Random propagation in complex systems : nonlinear matrix recursions and epidemic spread

This dissertation studies long-term behavior of random Riccati recursions and mathematical epidemic model. Riccati recursions are derived from Kalman filtering. The error covariance matrix of Kalman filtering satisfies Riccati recursions. Convergence condition of time-invariant Riccati recursions are well-studied by researchers. We focus on time-varying case, and assume that regressor matrix is random and identical and independently distributed according to given distribution whose probability distribution function is continuous, supported on whole space, and decaying faster than any polynomial. We study the geometric convergence of the probability distribution. We also study the global dynamics of the epidemic spread over complex networks for various models. For instance, in the discrete-time Markov chain model, each node is either healthy or infected at any given time. In this setting, the number of the state increases exponentially as the size of the network increases. The Markov chain has a unique stationary distribution where all the nodes are healthy with probability 1. Since the probability distribution of Markov chain defined on finite state converges to the stationary distribution, this Markov chain model concludes that epidemic disease dies out after long enough time. To analyze the Markov chain model, we study nonlinear epidemic model whose state at any given time is the vector obtained from the marginal probability of infection of each node in the network at that time. Convergence to the origin in the epidemic map implies the extinction of epidemics. The nonlinear model is upper-bounded by linearizing the model at the origin. As a result, the origin is the globally stable unique fixed point of the nonlinear model if the linear upper bound is stable. The nonlinear model has a second fixed point when the linear upper bound is unstable. We work on stability analysis of the second fixed point for both discrete-time and continuous-time models. Returning back to the Markov chain model, we claim that the stability of linear upper bound for nonlinear model is strongly related with the extinction time of the Markov chain. We show that stable linear upper bound is sufficient condition of fast extinction and the probability of survival is bounded by nonlinear epidemic map.

Estudo do envelhecimento de poliuretanos aplicados na indústria de petróleo

A indústria do petróleo é um dos setores com maior número de sistemas produtivos empregando alta tecnologia. O Brasil é mundialmente renomado como um líder na extração de petróleo, em águas profundas e ultraprofundas. Dentro da cadeia produtiva, grande parte do petróleo e do gás produzido é escoado através de dutos flexíveis que conectam os poços de produção com as plataformas. Existem dois segmentos dessas linhas que recebem diferentes denominações de acordo com o seu local de aplicação. Quando estão apoiadas sobre o fundo do mar, em condição de serviço estático, são denominados flowlines e quando se elevam do fundo do mar até a plataforma, em condição de serviço dinâmico, são denominados risers. Os tubos projetados para aplicações dinâmicas são dotados de bends stiffeners, componentes com formato cônico e, em geral, de base uretânica que têm a função de fornecer uma transição de rigidez suave entre a estrutura dos tubos flexíveis e a extremamente rígida, à plataforma, não permitindo que este componente infrinja seu raio mínimo de operação. A adequada compreensão dos enrijecedores de curvatura e do material empregado em sua fabricação vem se tornando cada vez mais importante na indústria devido à sua crescente utilização, bem como à ocorrência de falhas que vem sendo constatada nos últimos anos. Este trabalho abordou a variação das propriedades mecânicas de poliuretanos pela ação da hidrólise, calor e pela ação dos raios-UV por envelhecimento acelerado, assim como variação de massa, considerando que esses materiais são projetados para uma vida útil superior a vinte anos para trabalhos imersos em meio aquoso.

Value chain analysis for sea cucumber in the Philippines

This study examined the sea cucumber industry in the Philippines through the value chain lens. The intent was to identify effective pathways for the successful introduction of sandfish culture as livelihood support for coastal communities. Value chain analysis is a high-resolution analytical tool that enables industry examination at a detailed level. Previous industry assessments have provided a general picture of the sea cucumber industry in the country. The present study builds on the earlier work and supplies additional details for a better understanding of the industry's status and problems, especially their implications for the Australian Center for International Agricultural Research (ACIAR) funded sandfish project "Culture of sandfish (Holothuria scabra) in Asia- Pacific" (FIS/2003/059). (PDF contains 54 pages)

Optimized condition for etching fused-silica phase gratings with inductively coupled plasma technology

Polymer deposition is a serious problem associated with the etching of fused silica by use of inductively coupled plasma (ICP) technology, and it usually prevents further etching. We report an optimized etching condition under which no polymer deposition will occur for etching fused silica with ICP technology. Under the optimized etching condition, surfaces of the fabricated fused silica gratings are smooth and clean. Etch rate of fused silica is relatively high, and it demonstrates a linear relation between etched depth and working time. Results of the diffraction of gratings fabricated under the optimized etching condition match theoretical results well. (c) 2005 Optical Society of America.

Paranormal operator on a Hilbert space

In this thesis an extensive study is made of the set P of all paranormal operators in B(H), the set of all bounded endomorphisms on the complex Hilbert space H. T ϵ B(H) is paranormal if for each z contained in the resolvent set of T, d(z, σ(T))//(T-zI)^-1 = 1 where d(z, σ(T)) is the distance from z to σ(T), the spectrum of T. P contains the set N of normal operators and P contains the set of hyponormal operators. However, P is contained in L, the set of all T ϵ B(H) such that the convex hull of the spectrum of T is equal to the closure of the numerical range of T. Thus, N≤P≤L.

If the uniform operator (norm) topology is placed on B(H), then the relative topological properties of N, P, L can be discussed. In Section IV, it is shown that: 1) N P and L are arc-wise connected and closed, 2) N, P, and L are nowhere dense subsets of B(H) when dim H ≥ 2, 3) N = P when dimH ˂ ∞ , 4) N is a nowhere dense subset of P when dimH ˂ ∞ , 5) P is not a nowhere dense subset of L when dimH ˂ ∞ , and 6) it is not known if P is a nowhere dense subset of L when dimH ˂ ∞.

