On the Error-Correcting Performance of some Binary and Ternary Linear Codes

In this work, we determine the coset weight spectra of all binary cyclic codes of lengths up to 33, ternary cyclic and negacyclic codes of lengths up to 20 and of some binary linear codes of lengths up to 33 which are distance-optimal, by using some of the algebraic properties of the codes and a computer assisted search. Having these weight spectra the monotony of the function of the undetected error probability after t-error correction P(t)ue (C,p) could be checked with any precision for a linear time. We have used a programm written in Maple to check the monotony of P(t)ue (C,p) for the investigated codes for a finite set of points of p € [0, p/(q-1)] and in this way to determine which of them are not proper.

Improving the Watermarking Process with Usage of Block Error-Correcting Codes

The emergence of digital imaging and of digital networks has made duplication of original artwork easier. Watermarking techniques, also referred to as digital signature, sign images by introducing changes that are imperceptible to the human eye but easily recoverable by a computer program. Usage of error correcting codes is one of the good choices in order to correct possible errors when extracting the signature. In this paper, we present a scheme of error correction based on a combination of Reed-Solomon codes and another optimal linear code as inner code. We have investigated the strength of the noise that this scheme is steady to for a fixed capacity of the image and various lengths of the signature. Finally, we compare our results with other error correcting techniques that are used in watermarking. We have also created a computer program for image watermarking that uses the newly presented scheme for error correction.

Experiments in Detection and Correction of Russian Malapropisms by Means of the WEB

Malapropism is a semantic error that is hardly detectable because it usually retains syntactical links between words in the sentence but replaces one content word by a similar word with quite different meaning. A method of automatic detection of malapropisms is described, based on Web statistics and a specially defined Semantic Compatibility Index (SCI). For correction of the detected errors, special dictionaries and heuristic rules are proposed, which retains only a few highly SCI-ranked correction candidates for the user’s selection. Experiments on Web-assisted detection and correction of Russian malapropisms are reported, demonstrating efficacy of the described method.

Paronyms for Accelerated Correction of Semantic Errors

* Work done under partial support of Mexican Government (CONACyT, SNI), IPN (CGPI, COFAA) and Korean Government (KIPA Professorship for Visiting Faculty Positions). The second author is currently on Sabbatical leave at Chung-Ang University.

Error tolerance of topological codes with independent bit-flip and measurement errors

Topological quantum error correction codes are currently among the most promising candidates for efficiently dealing with the decoherence effects inherently present in quantum devices. Numerically, their theoretical error threshold can be calculated by mapping the underlying quantum problem to a related classical statistical-mechanical spin system with quenched disorder. Here, we present results for the general fault-tolerant regime, where we consider both qubit and measurement errors. However, unlike in previous studies, here we vary the strength of the different error sources independently. Our results highlight peculiar differences between toric and color codes. This study complements previous results published in New J. Phys. 13, 083006 (2011).

Iterative Phase Optimization of Elementary Quantum Error Correcting Codes

Performing experiments on small-scale quantum computers is certainly a challenging endeavor. Many parameters need to be optimized to achieve high-fidelity operations. This can be done efficiently for operations acting on single qubits, as errors can be fully characterized. For multiqubit operations, though, this is no longer the case, as in the most general case, analyzing the effect of the operation on the system requires a full state tomography for which resources scale exponentially with the system size. Furthermore, in recent experiments, additional electronic levels beyond the two-level system encoding the qubit have been used to enhance the capabilities of quantum-information processors, which additionally increases the number of parameters that need to be controlled. For the optimization of the experimental system for a given task (e.g., a quantum algorithm), one has to find a satisfactory error model and also efficient observables to estimate the parameters of the model. In this manuscript, we demonstrate a method to optimize the encoding procedure for a small quantum error correction code in the presence of unknown but constant phase shifts. The method, which we implement here on a small-scale linear ion-trap quantum computer, is readily applicable to other AMO platforms for quantum-information processing.

Adaptive Brain-Computer Interface Systems For Communication in People with Severe Neuromuscular Disabilities

Brain-computer interfaces (BCI) have the potential to restore communication or control abilities in individuals with severe neuromuscular limitations, such as those with amyotrophic lateral sclerosis (ALS). The role of a BCI is to extract and decode relevant information that conveys a user's intent directly from brain electro-physiological signals and translate this information into executable commands to control external devices. However, the BCI decision-making process is error-prone due to noisy electro-physiological data, representing the classic problem of efficiently transmitting and receiving information via a noisy communication channel.

