Typical kernel size and number of sparse random matrices over Galois fields: a statistical physics approach

Using methods of statistical physics, we study the average number and kernel size of general sparse random matrices over GF(q), with a given connectivity profile, in the thermodynamical limit of large matrices. We introduce a mapping of GF(q) matrices onto spin systems using the representation of the cyclic group of order q as the q-th complex roots of unity. This representation facilitates the derivation of the average kernel size of random matrices using the replica approach, under the replica symmetric ansatz, resulting in saddle point equations for general connectivity distributions. Numerical solutions are then obtained for particular cases by population dynamics. Similar techniques also allow us to obtain an expression for the exact and average number of random matrices for any general connectivity profile. We present numerical results for particular distributions.

Spatial aspects of MRSA epidemiology:A case study using stochastic simulation, kernel estimation and SaTScan

The identification of disease clusters in space or space-time is of vital importance for public health policy and action. In the case of methicillin-resistant Staphylococcus aureus (MRSA), it is particularly important to distinguish between community and health care-associated infections, and to identify reservoirs of infection. 832 cases of MRSA in the West Midlands (UK) were tested for clustering and evidence of community transmission, after being geo-located to the centroids of UK unit postcodes (postal areas roughly equivalent to Zip+4 zip code areas). An age-stratified analysis was also carried out at the coarser spatial resolution of UK Census Output Areas. Stochastic simulation and kernel density estimation were combined to identify significant local clusters of MRSA (p<0.025), which were supported by SaTScan spatial and spatio-temporal scan. In order to investigate local sampling effort, a spatial 'random labelling' approach was used, with MRSA as cases and MSSA (methicillin-sensitive S. aureus) as controls. Heavy sampling in general was a response to MRSA outbreaks, which in turn appeared to be associated with medical care environments. The significance of clusters identified by kernel estimation was independently supported by information on the locations and client groups of nursing homes, and by preliminary molecular typing of isolates. In the absence of occupational/ lifestyle data on patients, the assumption was made that an individual's location and consequent risk is adequately represented by their residential postcode. The problems of this assumption are discussed, with recommendations for future data collection.

Analysis of nocturnal oxygen saturation recordings using kernel entropy to assist in sleep apnea-hypopnea diagnosis

In this study, a new entropy measure known as kernel entropy (KerEnt), which quantifies the irregularity in a series, was applied to nocturnal oxygen saturation (SaO 2) recordings. A total of 96 subjects suspected of suffering from sleep apnea-hypopnea syndrome (SAHS) took part in the study: 32 SAHS-negative and 64 SAHS-positive subjects. Their SaO 2 signals were separately processed by means of KerEnt. Our results show that a higher degree of irregularity is associated to SAHS-positive subjects. Statistical analysis revealed significant differences between the KerEnt values of SAHS-negative and SAHS-positive groups. The diagnostic utility of this parameter was studied by means of receiver operating characteristic (ROC) analysis. A classification accuracy of 81.25% (81.25% sensitivity and 81.25% specificity) was achieved. Repeated apneas during sleep increase irregularity in SaO 2 data. This effect can be measured by KerEnt in order to detect SAHS. This non-linear measure can provide useful information for the development of alternative diagnostic techniques in order to reduce the demand for conventional polysomnography (PSG). © 2011 IEEE.

Reduced postprandial proinsulinaemia and 32-33 split proinsulinaemia after a mixed meal in type 2 diabetic patients following sensitization to insulin with pioglitazone

Objective: Reduced insulin sensitivity associated with fasting hyperproinsulinaemia is common in type 2 diabetes. Proinsulinaemia is an established independent cardiovascular risk factor. The objective was to investigate fasting and postprandial release of insulin, proinsulin (PI) and 32-33 split proinsulin (SPI) before and after sensitization to insulin with pioglitazone compared to a group treated with glibenclamide. Design and patients: A randomized double-blind placebo-controlled trial. Twenty-two type 2 diabetic patients were recruited along with 10 normal subjects. After 4 weeks washout, patients received a mixed meal and were assigned to receive pioglitazone or glibenclamide for 20 weeks, after which patients received another identical test meal. The treatment regimes were designed to maintain glycaemic control (HbA1c) at pretreatment levels so that ß-cells received an equivalent glycaemic stimulus for both test meals. Measurements: Plasma insulin, PI, SPI and glucose concentrations were measured over an 8-h postprandial period. The output of PI and SPI was measured as the integrated postprandial response (area under the curve, AUC). Results: Pioglitazone treatment resulted in a significant reduction in fasting levels of PI and SPI compared to those of the controls. Postprandially, pioglitazone treatment had no effect on the insulin AUC response to the meal but significantly reduced the PI and SPI AUCs. Glibenclamide increased fasting insulin and the postprandial insulin AUC but had no effect on the PI and SPI AUCs. Conclusions: Sensitization to insulin with pioglitazone reduces the amount of insulin precursor species present in fasting and postprandially and may reduce cardiovascular risk. © 2007 The Authors.

