Structural Properties of Planar Graphs of Urban Street Patterns

Recent theoretical and empirical studies have focused on the structural properties of complex relational networks in social, biological and technological systems. Here we study the basic properties of twenty 1-square-mile samples of street patterns of different world cities. Samples are represented by spatial (planar) graphs, i.e. valued graphs defined by metric rather than topologic distance and where street intersections are turned into nodes and streets into edges. We study the distribution of nodes in the 2-dimensional plane. We then evaluate the local properties of the graphs by measuring the meshedness coefficient and counting short cycles (of three, four and five edges), and the global properties by measuring global efficiency and cost. As normalization graphs, we consider both minimal spanning trees (MST) and greedy triangulations (GT) induced by the same spatial distribution of nodes. The results indicate that most of the cities have evolved into networks as efficienct as GT, although their cost is closer to the one of a tree. An analysis based on relative efficiency and cost is able to characterize different classes of cities.Comment: 7 pages, 3 figures, 3 table

Spanning Trees and bootstrap reliability estimation in correlation based networks

We introduce a new technique to associate a spanning tree to the average linkage cluster analysis. We term this tree as the Average Linkage Minimum Spanning Tree. We also introduce a technique to associate a value of reliability to links of correlation based graphs by using bootstrap replicas of data. Both techniques are applied to the portfolio of the 300 most capitalized stocks traded at New York Stock Exchange during the time period 2001-2003. We show that the Average Linkage Minimum Spanning Tree recognizes economic sectors and sub-sectors as communities in the network slightly better than the Minimum Spanning Tree does. We also show that the average reliability of links in the Minimum Spanning Tree is slightly greater than the average reliability of links in the Average Linkage Minimum Spanning Tree.Comment: 17 pages, 3 figure

Dense sphere packings from optimized correlation functions

Elementary smooth functions (beyond contact) are employed to construct pair correlation functions that mimic jammed disordered sphere packings. Using the g2-invariant optimization method of Torquato and Stillinger [J. Phys. Chem. B 106, 8354, 2002], parameters in these functions are optimized under necessary realizability conditions to maximize the packing fraction phi and average number of contacts per sphere Z. A pair correlation function that incorporates the salient features of a disordered packing and that is smooth beyond contact is shown to permit a phi of 0.6850: this value represents a 45% reduction in the difference between the maximum for congruent hard spheres in three dimensions, pi/sqrt{18} ~ 0.7405, and 0.64, the approximate fraction associated with maximally random jammed (MRJ) packings in three dimensions. We show that, surprisingly, the continued addition of elementary functions consisting of smooth sinusoids decaying as r^{-4} permits packing fractions approaching pi/sqrt{18}. A translational order metric is used to discriminate between degrees of order in the packings presented. We find that to achieve higher packing fractions, the degree of order must increase, which is consistent with the results of a previous study [Torquato et al., Phys. Rev. Lett. 84, 2064, 2000].Comment: 26 pages, 9 figures, 1 table; added references, fixed typos, simplified argument and discussion in Section IV

Non-singular four-dimensional black holes and the Jackiw-Teitelboim theory

A four-dimensional dilaton-gravity action whose spherical reduction to two dimensions leads to the Jackiw-Teitelboim theory is presented. A nonsingular black hole solution of the theory is obtained and its physical interpretation is discussed. The classical and semiclassical properties of the solution and of its 2d counterpart are analysed. The 2d theory is also used to model the evaporation process of the near-extremal 4d black hole. We describe in detail the peculiarities of the black hole solutions, in particular the purely topological nature of the Hawking radiation, in the context of the Jackiw-Teitelboim theory.Comment: 24 pages, 6 figures available upon request, Plain Tex, INFN-CA-TH-94-2

Origins of Selectivity for the [2+2] Cycloaddition of α,β-unsaturated Ketones within a Porous Self-assembled Organic Framework

This article studies the origins of selectivity for the [2+2] cycloadditions of α,β-unsaturated ketones within a porous crystalline host. The host, formed by the self-assembly of a bis-urea macrocycle, contains accessible channels of ∼6 Å diameter and forms stable inclusion complexes with a variety of cyclic and acyclic α,β-unsaturated ketone derivatives. Host 1 crystals provide a robust confined reaction environment for the highly selective [2+2] cycloaddition of 3-methyl-2-cyclopentenone, 2-cyclohexenone, and 2-methyl-2-cyclopentenone, forming their respective exo head-to-tail dimers in high conversion. The products are readily extracted from the self-assembled host and the crystalline host can be efficiently recovered and reused. Molecular modeling studies indicate that the origin of the observed selectivity is due to the excellent match between the size and shape of these guests to dimensions of the host channel and to the preorganization of neighboring enones into favorable reaction geometries. Small substrates, such as acrylic acid and methylvinylketone, were bound by the host and were protected from photoreactions. Larger substrates, such as 4,4-dimethyl-2-cyclohexenone and mesityl oxide, do not undergo selective [2+2] cycloaddition reactions. In an effort to understand these differences in reactivity, we examined these host−guest complexes by thermogravimetric analysis (TGA), NMR, powder X-ray diffraction (PXRD) and molecular modeling

