HIERARCHICAL DECOMPOSITION OF MULTICLASS PROBLEMS

Several popular Machine Learning techniques are originally designed for the solution of two-class problems. However, several classification problems have more than two classes. One approach to deal with multiclass problems using binary classifiers is to decompose the multiclass problem into multiple binary sub-problems disposed in a binary tree. This approach requires a binary partition of the classes for each node of the tree, which defines the tree structure. This paper presents two algorithms to determine the tree structure taking into account information collected from the used dataset. This approach allows the tree structure to be determined automatically for any multiclass dataset.

Hierarchical spherical model from a geometric point of view

A continuous version of the hierarchical spherical model at dimension d=4 is investigated. Two limit distributions of the block spin variable X(gamma), normalized with exponents gamma = d + 2 and gamma=d at and above the critical temperature, are established. These results are proven by solving certain evolution equations corresponding to the renormalization group (RG) transformation of the O(N) hierarchical spin model of block size L(d) in the limit L down arrow 1 and N ->infinity. Starting far away from the stationary Gaussian fixed point the trajectories of these dynamical system pass through two different regimes with distinguishable crossover behavior. An interpretation of this trajectories is given by the geometric theory of functions which describe precisely the motion of the Lee-Yang zeroes. The large-N limit of RG transformation with L(d) fixed equal to 2, at the criticality, has recently been investigated in both weak and strong (coupling) regimes by Watanabe (J. Stat. Phys. 115:1669-1713, 2004) . Although our analysis deals only with N = infinity case, it complements various aspects of that work.

Hierarchical spatial organization of geographical networks

In this work, we propose a hierarchical extension of the polygonality index as the means to characterize geographical planar networks. By considering successive neighborhoods around each node, it is possible to obtain more complete information about the spatial order of the network at progressive spatial scales. The potential of the methodology is illustrated with respect to synthetic and real geographical networks.

Hierarchical Assembly of CaMoO(4) Nano-Octahedrons and Their Photoluminescence Properties

Hierarchical assemblies of CaMoO4 (CM) nano-octahedrons were obtained by microwave-assisted hydrothemial synthesis at 120 degrees C for different times. These structures were structurally, morphologically and optically characterized by X-ray diffraction, micro-Raman spectroscopy, field-emission gun scanning electron microscopy, ultraviolet-visible absorption spectroscopy and photoluminescence measurements. First-principle calculations have been carried out to understand the structural and electronic order-disorder effects as a function of the particle/region size. Supercells of different dimensions were constructed to simulate the geometric distortions along both they and z planes of the scheelite structure. Based on these experimental results and with the help of detailed structural simulations, we were able to model the nature of the order-disorder in this important class of materials and discuss the consequent implications on its physical properties, in particular, the photoluminescence properties of CM nanocrystals.

EXACT AND APPROXIMATE RELATIONS FOR THE SPIN-DEPENDENCE OF THE EXCHANGE ENERGY IN HIGH MAGNETIC FIELDS

The exchange energy of an arbitrary collinear-spin many-body system in an external magnetic field is a functional of the spin-resolved charge and current densities, E(x)[n(up arrow), n(down arrow), j(up arrow), j(down arrow)]. Within the framework of density-functional theory (DFT), we show that the dependence of this functional on the four densities can be fully reconstructed from either of two extreme limits: a fully polarized system or a completely unpolarized system. Reconstruction from the limit of an unpolarized system yields a generalization of the Oliver-Perdew spin scaling relations from spin-DFT to current-DFT. Reconstruction from the limit of a fully polarized system is used to derive the high-field form of the local-spin-density approximation to current-DFT and to magnetic-field DFT.

The Impact of Transnational Conflicts on Christian-Muslim Relations in Nigeria (2001-2006)

This Master’s Thesis examines transnational conflicts and Christian-Muslim relations in Nigeria between the years 2001 and 2006. It focuses on two major transnational conflicts: The September 11, 2001 attacks in the United States and the Danish cartoon controversy of 2005/2006. It discusses the impact of these transnational conflicts on Christian-Muslim relations in Nigeria in the light of the implementation of the Sharia Law in some northern Nigerian states and the improved access to the broadcast media and mobile telephone communication in Nigeria. By underscoring the relationship between transnational conflicts and the local context, this study provides a new perspective for understanding Christian-Muslim relations in Nigeria

Estimation of genetic variance for macro- and micro-environmental sensitivity using double hierarchical generalized linear models

