1 
Code constructions and code families for nonbinary quantum stabilizer codeKetkar, Avanti Ulhas 01 November 2005 (has links)
Stabilizer codes form a special class of quantum error correcting codes. Nonbinary quantum stabilizer codes are studied in this thesis. A lot of work on binary quantum stabilizer codes has been done. Nonbinary stabilizer codes have received much less attention. Various results on binary stabilizer codes such as various code families and general code constructions are generalized to the nonbinary case in this thesis. The lower bound on the minimum distance of a code is nothing but the minimum distance of the currently best known code. The focus of this research is to improve the lower bounds on this minimum distance. To achieve this goal, various existing quantum codes are studied that have good minimum distance. Some new families of nonbinary stabilizer codes such as quantum BCH codes are constructed. Diﬀerent ways of constructing new codes from the existing ones are also found. All these constructions together help improve the lower bounds.

2 
Code constructions and code families for nonbinary quantum stabilizer codeKetkar, Avanti Ulhas 01 November 2005 (has links)
Stabilizer codes form a special class of quantum error correcting codes. Nonbinary quantum stabilizer codes are studied in this thesis. A lot of work on binary quantum stabilizer codes has been done. Nonbinary stabilizer codes have received much less attention. Various results on binary stabilizer codes such as various code families and general code constructions are generalized to the nonbinary case in this thesis. The lower bound on the minimum distance of a code is nothing but the minimum distance of the currently best known code. The focus of this research is to improve the lower bounds on this minimum distance. To achieve this goal, various existing quantum codes are studied that have good minimum distance. Some new families of nonbinary stabilizer codes such as quantum BCH codes are constructed. Diﬀerent ways of constructing new codes from the existing ones are also found. All these constructions together help improve the lower bounds.

3 
Color Segmentation on FPGA for Automatic Road Sign RecognitionZhao, Jingbo January 2012 (has links)
No description available.

4 
A New Algorithm for Finding the Minimum Distance between Two Convex HullsKaown, Dougsoo 05 1900 (has links)
The problem of computing the minimum distance between two convex hulls has applications to many areas including robotics, computer graphics and path planning. Moreover, determining the minimum distance between two convex hulls plays a significant role in support vector machines (SVM). In this study, a new algorithm for finding the minimum distance between two convex hulls is proposed and investigated. A convergence of the algorithm is proved and applicability of the algorithm to support vector machines is demostrated. The performance of the new algorithm is compared with the performance of one of the most popular algorithms, the sequential minimal optimization (SMO) method. The new algorithm is simple to understand, easy to implement, and can be more efficient than the SMO method for many SVM problems.

5 
Classification of image pixels based on minimum distance and hypothesis testingGhimire, Santosh January 1900 (has links)
Master of Science / Department of Statistics / Haiyan Wang / We introduce a new classification method that is applicable to classify image pixels. This
work was motivated by the testbased classification (TBC) introduced by Liao and Akritas(2007). We found that direct application of TBC on image pixel classification can lead to high misclassification rate. We propose a method that combines the minimum distance
and evidence from hypothesis testing to classify image pixels. The method is implemented in R programming language. Our method eliminates the drawback of Liao and Akritas (2007).Extensive experiments show that our modified method works better in the classification of image pixels in comparison with some standard methods of classification; namely, Linear Discriminant Analysis (LDA), Quadratic Discriminant Analysis (QDA), Classification Tree(CT), Polyclass classification, and TBC. We demonstrate that our method works well in the case of both grayscale and color images.

6 
Critical knots for minimum distance energy and complementary domains of arrangements of hypersurfacesHager, William George 01 July 2010 (has links)
In this thesis, we will discuss two separate topics. First, we find a critical knot for an knot energy function. A knot is a closed curve or polygon in three space. It is possible to for a computer to simulate the flow of a knot to its minimum energy conformation. There is no guarantee, however, that a true minimizer exists near the computer's alleged minimizer. We take advantage of both the symmetry of the minimizer and the symmetry invariance of the energy function to prove that there is a critical point of the energy function near the computer's minimizer.
Second, we will discuss how to determine the number of complementary domains of arrangements of algebraic curves in 2space and ellipsoids in 3space. In each of these situations, we supply equations that provide an upper bound for the number of complementary domains. These upper bounds are applicable even when the exact intersections between the curves or surfaces are unknown.

