Critical random graphs: limiting constructions and distributional properties

We consider the Erdos-Renyi random graph G(n,p) inside the critical window, where p = 1/n + lambda * n^{-4/3} for some lambda in R. We proved in a previous paper (arXiv:0903.4730) that considering the connected components of G(n,p) as a sequence of metric spaces with the graph distance rescaled by n^{-1/3} and letting n go to infinity yields a non-trivial sequence of limit metric spaces C = (C_1, C_2, ...). These limit metric spaces can be constructed from certain random real trees with vertex-identifications. For a single such metric space, we give here two equivalent constructions, both of which are in terms of more standard probabilistic objects. The first is a global construction using Dirichlet random variables and Aldous' Brownian continuum random tree. The second is a recursive construction from an inhomogeneous Poisson point process on R_+. These constructions allow us to characterize the distributions of the masses and lengths in the constituent parts of a limit component when it is decomposed according to its cycle structure. In particular, this strengthens results of Luczak, Pittel and Wierman by providing precise distributional convergence for the lengths of paths between kernel vertices and the length of a shortest cycle, within any fixed limit component.Comment: 30 pages, 4 figure

Interrelated structure of high altitude atmospheric profiles

A preliminary development of a mathematical model to compute probabilities of thermodynamic profiles is presented. The model assumes an exponential expression for pressure and utilizes the hydrostatic law and equation of state in the determination of density and temperature. It is shown that each thermodynamic variable can be factored into the produce of steady state and perturbation functions. The steady state functions have profiles similar to those of the 1962 standard atmosphere while the perturbation functions oscillate about 1. Limitations of the model and recommendations for future work are presented

Culture Rules: The Foundations of the Rule of Law and Other Norms of Governance

This study presents evidence about relations between national culture and social institutions. We operationalize culture with data on cultural dimensions for over 50 nations adopted from cross-cultural psychology and generate testable hypotheses about three basic social norms of governance: the rule of law, corruption, and accountability. These norms correlate systematically and strongly with national scores on cultural dimensions and also differ across cultural regions of the world. Regressions indicate that quantitative measures of national culture are alone remarkably predictive of governance, that economic inequality and British heritage add to predictive power, but that economic development and other factors add little. The results suggest a framework for understanding the relations between fundamental institutions of social order as well as policy implications for reform programs in transition economies.http://deepblue.lib.umich.edu/bitstream/2027.42/39991/3/wp605.pd

Critical random graphs : limiting constructions and distributional properties

We consider the Erdos-Renyi random graph G(n, p) inside the critical window, where p = 1/n + lambda n(-4/3) for some lambda is an element of R. We proved in Addario-Berry et al. [2009+] that considering the connected components of G(n, p) as a sequence of metric spaces with the graph distance rescaled by n(-1/3) and letting n -> infinity yields a non-trivial sequence of limit metric spaces C = (C-1, C-2,...). These limit metric spaces can be constructed from certain random real trees with vertex-identifications. For a single such metric space, we give here two equivalent constructions, both of which are in terms of more standard probabilistic objects. The first is a global construction using Dirichlet random variables and Aldous' Brownian continuum random tree. The second is a recursive construction from an inhomogeneous Poisson point process on R+. These constructions allow us to characterize the distributions of the masses and lengths in the constituent parts of a limit component when it is decomposed according to its cycle structure. In particular, this strengthens results of Luczak et al. [1994] by providing precise distributional convergence for the lengths of paths between kernel vertices and the length of a shortest cycle, within any fixed limit component

Poetry, Prosecution, and the Author Function

This chapter draws on Foucault’s ‘author function’ to expose the ways in which the beginnings of Latin literature were predicated on interactions with Roman law. Foucault stipulates two principal conditions for the cultural emergence of the author, both broadly juridical in nature: penal appropriation and ownership of texts. For Foucault and others, these conditions only pertained more or less when modern copyright laws began to come into play in Europe. But penal appropriation and textual ownership were a central factor in the emergence of Latin literature in third-century BCE Rome. Poetic authorship in Latin emerged late, when juridical discourse was already well established. As I argue here, the resulting dynamic between law and literature crystallizes the Foucauldian author function in fundamental ways. The stipulation against mala carmina in the XII Tables and the concept of literary ‘theft’ — naturalized from Alexandria into Roman legal language — suggest that Foucault’s conditions were a legible part of the cultural landscape of Republican Rome. As later readers saw it in particular, from the legendary curbing of Fescennina licentia to Gnaeus Naevius’ infamous clash with the Metelli, Roman poetic authorship fundamentally emerged in the shadow of the law