The spectral properties of paranormal operators are of current interest in the literature. Putnam [22, 23] has shown that certain points on the boundary of the spectrum of a paranormal operator are either normal eigenvalues or normal approximate eigenvalues. Stampfli [26] has shown that a hyponormal operator with countable spectrum is normal. However, in Theorem 3.3, it is shown that a paranormal operator T with countable spectrum can be written as the direct sum, N ⊕ A, of a normal operator N with σ(N) = σ(T) and of an operator A with σ(A) a subset of the derived set of σ(T). It is then shown that A need not be normal. If we restrict the countable spectrum of T ϵ P to lie on a C²-smooth rectifiable Jordan curve G_o, then T must be normal [see Theorem 3.5 and its Corollary]. If T is a scalar paranormal operator with countable spectrum, then in order to conclude that T is normal the condition of σ(T) ≤ G_o can be relaxed [see Theorem 3.6]. In Theorem 3.7 it is then shown that the above result is not true when T is not assumed to be scalar. It was then conjectured that if T ϵ P with σ(T) ≤ G_o, then T is normal. The proof of Theorem 3.5 relies heavily on the assumption that T has countable spectrum and cannot be generalized. However, the corollary to Theorem 3.9 states that if T ϵ P with σ(T) ≤ G_o, then T has a non-trivial lattice of invariant subspaces. After the completion of most of the work on this thesis, Stampfli [30, 31] published a proof that a paranormal operator T with σ(T) ≤ G_o is normal. His proof uses some rather deep results concerning numerical ranges whereas the proof of Theorem 3.5 uses relatively elementary methods.

Diet and condition of American Alligators (Alligator mississippiensis)in three central Florida lakes

Understanding the diet of crocodilians is important because diet affects condition, behavior, growth, and reproduction. By examining the diet of crocodilians, valuable knowledge is gained about predator-prey interactions and prey utilization among habitats. In this study, I examined the diet and condition of adult American alligators (Alligator mississippiensis) in three central Florida lakes, Griffin, Apopka, and Woodruff. Two hundred adult alligators were captured and lavaged from March through October 2001, from April through October 2002, and from April through August 2003. Alligators ate a variety of vertebrate and invertebrate prey, but vertebrates were more abundant and fish dominated alligator diets in the lakes. Species composition of fish varied among the lakes. The majority of the diet of alligators from Lakes Apopka and Woodruff was fish, 90% and 84% respectively. Lake Apopka alligators consumed a significantly (P = 0.006) higher proportion of fish in their diet. Fish were 54% of the diet of Lake Griffin alligators and the infrequent occurrence of reptiles, mammals, birds, and amphibians often resulted in a large biomass. Differences in alligator diets among lakes may be due to differences in sample size (higher numbers of samples from Lake Griffin), prey availability, habitat, prey vulnerability, or prey size. Alligator condition (Fulton’s Condition Factor, K) was significantly (P < 0.001) different among the lakes. Alligators from Lake Apopka had the highest condition, followed by those from Lake Griffin, and alligators from Lake Woodruff had the lowest condition. Composition of fish along with diversity and equitability of fish in alligator diets may have contributed to differences in condition among lakes. Condition was probably also due to factors other than diet such as alligator hunting behavior, alligator density, or year-round optimal temperature that prolongs feeding. The observed diet and condition differences probably reflect both habitat differences and prey availability in these three lakes.

Entanglement negativity in the harmonic chain out of equilibrium

We study the entanglement in a chain of harmonic oscillators driven out of equilibrium by preparing the two sides of the system at different temperatures, and subsequently joining them together. The steady state is constructed explicitly and the logarithmic negativity is calculated between two adjacent segments of the chain. We find that, for low temperatures, the steady-state entanglement is a sum of contributions pertaining to left-and right-moving excitations emitted from the two reservoirs. In turn, the steady-state entanglement is a simple average of the Gibbs-state values and thus its scaling can be obtained from conformal field theory. A similar averaging behaviour is observed during the entire time evolution. As a particular case, we also discuss a local quench where both sides of the chain are initialized in their respective ground states.

White spot syndrome virus (WSSV) transmission risk through infected cooked shrimp products assessed by polymerase chain reaction (PCR) and bio-inoculation studies

The aim of the study was to evaluate the resistance of white spot syndrome virus (WSSV) in shrimps (Penaeus monodon) to the process of cooking. The cooking was carried out at 1000C six different durations 5, 10, 15, 20, 25 and 30 min. The presence of WSSV was tested by single step and nested polymerase chain reaction (PCR). In the single step PCR, the primers 1s5 & 1a16 and IK1 & IK2 were used. While in the nested PCR, primers IK1 &IK2 – IK3 & IK4 were used for the detection of WSSV. WSSV was detected in the single step PCR with the primers 1s5 and 1a16 and the nested PCR with the primers IK1 and IK2 – IK3 & IK4 from the cooked shrimp samples. The cooked shrimps, which gave positive results for WSSV by PCR, were further confirmed for the viability of WSSV by conducting the bio-inoculation studies. Mortality (100%) was observed within 123 h of intra-muscular post injection (P.I) into the live healthy WSSV-free shrimps (P. monodon). These results show that the WSSV survive the cooking process and even infected cooked shrimp products may pose a transmission risk for WSSV to the native shrimp farming systems.