Nested Sampling and its Applications in Stable Compressive Covariance Estimation and Phase Retrieval with Near-Minimal Measurements

Compressed covariance sensing using quadratic samplers is gaining increasing interest in recent literature. Covariance matrix often plays the role of a sufficient statistic in many signal and information processing tasks. However, owing to the large dimension of the data, it may become necessary to obtain a compressed sketch of the high dimensional covariance matrix to reduce the associated storage and communication costs. Nested sampling has been proposed in the past as an efficient sub-Nyquist sampling strategy that enables perfect reconstruction of the autocorrelation sequence of Wide-Sense Stationary (WSS) signals, as though it was sampled at the Nyquist rate. The key idea behind nested sampling is to exploit properties of the difference set that naturally arises in quadratic measurement model associated with covariance compression. In this thesis, we will focus on developing novel versions of nested sampling for low rank Toeplitz covariance estimation, and phase retrieval, where the latter problem finds many applications in high resolution optical imaging, X-ray crystallography and molecular imaging. The problem of low rank compressive Toeplitz covariance estimation is first shown to be fundamentally related to that of line spectrum recovery. In absence if noise, this connection can be exploited to develop a particular kind of sampler called the Generalized Nested Sampler (GNS), that can achieve optimal compression rates. In presence of bounded noise, we develop a regularization-free algorithm that provably leads to stable recovery of the high dimensional Toeplitz matrix from its order-wise minimal sketch acquired using a GNS. Contrary to existing TV-norm and nuclear norm based reconstruction algorithms, our technique does not use any tuning parameters, which can be of great practical value. The idea of nested sampling idea also finds a surprising use in the problem of phase retrieval, which has been of great interest in recent times for its convex formulation via PhaseLift, By using another modified version of nested sampling, namely the Partial Nested Fourier Sampler (PNFS), we show that with probability one, it is possible to achieve a certain conjectured lower bound on the necessary measurement size. Moreover, for sparse data, an l1 minimization based algorithm is proposed that can lead to stable phase retrieval using order-wise minimal number of measurements.

Towards realistic simulations of lava dome growth using the level set method

The level set method has been implemented in a computational volcanology context. New techniques are presented to solve the advection equation and the reinitialisation equation. These techniques are based upon an algorithm developed in the finite difference context, but are modified to take advantage of the robustness of the finite element method. The resulting algorithm is tested on a well documented Rayleigh–Taylor instability benchmark [19], and on an axisymmetric problem where the analytical solution is known. Finally, the algorithm is applied to a basic study of lava dome growth.

Finite-difference time-domain-based studies of MRI pulsed field gradient-induced eddy currents inside the human body

In modern magnetic resonance imaging (MRI), patients are exposed to strong, rapidly switching magnetic gradient fields that, in extreme cases, may be able to elicit nerve stimulation. This paper presents theoretical investigations into the spatial distribution of induced current inside human tissues caused by pulsed z-gradient fields. A variety of gradient waveforms have been studied. The simulations are based on a new, high-definition, finite-difference time-domain method and a realistic inhomogeneous 10-mm resolution human body model with appropriate tissue parameters. it was found that the eddy current densities are affected not only by the pulse sequences but by many parameters such as the position of the body inside the gradient set, the local biological material properties and the geometry of the body. The discussion contains a comparison of these results with previous results found in the literature. This study and the new methods presented herein will help to further investigate the biological effects caused by the switched gradient fields in a MRI scan. (C) 2002 Wiley Periodicals, Inc.

Representational Difference Analysis (RDA) reveals differential expression of conserved as well as novel genes during caste-specific development of the honey bee (Apis mellifera L.) ovary

In highly eusocial insects, such as the honey bee, Apis mellifera, the reproductive bias has become embedded in morphological caste differences. These are most expressively denoted in ovary size, with adult queens having large ovaries consisting of 150-200 ovarioles each, while workers typically have only 1-20 ovarioles per ovary. This morphological differentiation is a result of hormonal signals triggered by the diet change in the third larval instar, which eventually generate caste-specific gene expression patterns. To reveal these we produced differential gene expression libraries by Representational Difference Analysis (RDA) for queen and worker ovaries in a developmental stage when cell death is a prominent feature in the ovarioles of workers, whereas all ovarioles are maintained and extend in length in queens. In the queen library, 48% of the gene set represented homologs of known Drosophila genes, whereas in the worker ovary, the largest set (59%) were ESTs evidencing novel genes, not even computationally predicted in the honey bee genome. Differential expression was confirmed by quantitative RT-PCR for a selected gene set, denoting major differences for two queen and two worker library genes. These included two unpredicted genes located in chromosome 11 (Group11.35 and Group11.31, respectively) possibly representing long non-coding RNAs. Being candidates as modulators of ovary development, their expression and functional analysis should be a focal point for future studies. (C) 2011 Elsevier Ltd. All rights reserved.

