In this paper, we focus on the goodness of fit test for self-similar property of two well-known processes: the fractional Brownian motion and the fractional autoregressive integrated moving average process. The Hurst parameter of the self-similar process is estimated by the embedding branching process method proposed by Jones and Shen (2004). The goodness of fit test for self-similarity is based on the Pearson chi-square test statistic. We approximate the null distribution of the test statistic by a scaled chi-square distribution to correct the size bias problem of the conventional chi-square distribution. The scale parameter and degrees of freedom of the test statistic are determined via regression method. Simulations are performed to show the finite sample size and power of the proposed test. Empirical applications are conducted for the high frequency financial data and human heart rate data.

Quantum coherence and interference(QCI) effects have been studied for decades and are widely exploited in many areas. For media with QCI effect, the optical properties can change drastically, which leads to many interesting effects, such as coherent population trapping, electromagnetically induced transparency(EIT), lasing without population inversion(LWI) and so on. We have theoretically studied the pulsed regime of EIT. In particular, simulations of propagation of gaussian and 0 - pi co-propagating laser pulses in a medium consisting of 3-level Lambda-atoms have been performed. It has been found that, even at the two-photon resonance, the length of propagation for the 0 - pi pulses is much smaller than that for the Gaussian probe pulses. We explained such a behavior using the dark and bright basis and the dressed state basis. Some possible applications are discussed. We also investigated the collision-induced coherence of two decay channels along two optical transitions. Quantum interference will suppress the spontaneous emission. The degree of this suppression is measured by the branch ratio of these two transitions. Our preliminary calculations show that a significant decrease of the branching ratio with increase of electron densities is reproduced in the theory. We have developed a new variant of Raman spectroscopy with shaped femtosecond pulses. It has several advantages to be applied in multiscatterd media. It is based on change of the spectra of femtopulses due to Raman scattering (stimulated or coherent). The technique can be used for a broad range of applications from atomic and molecular optical and IR spectroscopy to spore detection and tissue microscopy. Finally, we have shown that Fano interference in the decay channels of three levels system can lead to considerably different absorption and emission profiles. We found that a coherence can be built up in the ground state doublet whose strength depends on a coupling parameter that arises from Fano interference. This can in principle lead to breaking of the detail balance between the absorption and emission processes in atomic systems.

1 x N optical power splitters using hybrid sol-gel glasses based on buried waveguide structure on silicon substrate were fabricated. The advantage over conventional ridge structures is the fact that Y branch of the splitters can be easily obtained with the buried structure using standard photo lithography processes. Now we can successfully make the width of Y branch of less of 1um. Proximity printing was used to define the waveguide trench on sol-gel films. Then burying the sol-gel glass into the trench to define waveguide core. Finally the waveguide was packaged for measurement after coating a sol-gel top cladding layer onto the guiding layer. The propagation losses of this waveguide device are 0.69 dB/cm and 0.70 dB/cm for TE and TM polarized lights. The coupling losses are 1.57 dB and 1.89 dB for TE and TM lights with a index contrast of 0.66 %. The insertion loss and the branching loss of the 1¡Ñ2 splitter are 5.7 dB and 0.3 dB¡Arespectively.