A high-fat meal induces low-grade endotoxemia:evidence of a novel mechanism of postprandial inflammation

Background: Bacterial endotoxin is a potently inflammatory antigen that is abundant in the human gut. Endotoxin circulates at low concentrations in the blood of all healthy individuals, although elevated concentrations are associated with an increased risk of atherosclerosis. Objective: We sought to determine whether a high-fat meal or smoking increases plasma endotoxin concentrations and whether such concentrations are of physiologic relevance. Design: Plasma endotoxin and endotoxin neutralization capacity were measured for 4 h in 12 healthy men after no meal, 3 cigarettes, a high-fat meal, or a high-fat meal with 3 cigarettes by using the limulus assay. Results: Baseline endotoxin concentrations were 8.2 pg/mL (interquartile range: 3.4–13.5 pg/mL) but increased significantly (P < 0.05) by ≈50% after a high-fat meal or after a high-fat meal with cigarettes but not after no meal or cigarettes alone. These results were validated by the observations that a high-fat meal with or without cigarettes, but not no meal or smoking, also significantly (P < 0.05) reduced plasma endotoxin neutralization capacity, which is an indirect measure of endotoxin exposure. Human monocytes, but not aortic endothelial cells, were responsive to transient (30 s) or low-dose (10 pg/mL) exposure to endotoxin. However, plasma from whole blood treated with as little as 10 pg endotoxin/mL increased the endothelial cell expression of E-selectin, at least partly via tumor necrosis factor-α–induced cellular activation. Conclusions: Low-grade endotoxemia may contribute to the postprandial inflammatory state and could represent a novel potential contributor to endothelial activation and the development of atherosclerosis.

Predicting class II MHC-Peptide binding:a kernel based approach using similarity scores

Background - Modelling the interaction between potentially antigenic peptides and Major Histocompatibility Complex (MHC) molecules is a key step in identifying potential T-cell epitopes. For Class II MHC alleles, the binding groove is open at both ends, causing ambiguity in the positional alignment between the groove and peptide, as well as creating uncertainty as to what parts of the peptide interact with the MHC. Moreover, the antigenic peptides have variable lengths, making naive modelling methods difficult to apply. This paper introduces a kernel method that can handle variable length peptides effectively by quantifying similarities between peptide sequences and integrating these into the kernel. Results - The kernel approach presented here shows increased prediction accuracy with a significantly higher number of true positives and negatives on multiple MHC class II alleles, when testing data sets from MHCPEP [1], MCHBN [2], and MHCBench [3]. Evaluation by cross validation, when segregating binders and non-binders, produced an average of 0.824 AROC for the MHCBench data sets (up from 0.756), and an average of 0.96 AROC for multiple alleles of the MHCPEP database. Conclusion - The method improves performance over existing state-of-the-art methods of MHC class II peptide binding predictions by using a custom, knowledge-based representation of peptides. Similarity scores, in contrast to a fixed-length, pocket-specific representation of amino acids, provide a flexible and powerful way of modelling MHC binding, and can easily be applied to other dynamic sequence problems.

An investigation of management accounting control systems in the palm oil industry:a sociomaterial approach to practice change

The primary aim of this research is to understand what constitutes management accounting and control (MACs) practice and how these control processes are implicated in the day to day work practices and operations of the organisation. It also examines the changes that happen in MACs practices over time as multiple actors within organisational settings interact with each other. I adopt a distinctive practice theory approach (i.e. sociomateriality) and the concept of imbrication in this research to show that MACs practices emerge from the entanglement between human/social agency and material/technological agency within an organisation. Changes in the pattern of MACs practices happens in imbrication processes which are produced as the two agencies entangle. The theoretical approach employed in this research offers an interesting and valuable lens which seeks to reveal the depth of these interactions and uncover the way in which the social and material imbricate. The theoretical framework helps to reveal how these constructions impact on and produce modifications of MACs practices. The exploration of the control practices at different hierarchical levels (i.e. from the operational to middle management and senior level management) using the concept of imbrication process also maps the dynamic flow of controls from operational to top management and vice versa in the organisation. The empirical data which is the focus of this research has been gathered from a case study of an organisation involved in a large vertically integrated palm oil industry company in Malaysia specifically the refinery sector. The palm oil industry is a significant industry in Malaysia as it contributed an average of 4.5% of Malaysian Gross Domestic Product, over the period 1990 -2010. The Malaysian palm oil industry also has a significant presence in global food oil supply where it contributed 26% of the total oils and fats global trade in 2010. The case organisation is a significant contributor to the Malaysian palm oil industry. The research access has provided an interesting opportunity to explore the interactions between different groups of people and material/technology in a relatively heavy process food industry setting. My research examines how these interactions shape and are shaped by control practices in a dynamic cycle of imbrications over both short and medium time periods.

Perturbed Proximal Point Algorithm with Nonquadratic Kernel

Let H be a real Hilbert space and T be a maximal monotone operator on H. A well-known algorithm, developed by R. T. Rockafellar [16], for solving the problem (P) ”To find x ∈ H such that 0 ∈ T x” is the proximal point algorithm. Several generalizations have been considered by several authors: introduction of a perturbation, introduction of a variable metric in the perturbed algorithm, introduction of a pseudo-metric in place of the classical regularization, . . . We summarize some of these extensions by taking simultaneously into account a pseudo-metric as regularization and a perturbation in an inexact version of the algorithm.