Parameter estimation and the statistics of nonlinear cosmic fields

The large scale distribution of matter in the universe contains valuable information about fundamental cosmological parameters, the properties of dark matter and the formation processes of galaxies. The best hope of retrieving this information lies in providing a statistical description of the matter distribution that may be used for comparing models with observation. Unfortunately much of the important information lies on scales below which nonlinear gravitational effects have taken hold, complicating both models and statistics considerably. This thesis deals with the distribution of matter - mass and galaxies - on such scales. The aim is to develop new statistical tools that make use of the nonlinear evolution for the purposes of constraining cosmological models.A new derivation for the 1 -point probability distribution function (PDF) for density inhomogeneities is presented first. The calculation is based upon an exact statistical treatment, using the Chapman -Kolmogorov equation and second order Eulerian perturbation theory to propagate the initial density field into the nonlinear regime. The analysis yields the generating function for moments, allowing for a straightforward derivation of the skewness. A new dependance upon the perturbation spectrum is found for the skewness at second order. The results of the analysis are compared against other methods for deriving the 1 -point PDF and against data from numerical N -body simulations. Good agreement is found in both cases.The 1 -point PDF for galaxies is derived next, taking into account nonlinear biasing of the density field and the distorting effects associated with working in redshift space. Once again perturbation theory is used to evolve the density field into the nonlinear regime and the Chapman -Kolmogorov equation to propagate the initial probabilities. Transformation of the dark matter density to a biased galaxy distribution is done through an Eulerian biasing prescription, expanding the nonlinear bias function to second order. An advantage of the Chapman- Kolmogorov approach is the natural way that different initial conditions and biasing models may be incorporated. It is shown that the method is general enough to allow a non -deterministic (hidden variable) bias. The dependance on cosmological parameters of the evolution of the galaxy 1 -point PDF is demonstrated and a method for differentiating between degenerate models in linear theory is presented. A new derivation of the skewness for a biased density field in red - shift space is also given and shown to depend significantly on the density and bias parameters. The results are compared favourably with those of numerical simulations.Finally a new, general formalism for analysing parameter information from non - Gaussian cosmic fields is developed. The method is general enough for application to a range of problems including the measurement of parameters from galaxy redshift surveys, weak lensing surveys and velocity field surveys. It may also be used to test for non -Gaussianity in the Cosmic Microwave Background. Generalising maximum likelihood analysis to second order, the non -Gaussian Fisher information matrix is derived and the detailed shapes of likelihood surfaces in parameter space are explored via a parameter entropy function. Concentrating on non -Gaussianity due to nonlinear evolution under gravity, the generalised Fisher analysis is applied to a model of a Galaxy redshift survey, including the effects of biasing, redshift space distortions and shot noise. Incorporating second order moments into the parameter estimation is found to have a large effect, breaking all of the degeneracies between parameters. The results indicate that using nonlinear likelihood analysis may yield parameter uncertainties around the few percent level from forthcoming large galaxy redshift surveys

Finite size effects in perturbed boundary conformal field theories

We discuss the finite-size properties of a simple integrable quantum field theory in 1+1 dimensions with non-trivial boundary conditions. Novel off-critical identities between cylinder partition functions of models with differing boundary conditions are derived.Comment: 7 pages, 11 figures, JHEP proceedings style. Uses epsfig, amssymb. Talk given at the conference `Nonperturbative Quantum Effects 2000', Pari

Radiation exposure of LDEF: Initial results

Initial results from LDEF include radiation detector measurements from four experiments, P0006, P0004, M0004, and A0015. The detectors were located on both the leading and trailing edges of the orbiter and also on the Earthside end. This allowed the directional dependence of the incoming radiation to be measured. Total absorbed doses from thermoluminescent detectors (TLDs) verified the predicted spatial east-west dose ratio dependence of a factor approx. 2.5, due to trapped proton anisotropy in the South Atlantic Anomaly. On the trailing edge of the orbiter a range of doses from 6.64 to 2.91 Gy were measured under Al equivalent shielding of 0.42 to 1.11 g/sq cm. A second set of detectors near this location yielded doses of 6.48 to 2.66 Gy under Al equivalent shielding of 0.48 to 15.4 g/sq cm. On the leading edge, doses of 2.58 to 2.10 Gy were found under Al equivalent shielding of 1.37 to 2.90 g/sq cm. Initial charged particle LET (linear energy transfer) spectra, fluxes, doses and dose equivalents, for LET in H2O greater than or = 8 keV/micron, were measured with plastic nuclear track detectors (PNTDs) located in two experiments. Also preliminary data on low energy neutrons were obtained from detectors containing (6)LiF foils

