On the Properties and Cosmology of Q-balls

The properties and cosmological importance of a class of non-topological solitons, Q-balls, are studied. Aspects of Q-ball solutions and Q-ball cosmology discussed in the literature are reviewed. Q-balls are particularly considered in the Minimal Supersymmetric Standard Model with supersymmetry broken by a hidden sector mechanism mediated by either gravity or gauge interactions. Q-ball profiles, charge-energy relations and evaporation rates for realistic Q-ball profiles are calculated for general polynomial potentials and for the gravity mediated scenario. In all of the cases, the evaporation rates are found to increase with decreasing charge. Q-ball collisions are studied by numerical means in the two supersymmetry breaking scenarios. It is noted that the collision processes can be divided into three types: fusion, charge transfer and elastic scattering. Cross-sections are calculated for the different types of processes in the different scenarios. The formation of Q-balls from the fragmentation of the Aflieck-Dine -condensate is studied by numerical and analytical means. The charge distribution is found to depend strongly on the initial energy-charge ratio of the condensate. The final state is typically noted to consist of Q- and anti-Q-balls in a state of maximum entropy. By studying the relaxation of excited Q-balls the rate at which excess energy can be emitted is calculated in the gravity mediated scenario. The Q-ball is also found to withstand excess energy well without significant charge loss. The possible cosmological consequences of these Q-ball properties are discussed.

Development of phase retrieval algorithm and techniques for optical spectrum analysis

Coherent anti-Stokes Raman scattering is the powerful method of laser spectroscopy in which significant successes are achieved. However, the non-linear nature of CARS complicates the analysis of the received spectra. The objective of this Thesis is to develop a new phase retrieval algorithm for CARS. It utilizes the maximum entropy method and the new wavelet approach for spectroscopic background correction of a phase function. The method was developed to be easily automated and used on a large number of spectra of different substances.. The algorithm was successfully tested on experimental data.

Multifrequency VLBI Observations of Selected Active Galactic Nuclei

In this dissertation, active galactic nuclei (AGN) are discussed, as they are seen with the high-resolution radio-astronomical technique called Very Long Baseline Interferometry (VLBI). This observational technique provides very high angular resolution (_ 10−300 = 1 milliarcsecond). VLBI observations, performed at different radio frequencies (multi-frequency VLBI), allow to penetrate deep into the core of an AGN to reveal an otherwise obscured inner part of the jet and the vicinity of the AGN’s central engine. Multi-frequency VLBI data are used to scrutinize the structure and evolution of the jet, as well as the distribution of the polarized emission. These data can help to derive the properties of the plasma and the magnetic field, and to provide constraints to the jet composition and the parameters of emission mechanisms. Also VLBI data can be used for testing the possible physical processes in the jet by comparing observational results with results of numerical simulations. The work presented in this thesis contributes to different aspects of AGN physics studies, as well as to the methodology of VLBI data reduction. In particular, Paper I reports evidence of optical and radio emission of AGN coming from the same region in the inner jet. This result was obtained via simultaneous observations of linear polarization in the optical and in radio using VLBI technique of a sample of AGN. Papers II and III describe, in detail, the jet kinematics of the blazar 0716+714, based on multi-frequency data, and reveal a peculiar kinematic pattern: plasma in the inner jet appears to move substantially faster that that in the large-scale jet. This peculiarity is explained by the jet bending, in Paper III. Also, Paper III presents a test of the new imaging technique for VLBI data, the Generalized Maximum Entropy Method (GMEM), with the observed (not simulated) data and compares its results with the conventional imaging. Papers IV and V report the results of observations of the circularly polarized (CP) emission in AGN at small spatial scales. In particular, Paper IV presents values of the core CP for 41 AGN at 15, 22 and 43 GHz, obtained with the help of the standard Gain transfer (GT) method, which was previously developed by D. Homan and J.Wardle for the calibration of multi-source VLBI observations. This method was developed for long multi-source observations, when many AGN are observed in a single VLBI run. In contrast, in Paper V, an attempt is made to apply the GT method to single-source VLBI observations. In such observations, the object list would include only a few sources: a target source and two or three calibrators, and it lasts much shorter than the multi-source experiment. For the CP calibration of a single-source observation, it is necessary to have a source with zero or known CP as one of the calibrators. If the archival observations included such a source to the list of calibrators, the GT could also be used for the archival data, increasing a list of known AGN with the CP at small spatial scale. Paper V contains also calculation of contributions of different sourced of errors to the uncertainty of the final result, and presents the first results for the blazar 0716+714.

