Covering maps and fibrations of spaces fulfilling certain technical conditions are known to satisfy a multiplicative formula relating the Euler characteristic of the domain to that of the codomain. An open question posed by Albrecht Dold in 1980 asks in general when this is true and can be stated as: for which classes of maps is it true that if χ(X) denotes the Euler characteristic of a space X, and if f : X → Y has the property that the Euler characteristic of the preimage of y is k for all y ∈ Y and for some integer k, the multiplicative formula χ(X) = k · χ(Y ) holds? A corroborative answer is given herein for simplicial maps of finite simplicial complexes, while counterexamples are constructed for cellular maps of finite CW complexes, continuous maps of closed topological manifolds, and even smooth maps of smooth manifolds. / 1 / Kelley Brook Johnson

Neointimal proliferation is a key process underlying many cardiovascular diseases such as atherosclerosis and angioplasty-induced restenosis. Vascular smooth muscle cells (SMC) are significant contributors to the development and stability of the neointimal lesion. This is due, in part, to their capacity to be phenotypically modulated, facilitating SMC proliferation in response to mechanical injury, their subsequent migration, and deposition of extracellular matrix. The aim of this thesis was to characterize the function of two genes identified in our laboratory to be upregulated shortly after mechanical injury of vascular SMC and their exposure to fibroblast growth factor (FGF)-2, an injury-induced cytokine. The first is activation transcription factor (ATF) 4, which is upregulated by FGF-2 and mechanical injury in vascular SMC in vitro, and by balloon-injury in the artery wall. The induction of ATF4 by FGF-2 was shown to be mediated through the PI3K pathway, and preceded by phoshorylation of eIF2alpha, a known upstream effector of ATF4 activation. Knock-down of ATF4 expression inhibited balloon-injury induced neointimal hyperplasia, suggesting that ATF4 is a key player in the SMC response to injury. Furthermore, microarray analysis identified several genes whose transcription in response to FGF-2 may be regulated by ATF4. In particular, this work demonstrates that ATF4 is necessary for VEGF-A upregulation in SMC in response to FGF-2 and mechanical injury in vitro and in the artery wall following balloon-injury. The second is a translation factor, YrdC203. Using confocal fluorescence microscopy, YrdC203 was found to localize partially to the ER, and with RPL12, a component of the 60S ribosomal subunit. Immunoprecipitation studies demonstrate that YrdC203 also interacts with an initiation factor, eIF5B. Mutation of an initiation factor’s signature on the exterior of YrdC203 perturbed its interaction with RPL12 and eIF5B, and inhibited the increase in protein synthesis observed with overexpression of YrdC203. This implicates YrdC203 as a translation factor responsible for ensuring protein synthesis in vascular SMC in response to injury. The present work provides evidence for new molecular mechanisms, transcriptional and translational, regulating the response of vascular SMC to injury. This would provide leads for future therapeutic targets.

The exchange rate target zone has been paid much attention in the early 1990 initially by Krugman (1991).It expressed when exchange rate surpasses the band of exchange rate that implicitly or explicitly determined by the central bank, the central Bank will intervene the foreign exchange by buying or selling foreign exchange to ensure the exchange rate staying inside the band, otherwise, the exchange rate will be allowed to fluctuate inside the band freely.According to Krugman (1991), when economic system faces random disturbances, the exchange rate target zone regime is helpful to narrow down the exchange rate volatility contrast to that in the floating exchange rate regime. That is, the exchange rate target zone has more essential stability,which is called ``honeymoon effect". In recent decade, Krugman's exchange rate target zone model has been tested empirically.In this thesis, the smooth transition autoregression with target zone (STARTZ) proposed originally by Lundbergh and Ter"{a}svirta (2006) and logistic smooth transition regression with two thresholds (LSTR2) are used to make comparisons for in-sample fitness and out-of-sample forcastability.Furthermore, we also test two important assumptions of the exchange rate target zone model: the credibility assumption and marginal interventions. The data are constructed with 755 daily spot exchange rates, denominated in Eurpean Currency Unit (ECU), from January 14, 1987 to December 29, 1989, in German, France, and Italy.We split the sample into in-sample (570 observations), and out-of-sample (185 observations), and make use of STARTZ-GARCH and LSTR2-STGARCH to fit the in-sample regimes, and apply Rapach and Wohard (2006)'s Bootstapping to generate the out-of-sample forecasts. Finally,we make use of Diebold and Mariano (1995)'s predictive accuracy tests to compare the out-of-sample forecastability between STARTZ and LSTR2 models.According to the empirical results, we can find that LSTR2 model has not bad performance in fitting the in-sample and forecasting the out-of-sample data compared to STARTZ model.

