Investigating Nonlinearity: A Note on the Implementation of Hamilton's Methodology

In this paper we give an account of the new approach to nonlinear econometric modelling proposed by Hamilton (2001) and briefly describe some of the methods of nonlinear optimization that may be used in the Gauss computer program provided by Hamilton for the implementation of his methodology. The performance of this program is investigated using data relating to Hamilton's example concerning the US Phillips curve, two versions of the Gauss software and a range of alternative numerical optimization options and values for the important Gauss parameter _oprteps. Finally, the effects of changes in the sample data on the results produced by Hamilton's procedure are explored. The results presented suggest some clear conclusions, which will be of value to those contemplating working with Hamilton's new method.

Investigating Nonlinearity: A Note on the Estimation of Hamilton’s Random Field Regression Model

This is a revised and extended version of the authors’ 2003 Trinity Economic Paper. It describes Hamilton’s (2001) approach to nonlinear econometric modelling and some of the methods of nonlinear optimization, as before, but adds significantly to the investigation of Hamilton’s Gauss program for the implementation of his methodology. Specifically, it reports on the performance of this program using data relating to Hamilton’s US Phillips curve example, the use of two versions of the Gauss software and a range of numerical optimization options. It also examines the impact of changes in initial parameter estimates, the use of algorithm switching strategies, and the e?ects of changes in the sample data on the results produced by Hamilton’s procedure. The new results presented suggest some further clear conclusions that will be of value to those using Hamilton’s method.

Structure Formation with Majoron Supermultiplet

We show that the late-decaying particle scenario may be realized in the supersymmetric singlet majoron model with the majoron scale $10-200$ TeV. The smajoron decaying into two neutrinos is the late-decaying particle with the mass $0.1-1$ TeV and the life-time $2\times10^3-8\times10^4$ seconds. The lower limit of the majorino mass is $4-40$ TeV in order to avoid the overclosure of the universe due to the decay-produced LSP. The muon neutrino and the tau neutrino can be used to explain the atmospheric and the solar neutrino deficit.Comment: 9 pages, latex; some changes in the main text, but none in conclusio

Sociological variety and the transmission efficiency of Mycobacterium tuberculosis: a secondary analysis of qualitative and quantitative data from 15 communities in Zambia

Objectives: Selected Zambian communities formed part of a cluster randomised trial: the Zambia and South Africa TB and AIDS Reduction study (ZAMSTAR). There was wide variability in the prevalence of Mycobacterium tuberculosis infection and tuberculosis (TB) disease across these communities. We sought to clarify whether specific communities could have been more/less vulnerable to M. tuberculosis transmission as a result of sociological variety relevant to transmission efficiency. Design: We conducted a mixed methods secondary analysis using existing data sets. First, we analysed qualitative data to categorise and synthesise patterns of socio-spatial engagement across communities. Second, we compared emergent sociological variables with a measure of transmission efficiency: the ratio of the annual risk of infection to TB prevalence. Setting: ZAMSTAR communities in urban and peri-urban Zambia, spanning five provinces. Participants Fifteen communities, each served by a health facility offering TB treatment to a population of at least 25 000. TB notification rates were at least 400 per 100 000 per annum and HIV seroprevalence was estimated to be high. Results: Crowding, movement, livelihoods and participation in recreational activity differed across communities. Based on 12 socio-spatial indicators, communities were qualitatively classified as more/less spatially crowded and as more/less socially ‘open’ to contact with others, with implications for the presumptive risk of M. tuberculosis transmission. For example, watching video shows in poorly ventilated structures posed a presumptive risk in more socially open communities, while outdoor farming and/or fishing were particularly widespread in communities with lower transmission measures. Conclusions: A dual dynamic of ‘social permeability’ and crowding appeared relevant to disparities in M. tuberculosis transmission efficiency. To reduce transmission, certain socio-spatial aspects could be adjusted (eg, increasing ventilation on transport), while more structural aspects are less malleable (eg, reliance on public transport). We recommend integrating community level typologies with genome sequencing techniques to further explore the significance of ‘social permeability’. Trial registration number: ISRCTN36729271

Cosmic Microwave Background Anisotropy with Cosine-Type Quintessence

We study the Cosmic Microwave Background (CMB) anisotropies produced by cosine-type quintessence models. In our analysis, effects of the adiabatic and isocurvature fluctuations are both taken into account. For purely adiabatic fluctuations with scale invariant spectrum, we obtain a stringent constraint on the model parameters using the CMB data from COBE, BOOMERanG and MAXIMA. Furthermore, it is shown that isocurvature fluctuations have significant effects on the CMB angular power spectrum at low multipoles in some parameter space, which may be detectable in future satellite experiments. Such a signal may be used to test the cosine-type quintessence models.Comment: 21 pages, 9 figure

Is the evidence for dark energy secure?

