960 resultados para Log-Euclidean Potentials


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MSC 2010: 30C45, 30C55

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2010 Mathematics Subject Classification: 53A07, 53A35, 53A10.

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2000 Mathematics Subject Classification: 49L20, 60J60, 93E20

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2000 Mathematics Subject Classification: 62P10, 92C20

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This paper examines whether the observed long memory behavior of log-range series is to some extent spurious and whether it can be explained by the presence of structural breaks. Utilizing stock market data we show that the characterization of log-range series as long memory processes can be a strong assumption. Moreover, we find that all examined series experience a large number of significant breaks. Once the breaks are accounted for, the volatility persistence is eliminated. Overall, the findings suggest that volatility can be adequately represented, at least in-sample, through a multiple breaks process and a short run component.

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2000 Mathematics Subject Classification: Primary 42A38. Secondary 42B10.

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We consider an optical fiber with a nanoscale variation of the effective fiber radius that supports whispering gallery modes slowly propagating along the fiber, and reveal that the radius variation can be designed to support the reflectionless propagation of these modes. We show that reflectionless modulations can realize control of the transmission amplitude and temporal delay, while enabling close packing due to the absence of cross talk, in contrast to the conventional potentials.

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Diabetes mellitus (DM) is a metabolic disorder which is characterised by hyperglycaemia resulting from defects in insulin secretion, insulin action or both. The long-term specific effects of DM include the development of retinopathy, nephropathy and neuropathy. Cardiac disease, peripheral arterial and cerebrovascular disease are also known to be linked with DM. Type 1 diabetes mellitus (T1DM) accounts for approximately 10% of all individuals with DM, and insulin therapy is the only available treatment. Type 2 diabetes mellitus (T2DM) accounts for 90% of all individuals with DM. Diet, exercise, oral hypoglycaemic agents and occasionally exogenous insulin are used to manage T2DM. The diagnosis of DM is made where the glycated haemoglobin (HbA1c) percentage is greater than 6.5%. Pattern-reversal visual evoked potential (PVEP) testing is an objective means of evaluating impulse conduction along the central nervous pathways. Increased peak time of the visual P100 waveform is an expression of structural damage at the level of myelinated optic nerve fibres. This was an observational cross sectional study. The participants were grouped into two phases. Phase 1, the control group, consisted of 30 healthy non-diabetic participants. Phase 2 comprised of 104 diabetic participants of whom 52 had an HbA1c greater than 10% (poorly controlled DM) and 52 whose HbA1c was 10% and less (moderately controlled DM). The aim of this study was to firstly observe the possible association between glycated haemoglobin levels and P100 peak time of pattern-reversal visual evoked potentials (PVEPs) in DM. Secondly, to assess whether the central nervous system (CNS) and in particular visual function is affected by type and/or duration of DM. The cut-off values to define P100 peak time delay was calculated as the mean P100 peak time plus 2.5 X standard deviations as measured for the non-diabetic control group, and were 110.64 ms for the right eye. The proportion of delayed P100 peak time amounted to 38.5% for both diabetic groups, thus the poorly controlled group (HbA1c > 10%) did not pose an increased risk for delayed P100 peak time, relative to the moderately controlled group (HbA1c ≤ 10%). The P100 PVEP results for this study, do however, reflect significant delay (p < 0.001) of the DM group as compared to the non-diabetic group; thus, subclincal neuropathy of the CNS occurs in 38.5% of cases. The duration of DM and type of DM had no influence on the P100 peak time measurements.

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This dissertation develops a new mathematical approach that overcomes the effect of a data processing phenomenon known as “histogram binning” inherent to flow cytometry data. A real-time procedure is introduced to prove the effectiveness and fast implementation of such an approach on real-world data. The histogram binning effect is a dilemma posed by two seemingly antagonistic developments: (1) flow cytometry data in its histogram form is extended in its dynamic range to improve its analysis and interpretation, and (2) the inevitable dynamic range extension introduces an unwelcome side effect, the binning effect, which skews the statistics of the data, undermining as a consequence the accuracy of the analysis and the eventual interpretation of the data. ^ Researchers in the field contended with such a dilemma for many years, resorting either to hardware approaches that are rather costly with inherent calibration and noise effects; or have developed software techniques based on filtering the binning effect but without successfully preserving the statistical content of the original data. ^ The mathematical approach introduced in this dissertation is so appealing that a patent application has been filed. The contribution of this dissertation is an incremental scientific innovation based on a mathematical framework that will allow researchers in the field of flow cytometry to improve the interpretation of data knowing that its statistical meaning has been faithfully preserved for its optimized analysis. Furthermore, with the same mathematical foundation, proof of the origin of such an inherent artifact is provided. ^ These results are unique in that new mathematical derivations are established to define and solve the critical problem of the binning effect faced at the experimental assessment level, providing a data platform that preserves its statistical content. ^ In addition, a novel method for accumulating the log-transformed data was developed. This new method uses the properties of the transformation of statistical distributions to accumulate the output histogram in a non-integer and multi-channel fashion. Although the mathematics of this new mapping technique seem intricate, the concise nature of the derivations allow for an implementation procedure that lends itself to a real-time implementation using lookup tables, a task that is also introduced in this dissertation. ^