This research focuses on P300-based BCIs which rely predominantly on event-related potentials (ERP) that are elicited as a function of a user's uncertainty regarding stimulus events, in either an acoustic or a visual oddball recognition task. The P300-based BCI system enables users to communicate messages from a set of choices by selecting a target character or icon that conveys a desired intent or action. P300-based BCIs have been widely researched as a communication alternative, especially in individuals with ALS who represent a target BCI user population. For the P300-based BCI, repeated data measurements are required to enhance the low signal-to-noise ratio of the elicited ERPs embedded in electroencephalography (EEG) data, in order to improve the accuracy of the target character estimation process. As a result, BCIs have relatively slower speeds when compared to other commercial assistive communication devices, and this limits BCI adoption by their target user population. The goal of this research is to develop algorithms that take into account the physical limitations of the target BCI population to improve the efficiency of ERP-based spellers for real-world communication.

In this work, it is hypothesised that building adaptive capabilities into the BCI framework can potentially give the BCI system the flexibility to improve performance by adjusting system parameters in response to changing user inputs. The research in this work addresses three potential areas for improvement within the P300 speller framework: information optimisation, target character estimation and error correction. The visual interface and its operation control the method by which the ERPs are elicited through the presentation of stimulus events. The parameters of the stimulus presentation paradigm can be modified to modulate and enhance the elicited ERPs. A new stimulus presentation paradigm is developed in order to maximise the information content that is presented to the user by tuning stimulus paradigm parameters to positively affect performance. Internally, the BCI system determines the amount of data to collect and the method by which these data are processed to estimate the user's target character. Algorithms that exploit language information are developed to enhance the target character estimation process and to correct erroneous BCI selections. In addition, a new model-based method to predict BCI performance is developed, an approach which is independent of stimulus presentation paradigm and accounts for dynamic data collection. The studies presented in this work provide evidence that the proposed methods for incorporating adaptive strategies in the three areas have the potential to significantly improve BCI communication rates, and the proposed method for predicting BCI performance provides a reliable means to pre-assess BCI performance without extensive online testing.

Combining Information from Multiple Sources in Bayesian Modeling

Surveys can collect important data that inform policy decisions and drive social science research. Large government surveys collect information from the U.S. population on a wide range of topics, including demographics, education, employment, and lifestyle. Analysis of survey data presents unique challenges. In particular, one needs to account for missing data, for complex sampling designs, and for measurement error. Conceptually, a survey organization could spend lots of resources getting high-quality responses from a simple random sample, resulting in survey data that are easy to analyze. However, this scenario often is not realistic. To address these practical issues, survey organizations can leverage the information available from other sources of data. For example, in longitudinal studies that suffer from attrition, they can use the information from refreshment samples to correct for potential attrition bias. They can use information from known marginal distributions or survey design to improve inferences. They can use information from gold standard sources to correct for measurement error.

This thesis presents novel approaches to combining information from multiple sources that address the three problems described above.

The first method addresses nonignorable unit nonresponse and attrition in a panel survey with a refreshment sample. Panel surveys typically suffer from attrition, which can lead to biased inference when basing analysis only on cases that complete all waves of the panel. Unfortunately, the panel data alone cannot inform the extent of the bias due to attrition, so analysts must make strong and untestable assumptions about the missing data mechanism. Many panel studies also include refreshment samples, which are data collected from a random sample of new

individuals during some later wave of the panel. Refreshment samples offer information that can be utilized to correct for biases induced by nonignorable attrition while reducing reliance on strong assumptions about the attrition process. To date, these bias correction methods have not dealt with two key practical issues in panel studies: unit nonresponse in the initial wave of the panel and in the

refreshment sample itself. As we illustrate, nonignorable unit nonresponse

can significantly compromise the analyst's ability to use the refreshment samples for attrition bias correction. Thus, it is crucial for analysts to assess how sensitive their inferences---corrected for panel attrition---are to different assumptions about the nature of the unit nonresponse. We present an approach that facilitates such sensitivity analyses, both for suspected nonignorable unit nonresponse

in the initial wave and in the refreshment sample. We illustrate the approach using simulation studies and an analysis of data from the 2007-2008 Associated Press/Yahoo News election panel study.

The second method incorporates informative prior beliefs about

marginal probabilities into Bayesian latent class models for categorical data.

The basic idea is to append synthetic observations to the original data such that

(i) the empirical distributions of the desired margins match those of the prior beliefs, and (ii) the values of the remaining variables are left missing. The degree of prior uncertainty is controlled by the number of augmented records. Posterior inferences can be obtained via typical MCMC algorithms for latent class models, tailored to deal efficiently with the missing values in the concatenated data.

We illustrate the approach using a variety of simulations based on data from the American Community Survey, including an example of how augmented records can be used to fit latent class models to data from stratified samples.

