Transient solution of the M/Ek/1 queueing system

In this thesis, the Erlang queueing model Af/i/l, where customers arrive at random mean rate A and service times have an Erlang distribution with parameter k and iro service rate u, has been considered from different perspectives. Firstly, an analytic metl of obtaining the time-dependent probabilities, pn,,(() for the M/Ek/l system have t> proposed in terms of a new generalisation of the modified Bessel function when initk there are no customers in the system. Results have been also generalised to the case wl initially there are a customers in the system. Secondly, a new generalisation of the modified Bessei function and its generating function have been presented with its main properties and relations to other special functii (generalised Wright function and Mittag-Leffler function) haw been noted. Thirdly, the mean waiting tune in the queue, H',(f), has been evaluated, using Lucha results. The double-exponential approximation of computing Yq(t) has been proposed different values of p. which gives results within about % of the 'exact1 values obtained fr numerical solution of the differential-difference equations. The advantage of this approximation is that it provides additional information, via its functional form of the characterisl of the transient solution. Fourthly, the inversion of the Laplace transform with the application to the queues 1 been studied and verified for A//A//1 and M/Ek/l models of computing Wq{t}. Finally, an application of the A//fi/l queue has been provided in the example of hour traffic flow for the Severn Bridge. One of the main reasons for studying queue models from a theoretical point of view is to develop ways of modelling real-life system. The analytic results have been confirmed with the simulation

Numerical approximation of high-dimensional Fokker-Planck equations with polynomial coefficients

This paper is concerned with the numerical solution of high-dimensional Fokker- Planck equations related to multi-dimensional diffusion with polynomial coefficients or Pearson diffusions. Classification of multi-dimensional Pearson diffusion follows from the classification of one-dimensional Pearson diffusion. There are six important classes of Pearson diffusion - three of them possess an infinite system of moments (Gaussian, Gamma, Beta) while the other three possess a finite number of moments (inverted Gamma, Student and Fisher-Snedecor). Numerical approximations to the solution of the Fokker-Planck equation are generated using the spectral method. The use of an adaptive reduced basis technique facilitates a significant reduction in the number of degrees of freedom required in the approximation through the determination of an optimal basis using the singular value decomposition (SVD). The basis functions are constructed dynamically so that the numerical approximation is optimal in the current finite-dimensional subspace of the solution space. This is achieved through basis enrichment and projection stages. Numerical results with different boundary conditions are presented to demonstrate the accuracy and efficiency of the numerical scheme

Determination of Fenspiride Hydrochloride Residues on Pharmaceutical Manufacturing Equipment Surfaces by HPLC Method

The cleaning procedure must be validated, so special attention must be devoted to the methods used for determination of trace amounts of drugs. A rapid, sensitive, and specific reverse phase high-performance liquid chromatographic (HPLC) method was developed for the quantitative determination of fenspiride hydrochloride residues on pharmaceutical manufacturing equipment surfaces. The calibration curve was linear over a concentration range from 1.0 to 100.0 μg/ml with a correlation coefficient of 0.99994. The detection limit and quantitation limit were 0.41 μg/ml and 1.25 μg/ml, respectively. The developed method was validated with respect to specificity, linearity, limit of detection, accuracy and precision

Genetic analysis suggests high misassignment rates in clinical Alzheimer's cases and controls

Genetic case-control association studies are often based on clinically ascertained cases and population or convenience controls. It is known that some of the controls will contain cases, as they are usually not screened for the disease of interest. However, even clinically assessed cases and controls can be misassigned. For Alzheimer's disease (AD), it is important to know the accuracy of the clinical assignment. The predictive accuracy of AD risk by polygenic risk score analysis has been reported in both clinical and pathologically confirmed cohorts. The genetic risk prediction can provide additional insights to inform classification of subjects to case and control sets at a preclinical stage. In this study, we take a mathematical approach and aim to assess the importance of a genetic component for the assignment of subjects to AD-positive and -negative groups, and provide an estimate of misassignment rates (MARs) in AD case/control cohorts accounting for genetic prediction modeling results. The derived formulae provide a tool to estimate MARs in any sample. This approach can also provide an estimate of the maximal and minimal MARs and therefore could be useful for statistical power estimation at the study design stage. We illustrate this approach in 2 independent clinical cohorts and estimate misdiagnosis rate up to 36% in controls unscreened for the APOE genotype, and up to 29% when E3 homozygous subjects are used as controls in clinical studies