Open Access Article

In this thesis, we use multitype Galton-Watson branching processes in random environments as individual-based models for the evolution of structured populations with both demographic stochasticity and environmental stochasticity, and investigate the phenotype allocation problem. We explore a variational characterization for the stochastic evolution of a structured population modeled by a multitype Galton-Watson branching process. When the population under consideration is large and the time scale is fast, we deduce the continuous approximation for multitype Markov branching processes in random environments. Many problems in evolutionary biology involve the allocation of some limited resource among several investments. It is often of interest to know whether, and how, allocation strategies can be optimized for the evolution of a structured population with randomness. In our work, the investments represent different types of offspring, or alternative strategies for allocations to offspring. As payoffs we consider the long-term growth rate, the expected number of descendants with some future discount factor, the extinction probability of the lineage, or the expected survival time. Two different kinds of population randomness are considered: demographic stochasticity and environmental stochasticity. In chapter 2, we solve the allocation problem w.r.t. the above payoff functions in three stochastic population models depending on different kinds of population randomness. Evolution is often understood as an optimization problem, and there is a long tradition to look at evolutionary models from a variational perspective. In chapter 3, we deduce a variational characterization for the stochastic evolution of a structured population modeled by a multitype Galton-Watson branching process. In particular, the so-called retrospective process plays an important role in the description of the equilibrium state used in the variational characterization. We define the retrospective process associated with a multitype Galton-Watson branching process and identify it with the mutation process describing the type evolution along typical lineages of the multitype Galton-Watson branching process. Continuous approximation of branching processes is of both practical and theoretical interest. However, to our knowledge, there is no literature on approximation of multitype branching processes in random environments. In chapter 4, we firstly construct a multitype Markov branching process in a random environment. When conditioned on the random environment, we deduce the Kolmogorov equations and the mean matrix for the conditioned branching process. Then we introduce a parallel mutation-selection Markov branching process in a random environment and analyze its instability property. Finally, we deduce a weak convergence result for a sequence of the parallel Markov branching processes in random environments and give examples for applications.

The aim with this study was to develop a method to estimate total area of hair lichens and to compare morphological traits and water storage in them. Hair lichens are an important component of the epiphytic flora in boreal forests. Their growth is primarily regulated by available water, and light when hydrated. Lichens have no active mechanism to regulate their water content and their water holding capacity (WHC, mg H2O/cm2) is thus an important factor for how long they remain wet and metabolically active. In this study, the water uptake and loss in five hair lichens (Alectoria sarmentosa, three Bryoria spp. and Usnea dasypoga) were compared. Their area were estimated by combining photography, scanning and a computer programme that estimates the area of objects. Total area overlap of individual branches was calculated for each species, to estimate total area of the lichen. WHC and specific thallus mass (STM) (mg DM/cm2) of the lichens were calculated. Bryoria spp. had a significantly lower STM compared to U. dasypoga and A. sarmentosa, due to its thinner branches and higher branch density. Bryoria also had a lower WHC compared to A. sarmentosa, promoting a rapid uptake and loss of water. All species had a significant relationship between STM and WHC, above a 1:1 line for all species except U. dasypoga. The lower relationship in U. dasypoga is explained by its less developed branching in combination with its thick branches.

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Biennial bearing, low precocity, and vigorous vegetative growth are major production constraints of ‘Northern Spy’ apple trees. Experiments were conducted in bearing and non-bearing ‘Northern Spy’/M.9 orchards to determine whether plant bioregulator applications of ethephon (ETH), napthaleneacetic acid (NAA), prohexadione-calcium (P-Ca), and/or benzyladenine (BA) could be used to overcome these production constraints of ‘Northern Spy’. Ethephon application at 150, 300, or 450 mg∙L-1 in the ‘on’ year increased return bloom, fruit yield, and alleviated biennial bearing in the ‘off’ year in a positive linear relationship to concentration when trees were moderately biennial in cropping. Applications applied 22 June were more effective than 27 July or 31 Aug. applications. However, single or multiple (2, 3, or 4) application(s) of 150 mg∙L-1 ETH or 5 mg∙L-1 NAA were ineffective when trees were not biennial. Two ETH applications at 1500 mg∙L-1 to non-bearing trees significantly increased flowering and fruit yield the year following treatment. The combination of P-Ca with ETH had an additive effect on shoot growth and improved growth control compared to P-Ca alone. Two BA applications at 500 mg∙L-1 had no effect on lateral branching of young trees. / Chudleigh's Limited, MITACS Accelerate

