Ensemble codes involving hippocampal neurons are at risk during delayed performance tests

Multielectrode recording techniques were used to record ensemble activity from 10 to 16 simultaneously active CA1 and CA3 neurons in the rat hippocampus during performance of a spatial delayed-nonmatch-to-sample task. Extracted sources of variance were used to assess the nature of two different types of errors that accounted for 30% of total trials. The two types of errors included ensemble “miscodes” of sample phase information and errors associated with delay-dependent corruption or disappearance of sample information at the time of the nonmatch response. Statistical assessment of trial sequences and associated “strength” of hippocampal ensemble codes revealed that miscoded error trials always followed delay-dependent error trials in which encoding was “weak,” indicating that the two types of errors were “linked.” It was determined that the occurrence of weakly encoded, delay-dependent error trials initiated an ensemble encoding “strategy” that increased the chances of being correct on the next trial and avoided the occurrence of further delay-dependent errors. Unexpectedly, the strategy involved “strongly” encoding response position information from the prior (delay-dependent) error trial and carrying it forward to the sample phase of the next trial. This produced a miscode type error on trials in which the “carried over” information obliterated encoding of the sample phase response on the next trial. Application of this strategy, irrespective of outcome, was sufficient to reorient the animal to the proper between trial sequence of response contingencies (nonmatch-to-sample) and boost performance to 73% correct on subsequent trials. The capacity for ensemble analyses of strength of information encoding combined with statistical assessment of trial sequences therefore provided unique insight into the “dynamic” nature of the role hippocampus plays in delay type memory tasks.

Clinical validation of an algorithm to correct the error in the keratometric estimation of corneal power for normal eyes

To validate clinically an algorithm for correcting the error in the keratometric estimation of corneal power by using a variable keratometric index of refraction (nk) in a normal healthy population.

Continuous quantum error correction by cooling

We describe an implementation of quantum error correction that operates continuously in time and requires no active interventions such as measurements or gates. The mechanism for carrying away the entropy introduced by errors is a cooling procedure. We evaluate the effectiveness of the scheme by simulation, and remark on its connections to some recently proposed error prevention procedures.

Stabilizer formalism for operator quantum error correction

Operator quantum error correction is a recently developed theory that provides a generalized and unified framework for active error correction and passive error avoiding schemes. In this Letter, we describe these codes using the stabilizer formalism. This is achieved by adding a gauge group to stabilizer codes that defines an equivalence class between encoded states. Gauge transformations leave the encoded information unchanged; their effect is absorbed by virtual gauge qubits that do not carry useful information. We illustrate the construction by identifying a gauge symmetry in Shor's 9-qubit code that allows us to remove 3 of its 8 stabilizer generators, leading to a simpler decoding procedure and a wider class of logical operations without affecting its essential properties. This opens the path to possible improvements of the error threshold of fault-tolerant quantum computing.

Operator quantum error correction

This paper is an expanded and more detailed version of the work [1] in which the Operator Quantum Error Correction formalism was introduced. This is a new scheme for the error correction of quantum operations that incorporates the known techniques - i.e. the standard error correction model, the method of decoherence-free subspaces, and the noiseless subsystem method - as special cases, and relies on a generalized mathematical framework for noiseless subsystems that applies to arbitrary quantum operations. We also discuss a number of examples and introduce the notion of unitarily noiseless subsystems.

Correcting errors in optical data transmission using neural networks

Optical data communication systems are prone to a variety of processes that modify the transmitted signal, and contribute errors in the determination of 1s from 0s. This is a difficult, and commercially important, problem to solve. Errors must be detected and corrected at high speed, and the classifier must be very accurate; ideally it should also be tunable to the characteristics of individual communication links. We show that simple single layer neural networks may be used to address these problems, and examine how different input representations affect the accuracy of bit error correction. Our results lead us to conclude that a system based on these principles can perform at least as well as an existing non-trainable error correction system, whilst being tunable to suit the individual characteristics of different communication links.