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Hydrophobicity as measured by Log P is an important molecular property related to toxicity and carcinogenicity. With increasing public health concerns for the effects of Disinfection By-Products (DBPs), there are considerable benefits in developing Quantitative Structure and Activity Relationship (QSAR) models capable of accurately predicting Log P. In this research, Log P values of 173 DBP compounds in 6 functional classes were used to develop QSAR models, by applying 3 molecular descriptors, namely, Energy of the Lowest Unoccupied Molecular Orbital (ELUMO), Number of Chlorine (NCl) and Number of Carbon (NC) by Multiple Linear Regression (MLR) analysis. The QSAR models developed were validated based on the Organization for Economic Co-operation and Development (OECD) principles. The model Applicability Domain (AD) and mechanistic interpretation were explored. Considering the very complex nature of DBPs, the established QSAR models performed very well with respect to goodness-of-fit, robustness and predictability. The predicted values of Log P of DBPs by the QSAR models were found to be significant with a correlation coefficient R2 from 81% to 98%. The Leverage Approach by Williams Plot was applied to detect and remove outliers, consequently increasing R 2 by approximately 2% to 13% for different DBP classes. The developed QSAR models were statistically validated for their predictive power by the Leave-One-Out (LOO) and Leave-Many-Out (LMO) cross validation methods. Finally, Monte Carlo simulation was used to assess the variations and inherent uncertainties in the QSAR models of Log P and determine the most influential parameters in connection with Log P prediction. The developed QSAR models in this dissertation will have a broad applicability domain because the research data set covered six out of eight common DBP classes, including halogenated alkane, halogenated alkene, halogenated aromatic, halogenated aldehyde, halogenated ketone, and halogenated carboxylic acid, which have been brought to the attention of regulatory agencies in recent years. Furthermore, the QSAR models are suitable to be used for prediction of similar DBP compounds within the same applicability domain. The selection and integration of various methodologies developed in this research may also benefit future research in similar fields.

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This dissertation develops a new mathematical approach that overcomes the effect of a data processing phenomenon known as "histogram binning" inherent to flow cytometry data. A real-time procedure is introduced to prove the effectiveness and fast implementation of such an approach on real-world data. The histogram binning effect is a dilemma posed by two seemingly antagonistic developments: (1) flow cytometry data in its histogram form is extended in its dynamic range to improve its analysis and interpretation, and (2) the inevitable dynamic range extension introduces an unwelcome side effect, the binning effect, which skews the statistics of the data, undermining as a consequence the accuracy of the analysis and the eventual interpretation of the data. Researchers in the field contended with such a dilemma for many years, resorting either to hardware approaches that are rather costly with inherent calibration and noise effects; or have developed software techniques based on filtering the binning effect but without successfully preserving the statistical content of the original data. The mathematical approach introduced in this dissertation is so appealing that a patent application has been filed. The contribution of this dissertation is an incremental scientific innovation based on a mathematical framework that will allow researchers in the field of flow cytometry to improve the interpretation of data knowing that its statistical meaning has been faithfully preserved for its optimized analysis. Furthermore, with the same mathematical foundation, proof of the origin of such an inherent artifact is provided. These results are unique in that new mathematical derivations are established to define and solve the critical problem of the binning effect faced at the experimental assessment level, providing a data platform that preserves its statistical content. In addition, a novel method for accumulating the log-transformed data was developed. This new method uses the properties of the transformation of statistical distributions to accumulate the output histogram in a non-integer and multi-channel fashion. Although the mathematics of this new mapping technique seem intricate, the concise nature of the derivations allow for an implementation procedure that lends itself to a real-time implementation using lookup tables, a task that is also introduced in this dissertation.

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Acknowledgements This paper constitutes an output of the Belmont Forum/FACCE-JPI funded DEVIL project (NE/M021327/1). Financial support from the CGIAR Program on Climate Change, Agriculture and Food Security (CCAFS) and the EU-FP7 AnimalChange project is also recognized. P.K.T. acknowledges the support of a CSIRO McMaster Research Fellowship.

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5 pages, 4 figures