High-precision half-life and branching-ratio measurements for the superallowed beta+ emitter 26Alm were performed at the TRIUMF-ISAC radioactive ion beam facility located in Vancouver, Canada. The branching ratio measurement was performed with the 8pi Spectrometer, an array of 20 high-purity germanium detectors, in conjunction with SCEPTAR, a plastic scintillator array used to detect the emitted beta particles. An upper limit of <= 12 ppm at 90% confidence level was found for the second forbidden beta + decay of 26Alm to the first 2+ state at 1809 keV in 26Mg. An inclusive upper limit of <= 15 ppm at 90% confidence level was found when considering all possible non-analogue beta +/EC decay branches of 26Alm, resulting in a superallowed branching ratio of 100.0000+0−0.0015%. The half-life measurement was performed using a 4pi continuous-flow gas proportional counter and fast tape transport system. The resulting value for the 26Alm half-life, T1/2 = 6.34654(76) s, is consistent with, but 2.5 times more precise than, the previous world average, and represents the single most precisely measured half-life of any superallowed emitting nucleus to date. Combining these results with world-average Q-value measurements yields a superallowed beta -decay ft value of 3037.58(60) s, the most precisely determined ft value for any superallowed emitting nucleus to date. Combined with the small, and precisely quoted, theoretical isospin-symmetry-breaking corrections for this nucleus, the corrected Ft value for 26Alm of 3073.1(12) s is also the most precisely determined for any superallowed emitter by nearly a factor of two and now rivals the precision of all the other 12 precisely measured superallowed beta decays combined. The high-precision experimental ft value for 26Alm superallowed decay reported here provides a new benchmark to refine theoretical models of isospin-symmetry-breaking effects in superallowed Fermi beta decays.

<p>The first part of the thesis focuses on the development of Bayesian modeling motivated by geophysics applications. In Chapter 2, we model the frequency of pyroclastic flows collected from the Soufriere Hills volcano. Multiple change points within the dataset reveal several limitations of existing methods in literature. We propose Bayesian hierarchical models (BBH) by introducing an extra level of hierarchy with hyper parameters, adding a penalty term to constrain close consecutive rates, and using a mixture prior distribution to more accurately match certain circumstances in reality. We end the chapter with a description of the prediction procedure, which is the biggest advantage of the BBH in comparison with other existing methods. In Chapter 3, we develop new statistical techniques to model and relate three complex processes and datasets: the process of extrusion of magma into the lava dome, the growth of the dome as measured by its height, and the rockfalls as an indication of the dome's instability. First, we study the dynamic Negative Binomial branching process and use it to model the rockfalls. Moreover, a generalized regression model is proposed to regress daily rockfall numbers on the extrusion rate and dome height. Furthermore, we solve an inverse problem from the regression model and predict extrusion rate based on rockfalls and dome height.</p><p>The other focus of the thesis is adaptive Markov chain Monte Carlo (MCMC) method. In Chapter 4, we improve upon the Wang-Landau (WL) algorithm. The WL algorithm is an adaptive sampling scheme that modifies the target distribution to enable the chain to visit low-density regions of the state space. However, the approach relies heavily on a partition of the state space that is left to the user to specify. As a result, the implementation and the use of the algorithm are time-consuming and less automatic. We propose an automatic, adaptive partitioning scheme which continually refines the initial partition as needed during sampling. We show that this overcomes the limitations of the input user-specified partition, making the algorithm significantly more automatic and user-friendly while also making the performance dramatically more reliable and robust. In Chapter 5, we consider the convergence and autocorrelation aspects of MCMC. We propose an Exploration/Exploitation (XX) approach to constructing adaptive MCMC algorithms, which combines adaptation schemes of distinct types. The exploration piece uses adaptation strategies aiming at exploring new regions of the target distribution and thus improving the rate of convergence to equilibrium. The exploitation piece involves an adaptation component which decreases autocorrelation for sampling among regions already discovered. We demonstrate that the combined XX algorithm significantly outperforms either original algorithm on difficult multimodal sampling problems.</p> / Dissertation