A global **minimum** **distance** **error** correcting parser for a context-free grammar G = (N , Σ, P, S) takes any x in Σ * and produces a parse for some w in L(G) such that the **minimum** **distance** between w and x is as small as possible. Thus a global **correction** scheme does not handle each **error** in the input separately, but finds a best approximation to incorrect input over the whole input string. Such a scheme is not held to be practical: "Unfortunately, global **correction** techniques cannot be incorporated in practical parsers without drastically affecting the parsing speed even of correct sentences. In fact, the global **correction** approach seems to fit conveniently only general context- free parsing algorithms" [12]. Aho and Peterson [2] present an O(n 3 ) algorithm for **minimum** dis- tance **error** **correction** for any context-free grammar G. They add a set of **error** produc- tions to give a covering grammar G ′ which generates Σ *, and design a parser for G ′ that uses as few **error** productions as possible in parsing any string w. The **error** productions used in a parse indicate the errors in w. G ′ is ambiguous and the parser is a variation of Earley’s algorithm [5] which includes a count of the number of **error** productions used. An alternative approach is used by Mauney and Fischer [10] to achieve what they term "regional least-cost repair", i.e. **minimum** **distance** **error** **correction** over a bounded region of the input string. They dev elop a global least-cost **error** correcting parser and then restrict it to regional least-cost. Instead of extending the original grammar with **error** pro- ductions, the parser is modified so that it can simulate insertions, deletions and replace- ments on the input string. For the general context-free parsing method required, they choose the Graham, Harrison, Ruzzo algorithm [6]. This method, which is similar to Ear- ley, finds the parse in time O(n 3 ). To achieve a more practical method, they propose using an O(n) parser and calling the repair algorithm only when needed, to parse a sub- string of the input. An algorithm is needed to output a string which can follow the input accepted so far, for example a context-free grammar which describes the legal suffixes. This however is not presented.

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The advantages of the method used here lie in its formality: it is precise, objective, and could be automated (although we have not done so). A potential disadvantage also lies in the method's formality: if the model of **minimum**-**distance** errors were not to correspond closely with the human user's concept of syntax errors, the method would provide an inap- propriate measure of performance. We claim that the models are valid. The justication for this claim is given by analysis of the Ripley suite of Pascal programs, which shows that the **minimum**-**distance** **error** **correction** corresponds with the human's perception (as given by Ripley and Druseikis 18 ) in 106 of the 121 programs (88%).

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The module for handling keyboard-related (typographical) errors uses a constant weight for all pairs of horizontally contiguous neighbors on the QWERTY keyboard (e.g., {C,V}). The module also includes, at a slightly smaller cost, the pair {:,;} which differ only in use of the shift key, and (at a greater cost) the pairs {l,:} and {",;} which involve both a horizontal slip and a misuse of the shift key. No insertions or deletions are used in this module. Preliminary tests by potential users of this tool indicated that correcting for keyboard-related errors was less useful than corrections from the other two modules; the costs of operations from this module were increased accordingly (making these substitutions less likely to be used). The modules are combined into a single weighted FST by taking a union of operations found in the three modules. If two modules allow the same operation but assign different weights, the weight corresponding to the **minimum** cost is used. Transitive operations are assigned the sum of their costs. For example, since emphatic /d / (SATTS V) is phonetically confusable with unemphatic /d/ (SATTS D), and V can be mistyped as C (due to keyboard proximity), then the ‘double’ substitution of DC would require two errors on the part of the user. The cost of the corresponding **correction** (C D) is equal to the summed cost of the corrections (C V) and (VD).

