A Simple Approach to Maximum Intractable Likelihood Estimation

Approximate Bayesian Computation (ABC) can be viewed as an analytic approximation of an intractable likelihood coupled with an elementary simulation step. Such a view, combined with a suitable instrumental prior distribution permits maximum-likelihood (or maximum-a-posteriori) inference to be conducted, approximately, using essentially the same techniques. An elementary approach to this problem which simply obtains a nonparametric approximation of the likelihood surface which is then used as a smooth proxy for the likelihood in a subsequent maximisation step is developed here and the convergence of this class of algorithms is characterised theoretically. The use of non-sufficient summary statistics in this context is considered. Applying the proposed method to four problems demonstrates good performance. The proposed approach provides an alternative for approximating the maximum likelihood estimator (MLE) in complex scenarios

Economics of Disability Research Report #4: Estimates of the Prevalence of Disability, Employment Rates, and Median Household Size-Adjusted Income for People with Disabilities Aged 18 though 64 in the United States by State, 1980 through 2000

This report replicates Economics of Disability Reports 1, 2, and 3, with some minor changes. These reports contain the prevalence of a disability, employment rates, and median household size-adjusted income between states over the 1980s and 1990s. In response to the requests of state officials to generate statistics that reflect the population they serve, this report includes people aged 18 through 64 rather than people aged 25 through 61. The new age group is more likely to include those who enter the labor force after high school, during college, and post-college as well as those people who have decided not to take early retirement. In addition, at the request of state officials, the statistics in this report are not separated by gender because most government agencies do not make a strong distinction between men and women, even though men and women face different labor market conditions. This report uses data from the March Current Population Survey to estimate the prevalence of a disability, employment rate, and median household size-adjusted income among the non-institutionalized working-age (aged 18 through 64) civilian population in the United States, and for each state and the District of Columbia for the survey years 1981 through 2000 and income/employment years 1980 through 1999. Two definitions of disability that are commonly used in the literature—work limitation and work disability—are utilized. The prevalence of a work limitation and work disability varies greatly across states and over time. The employment rate of persons with work limitations relative to that of persons without a disability varies greatly across states. However, over the last 20 years the relative employment rate of those with work limitations dramatically declined overall and in most states. Consequently, the decrease in the relative employment rate for persons with work limitations induced the growth in the median household size-adjusted income of those with work limitations

Limitations of the Hodgkin-Huxley formalism : effects of single channel kinetics on transmembrane voltage dynamics

A standard membrane model, based on the continuous deterministic Hodgkin-Huxley equations, is compared to an alternative membrane model, based on discrete stochastic ion channel populations represented through Marlcov processes. Simulations explore the relationship between these two levels of description: the behavior predicted by the macroscopic membrane currents versus the behavior predicted by their microscopic ion channels. Discussion considers the extent to which these random events underlying neural signals mediate random events in neural computation

A comprehensive treatment of electromagnetic interactions and the three-body spectator equations

We present a general derivation the three-body spectator (Gross) equations and the corresponding electromagnetic currents. As in previous paper on two-body systems, the wave equations and currents are derived from those for Bethe-Salpeter equation with the help of algebraic method using a concise matrix notation. The three-body interactions and currents introduced by the transition to the spectator approach are isolated and the matrix elements of the e.m. current are presented in detail for system of three indistinguishable particles, namely for elastic scattering and for two and three body break-up. The general expressions are reduced to the one-boson-exchange approximation to make contact with previous work. The method is general in that it does not rely on introduction of the electromagnetic interaction with the help of the minimal replacement. It would therefore work also for other external fields

Integrable subsystem of Yang--Mills dilaton theory

With the help of the Cho-Faddeev-Niemi-Shabanov decomposition of the SU(2) Yang-Mills field, we find an integrable subsystem of SU(2) Yang-Mills theory coupled to the dilaton. Here integrability means the existence of infinitely many symmetries and infinitely many conserved currents. Further, we construct infinitely many static solutions of this integrable subsystem. These solutions can be identified with certain limiting solutions of the full system, which have been found previously in the context of numerical investigations of the Yang-Mills dilaton theory. In addition, we derive a Bogomolny bound for the integrable subsystem and show that our static solutions are, in fact, Bogomolny solutions. This explains the linear growth of their energies with the topological charge, which has been observed previously. Finally, we discuss some generalisations.Comment: 25 pages, LaTex. Version 3: appendix added where the equivalence of the field equations for the full model and the submodel is demonstrated; references and some comments adde

