A statistical-mechanical analysis of coded CDMA with regular LDPC codes

We analyze, using the replica method of statistical mechanics, the theoretical performance of coded code-division multiple-access (CDMA) systems in which regular low-density parity-check (LDPC) codes are used for channel coding.

Statistical mechanics analysis of LDPC coding in MIMO Gaussian channels

Using analytical methods of statistical mechanics, we analyse the typical behaviour of a multiple-input multiple-output (MIMO) Gaussian channel with binary inputs under low-density parity-check (LDPC) network coding and joint decoding. The saddle point equations for the replica symmetric solution are found in particular realizations of this channel, including a small and large number of transmitters and receivers. In particular, we examine the cases of a single transmitter, a single receiver and symmetric and asymmetric interference. Both dynamical and thermodynamical transitions from the ferromagnetic solution of perfect decoding to a non-ferromagnetic solution are identified for the cases considered, marking the practical and theoretical limits of the system under the current coding scheme. Numerical results are provided, showing the typical level of improvement/deterioration achieved with respect to the single transmitter/receiver result, for the various cases. © 2007 IOP Publishing Ltd.

Composite CDMA—a statistical mechanics analysis

Code division multiple access (CDMA) in which the spreading code assignment to users contains a random element has recently become a cornerstone of CDMA research. The random element in the construction is particularly attractive as it provides robustness and flexibility in utilizing multiaccess channels, whilst not making significant sacrifices in terms of transmission power. Random codes are generated from some ensemble; here we consider the possibility of combining two standard paradigms, sparsely and densely spread codes, in a single composite code ensemble. The composite code analysis includes a replica symmetric calculation of performance in the large system limit, and investigation of finite systems through a composite belief propagation algorithm. A variety of codes are examined with a focus on the high multi-access interference regime. We demonstrate scenarios both in the large size limit and for finite systems in which the composite code has typical performance exceeding those of sparse and dense codes at equivalent signal to noise ratio.

The carbon dioxide emissions of firms:a spatial analysis

In order to gain a greater understanding of firms' 'environmental behaviour' this paper explores the factors that influence firms' emissions intensities and provides the first analysis of the determinants of firm level carbon dioxide (CO2) emissions. Focussing on Japan, the paper also examines whether firms' CO2 emissions are influenced by the emissions of neighbouring firms and other possible sources of spatial correlation. Results suggest that size, the capital-labour ratio, R&D expenditure, the extent of exports and concern for public profile are the key determinants of CO2 emissions. Local lobbying pressure, as captured by regional community characteristics, does not appear to play a role, however emissions are found to be spatially correlated. This raises implications for the manner in which the environmental performance of firms is modelled in future. © 2013 Elsevier Inc.

A multivariate spatial analysis of vowel formants in American English

This paper presents the results of a multivariate spatial analysis of 38 vowel formant variables in the language of 402 informants from 236 cities from across the contiguous United States, based on the acoustic data from the Atlas of North American English (Labov, Ash & Boberg, 2006). The results of the analysis both confirm and challenge the results of the Atlas. Most notably, while the analysis identifies similar patterns as the Atlas in the West and the Southeast, the analysis finds that the Midwest and the Northeast are distinct dialect regions that are considerably stronger than the traditional Midland and Northern dialect region indentified in the Atlas. The analysis also finds evidence that a western vowel shift is actively shaping the language of the Western United States.

Spatially clustered associations in health GIS

Overlaying maps using a desktop GIS is often the first step of a multivariate spatial analysis. The potential of this operation has increased considerably as data sources and Web services to manipulate them are becoming widely available via the Internet. Standards from the OGC enable such geospatial mashups to be seamless and user driven, involving discovery of thematic data. The user is naturally inclined to look for spatial clusters and correlation of outcomes. Using classical cluster detection scan methods to identify multivariate associations can be problematic in this context, because of a lack of control on or knowledge about background populations. For public health and epidemiological mapping, this limiting factor can be critical but often the focus is on spatial identification of risk factors associated with health or clinical status. Spatial entropy index HSu for the ScankOO analysis of the hypothetical dataset using a vicinity which is fixed by the number of points without distinction between their labels. (The size of the labels is proportional to the inverse of the index) In this article we point out that this association itself can ensure some control on underlying populations, and develop an exploratory scan statistic framework for multivariate associations. Inference using statistical map methodologies can be used to test the clustered associations. The approach is illustrated with a hypothetical data example and an epidemiological study on community MRSA. Scenarios of potential use for online mashups are introduced but full implementation is left for further research.

Spatially clustered associations in health related geospatial data

Overlaying maps using a desktop GIS is often the first step of a multivariate spatial analysis. The potential of this operation has increased considerably as data sources an dWeb services to manipulate them are becoming widely available via the Internet. Standards from the OGC enable such geospatial ‘mashups’ to be seamless and user driven, involving discovery of thematic data. The user is naturally inclined to look for spatial clusters and ‘correlation’ of outcomes. Using classical cluster detection scan methods to identify multivariate associations can be problematic in this context, because of a lack of control on or knowledge about background populations. For public health and epidemiological mapping, this limiting factor can be critical but often the focus is on spatial identification of risk factors associated with health or clinical status. In this article we point out that this association itself can ensure some control on underlying populations, and develop an exploratory scan statistic framework for multivariate associations. Inference using statistical map methodologies can be used to test the clustered associations. The approach is illustrated with a hypothetical data example and an epidemiological study on community MRSA. Scenarios of potential use for online mashups are introduced but full implementation is left for further research.