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EX500 excimer laser using photorefractive keratectomy (PRK) in patients with high myopia. Methods: A retrospective chart review of consecutive cases of high myopic eyes ($6.0 Diopters [D]) undergoing PRK with the Alcon Wavelight EX500 excimer laser (Alcon Labo- ratories, Fort Worth, TX, USA) was done. Moderately high myopic eyes (6.0 to ,8.0 D [6 D]) were compared with high myopic eyes (8.0 D or greater [8 D]). Outcomes measured included pre- and postoperative refractive **error**, uncorrected **distance** visual acuity (UDVA), corrected **distance** visual acuity, spherical equivalent **correction** (SEQ), haze incidence, and intraocular pressure (IOP).

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In this paper, we present two new algorithms in residue number systems for scaling and **error** **correction**. The first algo- rithm is the Cyclic Property of Residue-Digit Difference (CPRDD). It is used to speed up the residue multiple **error** cor- rection due to its parallel processes. The second is called the Target Race **Distance** (TRD). It is used to speed up residue scaling. Both of these two algorithms are used without the need for Mixed Radix Conversion (MRC) or Chinese Resi- due Theorem (CRT) techniques, which are time consuming and require hardware complexity. Furthermore, the residue scaling can be performed in parallel for any combination of moduli set members without using lookup tables.

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In this project we have used average **distance** estimation based DDoS detection technique. In this technique we estimate the mean value of **distance** in the next time period by using the exponential smoothing estimation technique. This **distance**-based traffic separation DDoS detection technique uses MMSE (**Minimum** Mean Square **Error**) linear predictor to estimate the traffic rates from different distances.We calculate the **distance** value based on the TTL field of an IP header directly during transit, each intermediate router deducts one from the TTL value of an IP packet. Therefore, the **distance** of the packet is the final TTL value subtracted from the initial value. Therefore, the initial value can be determined by choosing the smallest initial value of all the possible values which are larger than the final TTL value. The detection of anomaly relies on the description of normality and deviation. The exponential smoothing estimation technique is chosen because of its successful application in the real time measurement of the round trip time of IP traffic. The exponential smoothing estimation model predicts the mean value of **distance** dt+1 at time t+1 using:

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Theorem 7 gives the noncoherent capacity region. In the proof of Theorem 7 we show how to design noncoherent network codes that achieve upper bounds given by (5.4) when a **minimum** (or bounded) injection **distance** decoder is used at the sink nodes. Our code con- struction uses random linear network coding at intermediate nodes, single-source network **error** **correction** capacity-achieving codes at each source, and an overall global coding vector. Our choice of decoder relies on the observation that subspace erasures are not arbitrarily chosen by the adversary, but also depend on the network code. Since, as we show below, with high probability in a random linear network code, subspace erasures do not cause con- fusion between transmitted codewords, the decoder focuses on the discrepancy between the sent and the received codewords caused by subspace errors. The **error** analysis shows that injection **distance** decoding succeeds with high probability over the random network code. On the other hand, the subspace **minimum** **distance** of the code is insufficient to account for the total number of subspace errors and erasures that can occur. This is in contrast to constant dimension single-source codes, where subspace **distance** decoding is equivalent to injection **distance** decoding [32].

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The parallel corpora that we use to train the translation model come from two different sources. The first corpus is NUCLE (Dahlmeier et al., 2013), containing essays written by students at the National University of Singapore (NUS) which have been manually corrected by English instruc- tors at NUS. The other corpus is collected from the language exchange social networking website Lang-8. We develop two versions of SMT sys- tems: one with two phrase tables trained on NU- CLE and Lang-8 separately (S1), and the other with a single phrase table trained on the concate- nation of NUCLE and Lang-8 data (S2). Multiple phrase tables are used with alternative decoding paths (Birch et al., 2007). We add a word-level Levenshtein **distance** feature in the phrase table used by S2, similar to (Felice et al., 2014; Junczys- Dowmunt and Grundkiewicz, 2014). This feature is not included in S1.