The abundance and spatial distribution of ultra-diffuse galaxies in nearby galaxy clusters

Recent observations have highlighted a significant population of faint but large (r_eff>1.5 kpc) galaxies in the Coma cluster. The origin of these Ultra Diffuse Galaxies (UDGs) remains puzzling, as the interpretation of the observational results has been hindered by the subjective selection of UDGs, and the limited study of only the Coma (and some examples in the Virgo-) cluster. We extend the study of UDGs using 8 clusters in the redshift range 0.044<z<0.063 with deep g- and r-band imaging data taken with MegaCam at the CFHT. We describe an automatic selection pipeline for quantitative identification, tested for completeness using image simulations of these galaxies. We find that the abundance of the UDGs we can detect increases with cluster mass, reaching ~200 in typical haloes of M200~10^15 Msun. The cluster UDGs have colours consistent with the cluster red sequence, and have a steep size distribution that declines as n~r_eff^-3.4. Their radial distribution is significantly steeper than NFW in the outskirts, and is significantly shallower in the inner parts. They follow the same radial distribution as the more massive quiescent galaxies in the clusters, except within the core region of r<0.15XR200 (or <300 kpc). Within this region the number density of UDGs drops and is consistent with zero. These diffuse galaxies can only resist tidal forces down to this cluster-centric distance if they are highly centrally dark-matter dominated. The observation that the radial distribution of more compact dwarf galaxies (r_eff<1.0 kpc) with similar luminosities follows the same distribution as the UDGs, but exist down to a smaller distance of 100kpc from the cluster centres, indicates that they may have similarly massive sub-haloes as the UDGs. Although several scenarios can give rise to the UDG population, our results point to differences in the formation history as the most plausible explanation.Comment: 12 pages, 11 figures. Accepted for publication in A&A after minor revisio

Quark-Antiquark Bound States in the Relativistic Spectator Formalism

The quark-antiquark bound states are discussed using the relativistic spectator (Gross) equations. A relativistic covariant framework for analyzing confined bound states is developed. The relativistic linear potential developed in an earlier work is proven to give vanishing meson$\to$ $q+\bar{q}$ decay amplitudes, as required by confinement. The regularization of the singularities in the linear potential that are associated with nonzero energy transfers (i.e. $q^2=0,q^{\mu}\neq0$) is improved. Quark mass functions that build chiral symmetry into the theory and explain the connection between the current quark and constituent quark masses are introduced. The formalism is applied to the description of pions and kaons with reasonable results.Comment: 31 pages, 16 figure

Scaling study of Si and strained Si n-MOSFETs with different high-k gate stacks

Using ensemble Monte Carlo device simulations, this paper studies the impact of interface roughness and soft-optical phonon scattering on the performance of sub-100nm Si and strained Si MOSFETs with different high-k gate stacks. Devices with gate lengths down to 25nm have been investigated

The role of electron-electron interactions in two-dimensional Dirac fermions

The role of electron-electron interactions on two-dimensional Dirac fermions remains enigmatic. Using a combination of nonperturbative numerical and analytical techniques that incorporate both the contact and long-range parts of the Coulomb interaction, we identify the two previously discussed regimes: a Gross-Neveu transition to a strongly correlated Mott insulator, and a semi-metallic state with a logarithmically diverging Fermi velocity accurately described by the random phase approximation. Most interestingly, experimental realizations of Dirac fermions span the crossover between these two regimes providing the physical mechanism that masks this velocity divergence. We explain several long-standing mysteries including why the observed Fermi velocity in graphene is consistently about 20 percent larger than the best values calculated using ab initio and why graphene on different substrates show different behavior.Comment: 11 pages, 4 figure