Representation and parameterisation issues in genetic algorithms

A multi-chromosome GA (Multi-GA) was developed, based upon concepts from the natural world, allowing improved flexibility in a number of areas including representation, genetic operators, their parameter rates and real world multi-dimensional applications. A series of experiments were conducted, comparing the performance of the Multi-GA to a traditional GA on a number of recognised and increasingly complex test optimisation surfaces, with promising results. Further experiments demonstrated the Multi-GA's flexibility through the use of non-binary chromosome representations and its applicability to dynamic parameterisation. A number of alternative and new methods of dynamic parameterisation were investigated, in addition to a new non-binary 'Quotient crossover' mechanism. Finally, the Multi-GA was applied to two real world problems, demonstrating its ability to handle mixed type chromosomes within an individual, the limited use of a chromosome level fitness function, the introduction of new genetic operators for structural self-adaptation and its viability as a serious real world analysis tool. The first problem involved optimum placement of computers within a building, allowing the Multi-GA to use multiple chromosomes with different type representations and different operators in a single individual. The second problem, commonly associated with Geographical Information Systems (GIS), required a spatial analysis location of the optimum number and distribution of retail sites over two different population grids. In applying the Multi-GA, two new genetic operators (addition and deletion) were developed and explored, resulting in the definition of a mechanism for self-modification of genetic material within the Multi-GA structure and a study of this behaviour.

Regional variation in written American English

The first study of its kind, Regional Variation in Written American English takes a corpus-based approach to map over a hundred grammatical alternation variables across the United States. A multivariate spatial analysis of these maps shows that grammatical alternation variables follow a relatively small number of common regional patterns in American English, which can be explained based on both linguistic and extra-linguistic factors. Based on this rigorous analysis of extensive data, Grieve identifies five primary modern American dialect regions, demonstrating that regional variation is far more pervasive and complex in natural language than is generally assumed. The wealth of maps and data and the groundbreaking implications of this volume make it essential reading for students and researchers in linguistics, English language, geography, computer science, sociology and communication studies.

Generalized KPCA by adaptive rules in feature space

Principal component analysis (PCA) is well recognized in dimensionality reduction, and kernel PCA (KPCA) has also been proposed in statistical data analysis. However, KPCA fails to detect the nonlinear structure of data well when outliers exist. To reduce this problem, this paper presents a novel algorithm, named iterative robust KPCA (IRKPCA). IRKPCA works well in dealing with outliers, and can be carried out in an iterative manner, which makes it suitable to process incremental input data. As in the traditional robust PCA (RPCA), a binary field is employed for characterizing the outlier process, and the optimization problem is formulated as maximizing marginal distribution of a Gibbs distribution. In this paper, this optimization problem is solved by stochastic gradient descent techniques. In IRKPCA, the outlier process is in a high-dimensional feature space, and therefore kernel trick is used. IRKPCA can be regarded as a kernelized version of RPCA and a robust form of kernel Hebbian algorithm. Experimental results on synthetic data demonstrate the effectiveness of IRKPCA. © 2010 Taylor & Francis.

Spatial pattern analysis of beta-amyloid (A beta) deposits in Alzheimer disease by linear regression

The spatial patterns of discrete beta-amyloid (Abeta) deposits in brain tissue from patients with Alzheimer disease (AD) were studied using a statistical method based on linear regression, the results being compared with the more conventional variance/mean (V/M) method. Both methods suggested that Abeta deposits occurred in clusters (400 to <12,800 mu m in diameter) in all but 1 of the 42 tissues examined. In many tissues, a regular periodicity of the Abeta deposit clusters parallel to the tissue boundary was observed. In 23 of 42 (55%) tissues, the two methods revealed essentially the same spatial patterns of Abeta deposits; in 15 of 42 (36%), the regression method indicated the presence of clusters at a scale not revealed by the V/M method; and in 4 of 42 (9%), there was no agreement between the two methods. Perceived advantages of the regression method are that there is a greater probability of detecting clustering at multiple scales, the dimension of larger Abeta clusters can be estimated more accurately, and the spacing between the clusters may be estimated. However, both methods may be useful, with the regression method providing greater resolution and the V/M method providing greater simplicity and ease of interpretation. Estimates of the distance between regularly spaced Abeta clusters were in the range 2,200-11,800 mu m, depending on tissue and cluster size. The regular periodicity of Abeta deposit clusters in many tissues would be consistent with their development in relation to clusters of neurons that give rise to specific neuronal projections.

The usefulness of spatial pattern analysis in understanding the pathogenesis of neurodegenerative disorders, with particular reference to plaque formation in Alzheimer's disease

Discrete, microscopic lesions are developed in the brain in a number of neurodegenerative diseases. These lesions may not be randomly distributed in the tissue but exhibit a spatial pattern, i.e., a departure from randomness towards regularlity or clustering. The spatial pattern of a lesion may reflect its development in relation to other brain lesions or to neuroanatomical structures. Hence, a study of spatial pattern may help to elucidate the pathogenesis of a lesion. A number of statistical methods can be used to study the spatial patterns of brain lesions. They range from simple tests of whether the distribution of a lesion departs from random to more complex methods which can detect clustering and the size, distribution and spacing of clusters. This paper reviews the uses and limitations of these methods as applied to neurodegenerative disorders, and in particular to senile plaque formation in Alzheimer's disease.

A statistical analysis of regional variation in adverb position in a corpus of written Standard American English

This paper investigates whether the position of adverb phrases in sentences is regionally patterned in written Standard American English, based on an analysis of a 25 million word corpus of letters to the editor representing the language of 200 cities from across the United States. Seven measures of adverb position were tested for regional patterns using the global spatial autocorrelation statistic Moran’s I and the local spatial autocorrelation statistic Getis-Ord Gi*. Three of these seven measures were indentified as exhibiting significant levels of spatial autocorrelation, contrasting the language of the Northeast with language of the Southeast and the South Central states. These results demonstrate that continuous regional grammatical variation exists in American English and that regional linguistic variation exists in written Standard English.