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developed by Krishna et.al [6]. RNS offers better speed because of its underlying carry-free property. Because of this, a number of algorithms have been proposed to detect and correct errors in RRNS. In addition, the concepts of Hamming weight, **minimum** **distance**, weight distribution, **error** detection capabilities, and **error** **correction** capabilities are investigated. Goh and Siddiqui [9] proposed an algorithm that detects and corrects multiple bits errors in RNS using the Chinese Remainder Theorem (CRT). The CRT uses large numbers in its computations which results in reducing the performance of the algorithm. This is similar to the algorithms proposed by Sun & Krishna [7] and Yang & Hanzo [8]. Their proposed schemes however utilizes the MRC and syndrome check with the help of look-up table. The effect of this in terms of hardware resources and memory are more expensive when compared with proposed scheme. In addition, the proposed algorithm is straightforward and easier to implement. The proposed algorithm is also less computationally intensive and makes it more efficient in the detection and **correction** of multiple bit errors than the schemes in Sun & Krishna [7] and Yang & Hanzo [8]. Amusa & Nwoye [10] described a computationally efficient decoding procedure relying on the projection-depth theory for correcting multiple errors. The proposed scheme will eliminate multiple bit errors in RRNS by using other schemes like the MRC and the HD as a joint technique with lower complexity compared to higher order of complexity of CRT by detecting and correcting the errors. Because reliability in data transmission is a critical issue in digital systems, fault tolerance is an important feature of redundant residue number systems.

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were proposed. Based on the **minimum** **error** **correction** (MEC) model and the **minimum** **error** **correction** with genotype information (MEC/GI) model, Wang et al. [9] and Qian et al. [10] respectively proposed a genetic algorithm and a particle swarm optimization algorithm to reconstruct diploid individual haplotypes, both of which can be adapted to reconstructing the K-individual ones. The code length of the two algorithms is very long in practical applications, for it is equal to the number of sequencing SNP fragments. This brings huge solution space to these two algorithms and negatively affects the performance of them. Based on the **minimum** fragment removal (MFR) model [11], an exact exponential algo- rithm was introduced by Li et al. [11]. The time com- plexity of which is O(2 2t m 2 n + 2 (K +1)t m K+1 ) , where m denotes the number of SNP fragments, n denotes the number of SNP sites, and t is the max number of holes covered by a fragment. The algorithm can not perform well with large m, n and t. In 2013, Aguiar et al. [12] introduced the HapCompass model and the **minimum** weighted edge removal (MWER) optimization for hap- lotyping polyploid genomes. Algorithm HapCompass aims to remove a minimal weighted set of edges from the compass graph such that a unique phasing may be constructed. The HapCompass algorithm performs on the spanning-tree cycle basis of the compass graph to iteratively delete errors. However, in the same conflict cycle basis, there may be more than one edge having the same absolute value of weight. It may lead to the wrong SNP phasing to select the removed edge randomly. In 2014, Berger et al. [13] described a maximum-likelihood estimation framework HapTree for haplotyping a sin- gle polyploid. It can obtain better performance than the HapCompass algorithm [13]. In 2014, based on the MEC model, Wu et al. [14] presented a genetic algorithm GTIHR for reconstructing triploid haplotypes. Since the code length of algorithm GTIHR equals to the number of heterozygous sites in haplotype, the performance of the GTIHR algorithm is negatively affected by haplotype length and heterozygous rate. In this paper, the triploid individual haplotype assembly problem is studied based on the MEC/GI model. An enumeration-based algorithm enumeration haplotyping triploid with least difference (EHTLD) is proposed for solving it. Algorithm EHTLD reconstructs the three haplotypes according to the order of SNP loci along them. For reconstructing the three alleles of a given site, it enumerates three kinds of SNP values by using the site’s genotype, and chooses the kind of value resulting in the **minimum** difference between the reconstructed haplotypes and the sequenced fragments covering that SNP site. The experimental comparisons were performed between the EHTLD, the HapCompass