Stability of linear difference and differential inclusions

Any given n X n matrix A is shown to be a restriction, to the A-invariant subspace, of a nonnegative N x N matrix B of spectral radius p(B) arbitrarily close to p(A). A difference inclusion x(k+1) is an element of Ax(k), where A is a compact set of matrices, is asymptotically stable if and only if A can be extended to a set B of nonnegative matrices B with \ \B \ \ (1) < 1 or \ \B \ \ (infinity) < 1. Similar results are derived for differential inclusions.

Skolem-type difference sets for cycle systems

Cyclic m-cycle systems of order v are constructed for all m greater than or equal to 3, and all v = 1(mod 2m). This result has been settled previously by several authors. In this paper, we provide a different solution, as a consequence of a more general result, which handles all cases using similar methods and which also allows us to prove necessary and sufficient conditions for the existence of a cyclic m-cycle system of K-v - F for all m greater than or equal to 3, and all v = 2(mod 2m).

Human capital in growth regressions: how much difference does data quality make? An update and further results

We construct estimates of educational attainment for a sample of OECD countries using previously unexploited sources. We follow a heuristic approach to obtain plausible time profiles for attainment levels by removing sharp breaks in the data that seem to reflect changes in classification criteria. We then construct indicators of the information content of our series and a number of previously available data sets and examine their performance in several growth specifications. We find a clear positive correlation between data quality and the size and significance of human capital coefficients in growth regressions. Using an extension of the classical errors in variables model, we construct a set of meta-estimates of the coefficient of years of schooling in an aggregate Cobb-Douglas production function. Our results suggest that, after correcting for measurement error bias, the value of this parameter is well above 0.50.

Phylogenetic approach reveals that virus genotype largely determines HIV set-point viral load.

HIV virulence, i.e. the time of progression to AIDS, varies greatly among patients. As for other rapidly evolving pathogens of humans, it is difficult to know if this variance is controlled by the genotype of the host or that of the virus because the transmission chain is usually unknown. We apply the phylogenetic comparative approach (PCA) to estimate the heritability of a trait from one infection to the next, which indicates the control of the virus genotype over this trait. The idea is to use viral RNA sequences obtained from patients infected by HIV-1 subtype B to build a phylogeny, which approximately reflects the transmission chain. Heritability is measured statistically as the propensity for patients close in the phylogeny to exhibit similar infection trait values. The approach reveals that up to half of the variance in set-point viral load, a trait associated with virulence, can be heritable. Our estimate is significant and robust to noise in the phylogeny. We also check for the consistency of our approach by showing that a trait related to drug resistance is almost entirely heritable. Finally, we show the importance of taking into account the transmission chain when estimating correlations between infection traits. The fact that HIV virulence is, at least partially, heritable from one infection to the next has clinical and epidemiological implications. The difference between earlier studies and ours comes from the quality of our dataset and from the power of the PCA, which can be applied to large datasets and accounts for within-host evolution. The PCA opens new perspectives for approaches linking clinical data and evolutionary biology because it can be extended to study other traits or other infectious diseases.

A chemical Hamiltonian approach study of the basis set superposition error changes on electron densities and one- and two-center energy components

A comparision of the local effects of the basis set superposition error (BSSE) on the electron densities and energy components of three representative H-bonded complexes was carried out. The electron densities were obtained with Hartee-Fock and density functional theory versions of the chemical Hamiltonian approach (CHA) methodology. It was shown that the effects of the BSSE were common for all complexes studied. The electron density difference maps and the chemical energy component analysis (CECA) analysis confirmed that the local effects of the BSSE were different when diffuse functions were present in the calculations

Effect of basis set superposition error on the electron density of molecular complexes

The effect of basis set superposition error (BSSE) on molecular complexes is analyzed. The BSSE causes artificial delocalizations which modify the first order electron density. The mechanism of this effect is assessed for the hydrogen fluoride dimer with several basis sets. The BSSE-corrected first-order electron density is obtained using the chemical Hamiltonian approach versions of the Roothaan and Kohn-Sham equations. The corrected densities are compared to uncorrected densities based on the charge density critical points. Contour difference maps between BSSE-corrected and uncorrected densities on the molecular plane are also plotted to gain insight into the effects of BSSE correction on the electron density

