VictorJuiz/thesis huggingface dataset:
Ax-Schanuel type inequalities in differentially closed fields
Keywords: Ax-Schanuel theorem
Hrushovski construction
Abstract differential equation
Model theoretic algebra

In this thesis we study Ax-Schanuel type inequalities for abstract differential equations. A motivating example is the exponential differential equation. The Ax-Schanuel theorem states positivity of a predimension defined on its solutions. The notion of a predimension was introduced by Hrushovski in his work from the 1990s where he uses an amalgamation-with-predimension technique to refute Zilber's Trichotomy Conjecture. In the differential setting one can carry out a similar construction with the predimension given by Ax-Schanuel. In this way one constructs a limit structure whose theory turns out to be precisely the first-order theory of the exponential differential equation (this analysis is due to Kirby (for semiabelian varieties) and Crampin, and it is based on Zilber's work on pseudo-exponentiation). One says in this case that the inequality is adequate.
Thus, by an Ax-Schanuel type inequality we mean a predimension inequality for a differential equation. Our main question is to understand for which differential equations one can find an adequate predimension inequality. We show that this can be done for linear differential equations with constant coefficients by generalising the Ax-Schanuel theorem.
Further, the question turns out to be closely related to the problem of recovering the differential structure in reducts of differentially closed fields where we keep the field structure (which is quite an interesting problem in its own right). So we explore that question and establish some criteria for recovering the derivation of the field. We also show (under some assumptions) that when the derivation is definable in a reduct then the latter cannot satisfy a non-trivial adequate predimension inequality.
Another example of a predimension inequality is the analogue of Ax-Schanuel for the differential equation of the modular j-function due to Pila and Tsimerman. We carry out a Hrushovski construction with that predimension and give an axiomatisation of the first-order theory of the strong Fraïssé limit. It will be the theory of the differential equation of j under the assumption of adequacy of the predimension. We also show that if a similar predimension inequality (not necessarily adequate) is known for a differential equation then the fibres of the latter have interesting model theoretic properties such as strong minimality and geometric triviality. This, in particular, gives a new proof for a theorem of Freitag and Scanlon stating that the differential equation of j defines a trivial strongly minimal set.
Comparative planetary circulation regimes in simple general circulation models
Keywords: geophysical fluid dynamics
planetary science
atmospheric circulation

This thesis presents the studies of terrestrial planetary atmospheric circula- tion regimes using simplified GCMs with different levels of complexity. Two different versions of the simplified GCM PUMA (Portable University Model for the Atmosphere) are used — PUMA-S with Newtonian cooling scheme and PUMA-G with a semi-grey two-band radiative transfer scheme and dry convective adjustment. A series of controlled experiments are conducted by varying planetary rotation rate and imposed equator-to-pole temperature difference using PUMAS-S, and by varying rotation rate, planetary obliquity, and the ratio of optical depth in long-wave (thermal radiation) band to that in short-wave (stellar radiation) band using PUMA-G. These defining parameters are further combined with each other into dimensionless forms to establish parameter spaces, in which the occurences of different circulation regimes are mapped and classified. For the PUMA-S experiments, very coherent trends when varying planetary rotation rate (thermal Rossby number) is found. It is demonstrated that the GRW mechanism is mainly responsible for the equatorial super-rotation observed in our experiments. Regular baroclinic waves are obtained at intermediate values of thermal Rossby number and depend strongly on the strength of radiative and frictional damping. Global atmospheric energetics in terms of Lorenz energy cycle and meridional heat transport efficiency also exhibits strong dependence on planetary rotation rate from our PUMA-S experiments. Theories of geostrophic turbulence (especially the recently introduced zonostrophic turbulence) and jet formation are examined using the PUMA-S experiments. For the PUMA-G experiments, Similar trends are observed with respect to varying planetary rotation rate, while new regimes like strongly subrotating atmospheres are found when varying obliquity in PUMA- G. Tidally-locked planets are also studied by modifying the incoming stellar irradiation in PUMA-G. It is found that atmospheric optical depth in the longwave band plays an important role in setting the heat transport efficiency from day-side to night-side. These results provide significant insights into the terrestrial planetary atmospheric circulation dynamics and the inference of circulation regimes of extrasolar planets. Future studies will focus on the effect of seasonal/diurnal cycle, the parametrisation of eddy heat transport efficiency, as well as the modification of the two-band semi-grey radiative transfer scheme to incorporate pressure broadening effects.
Sand ramps as late Quaternary palaeoenvironmental archives: analysis from Southern Africa
Keywords: Sand ramp
OSL
aeolian geomorphology
Quaternary
Namibia