Cerebrovascular disease continues to be responsible for significant morbidity and mortality. There is a pressing need to better understand the biomechanics of both intracranial arteries and the extracranial arteries that feed these vessels. Histology and immunohistochemistry were performed on basilar and carotid arteries and elucidated their structural differences. Nonlinear optical microscopy (NLOM) provided collagen fiber orientation and distribution, which offered motivation for a more microstructrually-based model. Biaxial testing was performed on acute basilar and carotid arteries and cultured basilar arteries. We used a validated 2D, four fiber family constitutive relation to model passive biaxial stress-stretch behaviors of basilar and common carotid arteries, and we developed a new relation to model their active biaxial responses. Residual stress information from opening angles and collagen fiber orientation were used to create a 3D fiber distribution constitutive relation. Passive biaxial stress-stretch behavior of basilar arteries was modeled with the 3D fiber distribution constitutive relation and was combined with our new active relation to model the active response of basilar arteries. These data and 2D, four fiber family and active constitutive relation allow the first full comparison of circumferential and axial biomechanical behaviors between a muscular (basilar) and an elastic (carotid) artery from the same species. Our active model describes the responses by both types of vessels to four doses of the vasoconstrictor endothelin-1 (10^-10, 10^-9, 10^-8, 10^-7 M) and predicts levels of smooth muscle activation associated with basal tone under specific in vitro testing conditions. Cultured arteries revealed smooth muscle tone is necessary for vascular remodeling. Our 3D model allowed for the calculation of stress through the wall in passive basilar arteries. These results advance our understanding of the biomechanics of intracranial and extracranial arteries, which is needed to understand better their differential responses to similar perturbations in hemodynamic loading.

Recent advances in Wireless Mesh Networks (WMNs) have overcome the drawbacks of traditional wired networks and wireless ad hoc networks. WMNs will play a leading role in the next generation of networks, and the question of how to provide smooth mobility for WMNs is the driving force behind the research. The inherent characteristics of WMNs, such as relatively static backbones and highly mobile clients, require new handoff management solutions to be designed and implemented. This thesis first presents our research work on handoff management schemes in traditional WMNs. In general, a handoff process includes two parts, the MAC layer handoff and the network layer handoff. For the MAC layer handoff, a self-configured handoff scheme with dynamic adaptation is presented. Before the mobile node starts the probe process, it configures parameters for each channel to optimize the scan process. Moreover, a fast authentication scheme to reduce authentication latency for WiFi-based mesh networks is introduced. A tunnel is introduced to forward data packets between the new access router and the original reliable access router to recover data communication before the complete authentication process is finished. To minimize the network layer handoff latency, a hybrid routing protocol for forwarding packets is proposed: this involves both the link layer routing and the network layer routing. Based on the hybrid routing protocol, both intra-domain and inter-domain handoff management have been designed to support smooth roaming in WMNs. In addition, we extend our work to Vehicular Mesh Networks (VMNs). Considering the characteristics of VMNs, a fast handoff scheme is introduced to reduce handoff latency by using a multi-hop clustering algorithm. Using this scheme, vehicle nodes are divided into different multi-hop clusters according to the relative mobility. Some vehicle nodes are selected as assistant nodes; and these assistant nodes will help the cluster head node to determine the next access router for minimizing handoff latency. Extensive simulation results demonstrate that the proposed scheme can reduce handoff latency significantly.

A numerical method commonly referred to as smooth particle hydrodynamics (SPH) is implemented in two dimensions for solid mechanics in general and fracture mechanics in particular. The implementation is tested against a few analytical cases: a vibrating plate, a bending plate, a modus I crack and a modus II crack. A conclusion of these tests is that a better way of treating a shortcoming of SPH called tensile instability is needed. A study is made on the best choice of a vital parameter called the smoothing radius, and it is found that a good choice of the smoothing radius is roughly 1.5 times the initial particle spacing.

Let X. Y be compact Hausdorff spaces, and E, F be Banach spaces. A linear map T¡GC (X¡AE)¡÷C (Y¡AF) is separating if ¡üTf(y)¡ü¡üTg(y)¡ü¡×0 whenever ¡üf(x)¡ü¡üg(x)¡ü¡×0, for every x belonging to X, y belonging to Y. Gau, Jeang and Wong prove that a biseparating linear bijection T is a weighted composition oprator Tf¡×hf¡³£p where h is a function from Y into the set of inveritable linear operators from E onto F and £p is a homeomorphism from Y onto X. In this thesis, we extend this result to the case that continuous functions are defined to a locally compact Hausdorff space, which is either £m-compact or first countable. Moreover, we give a short proof of a recent result of Mrcun. Finally, we give an alternative approach to an Araujo's result concerning biseparating maps of smooth functions appeared in Adv. Math.

As the mobile communication devices become popular, getting the location data of various objects is more convenient than before. Mobile groups that exhibit spatial and temporal proximities can be used for marketing, criminal detection, and ecological studies, just to name a few. Although nowadays the most advanced position equipments are capable of achieving a high accuracy with the measurement error less than 10 meters, they are still expensive. Positioning equipments using different technologies incur different amount of measurement errors ranging from 10 meters to a few hundred meters. In this thesis, we examine the impact of measurement errors on the accuracy of identified valid mobile groups and apply Kalman Filter and RTS smoothing as the one-way and two-way correction to correct the measurement data. In most settings, the corrected location data yield more accurate valid mobile groups. However, when the measurement error is small and users do not make abrupt change in their speed, mining mobile groups directly on the measurement data, however, yield better results.

Thesis (M. Phil.)--University of Hong Kong, 2001. / Includes bibliographical references (leaves 134-145).

Thesis (Ph.D.)--Virginia Commonwealth University, 2009. / Prepared for: Dept. of Mechanical Engineering. Title from title-page of electronic thesis. Bibliography: leaves 98-106.