Bayesian nonparametric models for spatially indexed data of mixed type

We develop Bayesian nonparametric models for spatially indexed data of mixed type. Our work is motivated by challenges that occur in environmental epidemiology, where the usual presence of several confounding variables that exhibit complex interactions and high correlations makes it difficult to estimate and understand the effects of risk factors on health outcomes of interest. The modeling approach we adopt assumes that responses and confounding variables are manifestations of continuous latent variables, and uses multivariate Gaussians to jointly model these. Responses and confounding variables are not treated equally as relevant parameters of the distributions of the responses only are modeled in terms of explanatory variables or risk factors. Spatial dependence is introduced by allowing the weights of the nonparametric process priors to be location specific, obtained as probit transformations of Gaussian Markov random fields. Confounding variables and spatial configuration have a similar role in the model, in that they only influence, along with the responses, the allocation probabilities of the areas into the mixture components, thereby allowing for flexible adjustment of the effects of observed confounders, while allowing for the possibility of residual spatial structure, possibly occurring due to unmeasured or undiscovered spatially varying factors. Aspects of the model are illustrated in simulation studies and an application to a real data set

Flow Control in Wireless Ad-hoc Networks

We are interested in maximizing the Transmission Control Protocol (TCP) throughput between two nodes in a single cell wireless ad-hoc network. For this, we follow a cross-layer approach by first developing an analytical model that captures the effect of the wireless channel and the MAC layer to TCP. The analytical model gives the time evolution of the TCP window size which is described by a stochastic differential equation driven by a point process. The point process represents the arrival of acknowledgments sent by the TCP receiver to the sender as part of the self-regulating mechanism of the flow control protocol. Through this point process we achieve a cross-layer integration between the physical layer, the MAC layer and TCP. The intervals between successive points describe how the packet drops at the wireless channel and the delays because of retransmission at the MAC layer affect the window size at the TCP layer. We fully describe the statistical behavior of the point process by computing first the p.d.f. for the inter-arrival intervals and then the compensator and the intensity of the process parametrized by the quantities that describe the MAC layer and the wireless channel. To achieve analytical tractability we concentrate on the pure (unslotted) Aloha for the MAC layer and the Gilbert-Elliott model for the channel. Although the Aloha protocol is simpler than the more popular IEEE 802.11 protocol, it still exhibits the same exponential backoff mechanism which is a key factor for the performance of TCP in a wireless network. Moreover, another reason to study the Aloha protocol is that the protocol and its variants gain popularity as they are used in many of today's wireless networks. Using the analytical model for the TCP window size evolution, we try to increase the TCP throughput between two nodes in a single cell network. We want to achieve this by implicitly informing the TCP sender of the network conditions. We impose this additional constraint so we can achieve compatibility between the standard TCP and the optimized version. This allows the operation of both protocol stacks in the same network. We pose the optimization problem as an optimal stopping problem. For each packet transmitted by the TCP sender to the network, an optimal time instance has to be computed in the absence of an acknowledgment for this packet. This time instance indicates when a timeout has to be declared for the packet. In the absence of an acknowledgment, if the sender waits long for declaring a timeout, the network is underutilized. If the sender declares a timeout soon, it minimizes the transmission rate. Because of the analytical intractability of the optimal stopping time problem, we follow a Markov chain approximation method to solve the problem numerically

Galilean quantum gravity in 2+1 dimensions

In this thesis, we study the Galilean limit of gravity in 2+1 dimensions and give the necessary ingredients for its quantisation. We study two groups that play fundamental role in this thesis, the two-fold central extension of the Galilei and Newton-Hooke groups in 2+1 dimensions and their corresponding Lie algebras. We construct what we call \Galilean gravity in 2+1 dimensions" as the Chern-Simons theory of the Galilei group and generalise this construction to include a cosmological constant which, in the present setting corresponds to the Chern-Simons theory of the Newton-Hooke group. Finally, we apply the combinatorial quantisation program in detail to the Galilei group: we give the irreducible, unitary representation of the relevant quantum double and fully explore Galilean quantum gravity in this setting. We highlight the associated structures for the Newton-Hooke group and provide an outline for a similar quantisation. In doing so, we provide the link between Newton-Hooke gravity, and a deformation of an extension of the Heisenberg algebra that is well-studied