Quantum fluctuations and glassy behavior: The case of a quantum particle in a random potential

In this paper we expand our previous investigation of a quantum particle subject to the action of a random potential plus a fixed harmonic potential at a finite temperature T. In the classical limit the system reduces to a well-known ``toy'' model for an interface in a random medium. It also applies to a single quantum particle like an an electron subject to random interactions, where the harmonic potential can be tuned to mimic the effect of a finite box. Using the variational approximation, or alternatively, the limit of large spatial dimensions, together with the use the replica method, and are able to solve the model and obtain its phase diagram in the $T - (\hbar^2/m)$ plane, where $m$ is the particle's mass. The phase diagram is similar to that of a quantum spin-glass in a transverse field, where the variable $\hbar^2/m$ plays the role of the transverse field. The glassy phase is characterized by replica-symmetry-breaking. The quantum transition at zero temperature is also discussed.Comment: revised version, 23 pages, revtex, 5 postscript figures in a separate file figures.u

Culture Rules: The Foundations of the Rule of Law and Other Norms of Governance

This study presents evidence about relations between national culture and social institutions. We operationalize culture with data on cultural dimensions for over 50 nations adopted from cross-cultural psychology and generate testable hypotheses about three basic social norms of governance: the rule of law, corruption, and accountability. These norms correlate systematically and strongly with national scores on cultural dimensions and also differ across cultural regions of the world. Regressions indicate that quantitative measures of national culture are alone remarkably predictive of governance, that economic inequality and British heritage add to predictive power, but that economic development and other factors add little. The results suggest a framework for understanding the relations between fundamental institutions of social order as well as policy implications for reform programs in transition economies.Rule of Law, Corruption, Accountability, Culture, Governance, Economic Inequality, Economic Development

The importance of radio sources in accounting for the highest mass black holes

The most massive black holes lie in the most massive elliptical galaxies, and at low-z all radio-loud AGNs lie in giant ellipticals. This strongly suggests a link between radio-loudness and black hole mass. We argue that the increase in the radio-loud fraction with AGN luminosity in optically-selected quasar samples is consistent with this picture. We also use the ratio of black holes today to quasars at z~2 to conclude that the most bolometrically-luminous AGN, either radio-loud or radio quiet, are constrained to have lifetimes <~10^8 yr. If radio sources are associated with black holes of >~10^9 M_sun at all redshifts, then the same lifetime constraint applies to all radio sources with luminosities above L_5GHz ~ 10^24 W/Hz/sr.Comment: 6 pages, 2 figures. To appear in "Lifecycles of Radio Galaxies", ed J. Biretta et al., New Astronomy Review

Langevin Dynamics of the vortex matter two-stage melting transition in Bi_2Sr_2CaCu_2O8+δ_{8+\delta} in the presence of straight and of tilted columnar defects

In this paper we use London Langevin molecular dynamics simulations to investigate the vortex matter melting transition in the highly anisotropic high-temperature superconductor material Bi_2Sr_2CaCu_2O$_{8+\delta}$ in the presence of low concentration of columnar defects (CDs). We reproduce with further details our previous results obtained by using Multilevel Monte Carlo simulations that showed that the melting of the nanocrystalline vortex matter occurs in two stages: a first stage melting into nanoliquid vortex matter and a second stage delocalization transition into a homogeneous liquid. Furthermore, we report on new dynamical measurements in the presence of a current that identifies clearly the irreversibility line and the second stage delocalization transition. In addition to CDs aligned along the c-axis we also simulate the case of tilted CDs which are aligned at an angle with respect to the applied magnetic field. Results for CDs tilted by $45^{\circ}$ with respect to c-axis show that the locations of the melting and delocalization transitions are not affected by the tilt when the ratio of flux lines to CDs remains constant. On the other hand we argue that some dynamical properties and in particular the position of the irreversibility line should be affected.Comment: 13 pages, 11 figure