Persistent topology of the reionisation bubble network. I: Formalism & Phenomenology

We present a new formalism for studying the topology of HII regions during the Epoch of Reionisation, based on persistent homology theory. With persistent homology, it is possible to follow the evolution of topological features over time. We introduce the notion of a persistence field as a statistical summary of persistence data and we show how these fields can be used to identify different stages of reionisation. We identify two new stages common to all bubble ionisation scenarios. Following an initial pre-overlap and subsequent overlap stage, the topology is first dominated by neutral filaments (filament stage) and then by enclosed patches of neutral hydrogen undergoing outside-in ionisation (patch stage). We study how these stages are affected by the degree of galaxy clustering. We also show how persistence fields can be used to study other properties of the ionisation topology, such as the bubble size distribution and the fractal-like topology of the largest ionised region.Comment: 18 pages, 12 figures, 1 table. Submitted to MNRA

Estimating Vulnerability

Many existing measures of vulnerability lack a theoretical basis. In this paper we propose to measure vulnerability rigorously as the welfare of a household which solves an intertemporal optimisation model under risk.In such models, in essence a stochastic version of the Ramsey model, an important part of chronic poverty may be caused by the ex ante response of households to risks. Our simulation results indicate that whether or not a household is to be classified as vulnerable depends strongly on the time horizon considered. We use the model to assess the accuracy of existing regression-based vulnerability measures. We find that these methods can be vastly improved by including asset measures in the regression.Vulnerability, household models.

Geodesic motion and phase-space evolution of massive neutrinos

The non-trivial phase-space distribution of relic neutrinos is responsible for the erasure of primordial density perturbations on small scales, which is one of the main cosmological signatures of neutrino mass. In this paper, we present a new code,fastdf, for generating 1%-accurate particle realisations of the neutrino phase-space distribution using relativistic perturbation theory. We use the geodesic equation to derive equations of motion for massive particles moving in a weakly perturbed spacetime and integrate particles accordingly. We demonstrate how to combine geodesic-based initial conditions with the δf method to minimise shot noise and clarify the definition of the neutrino momentum, finding that large errors result if the wrong parametrisation is used. Compared to standard Lagrangian methods with ad-hoc thermal motions,fastdf achieves substantial improvements in accuracy. We outline the approximation schemes used to speed up the code and to ensure symplectic integration that preserves phase-space density. Finally, we discuss implications for neutrino particles in cosmological N-body simulations. In particular, we argue that particle methods can accurately describe the neutrino distribution from z = 109, when neutrinos are linear and ultra-relativistic, down to z = 0, when they are nonlinear and non-relativistic. fastdf can be used to set up accurate initial conditions (ICs) for N-body simulations and has been integrated into the higher-order IC code monofonic

Neutrinos from horizon to sub-galactic scales

A first determination of the mass scale set by the lightest neutrino remains a crucial outstanding challenge for cosmology and particle physics, with profound implications for the history of the Universe and physics beyond the Standard Model. In this thesis, we present the results from three methodological papers and two applications that contribute to our understanding of the cosmic neutrino background. First, we introduce a new method for the noise-suppressed evaluation of neutrino phase-space statistics. Its primary application is in cosmological N-body simulations, where it reduces the computational cost of simulating neutrinos by orders of magnitude without neglecting their nonlinear evolution. Second, using a recursive formulation of Lagrangian perturbation theory, we derive higher-order neutrino corrections and show that these can be used for the accurate and consistent initialisation of cosmological neutrino simulations. Third, we present a new code for the initialisation of neutrino particles, accounting both for relativistic effects and the full Boltzmann hierarchy. Taken together, these papers demonstrate that with the combination of the methods described therein, we can accurately simulate the evolution of the neutrino background over 13.8 Gyr from the linear and ultra-relativistic regime at $z=10^9$ down to the non-relativistic yet nonlinear regime at $z=0$. Moreover, they show that the accuracy of large-scale structure predictions can be controlled at the sub-percent level needed for a neutrino mass determination. In a first application of these methods, we present a forecast for direct detection of the neutrino background, taking into account the gravitational enhancement (or indeed suppression) of the local density due to the Milky Way and the observed large-scale structure within 200 Mpc/h. We determine that the large-scale structure is more important than the Milky Way for neutrino masses below 0.1 eV, predict the orientation of the neutrino dipole, and study small-scale anisotropies. We predict that the angular distribution of neutrinos is anti-correlated with the projected matter density, due to the capture or deflection of neutrinos by massive objects along the line of sight. Finally, we present the first results from a new suite of hydrodynamical simulations, which includes the largest ever simulation with neutrinos and galaxies. We study the extent to which variations in neutrino mass can be treated independently of astrophysical processes, such as feedback from supernovae and black holes. Our findings show that baryonic feedback is weakly dependent on neutrino mass, with feedback being stronger for models with larger neutrino masses. By studying individual dark matter halos, we attribute this effect to the increased baryon density relative to cold dark matter and a reduction in the binding energies of halos. We show that percent-level accurate modelling of the matter power spectrum in a cosmologically interesting parameter range is only possible if the cosmology-dependence of feedback is taken into account