Linear prediction in optical spectroscopy

A linear prediction procedure is one of the approved numerical methods of signal processing. In the field of optical spectroscopy it is used mainly for extrapolation known parts of an optical signal in order to obtain a longer one or deduce missing signal samples. The first is needed particularly when narrowing spectral lines for the purpose of spectral information extraction. In the present paper the coherent anti-Stokes Raman scattering (CARS) spectra were under investigation. The spectra were significantly distorted by the presence of nonlinear nonresonant background. In addition, line shapes were far from Gaussian/Lorentz profiles. To overcome these disadvantages the maximum entropy method (MEM) for phase spectrum retrieval was used. The obtained broad MEM spectra were further underwent the linear prediction analysis in order to be narrowed.

Statistical Methods for Conservation and Alignment Quality in Proteins

Construction of multiple sequence alignments is a fundamental task in Bioinformatics. Multiple sequence alignments are used as a prerequisite in many Bioinformatics methods, and subsequently the quality of such methods can be critically dependent on the quality of the alignment. However, automatic construction of a multiple sequence alignment for a set of remotely related sequences does not always provide biologically relevant alignments.Therefore, there is a need for an objective approach for evaluating the quality of automatically aligned sequences. The profile hidden Markov model is a powerful approach in comparative genomics. In the profile hidden Markov model, the symbol probabilities are estimated at each conserved alignment position. This can increase the dimension of parameter space and cause an overfitting problem. These two research problems are both related to conservation. We have developed statistical measures for quantifying the conservation of multiple sequence alignments. Two types of methods are considered, those identifying conserved residues in an alignment position, and those calculating positional conservation scores. The positional conservation score was exploited in a statistical prediction model for assessing the quality of multiple sequence alignments. The residue conservation score was used as part of the emission probability estimation method proposed for profile hidden Markov models. The results of the predicted alignment quality score highly correlated with the correct alignment quality scores, indicating that our method is reliable for assessing the quality of any multiple sequence alignment. The comparison of the emission probability estimation method with the maximum likelihood method showed that the number of estimated parameters in the model was dramatically decreased, while the same level of accuracy was maintained. To conclude, we have shown that conservation can be successfully used in the statistical model for alignment quality assessment and in the estimation of emission probabilities in the profile hidden Markov models.

Statistical Analysis of an SEIR Epidemic Model

This thesis was focussed on statistical analysis methods and proposes the use of Bayesian inference to extract information contained in experimental data by estimating Ebola model parameters. The model is a system of differential equations expressing the behavior and dynamics of Ebola. Two sets of data (onset and death data) were both used to estimate parameters, which has not been done by previous researchers in (Chowell, 2004). To be able to use both data, a new version of the model has been built. Model parameters have been estimated and then used to calculate the basic reproduction number and to study the disease-free equilibrium. Estimates of the parameters were useful to determine how well the model fits the data and how good estimates were, in terms of the information they provided about the possible relationship between variables. The solution showed that Ebola model fits the observed onset data at 98.95% and the observed death data at 93.6%. Since Bayesian inference can not be performed analytically, the Markov chain Monte Carlo approach has been used to generate samples from the posterior distribution over parameters. Samples have been used to check the accuracy of the model and other characteristics of the target posteriors.

