Modeling Multivariate Interest Rates Using Time-Varying Copulas and Reducible Nonlinear Stochastic Differential Equations

We propose a new approach for modeling nonlinear multivariate interest rate processes based on time-varying copulas and reducible stochastic differential equations (SDEs). In the modeling of the marginal processes, we consider a class of nonlinear SDEs that are reducible to Ornstein--Uhlenbeck (OU) process or Cox, Ingersoll, and Ross (1985) (CIR) process. The reducibility is achieved via a nonlinear transformation function. The main advantage of this approach is that these SDEs can account for nonlinear features, observed in short-term interest rate series, while at the same time leading to exact discretization and closed-form likelihood functions. Although a rich set of specifications may be entertained, our exposition focuses on a couple of nonlinear constant elasticity volatility (CEV) processes, denoted as OU-CEV and CIR-CEV, respectively. These two processes encompass a number of existing models that have closed-form likelihood functions. The transition density, the conditional distribution function, and the steady-state density function are derived in closed form as well as the conditional and unconditional moments for both processes. In order to obtain a more flexible functional form over time, we allow the transformation function to be time varying. Results from our study of U.S. and UK short-term interest rates suggest that the new models outperform existing parametric models with closed-form likelihood functions. We also find the time-varying effects in the transformation functions statistically significant. To examine the joint behavior of interest rate series, we propose flexible nonlinear multivariate models by joining univariate nonlinear processes via appropriate copulas. We study the conditional dependence structure of the two rates using Patton (2006a) time-varying symmetrized Joe--Clayton copula. We find evidence of asymmetric dependence between the two rates, and that the level of dependence is positively related to the level of the two rates. (JEL: C13, C32, G12) Copyright The Author 2010. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissions@oxfordjournals.org, Oxford University Press.

Weakly nonlinear effects associated with transverse oscillations in dusty plasma crystals

We study the amplitude modulation of transverse dust lattice waves (TDLW) propagating in a single- and double-layer dusty plasma (DP) crystal. It is shown that a modulational instability mechanism, which is related to an intrinsic nonlinearity of the sheath electric field, may occur under certain conditions. Possibility of the formation of localized excitations (envelope solitons) in the dusty plasma crystal is discussed.

Detecting the effects of diversity on measures of ecosystem function: experimental design, null models and empirical observations

Here we present a novel experimental approach to examine the relationship between diversity and ecosystem Function. We develop four null predictive models, with which to differentiate between the 'sampling effect' - the chance inclusion of a highly productive species, and 'species complementarity' - the complementary use of resources by species that differ in their niche or resource use. We investigate the effects of manipulating species and functional richness on ecosystem function in marine benthic system and using empirical data from our own experiments we illustrate the application of these models.

Nonlinear phenomena in multiferroic nanocapacitors:joule heating and electromechanical effects

We demonstrate an approach for probing nonlinear electromechanical responses in BiFeO(3) thin film nanocapacitors using half-harmonic band excitation piezoresponse force microscopy (PFM). Nonlinear PFM images of nanocapacitor arrays show clearly visible clusters of capacitors associated with variations of local leakage current through the BiFeO(3) film. Strain spectroscopy measurements and finite element modeling point to significance of the Joule heating and show that the thermal effects caused by the Joule heating can provide nontrivial contributions to the nonlinear electromechanical responses in ferroic nanostructures. This approach can be further extended to unambiguous mapping of electrostatic signal contributions to PFM and related techniques.

Therapeutic effects of PPARα agonists on diabetic retinopathy in type 1 diabetes models

Retinal vascular leakage, inflammation, and neovascularization (NV) are features of diabetic retinopathy (DR). Fenofibrate, a peroxisome proliferator-activated receptor a (PPARa) agonist, has shown robust protective effects against DR in type 2 diabetic patients, but its effects on DR in type 1 diabetes have not been reported. This study evaluated the efficacy of fenofibrate on DR in type 1 diabetes models and determined if the effect is PPARa dependent. Oral administration of fenofibrate significantly ameliorated retinal vascular leakage and leukostasis in streptozotocin-induced diabetic rats and in Akita mice. Favorable effects on DR were also achieved by intravitreal injection of fenofibrate or another specific PPARa agonist. Fenofibrate also ameliorated retinal NV in the oxygen-induced retinopathy (OIR) model and inhibited tube formation and migration in cultured endothelial cells. Fenofibrate also attenuated overexpression of intercellular adhesion molecule-1, monocyte chemoattractant protein-1, and vascular endothelial growth factor (VEGF) and blocked activation of hypoxia-inducible factor-1 and nuclear factor-?B in the retinas of OIR and diabetic models. Fenofibrate's beneficial effects were blocked by a specific PPARa antagonist. Furthermore, Ppara knockout abolished the fenofibrate-induced downregulation of VEGF and reduction of retinal vascular leakage in DR models. These results demonstrate therapeutic effects of fenofibrate on DR in type 1 diabetes and support the existence of the drug target in ocular tissues and via a PPARa-dependent mechanism.