Age-dependent effect of APOE and polygenic component on Alzheimer's disease

Alzheimer’s disease (AD) is a devastating neurodegenerative condition with significant genetic heritability. Several genes have been implicated in the onset of AD with the apolipoprotein E (APOE) gene being the strongest single genetic risk loci. Evidence suggests that the effect of APOE alters with age during disease progression. Here, we aim to investigate the impact of APOE and other variants outside the APOE region on AD risk in younger and older participants. Using data from both the Alzheimer’s Disease Neuroimaging Initiative (ADNI) and the UK Biobank (UKBB) we computed the polygenic risk score (PRS) of each individual informed by the latest genetic study from the International Genomics of Alzheimer’s Project (IGAP). Our analysis showed that the effect of APOE on the disease risk is greater in younger participants and reduces as participant age increases. Our findings indicate the increased impact of PRS as participant age increases. Therefore, AD in older individuals can potentially be triggered by the cumulative effect of genes which are outside the APOE region

Defining functional variants associated with Alzheimer's disease in the induced immune response

Defining the mechanisms involved in the aetiology of Alzheimer’s disease from genome-wide association studies alone is challenging since Alzheimer’s disease is polygenic and most genetic variants are non-coding. Non-coding Alzheimer’s disease risk variants can influence gene expression by affecting miRNA binding and those located within enhancers and within CTCF sites may influence gene expression through alterations in chromatin states. In addition, their function can be cell-type specific. They can function specifically in microglial enhancers thus affecting gene expression in the brain. Hence, transcriptome-wide association studies have been applied to test the genetic association between disease risk and cell-/tissue-specific gene expression. Many Alzheimer’s disease-associated loci are involved in the pathways of the innate immune system. Both microglia, the primary immune cells of the brain, and monocytes which can infiltrate the brain and differentiate into activated macrophages, have roles in neuroinflammation and β‐amyloid clearance through phagocytosis. In monocytes the function of regulatory variants can be context-specific after immune stimulation. To dissect the variants associated with Alzheimer’s disease in the context of monocytes, we utilized data from naïve monocytes and following immune stimulation in vitro, in combination with genome-wide association studies of Alzheimer’s disease in transcriptome-wide association studies. Of the nine genes with statistically independent transcriptome-wide association signals, seven are located in known Alzheimer’s disease risk loci: BIN1, PTK2B, SPI1, MS4A4A, MS4A6E, APOE and PVR. The transcriptome-wide association signal for MS4A6E, PTK2B and PVR and the direction of effect replicated in an independent genome-wide association studies. Our analysis identified two novel candidate genes for Alzheimer’s disease risk, LACTB2 and PLIN2/ADRP. LACTB2 replicated in a transcriptome-wide association study using independent expression weights. LACTB2 and PLIN2/ADRP are involved in mitochondrial function and lipid metabolism, respectively. Comparison of transcriptome-wide association study results from monocytes, whole blood and brain showed that the signal for PTK2B is specific to blood and MS4A6E is specific to LPS stimulated monocytes

Downregulation of Dickkopf-3, a Wnt antagonist elevated in Alzheimer’s disease, restores synapse integrity and memory in a disease mouse model

Increasing evidence supports a role for deficient Wnt signaling in Alzheimer’s disease (AD). Studies reveal that the secreted Wnt antagonist Dickkopf-3 (DKK3) colocalizes to amyloid plaques in AD patients. Here, we investigate the contribution of DKK3 to synapse integrity in healthy and AD brains. Our findings show that DKK3 expression is upregulated in the brains of AD subjects and that DKK3 protein levels increase at early stages in the disease. In hAPP-J20 and hAPPNL-G-F/NL-G-F mouse AD models, extracellular DKK3 levels are increased and DKK3 accumulates at dystrophic neuronal processes around plaques. Functionally, DKK3 triggers the loss of excitatory synapses through blockade of the Wnt/GSK3β signaling with a concomitant increase in inhibitory synapses via activation of the Wnt/JNK pathway. In contrast, DKK3 knockdown restores synapse number and memory in hAPP-J20 mice. Collectively, our findings identify DKK3 as a novel driver of synaptic defects and memory impairment in AD