The effect of three cognitive variables on students' understanding of the particulate nature of matter and its changes of state

In this study, students' understanding of the structure of matter and its changes of state, such as, melting, evaporation, boiling and condensation was investigated in relation to three cognitive variables: logical thinking, field-dependence/ field-independence and convergence/ divergence dimension. The study took place in Greece with the participation of 329 ninth-grade junior high school pupils (age 14-15). A stepwise multiple regression analysis revealed that all of the above mentioned cognitive variables were statistically significant predictors of the students' achievement. Among the three predictors, logical thinking was found to be the most dominant one. In addition, students’ understanding of the structure of matter, along with the cognitive variables, were shown to have an effect on their understanding the changes of states and on their competence to interpret these physical changes. Path analyses were implemented to depict these effects. Moreover, a theoretical analysis is provided that associates logical thinking and cognitive styles with the nature of mental tasks involved when learning the material concerning the particulate nature of matter and its changes of state. Implications for science education are also discussed

Hearing Through the Body: Expression and Movement in Music

This thesis engages with complex issues of musical expression and movement, and their relation, on the one hand, to musical structure and, on the other hand, to embodied musical experience. It aims to fill a gap in music theory and analysis: most methods overemphasise abstract conceptualisation of structural relations at the expense of the more dynamic, intuitive aspect of musical experience. As a solution, it offers a specific analytical method that can be used to explore dynamic aspects of music as experienced through the whole body. Drawing mainly on nineteenth-century piano music, I analyse aspects of structure in both composition and performance in terms of expressive and motional qualities, revealing the relationship between musical and physical movement. Expressivity in music derives its meaning, at least partly, from the embodied experience of music: performers shape expression through their whole body while listeners react to it in a comparable way, albeit less overtly. Two related systems of graphic notation are introduced, which provide a non-verbal means of representing expressive movement and at the same time encourage an immediate, visceral relationship to the music. The first notation captures the animated quality of expressive movement by analogy with the motion of a bouncing ball, while the second breaks down the expressive musical flow into discrete gestural patterns of specific motional character. While the ultimate value of this method lies in the analytical process it instigates, it also provides a novel theoretical framework that sheds light on the interaction, as well as integration, between structures such as metre, rhythm, harmony and voice-leading, which are traditionally studied mostly independently. In addition, it provides a useful tool for the study and communication of performance interpretation, based on data extracted from recordings in the form of tempo and dynamic fluctuation graphs

Constraining modified gravity theories with scalar fields using black-hole images

We study a number of well-motivated theories of modified gravity with the common overarching theme that they predict the existence of compact objects such as black holes and wormholes endowed with scalar hair. We compute the shadow radius of the resulting compact objects and demonstrate that black hole images such as that of M87$^*$ or the more recent SgrA$^*$ by the Einstein Horizon Telescope (EHT) collaboration may provide a powerful way to constrain deviations of the metric functions from what is expected from general relativity (GR) solutions. We focus our attention on Einstein-scalar-Gauss-Bonnet (EsGB) theory with three well motivated couplings, including the dilatonic and $Z_2$ symmetric cases. We then analyze the shadow radius of black holes in the contest of the spontaneous scalarization scenario within EsGB theory with an additional coupling to the Ricci scalar (EsRGB). Finally, we turn our attention to spontaneous scalarization in the Einstein-Maxwell-Scalar (EMS) theory and demonstrate the impact of the parameters on the black hole shadow. Our results show that black hole imaging is an important tool for constraining black holes with scalar hair and for some part of the parameter space, black holes solutions with scalar hair may be marginally favoured compared to solutions of GR.Comment: 17 pages, 9 figures, 2 table

BNSP: an R Package for fitting Bayesian semiparametric regression models and variable selection

The R package BNSP provides a unified framework for semiparametric location-scale regression and stochastic search variable selection. The statistical methodology that the package is built upon utilizes basis function expansions to represent semiparametric covariate effects in the mean and variance functions, and spike-slab priors to perform selection and regularization of the estimated effects. In addition to the main function that performs posterior sampling, the package includes functions for assessing convergence of the sampler, summarizing model fits, visualizing covariate effects and obtaining predictions for new responses or their means given feature/covariate vectors