A model for cascading failures in complex networks

Large but rare cascades triggered by small initial shocks are present in most of the infrastructure networks. Here we present a simple model for cascading failures based on the dynamical redistribution of the flow on the network. We show that the breakdown of a single node is sufficient to collapse the efficiency of the entire system if the node is among the ones with largest load. This is particularly important for real-world networks with an highly hetereogeneous distribution of loads as the Internet and electrical power grids.Comment: 4 pages, 4 figure

Cascade-based attacks on complex networks

We live in a modern world supported by large, complex networks. Examples range from financial markets to communication and transportation systems. In many realistic situations the flow of physical quantities in the network, as characterized by the loads on nodes, is important. We show that for such networks where loads can redistribute among the nodes, intentional attacks can lead to a cascade of overload failures, which can in turn cause the entire or a substantial part of the network to collapse. This is relevant for real-world networks that possess a highly heterogeneous distribution of loads, such as the Internet and power grids. We demonstrate that the heterogeneity of these networks makes them particularly vulnerable to attacks in that a large-scale cascade may be triggered by disabling a single key node. This brings obvious concerns on the security of such systems.Comment: 4 pages, 4 figures, Revte

Charged particle LET-spectra measurements aboard LDEF

The linear energy transfer (LET) spectra of charged particles was measured in the 5 to 250 keV/micron (water) interval with CR-39 and in the 500 to 1500 keV/micron (water) interval with polycarbonate plastic nuclear track detectors (PNTDs) under different shielding depths in the P0006 experiment. The optimal processing conditions were determined for both PNTDs in relation to the relatively high track densities due to the long term exposure in space. The total track density was measured over the selected samples, and tracks in coincidence on the facing surfaces of two detector sheets were selected for measuring at the same position on each sheet. The short range (SR) and Galactic Cosmic Ray (GCR) components were measured separately with CR-39 PNTDs and the integral dose and dose rate spectra of charged particles were also determined. The high LET portion of the LET spectra was measured with polycarbonate PNTDs with high statistical accuracy. This is a unique result of this exposure due to the low flux of these types of particles for typical spaceflight durations. The directional dependence of the charged particles at the position of the P0006 experiment was also studied by four small side stacks which surrounded the main stack and by analyzing the dip angle and polar angle distributions of the measured SR and GCR particle tracks in the main stack

Growing dynamics of Internet providers

In this paper we present a model for the growth and evolution of Internet providers. The model reproduces the data observed for the Internet connection as probed by tracing routes from different computers. This problem represents a paramount case of study for growth processes in general, but can also help in the understanding the properties of the Internet. Our main result is that this network can be reproduced by a self-organized interaction between users and providers that can rearrange in time. This model can then be considered as a prototype model for the class of phenomena of aggregation processes in social networks

LET spectra measurements of charged particles in the P0006 experiment on LDEF

Measurements are under way of the charged particle radiation environment of the Long Duration Exposure Facility (LDEF) satellite using stacks of plastic nuclear track detectors (PNTD's) placed in different locations of the satellite. In the initial work the charge, energy, and linear energy transfer (LET) spectra of charged particles were measured with CR-39 double layer PNTD's located on the west side of the satellite (Experiment P0006). Primary and secondary stopping heavy ions were measured separately from the more energetic particles. Both trapped and galactic cosmic ray (GCR) particles are included, with the latter component being dominated by relativistic iron particles. The results from the P0006 experiment will be compared with similar measurements in other locations on LDEF with different orientation and shielding conditions. The remarkably detailed investigation of the charged particle radiation environment of the LDEF satellite will lead to a better understanding of the radiation environment of the Space Station Freedom. It will enable more accurate prediction of single event upsets (SEU's) in microelectronics and, especially, more accurate assessment of the risk - contributed by different components of the radiation field (GCR's, trapped protons, secondaries and heavy recoils, etc.) - to the health and safety of crew members

Cooperation and Contagion in Web-Based, Networked Public Goods Experiments

A longstanding idea in the literature on human cooperation is that cooperation should be reinforced when conditional cooperators are more likely to interact. In the context of social networks, this idea implies that cooperation should fare better in highly clustered networks such as cliques than in networks with low clustering such as random networks. To test this hypothesis, we conducted a series of web-based experiments, in which 24 individuals played a local public goods game arranged on one of five network topologies that varied between disconnected cliques and a random regular graph. In contrast with previous theoretical work, we found that network topology had no significant effect on average contributions. This result implies either that individuals are not conditional cooperators, or else that cooperation does not benefit from positive reinforcement between connected neighbors. We then tested both of these possibilities in two subsequent series of experiments in which artificial seed players were introduced, making either full or zero contributions. First, we found that although players did generally behave like conditional cooperators, they were as likely to decrease their contributions in response to low contributing neighbors as they were to increase their contributions in response to high contributing neighbors. Second, we found that positive effects of cooperation were contagious only to direct neighbors in the network. In total we report on 113 human subjects experiments, highlighting the speed, flexibility, and cost-effectiveness of web-based experiments over those conducted in physical labs