Cognitive decline in Alzheimer’s disease is not associated with APOE

Background:The rate of cognitive decline in Alzheimer’s disease (AD) has been found to vary widely between individuals, with numerous factors driving this heterogeneity. Objective:This study aimed to compute a measure of cognitive decline in patients with AD based on clinical information and to utilize this measure to explore the genetic architecture of cognitive decline in AD. Methods:An in-house cohort of 616 individuals, hereby termed the Cardiff Genetic Resource for AD, as well as a subset of 577 individuals from the publicly available ADNI dataset, that have been assessed at multiple timepoints, were used in this study. Measures of cognitive decline were computed using various mixed effect linear models of Mini-Mental State Examination (MMSE). After an optimal model was selected, a metric of cognitive decline for each individual was estimated as the random slope derived from this model. This metric was subsequently used for testing the association of cognitive decline with apolipoprotein E (APOE) genotype. Results:No association was found between the number of APOE ɛ2 or ɛ4 alleles and the rate of cognitive decline in either of the datasets examined. Conclusion:Further exploration is required to uncover possible genetic variants that affect the rate of decline in patients with AD

Genetic risk for Alzheimer's disease is distinct from genetic risk for amyloid deposition

Objectives Alzheimer's disease (AD) is the most common form of dementia and is responsible for a huge and growing health care burden in the developed and developing world. The Polygenic Risk Score (PRS) approach has shown 75%‐84% prediction accuracy of identifying individuals with AD risk. Methods In this study we tested the prediction accuracy of AD, MCI and amyloid deposition risks with PRS, including and excluding APOE genotypes in a large publicly available data set with extensive phenotypic data: the Alzheimer's Disease Neuroimaging Initiative cohort. Among MCI individuals with amyloid positive status we examined PRS prediction accuracy in those who converted to AD. In addition, we divided polygenic risk score by biological pathways and tested them independently for distinguishing between AD, MCI and amyloid deposition. Results We found that AD and MCI are predicted by both APOE genotype and PRS (AUC=0.82% and 68%, respectively). Amyloid deposition is predicted by APOE only (AUC=79%). Further progression to AD of individuals with MCI and amyloid positive status is predicted by PRS over and above APOE (AUC=67%)

Investigation of relationships between bipolar disorder phenotypes and genome-wide significant loci from PGC2 schizophrenia

Background Schizophrenia (SZ) and Bipolar disorder (BD) show evidence for partial overlap in phenotypic and genetic influences based on family, twins, adoption and Psychiatric Genetic Consortium (PGC) studies. They have lifetime prevalence of about 1% and 2.4%, and heritability estimates of 60-80% and 40-70%, respectively. In the last decade BD has been investigated using dimensional structuring of psychoses based on symptomatic-functional checklists that provides reliable approach to phenotypic assessment. Recent research suggests moving towards developing Phenotype-based Genetic Association Studies. In this approach, patients will only be put into groups consisting of others with symptoms similar to their own. Canonical Correlation Analysis (CCA) is statistical technique designed to identify relationships (usually hidden) between two sets of variables. We use CCA to combine genotypic and phenotypic variables and measure correlation between those sets. This analysis estimates canonical correlation between psychotic symptoms measured using validated item check list (OPCRIT), and genome-wide significant (GWS) loci from PGC2 schizophrenia. Methods For our analysis we used phenotype and genetic data for 5,507 BD cases. Imputation of genetic data was performed with 1000Genomes (Phase 3, 2014) then quality control was applied (INFO>0.8, HWE>1e-6, MAF>0.01). Additional quality control was performed on phenotypic symptom coverage. CCA was employed as implemented in R, using package “CCA” with GWS loci from PGC2 SZ and OPCRIT items. SNPs were standardised and adjusted for 10 population covariates calculated from imputed data using principal component approach prior to CCA. Results Canonical correlation analysis was run on 4422 cases on 89 available GWS PGC2 SZ SNPs or their proxies (with r2>0.6). 60 phenotypic variables were taken from OPCRIT measurements including mood disturbance, biological indices, atypical depression, substance use, psychosis and social functioning. We found no significant canonical correlations indicating absence of hidden sub-clusters at individual symptom level of BD associated with SZ GWS loci. Discussion Our analysis was focused to find correlation from bipolar phenotype by using OPCRIT questionnaire and GWS SZ loci from PGC2. We have shown that there were no significant canonical correlation coefficients suggesting that there is no direct association between SZ associated genetic loci and BP at individual symptom level. CCA is canonical correlation analysis is one of potential of data-driven approaches to identify hidden genotype-phenotype relationships. It provides opportunities to generate and test different hypotheses and understand more about complex architecture of psychiatric disorders. In the next stage we plan to extend our analysis to more fine grained systematic descriptors of BD and test for correlation with genetic profiles from a number of co-morbid disorders, as well as the full range of phenotypic and genetic data that are available