Using Inside-Outside Algorithm for Estimation of the Offspring Distribution in Multitype Branching Processes

Multitype branching processes (MTBP) model branching structures, where the nodes of the resulting tree are particles of different types. Usually such a process is not observable in the sense of the whole tree, but only as the “generation” at a given moment in time, which consists of the number of particles of every type. This requires an EM-type algorithm to obtain a maximum likelihood (ML) estimate of the parameters of the branching process. Using a version of the inside-outside algorithm for stochastic context-free grammars (SCFG), such an estimate could be obtained for the offspring distribution of the process.

Em Estimation of the Offspring Distribution in Mutitype Branching Processes - a Model in Cell Kinetics

2000 Mathematics Subject Classification: 60J80, 60J85, 62P10, 92D25.

Bayesian and Frequentist Two-Sample Predictions of the Inverse Weibull Model Based on Generalized Order Statistics

2000 Mathematics Subject Classification: 62E16,62F15, 62H12, 62M20.

A timescale for diatom evolution based on four molecular markers: reassessment of ghost lineages and major steps defining diatom evolution.

ABSTRACT. – Phylogenies and molecular clocks of the diatoms have largely been inferred from SSU rDNA sequences. A new phylogeny of diatoms was estimated using four gene markers SSU and LSU rDNA rbcL and psbA (total 4352 bp) with 42 diatom species. The four gene trees analysed with a maximum likelihood (ML) and Baysian (BI) analysis recovered a monophyletic origin of the new diatom classes with high bootstrap support, which has been controversial with single gene markers using single outgroups and alignments that do not take secondary structure of the SSU gene into account. The divergence time of the classes were calculated from a ML tree in the MultliDiv Time program using a Bayesian estimation allowing for simultaneous constraints from the fossil record and varying rates of molecular evolution of different branches in the phylogenetic tree. These divergence times are generally in agreement with those proposed by other clocks using single genes with the exception that the pennates appear much earlier and suggest a longer Cretaceous fossil record that has yet to be sampled. Ghost lineages (i.e. the discrepancy between first appearance (FA) and molecular clock age of origin from an extant taxon) were revealed in the pennate lineage, whereas those ghost lineages in the centric lineages previously reported by others are reviewed and referred to earlier literature.

A timescale for diatom evolution based on four molecular markers: reassessment of ghost lineages and major steps defining diatom evolution.

ABSTRACT. – Phylogenies and molecular clocks of the diatoms have largely been inferred from SSU rDNA sequences. A new phylogeny of diatoms was estimated using four gene markers SSU and LSU rDNA rbcL and psbA (total 4352 bp) with 42 diatom species. The four gene trees analysed with a maximum likelihood (ML) and Baysian (BI) analysis recovered a monophyletic origin of the new diatom classes with high bootstrap support, which has been controversial with single gene markers using single outgroups and alignments that do not take secondary structure of the SSU gene into account. The divergence time of the classes were calculated from a ML tree in the MultliDiv Time program using a Bayesian estimation allowing for simultaneous constraints from the fossil record and varying rates of molecular evolution of different branches in the phylogenetic tree. These divergence times are generally in agreement with those proposed by other clocks using single genes with the exception that the pennates appear much earlier and suggest a longer Cretaceous fossil record that has yet to be sampled. Ghost lineages (i.e. the discrepancy between first appearance (FA) and molecular clock age of origin from an extant taxon) were revealed in the pennate lineage, whereas those ghost lineages in the centric lineages previously reported by others are reviewed and referred to earlier literature.

Non-line-of-sight localization with frequency-selective metasurfaces

An emerging technology, that Smart Radio Environments rely on to improve wireless link quality, are Reconfigurable Intelligent Surfaces (RISs). A RIS, in general, can be understood as a thin layer of EM composite material, typically mounted on the walls or ceilings of buildings, which can be reconfigured even after its deployment in the network. RISs made by composing artificial materials in an engineered way, in order to obtain unconventional characteristics, are called metasurfaces. Through the programming of the RIS, it is possible to control and/or modify the radio waves that affect it, thus shaping the radio environment. To overcome the limitations of RISs, the metaprism represents an alternative: it is a passive and non-reconfigurable frequency-selective metasurface that acts as a metamirror to improve the efficiency of the wireless link. In particular, using an OFDM (Orthogonal Frequency-Division Multiplexing) signaling it is possible to control the reflection of the signal, suitably selecting the sub-carrier assigned to each user, without having to interact with the metaprism or having to estimate the CSI. This thesis investigates how OFDM signaling and metaprism can be used for localization purposes, especially to extend the coverage area at low cost, in a scenario where the user is in NLoS (Non-line-of-sight) conditions with respect to the base station, both single antenna. In particular, the paper concerns the design of the analytical model and the corresponding Matlab implementation of a Maximum Likelihood (ML) estimator able to estimate the unknown position, behind an obstacle, from which a generic user transmits to a base station, exploiting the metaprism.