Sand ramps are widespread but understudied landforms which have the potential to provide detailed palaeoenvironmental information in dryland regions. This thesis investigates the utility of sand ramps as late Quaternary palaeoenvironmental archives by addressing two research questions: (1) What are the main controls on sand ramp formation in southern Africa? (2) What does the sand ramp record tell us about late Quaternary palaeoenvironments in southern Africa?
The distribution of sand ramps in southern Africa was surveyed using Google EarthTM and 75 features were identified in southern Namibia. Ten of these sand ramps, and an additional feature from South Africa, were studied in the field. Sediments and morphology were mapped and a total of 64 OSL dates, 96 sediment samples, 10 heavy mineral assemblages and OSL sensitivity data from 8 samples were examined.
The distribution of sand ramps suggests formation is dependent on (1) sediment supply, (2) accommodation space, (3) persistent unidirectional wind and (4) a variable semi-arid to arid climate. Chronologies and sediment analyses indicate individual sand ramp accumulation is locally controlled by sediment supply modulated by the availability, and nature, of the accommodation space. Comparison between the Namibian and South African sand ramps suggests considerable regional variation in the factors controlling sediment supply.
The Namibian sand ramps show an affinity to local ephemeral river channels. Periods of dated sand ramp activity in multiple features are interpreted as periods of increased regional fluvial activity. Significant activity occurred at &Tilde;21-12 ka (with peaks at 21-18.5 ka and 14.5-12 ka), &Tilde;8.5-7.5 ka and &Tilde;2 ka. Some activity is also indicated at 85-65 ka and 45-35 ka. These results correspond well to regional records.
Overall, this study demonstrates that sand ramps can provide palaeoclimatic information on both the local and regional scale but only if a number of caveats are taken into consideration.
Movement synchrony, social bonding and pro-sociality in ontogeny
Keywords: children
movement synchrony
social cognition
infants
dance and rhythm
intergroup behaviour
minimal group paradigm
cooperation
motor coordination
helping behavior
social preferences

Human sociality, with its wide scope, early ontogeny and pervasiveness across cultures, is remarkable from an evolutionary perspective. We form bonds with other individuals and live in large social groups. We help, empathise with and share our resources with others, who are unfamiliar and genetically unrelated to us. It has been suggested that interpersonal coordination and rhythmic synchronisation of movements may be one proximate mechanism that enables such widespread human sociality and facilitates cooperation. In the last decade, considerable research has examined the effect of movement synchrony on social bonding and cooperation. However, when this thesis started, there was virtually no experimental study investigating the ontogeny of the movement synchrony-social bonding link, which is proposed to have deep evolutionary roots and important, long-lasting consequences in social life.
This thesis aims to investigate the effects of movement synchrony on social bonding and cooperative behaviour across different time points in ontogeny. Three experimental studies were conducted examining infancy, early childhood and middle childhood. Each study explored a different aspect of social bonding and cooperation based on the motor, social and cognitive developments that mark that age group.
Study 1a found that at 12 months of age, infants prefer individuals who move in synchrony with them, when the individuals are social entities, but not when they are non-social. Study 1b showed no preferences for synchrony at 9 months in either social or non-social contexts, however. Study 2 revealed that in early childhood, performing synchronous movements actively with a peer facilitates helping behaviour among the children, as well as eye contact and mutual smiling during the interaction. Finally, Study 3 showed that the social bonding effects of movement synchrony applied to inter- group settings and that performing synchronous movements with out-groups increased bonding towards the out-group in middle childhood.
This thesis followed an interdisciplinary, integrative and naturalistic approach, where (i) literature from a wide range of disciplines motivated and guided the present research; (ii) links between motor, social and cognitive aspects of development, which are often investigated separately, are formed; and (iii) the experiments were designed in ways that represent the real-life occurrences of the investigated phenomena. The current findings provide the first substantial evidence that movement synchrony facilitates social bonding and cooperation in childhood and thereby provides a foundation for future research.
Functional characterisation of key residues in the photopigment melanopsin
Keywords: ipRGC
Opsin
Single Nucleotide Polymorphism
G-protein coupled receptor
Melanopsin
Missense Mutation
Photopigment
Pupillometry
Spectral Tuning
Multi-electrode array
Opn4
Adeno-associated virus
Circadian Rhythms