Background: Genetic variation for environmental sensitivity indicates that animals are genetically different in their response to environmental factors. Environmental factors are either identifiable (e.g. temperature) and called macro-environmental or unknown and called micro-environmental. The objectives of this study were to develop a statistical method to estimate genetic parameters for macro- and micro-environmental sensitivities simultaneously, to investigate bias and precision of resulting estimates of genetic parameters and to develop and evaluate use of Akaike’s information criterion using h-likelihood to select the best fitting model. Methods: We assumed that genetic variation in macro- and micro-environmental sensitivities is expressed as genetic variance in the slope of a linear reaction norm and environmental variance, respectively. A reaction norm model to estimate genetic variance for macro-environmental sensitivity was combined with a structural model for residual variance to estimate genetic variance for micro-environmental sensitivity using a double hierarchical generalized linear model in ASReml. Akaike’s information criterion was constructed as model selection criterion using approximated h-likelihood. Populations of sires with large half-sib offspring groups were simulated to investigate bias and precision of estimated genetic parameters. Results: Designs with 100 sires, each with at least 100 offspring, are required to have standard deviations of estimated variances lower than 50% of the true value. When the number of offspring increased, standard deviations of estimates across replicates decreased substantially, especially for genetic variances of macro- and micro-environmental sensitivities. Standard deviations of estimated genetic correlations across replicates were quite large (between 0.1 and 0.4), especially when sires had few offspring. Practically, no bias was observed for estimates of any of the parameters. Using Akaike’s information criterion the true genetic model was selected as the best statistical model in at least 90% of 100 replicates when the number of offspring per sire was 100. Application of the model to lactation milk yield in dairy cattle showed that genetic variance for micro- and macro-environmental sensitivities existed. Conclusion: The algorithm and model selection criterion presented here can contribute to better understand genetic control of macro- and micro-environmental sensitivities. Designs or datasets should have at least 100 sires each with 100 offspring.

Hglm: A package for fitting hierarchical generalized linear models

We present the hglm package for fitting hierarchical generalized linear models. It can be used for linear mixed models and generalized linear mixed models with random effects for a variety of links and a variety of distributions for both the outcomes and the random effects. Fixed effects can also be fitted in the dispersion part of the model.

Genetic heterogeneity of residual variance : estimation of variance components using double hierarchical generalized linear models

Background: The sensitivity to microenvironmental changes varies among animals and may be under genetic control. It is essential to take this element into account when aiming at breeding robust farm animals. Here, linear mixed models with genetic effects in the residual variance part of the model can be used. Such models have previously been fitted using EM and MCMC algorithms. Results: We propose the use of double hierarchical generalized linear models (DHGLM), where the squared residuals are assumed to be gamma distributed and the residual variance is fitted using a generalized linear model. The algorithm iterates between two sets of mixed model equations, one on the level of observations and one on the level of variances. The method was validated using simulations and also by re-analyzing a data set on pig litter size that was previously analyzed using a Bayesian approach. The pig litter size data contained 10,060 records from 4,149 sows. The DHGLM was implemented using the ASReml software and the algorithm converged within three minutes on a Linux server. The estimates were similar to those previously obtained using Bayesian methodology, especially the variance components in the residual variance part of the model. Conclusions: We have shown that variance components in the residual variance part of a linear mixed model can be estimated using a DHGLM approach. The method enables analyses of animal models with large numbers of observations. An important future development of the DHGLM methodology is to include the genetic correlation between the random effects in the mean and residual variance parts of the model as a parameter of the DHGLM.

Stratified resolution

We introduce a calculus of stratified resolution, in which special attention is paid to clauses that "define" relations. If such clauses are discovered in the initial set of clauses, they are treated using the rule of definition unfolding, i.e. the rule that replaces defined relations by their definitions. Stratified resolution comes with a powerful notion of redundancy: a clause to which definition unfolding has been applied can be removed from the search space. To prove the completeness of stratified resolution with redundancies, we use a novel combination of Bachmair and Ganzingerâ??s model construction technique and a hierarchical construction of orderings and least fixpoints.

Quantitative Information Flow, Relations and Polymorphic Types

This paper uses Shannon's information theory to give a quantitative definition of information flow in systems that transform inputs to outputs. For deterministic systems, the definition is shown to specialise to a simpler form when the information source and the known inputs jointly determine the inputs. For this special case, the definition is related to the classical security condition of non-interference and an equivalence is established between non-interference and independence of random variables. Quantitative information flow for deterministic systems is then presented in relational form. With this presentation, it is shown how relational parametricity can be used to derive upper and lower bounds on information flows through families of functions defined in the second order lambda calculus.