Space–Time Block Codes and the Complexity of Sphere Decoding

In wireless communications the transmitted signals may be affected by noise. The receiver must decode the received message, which can be mathematically modelled as a search for the closest lattice point to a given vector. This problem is known to be NP-hard in general, but for communications applications there exist algorithms that, for a certain range of system parameters, offer polynomial expected complexity. The purpose of the thesis is to study the sphere decoding algorithm introduced in the article On Maximum-Likelihood Detection and the Search for the Closest Lattice Point, which was published by M.O. Damen, H. El Gamal and G. Caire in 2003. We concentrate especially on its computational complexity when used in space–time coding. Computer simulations are used to study how different system parameters affect the computational complexity of the algorithm. The aim is to find ways to improve the algorithm from the complexity point of view. The main contribution of the thesis is the construction of two new modifications to the sphere decoding algorithm, which are shown to perform faster than the original algorithm within a range of system parameters.

Partitioned likelihood support and the evaluation of data set conflict

In simultaneous analyses of multiple data partitions, the trees relevant when measuring support for a clade are the optimal tree, and the best tree lacking the clade (i.e., the most reasonable alternative). The parsimony-based method of partitioned branch support (PBS) forces each data set to arbitrate between the two relevant trees. This value is the amount each data set contributes to clade support in the combined analysis, and can be very different to support apparent in separate analyses. The approach used in PBS can also be employed in likelihood: a simultaneous analysis of all data retrieves the maximum likelihood tree, and the best tree without the clade of interest is also found. Each data set is fitted to the two trees and the log-likelihood difference calculated, giving partitioned likelihood support (PLS) for each data set. These calculations can be performed regardless of the complexity of the ML model adopted. The significance of PLS can be evaluated using a variety of resampling methods, such as the Kishino-Hasegawa test, the Shimodiara-Hasegawa test, or likelihood weights, although the appropriateness and assumptions of these tests remains debated.

A note on the likelihood and moments of the skew-normal distribution

In this paper an alternative approach to the one in Henze (1986) is proposed for deriving the odd moments of the skew-normal distribution considered in Azzalini (1985). The approach is based on a Pascal type triangle, which seems to greatly simplify moments computation. Moreover, it is shown that the likelihood equation for estimating the asymmetry parameter in such model is generated as orthogonal functions to the sample vector. As a consequence, conditions for a unique solution of the likelihood equation are established, which seem to hold in more general setting.

Likelihood-based estimation of the regression model with scrambled responses

A significant problem in the collection of responses to potentially sensitive questions, such as relating to illegal, immoral or embarrassing activities, is non-sampling error due to refusal to respond or false responses. Eichhorn & Hayre (1983) suggested the use of scrambled responses to reduce this form of bias. This paper considers a linear regression model in which the dependent variable is unobserved but for which the sum or product with a scrambling random variable of known distribution, is known. The performance of two likelihood-based estimators is investigated, namely of a Bayesian estimator achieved through a Markov chain Monte Carlo (MCMC) sampling scheme, and a classical maximum-likelihood estimator. These two estimators and an estimator suggested by Singh, Joarder & King (1996) are compared. Monte Carlo results show that the Bayesian estimator outperforms the classical estimators in almost all cases, and the relative performance of the Bayesian estimator improves as the responses become more scrambled.

Robust Mixture Modelling Using the t Distribution

Normal mixture models are being increasingly used to model the distributions of a wide variety of random phenomena and to cluster sets of continuous multivariate data. However, for a set of data containing a group or groups of observations with longer than normal tails or atypical observations, the use of normal components may unduly affect the fit of the mixture model. In this paper, we consider a more robust approach by modelling the data by a mixture of t distributions. The use of the ECM algorithm to fit this t mixture model is described and examples of its use are given in the context of clustering multivariate data in the presence of atypical observations in the form of background noise.

