Grassmann integrals by machine

I present a numerical algorithm for direct evaluation of multiple Grassmann integrals. The approach is exact and suffers no Fermion sign problems. Memory requirements grow exponentially with the interaction range and the transverse size of the system. Low dimensional systems of order a thousand Grassmann variables can be evaluated on a workstation.Comment: LATTICE98(algorithms), 3 pages, 3 figures, uses espcrc2, revision darkens figure points, adding one from the RIKEN/BNL Supercompute

New indication for a dichotomy in the interior structure of Uranus and Neptune from the application of modified shape and rotation data

Since the Voyager fly-bys of Uranus and Neptune, improved gravity field data have been derived from long-term observations of the planets' satellite motions, and modified shape and solid-body rotation periods were suggested. A faster rotation period (-40 min) for Uranus and a slower rotation period (+1h20) of Neptune compared to the Voyager data were found to minimize the dynamical heights and wind speeds. We apply the improved gravity data, the modified shape and rotation data, and the physical LM-R equation of state to compute adiabatic three-layer structure models, where rocks are confined to the core, and homogeneous thermal evolution models of Uranus and Neptune. We present the full range of structure models for both the Voyager and the modified shape and rotation data. In contrast to previous studies based solely on the Voyager data or on empirical EOS, we find that Uranus and Neptune may differ to an observationally significant level in their atmospheric heavy element mass fraction Z1 and nondimensional moment of inertia, nI. For Uranus, we find Z1 < 8% and nI=0.2224(1), while for Neptune Z1 < 65% and nI=0.2555(2) when applying the modified shape and rotation data, while for the unmodified data we compute Z1 < 17% and nI=0.230(1) for Uranus and Z1 < 54% and nI=0.2410(8) for Neptune. In each of these cases, solar metallicity models (Z1=0.015) are still possible. The cooling times obtained for each planet are similar to recent calculations with the Voyager rotation periods: Neptune's luminosity can be explained by assuming an adiabatic interior while Uranus cools far too slowly. More accurate determinations of these planets' gravity fields, shapes, rotation periods, atmospheric heavy element abundances, and intrinsic luminosities are essential for improving our understanding of the internal structure and evolution of icy planets.Comment: accepted to Planet. Space Sci., special editio

The dynamic mature of the Adams ring arcs - Fraternite, Egalite (2,1), Liberte, Courage

By considering the finite mass of Fraternite, the dynamic nature of the Adams ring arcs is regarded as caused by the reaction of a test body (a minor arc) through the Lindblad resonance (LR). Assumming the eccentricity of the test body is larger than that of Galatea, this generates several locations along the ring in the neighborhood of Fraternite where the time averaged force on a test body vanishes. These locations appear to correspond to the time dependent configuration of Egalite (2,1), Liberte, and Courage, and seem to be able to account for the dynamics of the arcs. Such a configuration is a dynamic one because the minor arcs are not bounded by the corotation eccentricity resonance (CER) externally imposed by Galatea, but are self-generated by LR reacting to the external fields

A Comparison of the Interiors of Jupiter and Saturn

Interior models of Jupiter and Saturn are calculated and compared in the framework of the three-layer assumption, which rely on the perception that both planets consist of three globally homogeneous regions: a dense core, a metallic hydrogen envelope, and a molecular hydrogen envelope. Within this framework, constraints on the core mass and abundance of heavy elements (i.e. elements other than hydrogen and helium) are given by accounting for uncertainties on the measured gravitational moments, surface temperature, surface helium abundance, and on the inferred protosolar helium abundance, equations of state, temperature profile and solid/differential interior rotation.Comment: 25 pages, 6 tables, 10 figures Planetary and Space Science, in pres

