Finite mixture models: visualisation, localised regression, and prediction

Initially, this thesis introduces a new graphical tool, that can be used to summarise data possessing a mixture structure. Computation of the required summary statistics makes use of posterior probabilities of class membership obtained from a fitted mixture model. In this context, both real and simulated data are used to highlight the usefulness of the tool for the visualisation of mixture data in comparison to the use of a traditional boxplot. This thesis uses localised mixture models to produce predictions from time series data. Estimation method used in these models is achieved using a kernel-weighted version of an EM-algorithm: exponential kernels with different bandwidths are used as weight functions. By modelling a mixture of local regressions at a target time point, but using different bandwidths, an informative estimated mixture probabilities can be gained relating to the amount of information available in the data set. This information is given a scale of resolution, that corresponds to each bandwidth. Nadaraya-Watson and local linear estimators are used to carry out localised estimation. For prediction at a future time point, a new methodology of bandwidth selection and adequate methods are proposed for each local method, and then compared to competing forecasting routines. A simulation study is executed to assess the performance of this model for prediction. Finally, double-localised mixture models are presented, that can be used to improve predictions for a variable time series using additional information provided by other time series. Estimation for these models is achieved using a double-kernel-weighted version of the EM-algorithm, employing exponential kernels with different horizontal bandwidths and normal kernels with different vertical bandwidths, that are focused around a target observation at a given time point. Nadaraya-Watson and local linear estimators are used to carry out the double-localised estimation. For prediction at a future time point, different approaches are considered for each local method, and are compared to competing forecasting routines. Real data is used to investigate the performance of the localised and double-localised mixture models for prediction. The data used predominately in this thesis is taken from the International Energy Agency (IEA)

Verification estimates for the construction of Lyapunov functions using meshfree collocation

Lyapunov functions are functions with negative derivative along solutions of a given ordinary differential equation. Moreover, sub-level sets of a Lyapunov function are subsets of the domain of attraction of the equilibrium. One of the numerical construction methods for Lyapunov functions uses meshfree collocation with radial basis functions (RBF). In this paper, we propose two verification estimates combined with this RBF construction method to ensure that the constructed function is a Lyapunov function. We show that this combination of the RBF construction method and the verification estimates always succeeds in constructing and verifying a Lyapunov function for nonlinear ODEs in Rd with an exponentially stable equilibrium

Antiproliferative effect of the Red Sea cone snail, Conus geographus

Purpose: To investigate the antiproliferative effect of the Red Sea cone snail, Conus geographus, against 4 MCF-7 (breast), MDA-MB-231 (epithelial human breast), HepG2 (hepatocellular) and SKOV-3 (ovarian) cancer cell lines. Methods: Extraction of Red Sea cone snail sample with a mixture of CH2Cl2 and CH3OH (1:1, v/v) yielded 0.55 g of a green viscous material. The cytotoxic effects of the organic extract against the cancer cell lines were determined using cell proliferation (MTT) assay, and the half-maximal concentration (IC50) values measured. The effect of the crude extract on the cell cycle of the HepG-2 was determined by flow cytometry. Results: The extract produced significant inhibitory effects against SKOV-3, MDA-MB-231, MCF-7 and HepG2, with IC50 values of 22.7 ± 2.2, 68.7 ± 6.2, 47 ± 4.2 and 19 ± 2.1 μg/mL, respectively. Cell cycle analysis revealed that the extract enhanced accumulation of HepG2 cells in the Go/G1 phase, at a level of 23.4 and 24.1 % at IC50 (19 μg/mL) and ½ IC50 (9.5 μg/mL), respectively, when compared to the untreated cells. Conclusion: These results indicate that C. geographus extract exhibits potent cytotoxic effect against HepG2 cells via a mechanism involving G0/G1 cell cycle arrest. Thus, C. geographus is a potential source of a new anti-cancer agent. Keywords: Conus geographus, Marine invertebrate, HepG2, Antiproliferatio

Grid refinement and verification estimates for the RBF construction method of Lyapunov functions

Lyapunov functions are functions with negative orbital derivative, whose existence guarantee the stability of an equilibrium point of an ODE. Moreover, sub-level sets of a Lyapunov function are subsets of the domain of attraction of the equilibrium. In this thesis, we improve an established numerical method to construct Lyapunov functions using the radial basis functions (RBF) collocation method. The RBF collocation method approximates the solution of linear PDE's using scattered collocation points, and one of its applications is the construction of Lyapunov functions. More precisely, we approximate Lyapunov functions, that satisfy equations for their orbital derivative, using the RBF collocation method. Then, it turns out that the RBF approximant itself is a Lyapunov function. Our main contributions to improve this method are firstly to combine this construction method with a new grid refinement algorithm based on Voronoi diagrams. Starting with a coarse grid and applying the refinement algorithm, we thus manage to reduce the number of collocation points needed to construct Lyapunov functions. Moreover, we design two modified refinement algorithms to deal with the issue of the early termination of the original refinement algorithm without constructing a Lyapunov function. These algorithms uses cluster centres to place points where the Voronoi vertices failed to do so. Secondly, we derive two verification estimates, in terms of the first and second derivatives of the orbital derivative, to verify if the constructed function, with either a regular grid of collocation points or with one of the refinement algorithms, is a Lyapunov function, i.e., has negative orbital derivative over a given compact set. Finally, the methods are applied to several numerical examples up to 3 dimensions