Integro-difference equations for interacting species and the Neolithic transition

We introduce a set of sequential integro-difference equations to analyze the dynamics of two interacting species. Firstly, we derive the speed of the fronts when a species invades a space previously occupied by a second species, and check its validity by means of numerical random-walk simulations. As an example, we consider the Neolithic transition: the predictions of the model are consistent with the archaeological data for the front speed, provided that the interaction parameter is low enough. Secondly, an equation for the coexistence time between the invasive and the invaded populations is obtained for the first time. It agrees well with the simulations, is consistent with observations of the Neolithic transition, and makes it possible to estimate the value of the interaction parameter between the incoming and the indigenous populations

The cultural dimension in focus : promoting awareness of diversity and respect for difference in a Finland-Swedish EFL classroom

This study addresses the role of EFL education, its potential and shortcomings, and the challenges the future of EFL education will bring. It is argued that new societal demands and the limited time we have at our disposal in the classroom make it necessary to rethink goals and content and move away from the transmissionof limited sets of facts and information to helping students develop awareness and competences that can be applied in many different situations, also in a perspective of lifelong learning. The overall aim of the current study is to problematize and increase understanding of the implementation of cultural aspects in the language classroom by addressing the interrelated what, why and how of the cultural dimension within EFL education. This has been conducted by means of theoretical explorations into the area, alongside an attempt at promoting intercultural competence (IC) in a more systematic and insightful manner within my own educational praxis. The focus of the intercultural work in the classroom was on the promotion of awareness of difference and diversity, as well as respect for such difference through the ability to decenter from cultural norms and behavior that previously have been taken for granted. These are two elements that have been suggested as fundamental for other work with IC in the classroom and for the realization of important aspects of the underlying values of basic education. In the context of this study, IC comprises several interconnected components supportingeach other in a variety of ways, with the further aim being interaction with and respect for difference in general, not only concerning e.g. representatives ofcertain English-speaking communities. The methodology was informed by action research, with myself in the role of the teacher-researcher or the reflective practitioner. For the purpose of the project I was authorized to take on the EFL education for the three years of upper comprehensive school of one random class of students originally assigned to one of the language teachers of the selected Finland-Swedish school. Thus, the class of 17 students was not specifically chosen for the project, and the aims and contents chosen for the development project were placed within the framework of the ordinary curriculum. By exploring the students¿ insights concerning different English-speaking cultural groups, mainly through a set of questionnaires, it was possible to outline the work with the cultural dimension in the classroom for the following three years. Work progress was evaluated at specific stages, and the final project evaluations were conducted through individual student interviews in grade 9. The interviews were focused on possible development of students¿ insights concerning different aspects of the cultural dimension. In particular this concerned awareness of difference and diversity, including modification of stereotypes, as well as the ability to decenterin order to be better able to respect such difference. I also explored students¿ awareness and views of the activities and approaches used in class, as well asaffordances both inside and outside the EFL classroom in relation to these intended insights. A further focus area was the perceived relevance to students of different aspects of the cultural dimension. The frameworks and approaches adopted for the work in the classroom all have in common that they are based on a constructivist framework, where knowledge is constructed and reconstructed through interaction with one¿s social and cultural environment, including interaction with others. Reflective processes precede or are simultaneous with the learning of basic factual knowledge. This entails a view of learning as a progression from simple to more complex models rather than as a progression from facts to understanding and analysis. Here, the development of intercultural competence is seen asa cyclical process, or along a spiral curriculum, from simple to more complex levels through a combination of cognitive, affective and behavioral elements within a framework of experiential learning. This project has shown one possible wayforward concerning the development of intercultural competence within EFL education through a more systematic and comprehensive approach regarding linguistic and cultural aspects. The evaluation of the educational process explored in the study suggests the possibilities for work with the promotion of awareness of difference and diversity concerning some specific context that, based on students¿ prior knowledge and preconceptions, would benefit from further work. In this case, the specific context primarily concerned different aspects of both cultural and linguistic conditions in the UK. It is also suggested that many students developed the ability to decenter, described in the study as integral to being able to respect otherness. What still remains to be explored are more individualized approaches considering students¿ different levels of departure. Further work alsoneeds to be put into how to apply insights gained in these specific situations to more general contexts. It is also necessary to explore the use of the suggested approaches in a wider range of different contexts.