Understanding urban gentrification through machine learning

Recent developments in the field of machine learning offer new ways of modelling complex socio-spatial processes, allowing us to make predictions about how and where they might manifest in the future. Drawing on earlier empirical and theoretical attempts to understand gentrification and urban change, this paper shows it is possible to analyse existing patterns and processes of neighbourhood change to identify areas likely to experience change in the future. This is evidenced through an analysis of socio-economic transition in London neighbourhoods (based on 2001 and 2011 Census variables) which is used to predict those areas most likely to demonstrate ‘uplift’ or ‘decline’ by 2021. The paper concludes with a discussion of the implications of such modelling for the understanding of gentrification processes, noting that if qualitative work on gentrification and neighbourhood change is to offer more than a rigorous post-mortem then intensive, qualitative case studies must be confronted with – and complemented by – predictions stemming from other, more extensive approaches. As a demonstration of the capabilities of machine learning, this paper underlines the continuing value of quantitative approaches in understanding complex urban processes such as gentrification

Efficient data processing and quantum phenomena: Single-particle systems

We study the relation between the acquisition and analysis of data and quantum theory using a probabilistic and deterministic model for photon polarizers. We introduce criteria for efficient processing of data and then use these criteria to demonstrate that efficient processing of the data contained in single events is equivalent to the observation that Malus' law holds. A strictly deterministic process that also yields Malus' law is analyzed in detail. We present a performance analysis of the probabilistic and deterministic model of the photon polarizer. The latter is an adaptive dynamical system that has primitive learning capabilities. This additional feature has recently been shown to be sufficient to perform event-by-event simulations of interference phenomena, without using concepts of wave mechanics. We illustrate this by presenting results for a system of two chained Mach-Zehnder interferometers, suggesting that systems that perform efficient data processing and have learning capability are able to exhibit behavior that is usually attributed to quantum systems only.Comment: http://www.compphys.net/dl

Bosonization and even Grassmann variables

A new approach to bosonization in relativistic field theories and many-body systems, based on the use of fermionic composites as integration variables in the Berezin integral defining the partition function of the system, is tested. The method is applied to the study of a simplified version of the BCS model.Comment: 20 pages, LaTe

Superconductivity in the quasi-two-dimensional Hubbard model

On the basis of spin and pairing fluctuation-exchange approximation, we study the superconductivity in quasi-two-dimensional Hubbard model. The integral equations for the Green's function are self-consistently solved by numerical calculation. Solutions for the order parameter, London penetration depth, density of states, and transition temperature are obtained. Some of the results are compared with the experiments for the cuprate high-temperature superconductors. Numerical techniques are presented in details. With these techniques, the amount of numerical computation can be greatly reduced.Comment: 17 pages, 13 figure

Metal-Insulator transition in the Generalized Hubbard model

We present the exact ground-state wave function and energy of the generalized Hubbard model, subjected to the condition that the number of double occupied sites is conserved, for a wide, physically relevant range of parameters. For one hole and one double occupied site the existence of the ferromagnetic ground-state is proved which allow one to determine the critical value of the on-site repulsion corresponding to the point of metal-insulator transition. For the one dimensional model the exact solution for special values of the parameters is obtained.Comment: 20 pages, LaTex. Mod.Phys.Lett.B 7 (1993) 1397; Journal of Physics: Condensed Matter (to appear

Entry and exit patterns of "toxic" firms

We pair an establishment-level dataset from Texas with public information available in the Toxics Release Inventory (TRI) to evaluate the standing of dirty industries in Texas census tracts with a focus on environmental justice concerns. The share of nonwhite residents in a tract is positively correlated with the number of TRI-reporting firms and an inverse-U-shaped relationship characterizes the number of TRI-reporting firms and a tract's median income. Even after controlling for factor prices and other covariates which might drive firm location decisions, entrants that report to the TRI are more likely to locate in areas with a higher share of nonwhite residents. Firms that report to the TRI are also more likely to enter areas with a low share college graduates. In contrast, the number of entrants from industries which do not have TRI reporters is negatively related to the percent of nonwhite residents in a tract. Firms in these non-reporting industries are also more likely to enter areas with a high share of college graduates. Polluters appear to agglomerate, raising concerns about both chemical releases being concentrated in certain tracts and also affecting nonwhite-dense areas disproportionately. The strength of these effects often depend on an urban/rural classification, with rural areas experiencing the most pronounced concerns. Moreover, TRI-reporting firms are less likely to exit the market relative to their peers which operate in the same industry but do not need to file TRI reports, suggesting releases may affect a region in the long-run