Growth and Risk: Methodology and Micro Evidence

There has been a revival of interest in the effect of risk on economic growth. We quantify both ex ante and ex post effects of risk using a stochastic version of the Ramsey model. We develop a simulation-based econometric methodology which allows us to estimate the model in the structural form suggested by theory. The methodology is applied to micro data from a remarkable long-running panel data set for rural households in Zimbabwe. We find that risk substantially reduces growth: in the ergodic distribution the mean (across households) capital stock is 46% lower than in the absence of risk. About two-thirds of the impact of risk is due to the ex ante effect (i.e. the behavioral response to risk) which is usually not taken into account in policy design. Our results suggest that the e¤ectiveness of policy interventions which reduce exposure to shocks or help households in risk management may be seriously underestimated.Farm household models, stochastic Ramsey growth models, estimation by simulation.

Vulnerability in a Stochastic Dynamic Model

Most measures of vulnerability are a-theoretic and essentially static. In this paper we use a stochastic Ramsey model to find a household's optimal welfare and we measure vulnerability as the shortfall from the welfare attained if the household consumed permanently at the poverty line. The results indicate that vulnerability is very sensitive to the time horizon considered. We find that the accuracy of existing regression-based vulnerability measures can be greatly improved by including asset measures in the regression

Vulnerability in a Stochastic Dynamic Model

Most measures of vulnerability are a-theoretic and essentially static. In this paper we use a stochastic Ramsey model to find a household's optimal welfare and we measure vulnerability as the shortfall from the welfare attained if the household consumed permanently at the poverty line. The results indicate that vulnerability is very sensitive to the time horizon considered. We find that the accuracy of existing regression-based vulnerability measures can be greatly improved by including asset measures in the regression.vulnerability, expected poverty, risk, Ramsey model, consumption regressions

Optimizing WebPage Interest Research Proposal

Abstract In the rapidly evolving and growing environment of the internet, web site owners aim to maximize interest for their web site. How do you position a site optimally on the internet? Where does advertising generate the biggest increase in interest for your website? This document proposes a study to research these issues and develop an answer to these questions

Persistent topology of the reionization bubble network – II. Evolution and classification

We study the topology of the network of ionized and neutral regions that characterized the intergalactic medium during the Epoch of Reionization. Our analysis uses the formalism of persistent homology, which offers a highly intuitive and comprehensive description of the ionization topology in terms of the births and deaths of topological features. Features are identified as k-dimensional holes in the ionization bubble network, whose abundance is given by the kth Betti number: β0 for ionized bubbles, β1 for tunnels, and β2 for neutral islands. Using semi-numerical models of reionization, we investigate the dependence on the properties of sources and sinks of ionizing radiation. Of all topological features, we find that the tunnels dominate during reionization and that their number is easiest to observe and most sensitive to the astrophysical parameters of interest, such as the gas fraction and halo mass necessary for star formation. Seen as a phase transition, the importance of the tunnels can be explained by the entanglement of two percolating clusters and the fact that higher-dimensional features arise when lower-dimensional features link together. We also study the relation between the morphological components of the bubble network (bubbles, tunnels, and islands) and those of the cosmic web (clusters, filaments, and voids), describing a correspondence between the k-dimensional features of both. Finally, we apply the formalism to mock observations of the 21-cm signal. Assuming 1000 observation hours with HERA Phase II, we show that astrophysical models can be differentiated and confirm that persistent homology provides additional information beyond the power spectrum