The U -Radius And Hankel Determinant For Analytic Functions, And Product Of Logharmonic Mappings

This thesis studies geometric and analytic properties of complex-valued analytic functions and logharmonic mappings in the open unit disk D. It investigates four research problems. As a precursor to the first, let U be the class consisting of normalized analytic functions f satisfying |(z= f (z))2 f ′(z)−1| 0; or | f (z)=g(z)−1| < 1 in D; for g belonging to a certain class of analytic functions. In most instances, the exact U -radius are found. A recent conjecture by Obradovi´c and Ponnusamy concerning the radius of univalence for a product involving univalent functions is also shown to hold true. The second problem deals with the Hankel determinant of analytic functions. For a normalized analytic function f ; let z f ′(z)= f (z) or 1+z f ′′(z)= f ′(z) be subordinate to a given analytic function φ in D. Further let F be its kth-root transform, that is, F(z) = z[f(zk)=zk]1

Right Ventricle Outflow Obstruction in Biventricular Hypertrophic Cardiomyopathy in Amyloidosis

Light-chain (AL) amyloidosis is the most common type of amyloidosis; cardiac involvement is rare but has a poor prognosis. Biventricular hypertrophic cardiomyopathy is an exceptional finding in amyloidosis and its association with obstructive right ventricular gradient is even rarer. We report the case of a male patient with biventricular hypertrophy suggesting amyloidosis, with an obstructive gradient in the right ventricle

Modified refinement algorithm to construct lyapunov functions using meshless collocation

Contraction analysis considers the distance between two adjacent trajectories. If this distance is contracting, then trajectories have the same long-term behavior. The main advantage of this analysis is that it is independent of the solutions under consideration. Using an appropriate metric, with respect to which the distance is contracting, one can show convergence to a unique equilibrium or, if attraction only occurs in certain directions, to a periodic orbit. Contraction analysis was originally considered for ordinary differential equations, but has been extended to discrete-time systems, control systems, delay equations and many other types of systems. Moreover, similar techniques can be applied for the estimation of the dimension of attractors and for the estimation of different notions of entropy (including topological entropy). This review attempts to link the references in both the mathematical and the engineering literature and, furthermore, point out the recent developments and algorithms in the computation of contraction metrics

Prevalence, Risk Factors and Antibiotic Susceptibility of Urinary Tract Infections among Pregnant Women: A Study in Damt District Yemen

Urinary tract infections are the most common illnesses that impact pregnant women. This study aimed to investigate bacterial urinary tract infections and antibiotic susceptibility profiles in pregnant women. This study was conducted on pregnant women between April and October 2021 in clinics and hospitals in the Damt district. Midstream urine samples were collected, cultured, identified and tested for antibiotic susceptibility. The prevalence of UTI in pregnant women was 210/350 (60%). Escherichia coli accounted for 90/210 (42.9%), Staphylococcus aureus 50/210 (23.8%), and Klebsiella pneumoniae 25/210 (11.9%). Staphylococcus epidermidis, Pseudomonas aeruginosa, and Proteus mirabilis exhibited 15/210 (7.1%) of each with the moderately identified bacterial species. Antimicrobial sensitivity testing showed that bacterial isolates were resistant to amoxicillin (80-100%), ceftriaxone (40-70%), gentamycin (0-60%), amikacin (0-50%), tetracycline, ciprofloxacin, azithromycin, and amoxiclav (0-40%), and azithromycin (0-30%). Significant bacteriuria was associated with age (p = 0.01), pregnancy trimesters (p = 0.00), gestation (p = 0.00), and residence (p = 0.03), whereas there was no association with education (p = 0.05). Most isolates have become resistant toward antibiotic used in the study treatments, especially ceftriaxone and amoxicillin. Therefore, it is recommended that pregnant women undergo health education on the prevalence and causes of urinary tract infections

The Role of HR Practices on Turnover Intentions Directly and Through Organizational Citizenship Behavior in the Banking Sector of Malaysia

In the recent years, the banking industry of Malaysia has grown rapidly and the roles of employees are undeniable. In todays, dynamic environment banking industry is striving hard to retain the employees in the organization. Employee provides the basis for organization to be successful. The aim of this paper was to investigate the role of HR practices on turnover intentions directly and indirectly through organizational citizenship behavior in banking sector of Malaysia. Data collected through 510 questionnaires from top five banks (by Capital) branches in Kuala Lumpur, Malaysia. In order to investigate the hypotheses, this study applied Structural equation modelling (AMOS). Findings of this study portray that HR practices had negative effect on turnover intentions while the interesting finding is that indirect effect of HR practices through organizational citizenship were also significant. The results are beneficial for top management of banking sector of Malaysia in order to keep motivating employees and to retain them through proper implementation of OCB. To build and align the HR practices and OCB which results in reducing turnover intentions of employees. Keywords: HR Practices, Organizational Citizenship Behavior, Turnover Intentions, SEM. JEL Classifications: H11; S12 DOI: https://doi.org/10.32479/irmm.1076