Synergistic effects of proteasome inhibitor carfilzomib in combination with tyrosine kinase inhibitors in imatinib-sensitive and -resistant chronic myeloid leukemia models

The tyrosine kinase inhibitor (TKI) imatinib has transformed the treatment and outlook of chronic myeloid leukemia (CML); however, the development of drug resistance and the persistence of TKI-resistant stem cells remain obstacles to eradicating the disease. Inhibition of proteasome activity with bortezomib has been shown to effectively induce apoptosis in TKI-resistant cells. In this study, we show that exposure to the next generation proteasome inhibitor carfilzomib is associated with a decrease in ERK signaling and increased expression of Abelson interactor proteins 1 and 2 (ABI-1/2). We also investigate the effect of carfilzomib in models of imatinib-sensitive and -resistant CML and demonstrate a potent reduction in proliferation and induction of apoptosis in a variety of models of imatinib-resistant CML, including primitive CML stem cells. Carfilzomib acts synergistically with the TKIs imatinib and nilotinib, even in imatinib-resistant cell lines. In addition, we found that the presence of immunoproteasome subunits is associated with an increased sensitivity to carfilzomib. The present findings provide a rational basis to examine the potential of carfilzomib in combination with TKIs as a potential therapy for CML, particularly in imatinib-resistant disease.

The organizational ecology of ethnic cleavages: The nonlinear effects of ethnic diversity on party system fragmentation

The conventional wisdom regarding party system fragmentation assumes that the effects of electoral systems and social cleavages are linear. However, recent work applying organizational ecology theories to the study of party systems has challenged the degree to which electoral system effects are linear. This paper applies such concepts to the study of social cleavages. Drawing from theories of organizational ecology and the experience of many ethnically diverse African party systems, I argue that the effects of ethnic diversity are nonlinear, with party system fragmentation increasing until reaching moderate levels of diversity before declining as diversity reaches extreme values. Examining this argument cross-nationally, the results show that accounting for nonlinearity in ethnic diversity effects significantly improves model fit.

Pressure anisotropy effects on nonlinear electrostatic excitations in magnetized electron-positron-ion plasmas

The propagation of linear and nonlinear electrostatic waves is investigated in a magnetized anisotropic electron-positron-ion (e-p-i) plasma with superthermal electrons and positrons. A two-dimensional plasma geometry is assumed. The ions are assumed to be warm and anisotropic due to an external magnetic field. The anisotropic ion pressure is defined using the double adiabatic Chew-Golberger-Low (CGL) theory. In the linear regime, two normal modes are predicted, whose characteristics are investigated parametrically, focusing on the effect of superthermality of electrons and positrons, ion pressure anisotropy, positron concentration and magnetic field strength. A Zakharov-Kuznetsov (ZK) type equation is derived for the electrostatic potential (disturbance) via a reductive perturbation method. The parametric role of superthermality, positron content, ion pressure anisotropy and magnetic field strength on the characteristics of solitary wave structures is investigated. Following Allen and Rowlands [J. Plasma Phys. 53, 63 (1995)], we have shown that the pulse soliton solution of the ZK equation is unstable to oblique perturbations, and have analytically traced the dependence of the instability growth rate on superthermality and ion pressure anisotropy.

Outlier effects on robust joint modelling of longitudinal and survival data

Robust joint modelling is an emerging field of research. Through the advancements in electronic patient healthcare records, the popularly of joint modelling approaches has grown rapidly in recent years providing simultaneous analysis of longitudinal and survival data. This research advances previous work through the development of a novel robust joint modelling methodology for one of the most common types of standard joint models, that which links a linear mixed model with a Cox proportional hazards model. Through t-distributional assumptions, longitudinal outliers are accommodated with their detrimental impact being down weighed and thus providing more efficient and reliable estimates. The robust joint modelling technique and its major benefits are showcased through the analysis of Northern Irish end stage renal disease patients. With an ageing population and growing prevalence of chronic kidney disease within the United Kingdom, there is a pressing demand to investigate the detrimental relationship between the changing haemoglobin levels of haemodialysis patients and their survival. As outliers within the NI renal data were found to have significantly worse survival, identification of outlying individuals through robust joint modelling may aid nephrologists to improve patient's survival. A simulation study was also undertaken to explore the difference between robust and standard joint models in the presence of increasing proportions and extremity of longitudinal outliers. More efficient and reliable estimates were obtained by robust joint models with increasing contrast between the robust and standard joint models when a greater proportion of more extreme outliers are present. Through illustration of the gains in efficiency and reliability of parameters when outliers exist, the potential of robust joint modelling is evident. The research presented in this thesis highlights the benefits and stresses the need to utilise a more robust approach to joint modelling in the presence of longitudinal outliers.