Correcting errors in optical data transmission using neural networks

Optical data communication systems are prone to a variety of processes that modify the transmitted signal, and contribute errors in the determination of 1s from 0s. This is a difficult, and commercially important, problem to solve. Errors must be detected and corrected at high speed, and the classifier must be very accurate; ideally it should also be tunable to the characteristics of individual communication links. We show that simple single layer neural networks may be used to address these problems, and examine how different input representations affect the accuracy of bit error correction. Our results lead us to conclude that a system based on these principles can perform at least as well as an existing non-trainable error correction system, whilst being tunable to suit the individual characteristics of different communication links.

Interleavers and BCH codes for coherent DQPSK systems with laser phase noise

The relatively high phase noise of coherent optical systems poses unique challenges for forward error correction (FEC). In this letter, we propose a novel semianalytical method for selecting combinations of interleaver lengths and binary Bose-Chaudhuri-Hocquenghem (BCH) codes that meet a target post-FEC bit error rate (BER). Our method requires only short pre-FEC simulations, based on which we design interleavers and codes analytically. It is applicable to pre-FEC BER ∼10-3, and any post-FEC BER. In addition, we show that there is a tradeoff between code overhead and interleaver delay. Finally, for a target of 10-5, numerical simulations show that interleaver-code combinations selected using our method have post-FEC BER around 2× target. The target BER is achieved with 0.1 dB extra signal-to-noise ratio.

Dimensioning BCH codes for coherent DQPSK systems with laser phase noise and cycle slips

Forward error correction (FEC) plays a vital role in coherent optical systems employing multi-level modulation. However, much of coding theory assumes that additive white Gaussian noise (AWGN) is dominant, whereas coherent optical systems have significant phase noise (PN) in addition to AWGN. This changes the error statistics and impacts FEC performance. In this paper, we propose a novel semianalytical method for dimensioning binary Bose-Chaudhuri-Hocquenghem (BCH) codes for systems with PN. Our method involves extracting statistics from pre-FEC bit error rate (BER) simulations. We use these statistics to parameterize a bivariate binomial model that describes the distribution of bit errors. In this way, we relate pre-FEC statistics to post-FEC BER and BCH codes. Our method is applicable to pre-FEC BER around 10-3 and any post-FEC BER. Using numerical simulations, we evaluate the accuracy of our approach for a target post-FEC BER of 10-5. Codes dimensioned with our bivariate binomial model meet the target within 0.2-dB signal-to-noise ratio.

Low-complexity BCH codes with optimized interleavers for DQPSK systems with laser phase noise

The presence of high phase noise in addition to additive white Gaussian noise in coherent optical systems affects the performance of forward error correction (FEC) schemes. In this paper, we propose a simple scheme for such systems, using block interleavers and binary Bose–Chaudhuri–Hocquenghem (BCH) codes. The block interleavers are specifically optimized for differential quadrature phase shift keying modulation. We propose a method for selecting BCH codes that, together with the interleavers, achieve a target post-FEC bit error rate (BER). This combination of interleavers and BCH codes has very low implementation complexity. In addition, our approach is straightforward, requiring only short pre-FEC simulations to parameterize a model, based on which we select codes analytically. We aim to correct a pre-FEC BER of around (Formula presented.). We evaluate the accuracy of our approach using numerical simulations. For a target post-FEC BER of (Formula presented.), codes selected using our method result in BERs around 3(Formula presented.) target and achieve the target with around 0.2 dB extra signal-to-noise ratio.