Comparison of two population pharmacokinetic programs, NONMEM and P-PHARM, for tacrolimus

Objectives: To compare the population modelling programs NONMEM and P-PHARM during investigation of the pharmacokinetics of tacrolimus in paediatric liver-transplant recipients. Methods: Population pharmacokinetic analysis was performed using NONMEM and P-PHARM on retrospective data from 35 paediatric liver-transplant patients receiving tacrolimus therapy. The same data were presented to both programs. Maximum likelihood estimates were sought for apparent clearance (CL/F) and apparent volume of distribution (V/F). Covariates screened for influence on these parameters were weight, age, gender, post-operative day, days of tacrolimus therapy, transplant type, biliary reconstructive procedure, liver function tests, creatinine clearance, haematocrit, corticosteroid dose, and potential interacting drugs. Results: A satisfactory model was developed in both programs with a single categorical covariate - transplant type - providing stable parameter estimates and small, normally distributed (weighted) residuals. In NONMEM, the continuous covariates - age and liver function tests - improved modelling further. Mean parameter estimates were CL/F (whole liver) = 16.3 1/h, CL/F (cut-down liver) = 8.5 1/h and V/F = 565 1 in NONMEM, and CL/F = 8.3 1/h and V/F = 155 1 in P-PHARM. Individual Bayesian parameter estimates were CL/F (whole liver) = 17.9 +/- 8.8 1/h, CL/F (cutdown liver) = 11.6 +/- 18.8 1/h and V/F = 712 792 1 in NONMEM, and CL/F (whole liver) = 12.8 +/- 3.5 1/h, CL/F (cut-down liver) = 8.2 +/- 3.4 1/h and V/F = 221 1641 in P-PHARM. Marked interindividual kinetic variability (38-108%) and residual random error (approximately 3 ng/ml) were observed. P-PHARM was more user friendly and readily provided informative graphical presentation of results. NONMEM allowed a wider choice of errors for statistical modelling and coped better with complex covariate data sets. Conclusion: Results from parametric modelling programs can vary due to different algorithms employed to estimate parameters, alternative methods of covariate analysis and variations and limitations in the software itself.

Reconstrução/processamento de imagem médica com GPU em tomossíntese

Dissertação para obtenção do Grau de Mestre em Engenharia Biomédica

Silver space-time trellis-coded modulation

Silver Code (SilC) was originally discovered in [1–4] for 2×2 multiple-input multiple-output (MIMO) transmission. It has non-vanishing minimum determinant 1/7, slightly lower than Golden code, but is fast-decodable, i.e., it allows reduced-complexity maximum likelihood decoding [5–7]. In this paper, we present a multidimensional trellis-coded modulation scheme for MIMO systems [11] based on set partitioning of the Silver Code, named Silver Space-Time Trellis Coded Modulation (SST-TCM). This lattice set partitioning is designed specifically to increase the minimum determinant. The branches of the outer trellis code are labeled with these partitions. Viterbi algorithm is applied for trellis decoding, while the branch metrics are computed by using a sphere-decoding algorithm. It is shown that the proposed SST-TCM performs very closely to the Golden Space-Time Trellis Coded Modulation (GST-TCM) scheme, yetwith a much reduced decoding complexity thanks to its fast-decoding property.

Biometrical analysis and selection of tetraploid progenies of Panicum maximum using mixed model methods

The objectives of this work were to estimate the genetic and phenotypic parameters and to predict the genetic and genotypic values of the selection candidates obtained from intraspecific crosses in Panicum maximum as well as the performance of the hybrid progeny of the existing and projected crosses. Seventy-nine intraspecific hybrids obtained from artificial crosses among five apomictic and three sexual autotetraploid individuals were evaluated in a clonal test with two replications and ten plants per plot. Green matter yield, total and leaf dry matter yields and leaf percentage were evaluated in five cuts per year during three years. Genetic parameters were estimated and breeding and genotypic values were predicted using the restricted maximum likelihood/best linear unbiased prediction procedure (REML/BLUP). The dominant genetic variance was estimated by adjusting the effect of full-sib families. Low magnitude individual narrow sense heritabilities (0.02-0.05), individual broad sense heritabilities (0.14-0.20) and repeatability measured on an individual basis (0.15-0.21) were obtained. Dominance effects for all evaluated characteristics indicated that breeding strategies that explore heterosis must be adopted. Less than 5% increase in the parameter repeatability was obtained for a three-year evaluation period and may be the criterion to determine the maximum number of years of evaluation to be adopted, without compromising gain per cycle of selection. The identification of hybrid candidates for future cultivars and of those that can be incorporated into the breeding program was based on the genotypic and breeding values, respectively. The prediction of the performance of the hybrid progeny, based on the breeding values of the progenitors, permitted the identification of the best crosses and indicated the best parents to use in crosses.