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Our team entry, known under the abbreviation ’ TILB ’ in the C ON LL-2013 Shared Task, is a sim- plistic text and grammar **correction** system based on five memory-based classifiers implementing eight different **error** correctors. The goal of the system is to be lightweight: simple to set up and train, fast in execution. It requires a preferably very large but unannotated corpus to train on, and closed lists of words that contain categories of in- terest (in our case, determiners and prepositions). The **error** correctors make use of information from a lemmatizer and a noun and verb inflection mod- ule. The amount of explicit grammatical infor- mation input in the system is purposely kept to a **minimum**, as accurate deep grammatical infor- mation cannot be assumed to be present in most

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Atmospheric refraction is the main one among the errors which influence the accuracy of the InSAR system. **Distance** errors caused by atmospheric refraction must be cor- rected to meet the accuracy demand of slant ranging in InSAR system with distributed satellites. Aiming at two satellites, **error** **correction** experiments were carried out in 2007 and 2008 by using the **error** **correction** method presented in the paper. The expe- riments have demonstrated that residual **error** is little and steady after using the dis- tance **error** **correction** for atmospheric refraction. It shows that the method discussed in the paper is effective, which can mainly eliminate the **distance** precision loss caused by Troposphere atmospheric refraction and Ionosphere atmospheric refraction.

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Reed Solomon codes really are a subclass of non-binary BCH codes built with symbols from the Galois Field. An RS code has got the following parameters: maximum block length n q x 1, quantity of parity check symbols n x k 2. All individuals parameters are expressed when it comes to q-ary symbols. When t 1, the **minimum** **distance** is three and then the code can correct single symbol errors. These errors can impact multiple bits as lengthy as these fit in with exactly the same symbol. RS codes are generally expressed as RS(n, k, m). The syndrome vector may be used to identify errors the delay and complexity of syndrome computation is dependent around the values from the parity check matrix. However, there's a common extension from the SEC RS code In conclusion, the deciphering of SEC RS codes requires numerous complex procedures over GF(q) specifically for **error** **correction** where division and logarithm have to be implemented. Syndrome computation only requires multiplications and additions and it is delay is dependent around the values of each one of the rows within the H matrix.

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This paper focuses on selection techniques for best **correction** of misspelt words at the lexical level. Spelling errors are introduced by either cognitive or typographical mistakes. A robust spelling **correction** algorithm is needed to cover both cognitive and typographical errors. For the most effective spelling **correction** system, various strategies are considered in this paper: ranking heuristics, **correction** algorithms, and **correction** priority strategies for the best selection. The strategies also take account of **error** types, syntactic information, word frequency statistics, and character **distance**. The findings show that it is very hard to generalise the spelling **correction** strategy for various types of data sets such as typographical, orthographical, and scanning errors.

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The circuits for measuring the stabilizers of the 5- qubit code were similar to the ones used in Fig. 2b (for an X Pauli replace the CNOT by an XNOT). For flag- FTEC methods, it can be seen that the [[5, 1, 3]] code always achieves lower logical failure rates compared to the [[7, 1, 3]] code. However, when p ˜ = p, both the d = 3 surface code as well as Steane-EC achieves lower logical failure rates (with Steane-EC achieving the best perfor- mance). For p ˜ = p/10, flag-EC applied to the [[5, 1, 3]] code achieves nearly identical logical failure rates com- pared to the d = 3 surface code. For p ˜ = p/100, flag 1-FTEC applied to the [[5, 1, 3]] code achieves lower log- ical failure rates than the d = 3 surface code but still has higher logical failure rates compared to Steane-EC. We also note that the pseudo-threshold increases when p ˜ goes from p to p/10 for both the [[5, 1, 3]] and [[7, 1, 3]] codes when implemented using the flag 1-FTEC protocol. This is primarily due to the large circuit depth in flag-EC protocols since idle qubits locations signifi- cantly outnumber other gate locations. For the surface code, the opposite behaviour is observed. As was shown in [9], CNOT gate failures have the largest impact on the pseudo-threshold of the surface code. Thus, when idle qubits have lower failure probability, lower physical **error** rates will be required in order to achieve better logical failure rates. For instance, if idle qubits never failed, then performing **error** **correction** would be guar-