Several kinds of astronomical observations, interpreted in the framework of the standard Friedmann-Robertson-Walker cosmology, have indicated that our universe is dominated by a Cosmological Constant. The dimming of distant Type Ia supernovae suggests that the expansion rate is accelerating, as if driven by vacuum energy, and this has been indirectly substantiated through studies of angular anisotropies in the cosmic microwave background (CMB) and of spatial correlations in the large-scale structure (LSS) of galaxies. However there is no compelling direct evidence yet for (the dynamical effects of) dark energy. The precision CMB data can be equally well fitted without dark energy if the spectrum of primordial density fluctuations is not quite scale-free and if the Hubble constant is lower globally than its locally measured value. The LSS data can also be satisfactorily fitted if there is a small component of hot dark matter, as would be provided by neutrinos of mass 0.5 eV. Although such an Einstein-de Sitter model cannot explain the SNe Ia Hubble diagram or the position of the `baryon acoustic oscillation' peak in the autocorrelation function of galaxies, it may be possible to do so e.g. in an inhomogeneous Lemaitre-Tolman-Bondi cosmology where we are located in a void which is expanding faster than the average. Such alternatives may seem contrived but this must be weighed against our lack of any fundamental understanding of the inferred tiny energy scale of the dark energy. It may well be an artifact of an oversimplified cosmological model, rather than having physical reality.Comment: 12 pages, 5 figures; to appear in a special issue of General Relativity and Gravitation, eds. G.F.R. Ellis et al; Changes: references reformatted in journal style - text unchange

Bounds from Primordial Black Holes with a Near Critical Collapse Initial Mass Function

Recent numerical evidence suggests that a mass spectrum of primordial black holes (PBHs) is produced as a consequence of near critical gravitational collapse. Assuming that these holes formed from the initial density perturbations seeded by inflation, we calculate model independent upper bounds on the mass variance at the reheating temperature by requiring the mass density not exceed the critical density and the photon emission not exceed current diffuse gamma-ray measurements. We then translate these results into bounds on the spectral index n by utilizing the COBE data to normalize the mass variance at large scales, assuming a constant power law, then scaling this result to the reheating temperature. We find that our bounds on n differ substantially (\delta n > 0.05) from those calculated using initial mass functions derived under the assumption that the black hole mass is proportional to the horizon mass at the collapse epoch. We also find a change in the shape of the diffuse gamma-ray spectrum which results from the Hawking radiation. Finally, we study the impact of a nonzero cosmological constant and find that the bounds on n are strengthened considerably if the universe is indeed vacuum-energy dominated today.Comment: 24 pages, REVTeX, 5 figures; minor typos fixed, two refs added, version to be published in PR

Detectability of Tensor Perturbations Through CBR Anisotropy (final published version)

Detection of the tensor perturbations predicted in inflationary models is important for testing inflation as well as for reconstructing the inflationary potential. We show that because of cosmic variance the tensor contribution to the square of the CBR quadrupole anisotropy must be greater than about 20\% of the scalar contribution to ensure a statistically significant detection of tensor perturbations. This sensitivity could be achieved by full-sky measurements on angular scales of $3^{\circ}$ and $0.5^\circ$.Comment: 10 pages, uu-encoded postscript file, FERMILAB-PUB-94/175-

Limits on the gravity wave contribution to microwave anisotropies

We present limits on the fraction of large angle microwave anisotropies which could come from tensor perturbations. We use the COBE results as well as smaller scale CMB observations, measurements of galaxy correlations, abundances of galaxy clusters, and Lyman alpha absorption cloud statistics. Our aim is to provide conservative limits on the tensor-to-scalar ratio for standard inflationary models. For power-law inflation, for example, we find T/S<0.52 at 95% confidence, with a similar constraint for phi^p potentials. However, for models with tensor amplitude unrelated to the scalar spectral index it is still currently possible to have T/S>1.Comment: 23 pages, 7 figures, accepted for publication in Phys. Rev. D. Calculations extended to blue spectral index, Fig. 6 added, discussion of results expande

Running coupling: Does the coupling between dark energy and dark matter change sign during the cosmological evolution?

In this paper we put forward a running coupling scenario for describing the interaction between dark energy and dark matter. The dark sector interaction in our scenario is free of the assumption that the interaction term $Q$ is proportional to the Hubble expansion rate and the energy densities of dark sectors. We only use a time-variable coupling $b(a)$ (with $a$ the scale factor of the universe) to characterize the interaction $Q$. We propose a parametrization form for the running coupling $b(a)=b_0a+b_e(1-a)$ in which the early-time coupling is given by a constant $b_e$, while today the coupling is given by another constant, $b_0$. For investigating the feature of the running coupling, we employ three dark energy models, namely, the cosmological constant model ($w=-1$), the constant $w$ model ($w=w_0$), and the time-dependent $w$ model ($w(a)=w_0+w_1(1-a)$). We constrain the models with the current observational data, including the type Ia supernova, the baryon acoustic oscillation, the cosmic microwave background, the Hubble expansion rate, and the X-ray gas mass fraction data. The fitting results indicate that a time-varying vacuum scenario is favored, in which the coupling $b(z)$ crosses the noninteracting line ($b=0$) during the cosmological evolution and the sign changes from negative to positive. The crossing of the noninteracting line happens at around $z=0.2-0.3$, and the crossing behavior is favored at about 1$\sigma$ confidence level. Our work implies that we should pay more attention to the time-varying vacuum model and seriously consider the phenomenological construction of a sign-changeable or oscillatory interaction between dark sectors.Comment: 8 pages, 5 figures; refs added; to appear in EPJ