7 
Parametric classification and variable selection by the minimum integrated squared error criterionJanuary 2012 (has links)
This thesis presents a robust solution to the classification and variable selection problem when the dimension of the data, or number of predictor variables, may greatly exceed the number of observations. When faced with the problem of classifying objects given many measured attributes of the objects, the goal is to build a model that makes the most accurate predictions using only the most meaningful subset of the available measurements. The introduction of [cursive l] 1 regularized model titling has inspired many approaches that simultaneously do model fitting and variable selection. If parametric models are employed, the standard approach is some form of regularized maximum likelihood estimation. While this is an asymptotically efficient procedure under very general conditions, it is not robust. Outliers can negatively impact both estimation and variable selection. Moreover, outliers can be very difficult to identify as the number of predictor variables becomes large. Minimizing the integrated squared error, or L 2 error, while less efficient, has been shown to generate parametric estimators that are robust to a fair amount of contamination in several contexts. In this thesis, we present a novel robust parametric regression model for the binary classification problem based on L 2 distance, the logistic L 2 estimator (L 2 E). To perform simultaneous model fitting and variable selection among correlated predictors in the high dimensional setting, an elastic net penalty is introduced. A fast computational algorithm for minimizing the elastic net penalized logistic L 2 E loss is derived and results on the algorithm's global convergence properties are given. Through simulations we demonstrate the utility of the penalized logistic L 2 E at robustly recovering sparse models from high dimensional data in the presence of outliers and inliers. Results on real genomic data are also presented.

8 
Minimum Distance Estimation in Categorical Conditional Independence ModelsJanuary 2012 (has links)
One of the oldest and most fundamental problems in statistics is the analysis of crossclassified data called contingency tables. Analyzing contingency tables is typically a question of association  do the variables represented in the table exhibit special dependencies or lack thereof? The statistical models which best capture these experimental notions of dependence are the categorical conditional independence models; however, until recent discoveries concerning the strongly algebraic nature of the conditional independence models surfaced, the models were widely overlooked due to their unwieldy implicit description. Apart from the inferential question above, this thesis asks the more basic question  suppose such an experimental model of association is known, how can one incorporate this information into the estimation of the joint distribution of the table? In the traditional parametric setting several estimation paradigms have been developed over the past century; however, traditional results are not applicable to arbitrary categorical conditional independence models due to their implicit nature. After laying out the framework for conditional independence and algebraic statistical models, we consider three aspects of estimation in the models using the minimum Euclidean (L2E), minimum Pearson chisquared, and minimum Neyman modified chisquared distance paradigms as well as the more ubiquitous maximum likelihood approach (MLE). First, we consider the theoretical properties of the estimators and demonstrate that under general conditions the estimators exist and are asymptotically normal. For small samples, we present the results of large scale simulations to address the estimators' bias and mean squared error (in the Euclidean and Frobenius norms, respectively). Second, we identify the computation of such estimators as an optimization problem and, for the case of the L2E, propose two different methods by which the problem can be solved, one algebraic and one numerical. Finally, we present an R implementation via two novel packages, mpoly for symbolic computing with multivariate polynomials and catcim for fitting categorical conditional independence models. It is found that in general minimum distance estimators in categorical conditional independence models behave as they do in the more traditional parametric setting and can be computed in many practical situations with the implementation provided.

9 
A brief survey of selfdual codesOktavia, Rini 2009 August 1900 (has links)
This report is a survey of selfdual binary codes. We present
the fundamental MacWilliams identity and Gleason’s theorem
on selfdual binary codes. We also examine the upper bound of
minimum weights of selfdual binary codes using the extremal
weight enumerator formula. We describe the shadow code of a
selfdual code and the restrictions of the weight enumerator of
the shadow code. Then using the restrictions, we calculate the
weight enumerators of selfdual codes of length 38 and 40 and we
obtain the known weight enumerators of this lengths. Finally, we
investigate the GaboritOtmani experimental construction of selfdual
binary codes. This construction involves a fixed orthogonal
matrix, and we compare the result to the results obtained using
other orthogonal matrices. / text

10 
Deconvolution in Random Effects Models via Normal MixturesLitton, Nathaniel A. 2009 August 1900 (has links)
This dissertation describes a minimum distance method for density estimation when the variable of interest is not directly observed. It is assumed that the underlying target density can be well approximated by a mixture of normals. The method compares a density estimate of observable data with a density of the observable data induced from assuming the target density can be written as a mixture of normals. The goal is to choose the parameters in the normal mixture that minimize the distance between the density estimate of the observable data and the induced density from the model. The method is applied to the deconvolution problem to estimate the density of $X_{i}$ when the variable $% Y_{i}=X_{i}+Z_{i}$, $i=1,\ldots ,n$, is observed, and the density of $Z_{i}$ is known. Additionally, it is applied to a location random effects model to estimate the density of $Z_{ij}$ when the observable quantities are $p$ data sets of size $n$ given by $X_{ij}=\alpha _{i}+\gamma Z_{ij},~i=1,\ldots ,p,~j=1,\ldots ,n$, where the densities of $\alpha_{i} $ and $Z_{ij}$ are both unknown.
The performance of the minimum distance approach in the measurement error model is compared with the deconvoluting kernel density estimator of Stefanski and Carroll (1990). In the location random effects model, the minimum distance estimator is compared with the explicit characteristic function inversion method from Hall and Yao (2003). In both models, the methods are compared using simulated and real data sets. In the simulations, performance is evaluated using an integrated squared error criterion. Results indicate that the minimum distance methodology is comparable to the deconvoluting kernel density estimator and outperforms the explicit characteristic function inversion method.

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