Size Effect and Notch Size Effect in Metal Fatigue

It is a well known phenomenon that the constant amplitude fatigue limit of a large component is lower than the fatigue limit of a small specimen made of the same material. In notched components the opposite occurs: the fatigue limit defined as the maximum stress at the notch is higher than that achieved with smooth specimens. These two effects have been taken into account in most design handbooks with the help of experimental formulas or design curves. The basic idea of this study is that the size effect can mainly be explained by the statistical size effect. A component subjected to an alternating load can be assumed to form a sample of initiated cracks at the end of the crack initiation phase. The size of the sample depends on the size of the specimen in question. The main objective of this study is to develop a statistical model for the estimation of this kind of size effect. It was shown that the size of a sample of initiated cracks shall be based on the stressed surface area of the specimen. In case of varying stress distribution, an effective stress area must be calculated. It is based on the decreasing probability of equally sized initiated cracks at lower stress level. If the distribution function of the parent population of cracks is known, the distribution of the maximum crack size in a sample can be defined. This makes it possible to calculate an estimate of the largest expected crack in any sample size. The estimate of the fatigue limit can now be calculated with the help of the linear elastic fracture mechanics. In notched components another source of size effect has to be taken into account. If we think about two specimens which have similar shape, but the size is different, it can be seen that the stress gradient in the smaller specimen is steeper. If there is an initiated crack in both of them, the stress intensity factor at the crack in the larger specimen is higher. The second goal of this thesis is to create a calculation method for this factor which is called the geometric size effect. The proposed method for the calculation of the geometric size effect is also based on the use of the linear elastic fracture mechanics. It is possible to calculate an accurate value of the stress intensity factor in a non linear stress field using weight functions. The calculated stress intensity factor values at the initiated crack can be compared to the corresponding stress intensity factor due to constant stress. The notch size effect is calculated as the ratio of these stress intensity factors. The presented methods were tested against experimental results taken from three German doctoral works. Two candidates for the parent population of initiated cracks were found: the Weibull distribution and the log normal distribution. Both of them can be used successfully for the prediction of the statistical size effect for smooth specimens. In case of notched components the geometric size effect due to the stress gradient shall be combined with the statistical size effect. The proposed method gives good results as long as the notch in question is blunt enough. For very sharp notches, stress concentration factor about 5 or higher, the method does not give sufficient results. It was shown that the plastic portion of the strain becomes quite high at the root of this kind of notches. The use of the linear elastic fracture mechanics becomes therefore questionable.

Statistical analysis of survey-based event history data with application to modeling of unemployment duration

Longitudinal surveys are increasingly used to collect event history data on person-specific processes such as transitions between labour market states. Surveybased event history data pose a number of challenges for statistical analysis. These challenges include survey errors due to sampling, non-response, attrition and measurement. This study deals with non-response, attrition and measurement errors in event history data and the bias caused by them in event history analysis. The study also discusses some choices faced by a researcher using longitudinal survey data for event history analysis and demonstrates their effects. These choices include, whether a design-based or a model-based approach is taken, which subset of data to use and, if a design-based approach is taken, which weights to use. The study takes advantage of the possibility to use combined longitudinal survey register data. The Finnish subset of European Community Household Panel (FI ECHP) survey for waves 1–5 were linked at person-level with longitudinal register data. Unemployment spells were used as study variables of interest. Lastly, a simulation study was conducted in order to assess the statistical properties of the Inverse Probability of Censoring Weighting (IPCW) method in a survey data context. The study shows how combined longitudinal survey register data can be used to analyse and compare the non-response and attrition processes, test the missingness mechanism type and estimate the size of bias due to non-response and attrition. In our empirical analysis, initial non-response turned out to be a more important source of bias than attrition. Reported unemployment spells were subject to seam effects, omissions, and, to a lesser extent, overreporting. The use of proxy interviews tended to cause spell omissions. An often-ignored phenomenon classification error in reported spell outcomes, was also found in the data. Neither the Missing At Random (MAR) assumption about non-response and attrition mechanisms, nor the classical assumptions about measurement errors, turned out to be valid. Both measurement errors in spell durations and spell outcomes were found to cause bias in estimates from event history models. Low measurement accuracy affected the estimates of baseline hazard most. The design-based estimates based on data from respondents to all waves of interest and weighted by the last wave weights displayed the largest bias. Using all the available data, including the spells by attriters until the time of attrition, helped to reduce attrition bias. Lastly, the simulation study showed that the IPCW correction to design weights reduces bias due to dependent censoring in design-based Kaplan-Meier and Cox proportional hazard model estimators. The study discusses implications of the results for survey organisations collecting event history data, researchers using surveys for event history analysis, and researchers who develop methods to correct for non-sampling biases in event history data.