The third method leverages the information from a gold standard survey to model reporting error. Survey data are subject to reporting error when respondents misunderstand the question or accidentally select the wrong response. Sometimes survey respondents knowingly select the wrong response, for example, by reporting a higher level of education than they actually have attained. We present an approach that allows an analyst to model reporting error by incorporating information from a gold standard survey. The analyst can specify various reporting error models and assess how sensitive their conclusions are to different assumptions about the reporting error process. We illustrate the approach using simulations based on data from the 1993 National Survey of College Graduates. We use the method to impute error-corrected educational attainments in the 2010 American Community Survey using the 2010 National Survey of College Graduates as the gold standard survey.

Performance Analysis of Topological Quantum Error Correcting Codes

In the last few years there has been a great development of techniques like quantum computers and quantum communication systems, due to their huge potentialities and the growing number of applications. However, physical qubits experience a lot of nonidealities, like measurement errors and decoherence, that generate failures in the quantum computation. This work shows how it is possible to exploit concepts from classical information in order to realize quantum error-correcting codes, adding some redundancy qubits. In particular, the threshold theorem states that it is possible to lower the percentage of failures in the decoding at will, if the physical error rate is below a given accuracy threshold. The focus will be on codes belonging to the family of the topological codes, like toric, planar and XZZX surface codes. Firstly, they will be compared from a theoretical point of view, in order to show their advantages and disadvantages. The algorithms behind the minimum perfect matching decoder, the most popular for such codes, will be presented. The last section will be dedicated to the analysis of the performances of these topological codes with different error channel models, showing interesting results. In particular, while the error correction capability of surface codes decreases in presence of biased errors, XZZX codes own some intrinsic symmetries that allow them to improve their performances if one kind of error occurs more frequently than the others.

State protection under collective damping and diffusion

In this paper we provide a recipe for state protection in a network of oscillators under collective damping and diffusion. Our strategy is to manipulate the network topology, i.e., the way the oscillators are coupled together, the strength of their couplings, and their natural frequencies, in order to create a relaxation-diffusion-free channel. This protected channel defines a decoherence-free subspace (DFS) for nonzero-temperature reservoirs. Our development also furnishes an alternative approach to build up DFSs that offers two advantages over the conventional method: it enables the derivation of all the network-protected states at once, and also reveals, through the network normal modes, the mechanism behind the emergence of these protected domains.

Teleportation using coupled oscillator states

We analyze the fidelity of teleportation protocols, as a function of resource entanglement, for three kinds of two-mode oscillator states: states with fixed total photon number, number states entangled at a beam splitter, and the two-mode squeezed vacuum state. We define corresponding teleportation protocols for each case including phase noise to model degraded entanglement of each resource.

Quantum control and quantum entanglement

We discuss quantum error correction for errors that occur at random times as described by, a conditional Poisson process. We shoo, how a class of such errors, detected spontaneous emission, can be corrected by continuous closed loop, feedback.

Flex cars and the alcohol price

We build a model that incorporates the effect of the innovative ""flex"" car, an automobile that is able to run with either gasoline or alcohol, on the dynamics of fuel prices in Brazil. Our model shows that differences regarding fuel prices will now depend on the proportions of alcohol, gasoline and flex cars in the total stock. Conversely, the demand for each type of car will also depend on the expected future prices of alcohol and gasoline (in addition to the car prices). The model reflects our findings that energy prices are tied in the long run and that causality runs stronger from gasoline to alcohol. The estimated error correction parameter is stable, implying that the speed of adjustment towards equilibrium remains unchanged. The latter result is probably due to a still small fraction of flex cars in the total stock (approx. 5%), despite the fact that its sales nearly reached 100% in 2006. (C) 2009 Elsevier B.V. All rights reserved.

Tests for the hysteresis hypothesis in Brazilian industrialized exports: A threshold cointegration analysis

This paper examines the hysteresis hypothesis in the Brazilian industrialized exports using a time series analysis. This hypothesis finds an empirical representation into the nonlinear adjustments of the exported quantity to relative price changes. Thus, the threshold cointegration analysis proposed by Balke and Fomby [Balke, N.S. and Fomby, T.B. Threshold Cointegration. International Economic Review, 1997; 38; 627-645.] was used for estimating models with asymmetric adjustment of the error correction term. Amongst sixteen industrial sectors selected, there was evidence of nonlinearities in the residuals of long-run relationships of supply or demand for exports in nine of them. These nonlinearities represent asymmetric and/or discontinuous responses of exports to different representative measures of real exchange rates, in addition to other components of long-run demand or supply equations. (C) 2007 Elsevier B.V. All rights reserved.

Correcting the effects of spontaneous emission on cold-trapped ions

We propose two quantum error-correction schemes which increase the maximum storage time for qubits in a system of cold-trapped ions, using a minimal number of ancillary qubits. Both schemes consider only the errors introduced by the decoherence due to spontaneous emission from the upper levels of the ions. Continuous monitoring of the ion fluorescence is used in conjunction with selective coherent feedback to eliminate these errors immediately following spontaneous emission events.