existing decoders and further improves upon them. In particular, we increase the minimal number of errors necessary for a logical error in a system of linear size L from to for any We apply our algorithm to decoding quantum double models and a non-Abelian anyon model with Fibonacci-like fusion rules, and show that it indeed significantly outperforms previous HDRG decoders. Furthermore, we provide the first study of continuous error correction with imperfect syndrome measurements for the quantum double models. The parallelized runtime of our algorithm is for the perfect measurement case. In the continuous case with imperfect syndrome measurements, the averaged runtime is for Abelian systems, while continuous error correction for non-Abelian anyons stays an open problem.

Many operating agencies are developing computerized traffic management systems that support traffic operations as part of intelligent transportation system (ITS) user service improvements. To facilitate the prediction, diagnosis, and control decisions made with uncertain information, several numerical analysis methods are available for predictive traffic control. However, these methods cannot predict short-term traffic demand accurately. A neural network approach was proposed to improve short-term traffic demand prediction for the development of advanced traffic control strategies. A promising neural network approach to improving demand prediction and traffic data modeling to support proactive traffic control was examined. Specifically, the use of time-series detector data from a real-world freeway management system that were processed through neural network models was analyzed and the results were compared with real-world observations. In all cases, the proposed neural network approach can successfully predict traffic demand patterns. The proposed study approach of combining both neural networks and error correction was found to be promising for traffic prediction. Once the neural nets are successfully trained, the system can quickly pick up traffic demand trends for proactive traffic demand management. The error correction algorithm can further smooth out errors that may be caused by sharp neural net prediction.