Melanopsin (Opn4) is the opsin photopigment of intrinsically photosensitive retinal ganglion cells (ipRGCs). It has a conserved opsin structure and activation mechanism, yet demonstrates unusual functional properties that suggest it will possess unique structure-function relationships. The aim of this thesis was to characterise key OPN4 residues by examining the impact of non-synonymous mutations on melanopsin function. A genotype-driven screen of a chemically-mutagenized mouse archive led to the identification of a novel Opn4 mutant, S310A, located at a known opsin spectral tuning site. Action spectra from ipRGC and pupil light responses (PLR) of Opn4S310A mice revealed no change in wavelength of peak sensitivity. However, Opn4S310A PLR was significantly less sensitive at longer wavelengths, consistent with a short-wavelength shift in spectral sensitivity. This suggests S310A acts as a spectral tuning site in melanopsin. Next, the impact of naturally-occurring missense variants in human melanopsin (hOPN4) was examined in vitro. Fluorescent calcium imaging of 16 hOPN4 variants expressed in HEK293 cells revealed four hOPN4 variants abolished or attenuated responses to light (Y146C, R168C, G208S and S308F). These variants were located in conserved opsin motifs for chromophore binding or hydrogen-bond networks, functional roles apparently shared by melanopsin. Finally, two hOPN4 single nucleotide polymorphisms (SNPs) P10L and T394I, associated with abnormal non-image forming behaviour in humans, were explored in vivo. Using targeted viral-delivery of hOPN4 SNPs to mouse ipRGCs, a range of OPN4-driven behaviours, such as circadian photoentrainment and pupil light responses, were found to be comparable with hOPN4 WT control. Multi-electrode array recordings of ipRGCs transduced with hOPN4 T394I virus had significantly attenuated sensitivity and faster response offset, indicating this site may be functionally important for melanopsin activity but compensatory rod and cone input limits changes to non-image forming behaviour.
The evolutionary ecology of animal information use and social dominance
Keywords: individual differences
inequality
social evolution
information use
game theory
social dominance
competition
exploitation
evolutionary demography
evolutionary ecology
social behaviour

Organisms are frequently faced with uncertainty regarding how best to exploit vital resources, and may benefit from collecting information about their distribution through space and time. However, the ways in which competition over resources might systematically facilitate or constrain an individual's ability to use information has been largely overlooked. In this thesis, I develop a conceptual framework for considering how the distribution of limited resources might underpin interdependencies between competition and information use. I focus on the evolutionary ecology of relationships between social dominance and social information use. I begin with an observational study of wild chacma baboons (Papio ursinus) suggesting that, when resources can be monopolised, individuals with low competitive ability are limited in their ability to use social information. Building on these findings, I then develop a general model exploring selection on social information use in a competitive context across three axes of 'resource ecology' (scarcity, depletion rate, monopolisability). This study makes predictions regarding the resource conditions under which competitive ability might constrain social information use, and the potential importance of social information use in the evolution of social dominance. I go on to test these predictions in chacma baboons using a field experiment. This experiment also explores whether the predictability of resource distribution might facilitate the decoupling of social information use from the competitive context in which it was collected. Taken together, these findings provide general insights into the combinations of ecological conditions and behavioural mechanisms that should underpin the benefits of social dominance. I end by building a simple population matrix model to study social dominance using an eco-evolutionary approach, in which feedback loops between ecological and evolutionary processes are considered. By modelling relationships between dominance rank and survival, reproduction, inheritance, and development, I am able to derive estimates of long-term fitness associated with dominance. Using these estimates, I generate predictions regarding how dominance hierarchies should impact the dynamics of group stability, viability, and fission.
Nature and narratives; landscapes, plants and animals in Palaiologan vernacular literature
Keywords: Byzantine
Ecocriticism

This thesis identifies the role of nature within Palaiologan entertainment literature. The texts on which this thesis focuses include a selection of the Palaiologan novels, namely the Achilleid, Velthandros and Chrysandza, Kallimachos and Chrysorroi and Livistros and Rodamni, as well as two other, more satirical works, The Synaxarion of the Honourable Donkey, and An Entertaining Tale of Quadrupeds. These texts seem to be different from earlier works in which nature is prominent, utilising such material in an innovative way. The study of these texts provides us with information both on the Byzantine view of the natural world and on the use of literature during a particularly troubled period of Byzantine history. My main questions therefore are how nature is portrayed in these texts and what can this tell us about the society that produced them. The study of these vernacular texts indicates that the natural world is given a prominent place in the literature of the period, using landscapes, plants and animals in diverse ways to express assorted ideas, or to stress particular aspects of the stories. The animals and landscapes provide hints of the plot to the audience, which the authors sometimes then subvert. The authors draw on earlier Greek material, but parallels with literature from other cultures show similarities which imply a shared medieval perspective on nature with local differences.
Algorithms for trigonometric polynomial and rational approximation
Keywords: rational approximations
algorithms
periodic functions
Hermite integral formula
numerical algorithms