The role of the emergency department in the management of acute heart failure: an international perspective on education and research

Emergency departments are a major entry point for the initial management of acute heart failure (AHF) patients throughout the world. The initial diagnosis, management and disposition - the decision to admit or discharge - of AHF patients in the emergency department has significant downstream implications. Misdiagnosis, under or overtreatment, or inappropriate admission may place patients at increased risk for adverse events, and add costs to the healthcare system. Despite the critical importance of initial management, data are sparse regarding the impact of early AHF treatment delivered in the emergency department compared to inpatient or chronic heart failure management. Unfortunately, outcomes remain poor, with nearly a third of patients dying or re-hospitalised within 3 months post-discharge. In the absence of robust research evidence, consensus is an important source of guidance for AHF care. Thus, we convened an international group of practising emergency physicians, cardiologists and advanced practice nurses with the following goals to improve outcomes for AHF patients who present to the emergency department or other acute care setting through: (a) a better understanding of the pathophysiology, presentation and management of the initial phase of AHF care; (b) improving initial management by addressing knowledge gaps between best practices and current practice through education and research; and (c) to establish a framework for future emergency department-based international education and research

Negative Poisson's ratio materials via isotropic interactions

We show that under tension, a classical many-body system with only isotropic pair interactions in a crystalline state can, counterintutively, have a negative Poisson's ratio, or auxetic behavior. We derive the conditions under which the triangular lattice in two dimensions and lattices with cubic symmetry in three dimensions exhibit a negative Poisson's ratio. In the former case, the simple Lennard-Jones potential can give rise to auxetic behavior. In the latter case, negative Poisson's ratio can be exhibited even when the material is constrained to be elastically isotropic.Comment: 10 pages, 2 figures, accepted in Physical Review Letter

Two-dimensional higher-derivative gravity and conformal transformations

We consider the lagrangian $L=F(R)$ in classical (=non-quantized) two-dimensional fourth-order gravity and give new relations to Einstein's theory with a non-minimally coupled scalar field. We distinguish between scale-invariant lagrangians and scale-invariant field equations. $L$ is scale-invariant for F = c_1 R\sp {k+1} and a divergence for $F=c_2 R$. The field equation is scale-invariant not only for the sum of them, but also for $F=R\ln R$. We prove this to be the only exception and show in which sense it is the limit of \frac{1}{k} R\sp{k+1} as $k\to 0$. More generally: Let $H$ be a divergence and $F$ a scale-invariant lagrangian, then $L= H\ln F$ has a scale-invariant field equation. Further, we comment on the known generalized Birkhoff theorem and exact solutions including black holes.Comment: 16 pages, latex, no figures, [email protected], Class. Quant. Grav. to appea

Mineralogy of Vera Rubin Ridge in Gale Crater from the Mars Science Laboratory CheMin instrument

Gale crater was selected as the landing site for the Mars Science Laboratory Curiosity rover because of orbital evidence for a variety of secondary minerals in the lower slopes of Aeolis Mons (aka Mount Sharp) that indicate changes in aqueous conditions over time. Distinct units demonstrate orbital spectral signatures of hematite, phyllosilicate (smectite), and sulfate minerals, which suggest that ancient aqueous environments in Gale crater varied in oxidation potential, pH, and water activity. Vera Rubin ridge (VRR) is the first of these units identified from orbit to have been studied by Curiosity. Orbital near-infrared data from VRR show a strong band at 860 nm indicative of hematite. Before Curiosity arrived at VRR, the hypotheses to explain the formation of hematite included (1) precipitation at a redox interface where aqueous Fe2+ was oxidized to Fe3+, and (2) acidic alteration of olivine in oxic fluids. Studying the composition and sedimentology of the rocks on VRR allow us to test and refine these hypotheses and flesh out the depositional and diagenetic history of the ridge. Here, we focus on the mineralogical results of four rock powders drilled from and immediately below VRR as determined by CheMin