A low overhead error confinement method based on application statistical characteristics

Reliability has emerged as a critical design constraint especially in memories. Designers are going to great lengths to guarantee fault free operation of the underlying silicon by adopting redundancy-based techniques, which essentially try to detect and correct every single error. However, such techniques come at a cost of large area, power and performance overheads which making many researchers to doubt their efficiency especially for error resilient systems where 100% accuracy is not always required. In this paper, we present an alternative method focusing on the confinement of the resulting output error induced by any reliability issues. By focusing on memory faults, rather than correcting every single error the proposed method exploits the statistical characteristics of any target application and replaces any erroneous data with the best available estimate of that data. To realize the proposed method a RISC processor is augmented with custom instructions and special-purpose functional units. We apply the method on the proposed enhanced processor by studying the statistical characteristics of the various algorithms involved in a popular multimedia application. Our experimental results show that in contrast to state-of-the-art fault tolerance approaches, we are able to reduce runtime and area overhead by 71.3% and 83.3% respectively.

A proposal for self-correcting stabilizer quantum memories in 3 dimensions (or slightly less)

We propose a family of local CSS stabilizer codes as possible candidates for self-correcting quantum memories in 3D. The construction is inspired by the classical Ising model on a Sierpinski carpet fractal, which acts as a classical self-correcting memory. Our models are naturally defined on fractal subsets of a 4D hypercubic lattice with Hausdorff dimension less than 3. Though this does not imply that these models can be realized with local interactions in R3, we also discuss this possibility. The X and Z sectors of the code are dual to one another, and we show that there exists a finite temperature phase transition associated with each of these sectors, providing evidence that the system may robustly store quantum information at finite temperature.

Quantum error correction with the IBM quantum experience

Mentre si svolgono operazioni su dei qubit, possono avvenire vari errori, modificando così l’informazione da essi contenuta. La Quantum Error Correction costruisce algoritmi che permettono di tollerare questi errori e proteggere l’informazione che si sta elaborando. Questa tesi si focalizza sui codici a 3 qubit, che possono correggere un errore di tipo bit-flip o un errore di tipo phase-flip. Più precisamente, all’interno di questi algoritmi, l’attenzione è posta sulla procedura di encoding, che punta a proteggere meglio dagli errori l’informazione contenuta da un qubit, e la syndrome measurement, che specifica su quale qubit è avvenuto un errore senza alterare lo stato del sistema. Inoltre, sfruttando la procedura della syndrome measurement, è stata stimata la probabilità di errore di tipo bit-flip e phase-flip su un qubit attraverso l’utilizzo della IBM quantum experience.

Refractive Error In School Children In Campinas, Brazil.

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An empirical evaluation of imputation accuracy for association statistics reveals increased type-I error rates in genome-wide associations

Background: Genome wide association studies (GWAS) are becoming the approach of choice to identify genetic determinants of complex phenotypes and common diseases. The astonishing amount of generated data and the use of distinct genotyping platforms with variable genomic coverage are still analytical challenges. Imputation algorithms combine directly genotyped markers information with haplotypic structure for the population of interest for the inference of a badly genotyped or missing marker and are considered a near zero cost approach to allow the comparison and combination of data generated in different studies. Several reports stated that imputed markers have an overall acceptable accuracy but no published report has performed a pair wise comparison of imputed and empiric association statistics of a complete set of GWAS markers. Results: In this report we identified a total of 73 imputed markers that yielded a nominally statistically significant association at P < 10(-5) for type 2 Diabetes Mellitus and compared them with results obtained based on empirical allelic frequencies. Interestingly, despite their overall high correlation, association statistics based on imputed frequencies were discordant in 35 of the 73 (47%) associated markers, considerably inflating the type I error rate of imputed markers. We comprehensively tested several quality thresholds, the haplotypic structure underlying imputed markers and the use of flanking markers as predictors of inaccurate association statistics derived from imputed markers. Conclusions: Our results suggest that association statistics from imputed markers showing specific MAF (Minor Allele Frequencies) range, located in weak linkage disequilibrium blocks or strongly deviating from local patterns of association are prone to have inflated false positive association signals. The present study highlights the potential of imputation procedures and proposes simple procedures for selecting the best imputed markers for follow-up genotyping studies.