Error detection and correction in binary parallel digital computers /

"Retyped October, 1964"

Improved Techniques for Video Compression and Communication

Thesis (Ph.D.)--University of Washington, 2016-06

Quantum-error correction on linear-nearest-neighbor qubit arrays

A quantum circuit implementing 5-qubit quantum-error correction on a linear-nearest-neighbor architecture is described. The canonical decomposition is used to construct fast and simple gates that incorporate the necessary swap operations allowing the circuit to achieve the same depth as the current least depth circuit. Simulations of the circuit's performance when subjected to discrete and continuous errors are presented. The relationship between the error rate of a physical qubit and that of a logical qubit is investigated with emphasis on determining the concatenated error correction threshold.

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.

Zero-non-zero patterned vector error correction modeling for I(2) cointegrated time series with applications in testing PPP and stock market relationships

Vector error-correction models (VECMs) have become increasingly important in their application to financial markets. Standard full-order VECM models assume non-zero entries in all their coefficient matrices. However, applications of VECM models to financial market data have revealed that zero entries are often a necessary part of efficient modelling. In such cases, the use of full-order VECM models may lead to incorrect inferences. Specifically, if indirect causality or Granger non-causality exists among the variables, the use of over-parameterised full-order VECM models may weaken the power of statistical inference. In this paper, it is argued that the zero–non-zero (ZNZ) patterned VECM is a more straightforward and effective means of testing for both indirect causality and Granger non-causality. For a ZNZ patterned VECM framework for time series of integrated order two, we provide a new algorithm to select cointegrating and loading vectors that can contain zero entries. Two case studies are used to demonstrate the usefulness of the algorithm in tests of purchasing power parity and a three-variable system involving the stock market.

Vector Error-Correction Models in a consumer packaged goods category forecasting decision support system

A framework for developing marketing category management decision support systems (DSS) based upon the Bayesian Vector Autoregressive (BVAR) model is extended. Since the BVAR model is vulnerable to permanent and temporary shifts in purchasing patterns over time, a form that can correct for the shifts and still provide the other advantages of the BVAR is a Bayesian Vector Error-Correction Model (BVECM). We present the mechanics of extending the DSS to move from a BVAR model to the BVECM model for the category management problem. Several additional iterative steps are required in the DSS to allow the decision maker to arrive at the best forecast possible. The revised marketing DSS framework and model fitting procedures are described. Validation is conducted on a sample problem.

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.

An econometric analysis of international tourism demand in Hong Kong : a cointegration and error correction approach

The purpose of this study is to develop econometric models to better understand the economic factors affecting inbound tourist flows from each of six origin countries that contribute to Hong Kong’s international tourism demand. To this end, we test alternative cointegration and error correction approaches to examine the economic determinants of tourist flows to Hong Kong, and to produce accurate econometric forecasts of inbound tourism demand. Our empirical findings show that permanent income is the most significant determinant of tourism demand in all models. The variables of own price, weighted substitute prices, trade volume, the share price index (as an indicator of changes in wealth in origin countries), and a dummy variable representing the Beijing incident (1989) are also found to be important determinants for some origin countries. The average long-run income and own price elasticity was measured at 2.66 and – 1.02, respectively. It was hypothesised that permanent income is a better explanatory variable of long-haul tourism demand than current income. A novel approach (grid search process) has been used to empirically derive the weights to be attached to the lagged income variable for estimating permanent income. The results indicate that permanent income, estimated with empirically determined relatively small weighting factors, was capable of producing better results than the current income variable in explaining long-haul tourism demand. This finding suggests that the use of current income in previous empirical tourism demand studies may have produced inaccurate results. The share price index, as a measure of wealth, was also found to be significant in two models. Studies of tourism demand rarely include wealth as an explanatory forecasting long-haul tourism demand. However, finding a satisfactory proxy for wealth common to different countries is problematic. This study indicates with the ECM (Error Correction Models) based on the Engle-Granger (1987) approach produce more accurate forecasts than ECM based on Pesaran and Shin (1998) and Johansen (1988, 1991, 1995) approaches for all of the long-haul markets and Japan. Overall, ECM produce better forecasts than the OLS, ARIMA and NAÏVE models, indicating the superiority of the application of a cointegration approach for tourism demand forecasting. The results show that permanent income is the most important explanatory variable for tourism demand from all countries but there are substantial variations between countries with the long-run elasticity ranging between 1.1 for the U.S. and 5.3 for U.K. Price is the next most important variable with the long-run elasticities ranging between -0.8 for Japan and -1.3 for Germany and short-run elasticities ranging between – 0.14 for Germany and -0.7 for Taiwan. The fastest growing market is Mainland China. The findings have implications for policies and strategies on investment, marketing promotion and pricing.

Pricing-to-market using EGARCH-error correction model

In this paper, the authors use an exponential generalized autoregressive conditional heteroscedastic (EGARCH) error-correction model (ECM), that is, EGARCH-ECM, to estimate the pass-through effects of foreign exchange (FX) rates and producers’ prices for 20 U.K. export sectors. The long-run adjustment of export prices to FX rates and producers’ prices is within the range of -1.02% (for the Textiles sector) and -17.22% (for the Meat sector). The contemporaneous pricing-to-market (PTM) coefficient is within the range of -72.84% (for the Fuels sector) and -8.05% (for the Textiles sector). Short-run FX rate pass-through is not complete even after several months. Rolling EGARCH-ECMs show that the short and long-run effects of FX rate and producers’ prices fluctuate substantially as are asymmetry and volatility estimates before equilibrium is achieved.

Pairing Repeated Reading and Systematic Error Correction: Impact on Fluency of 18 Year Old Students on a Small Caribbean Island

This study investigates the impact of a combined treatment of Systematic Error Correction and Repeated Reading on reading rate and errors for 18 year olds with undiagnosed reading difficulties on a Caribbean Island. In addition to direct daily measures of reading accuracy, the Reading Self Perception Scale was administered to determine whether the intervention was associated with changes in the way the student perceives himself as a reader.

Development of error correction techniques for nitrate-N load estimation models

Excess nutrient loads carried by streams and rivers are a great concern for environmental resource managers. In agricultural regions, excess loads are transported downstream to receiving water bodies, potentially causing algal blooms, which could lead to numerous ecological problems. To better understand nutrient load transport, and to develop appropriate water management plans, it is important to have accurate estimates of annual nutrient loads. This study used a Monte Carlo sub-sampling method and error-corrected statistical models to estimate annual nitrate-N loads from two watersheds in central Illinois. The performance of three load estimation methods (the seven-parameter log-linear model, the ratio estimator, and the flow-weighted averaging estimator) applied at one-, two-, four-, six-, and eight-week sampling frequencies were compared. Five error correction techniques; the existing composite method, and four new error correction techniques developed in this study; were applied to each combination of sampling frequency and load estimation method. On average, the most accurate error reduction technique, (proportional rectangular) resulted in 15% and 30% more accurate load estimates when compared to the most accurate uncorrected load estimation method (ratio estimator) for the two watersheds. Using error correction methods, it is possible to design more cost-effective monitoring plans by achieving the same load estimation accuracy with fewer observations. Finally, the optimum combinations of monitoring threshold and sampling frequency that minimizes the number of samples required to achieve specified levels of accuracy in load estimation were determined. For one- to three-weeks sampling frequencies, combined threshold/fixed-interval monitoring approaches produced the best outcomes, while fixed-interval-only approaches produced the most accurate results for four- to eight-weeks sampling frequencies.