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account when handling errors, with the aim of producing a minimum distance or least-cost error correction for an incorrect string.. Global correction is effected by adapting a general co[r]

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A recent systematic review and meta-analysis of data on the prevalence of myopia, defined as refractive **error** of minus 0.5D or more, used papers published since 1995. The findings were used to estimate the number of individuals with myopia in 2000 and to extrapolate the findings to the year 2050 [6]. The data were presented using the country groupings employed by the GBD project, and assumptions were made for countries or locations within countries, which lacked data. In the year 2000 there were an estimated 1,406 (95% CI 932-1932) million people with myopia i.e., almost a quarter of the world's population (22.9%). The number is projected to increase to 4,758 (95% CI 3,620-6,065) million by the year 2050, affecting almost half of the world's population (49.8%). The number of individuals with high myopia is projected to increase from 163 million to 938 million over the same period. In the Southeast Asia region, which includes Sri Lanka, the prevalence of myopia in all ages was estimated to be 33.8% in 2000, expected to increase to 62% by 2050. Given the projected increase in the number of people who will become myopic, it is important that countries assess the magnitude of visual impairment due to uncor- rected refractive errors, including that due to myopia, and the extent to which the current need for spectacle **correction** is being met. The purpose of this paper is to present findings on the prevalence and types of refractive **error**, and the proportion of the need for spectacles for **distance** **correction** that is currently being met, among individuals aged 40 years, who were examined in the Sri Lanka National Survey of Blindness, Visual Impairment and Disability.

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The proposed unsupervised synthetic **error** gen- eration method does not require a seed corpus with example errors as most other methods based on sta- tistical **error** injection (Felice and Yuan, 2014) or back-translation models (Rei et al., 2017; Kasewa et al., 2018; Htut and Tetreault, 2019). It also out- performs noising techniques that rely on random word replacements (Xie et al., 2018; Zhao et al., 2019). Contrary to Ge et al. (2018) or Lichtarge et al. (2018), our approach can be easily used for effective pre-training of full encoder-decoder mod- els as it is model-independent and only requires clean monolingual data and potentially an available spell-checker dictionary. 2 In comparison to pre- training with BERT (Devlin et al., 2019), synthetic errors provide more task-specific training exam- ples than masking. As an unsupervised approach, MAGEC is an alternative to recently proposed lan- guage model (LM) based approaches (Bryant and Briscoe, 2018; Stahlberg et al., 2019), but it does not require any amount of annotated sentences for tuning.

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This paper presents a hybrid model for the CoNLL-2013 shared task which focuses on the problem of grammatical **error** **correction**. This year’s task includes determiner, preposition, noun number, verb form, and subject-verb agreement errors which is more comprehen- sive than previous **error** **correction** tasks. We correct these five types of errors in different modules where either machine learning based or rule-based methods are applied. Pre- processing and post-processing procedures are employed to keep idiomatic phrases from be- ing corrected. We achieved precision of 35.65%, recall of 16.56%, F 1 of 22.61% in the

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In addition to learning about a potential long-run relationship between many series the concept of cointegration enriches the kinds of dynamic models at our disposal, this can be done through **error** **correction** model. In the case of a cointegration relationship, least squares estimators can be shown to be super consistent, in the sense that the parameter estimates approach their true value faster than they would in regression involving cross-section or stationary time series data (Stock, 1987). On its own a cointegration relationship sheds no light on short run dynamics, but its very existence indicates that there must be some short term forces responsible for keeping the relationship intact, and thus that it should be possible to construct a more comprehensive model that combines short run and long run dynamics, which is **error** **correction** model. The model states that the change in Y in any period will be governed by the change in X and the discrepancy between Y t-1 and the value

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