This thesis presents new numerical algorithms for approximating functions by trigonometric polynomials and trigonometric rational functions. We begin by reviewing trigonometric polynomial interpolation and the barycentric formula for trigonometric polynomial interpolation in Chapter 1. Another feature of this chapter is the use of the complex plane, contour integrals and phase portraits for visualising various properties and relationships between periodic functions and their Laurent and trigonometric series. We also derive a periodic analogue of the Hermite integral formula which enables us to analyze interpolation error using contour integrals. We have not been able to find such a formula in the literature.
Chapter 2 discusses trigonometric rational interpolation and trigonometric linearized rational least-squares approximations. To our knowledge, this is the first attempt to numerically solve these problems. The contribution of this chapter is presented in the form of a robust algorithm for computing trigonometric rational interpolants of prescribed numerator and denominator degrees at an arbitrary grid of interpolation points. The algorithm can also be used to compute trigonometric linearized rational least-squares and trigonometric polynomial least-squares approximations.
Chapter 3 deals with the problem of trigonometric minimax approximation of functions, first in a space of trigonometric polynomials and then in a set of trigonometric rational functions. The contribution of this chapter is presented in the form of an algorithm, which to our knowledge, is the first description of a Remez-like algorithm to numerically compute trigonometric minimax polynomial and rational approximations. Our algorithm also uses trigonometric barycentric interpolation and Chebyshev-eigenvalue based root finding.
Chapter 4 discusses the Fourier-Padé (called trigonometric Padé) approximation of a function. We review two existing approaches to the problem, both of which are based on rational approximations of a Laurent series. We present a numerical algorithm with examples and compute various type (m, n) trigonometric Padé approximants.
Food environments in Islamabad, Pakistan
Keywords: food consumption
Pakistan
organic food
sustainability
food environment
food systems
middle class
urban design
alternative food networks
rhythm
local food
commodity geography
fuel scarcity

This dissertation examines how concerns about food system transformations affect how middle class consumers in Islamabad, Pakistan, perceive and approach food consumption in their everyday lives. The dissertation is situated in the context of risky food environments and food fears resulting from intensified, industrialised, and increasingly lengthened global food systems. Working within food geography and food environments paradigms, this dissertation explores how the transformation of food systems is associated with increasing anxiety about food security and safety for middle class urban consumers in Islamabad. Qualitative data gathered from semi-structured interviews and participant observation is used to illustrate the effects external influences, such as energy scarcity and violent events, have on everyday food environments. The dissertation examines the ways in which conceptualisations of 'good food', and trust relationships are negotiated in these dynamic food environments. The intensely geographical nature of these food environments and food systems, and the role of place-specific contexts on perceptions and adaptations related to food anxieties are emphasised. Situated in literatures on food anxiety and food consumption emerging from geography, food studies, and anthropology, this dissertation challenges dominant discourses on alternative and ethical consumption in a globalising food system. The results of this research not only contribute to literature on South Asia, but also contribute to consumption practices of a burgeoning middle class in developing countries.
The interaction of positive and negative intergroup contact
Keywords: Intergroup Relations
Valenced Contact
Social Psychology
Psychology
Intergroup Contact
Negative Contact

In the sixty years following Allport's (1954) formulation of the contact hypothesis, very little research has tested the effect of negative intergroup contact. In recent years, several authors (e.g., Barlow et al., 2012; Pettigrew, 2008; Pettigrew & Tropp, 2013) have expressed concern over this positivity bias within the contact literature. In particular, Barlow et al. (2012) presented evidence that negative contact may have a larger effect on prejudice than positive contact. Barlow et al. argue that this contact valence asymmetry could mean that in socially diverse environments (which provide opportunities for both positive and negative contact), negative contact could counteract (or even reverse) the beneficial effects of positive contact. However, a number of studies have shown that rather than combining additively, positive and negative contact may in fact interact (i.e., the effects of negative contact may change depending upon the level of positive contact, and vice versa, e.g., Birtel & Crisp, 2012; Christ, Ullrich, & Wagner, 2008; Paolini et al., 2014). Unfortunately, the extent of evidence for these valenced contact interactions (and indeed for valenced contact effects in general) is severely limited, making it difficult to build any degree of theoretical (or methodological) consensus. The aims of this thesis are therefore twofold: first, to expand the body of evidence for the effects of negative intergroup contact; and second, to test the possible interaction between positive and negative contact as predictors of outgroup attitudes. With these aims in mind, this thesis presents four survey studies and three experiments testing the main effects and interactions of positive and negative contact across six different contact settings. In so doing, it reports strong evidence for the existence of valenced contact interactions. Based on the profiles of these interaction effects, the thesis ends by discussing possible causal explanations, and their implications for the field of valenced contact research.