Fluctuation Scaling, Taylor’s Law, and Crime

Fluctuation scaling relationships have been observed in a wide range of processes ranging from internet router traffic to measles cases. Taylor’s law is one such scaling relationship and has been widely applied in ecology to understand communities including trees, birds, human populations, and insects. We show that monthly crime reports in the UK show complex fluctuation scaling which can be approximated by Taylor’s law relationships corresponding to local policing neighborhoods and larger regional and countrywide scales. Regression models applied to local scale data from Derbyshire and Nottinghamshire found that different categories of crime exhibited different scaling exponents with no significant difference between the two regions. On this scale, violence reports were close to a Poisson distribution (α = 1.057±0.026) while burglary exhibited a greater exponent (α = 1.292±0.029) indicative of temporal clustering. These two regions exhibited significantly different pre-exponential factors for the categories of anti-social behavior and burglary indicating that local variations in crime reports can be assessed using fluctuation scaling methods. At regional and countrywide scales, all categories exhibited scaling behavior indicative of temporal clustering evidenced by Taylor’s law exponents from 1.43±0.12 (Drugs) to 2.094±0081 (Other Crimes). Investigating crime behavior via fluctuation scaling gives insight beyond that of raw numbers and is unique in reporting on all processes contributing to the observed variance and is either robust to or exhibits signs of many types of data manipulation

Nonlocal competition and logistic growth: patterns, defects and fronts

Logistic growth of diffusing reactants on spatial domains with long range competition is studied. The bifurcations cascade involved in the transition from the homogenous state to a spatially modulated stable solution is presented, and a distinction is made between a modulated phase, dominated by single or few wavenumbers, and the spiky phase, where localized colonies are separated by depleted region. The characteristic defects in the periodic structure are presented for each phase, together with the invasion dynamics in case of local initiation. It is shown that the basic length scale that controls the bifurcation is the width of the Fisher front, and that the total population grows as this width decreases. A mix of analytic results and extensive numerical simulations yields a comprehensive examination of the possible phases for logistic growth in the presence of nonlocal competition

Quasi-Local Linear Momentum in Black-Hole Binaries

We propose a quasi-local formula for the linear momentum of black-hole horizons inspired by the formalism of quasi-local horizons. We test this formula using two complementary configurations: (i) by calculating the large orbital linear momentum of the two black holes in an unequal-mass, zero-spin, quasi-circular binary and (ii) by calculating the very small recoil momentum imparted to the remnant of the head-on collision of an equal-mass, anti-aligned-spin binary. We obtain results consistent with the horizon trajectory in the orbiting case, and consistent with the net radiated linear momentum for the much smaller head-on recoil velocity.Comment: 5 pages, 3 figures, revtex

Lessons from Recent Measurements of D-\bar D Mixing

An impressive progress in measurements of the D-\bar D mixing parameters has been made in recent years. We explore the implications of these measurements to models of new physics, especially in view of recent upper bounds on the amount of CP violation. We update the constraints on non-renormalizable four-quark operators. We show that the experiments are close to probing minimally flavor violating models with large tan beta. The data challenge models with a scale of order TeV where the flavor violation in the down sector is suppressed by alignment and, in particular, certain classes of supersymmetric models and of warped extra dimension models.Comment: 20 pages, 1 figure. Added references, minor corrections and clarifications. Matches published versio

The Birth-Death-Mutation process: a new paradigm for fat tailed distributions

Fat tailed statistics and power-laws are ubiquitous in many complex systems. Usually the appearance of of a few anomalously successful individuals (bio-species, investors, websites) is interpreted as reflecting some inherent "quality" (fitness, talent, giftedness) as in Darwin's theory of natural selection. Here we adopt the opposite, "neutral", outlook, suggesting that the main factor explaining success is merely luck. The statistics emerging from the neutral birth-death-mutation (BDM) process is shown to fit marvelously many empirical distributions. While previous neutral theories have focused on the power-law tail, our theory economically and accurately explains the entire distribution. We thus suggest the BDM distribution as a standard neutral model: effects of fitness and selection are to be identified by substantial deviations from it

Leptogenesis from Supersymmetry Breaking

We show that soft supersymmetry breaking terms involving the heavy sneutrinos can lead to sneutrino-antisneutrino mixing and to new sources of CP violation, which are present even if a single generation is considered. These terms are naturally present in supersymmetric versions of leptogenesis scenarios, and they induce indirect CP violation in the decays of the heavy sneutrinos, eventually generating a baryon asymmetry. This new contribution can be comparable to or even dominate over the asymmetry produced in traditional leptogenesis scenarios.Comment: 4 pages; An improved discussion of the relevant numerical range of the soft breaking terms (in agreement with hep-ph/0308031

Relating leptogenesis parameters to light neutrino masses

We obtain model independent relations among neutrino masses and leptogenesis parameters. We find exact relations that involve the CP asymmetries $\epsilon_{N_\alpha}$, the washout parameters $\tilde m_\alpha$ and $\theta_{\alpha\beta}$, and the neutrino masses $m_i$ and $M_\alpha$, as well as powerful inequalities that involve just $\tilde m_\alpha$ and $m_i$. We prove that the Yukawa interactions of at least two of the heavy singlet neutrinos are in the strong washout region ($\tilde m_\alpha\gg10^{-3} eV$).Comment: 5 pages, 1 figur

Ancient technology and punctuated change: Detecting the emergence of the Edomite Kingdom in the Southern Levant.

While the punctuated equilibrium model has been employed in paleontological and archaeological research, it has rarely been applied for technological and social evolution in the Holocene. Using metallurgical technologies from the Wadi Arabah (Jordan/Israel) as a case study, we demonstrate a gradual technological development (13th-10th c. BCE) followed by a human agency-triggered punctuated "leap" (late-10th c. BCE) simultaneously across the entire region (an area of ~2000 km2). Here, we present an unparalleled, diachronic archaeometallurgical dataset focusing on elemental analysis of dozens of well-dated slag samples. Based on the results, we suggest punctuated equilibrium provides an innovative theoretical model for exploring ancient technological changes in relation to larger sociopolitical conditions-in the case at hand the emergence of biblical Edom-, exemplifying its potential for more general cross-cultural applications

Reflectance in the Red and Near Infra-Red Ranges of the Spectrum as Tool for Remote Chlorophyll Estimation in Inland Waters: Lake Kinneret Case Study

Signature analysis of reflectance spectra was used for the selection of the most suitable spectral bands for remote sensing of chlorophyll in inland waters. The parameters of the reflectance peak near 700 nm were employed for construction of algorithms for chlorophyll determination. The best model, validated by independent data sets, enabled estimation of chlorophyll concentration with an error \u3c 0.6 mg/m3 for period of low Chl concentration and \u3c 6.5 mg/m3 for period of the phytoplankton bloom. For the purpose of chlorophyll mapping in Lake Kinneret, the use of three relatively narrow spectral bands was sufficient. Radiometric data were also used to simulate radiances in the channels of TM Landsat and to find algorithm for chlorophyll assessment. The ratio (TM2-TM3)/TMl was used to retrieve chlorophyll in the range 3-10 mg/m3 with an error of \u3c 1 mg.m-3; the ratio TM4/TM3 was used to map chlorophyll in the range 10-200 mg/m3 with 10 gradations

Maximum gravitational recoil

Recent calculations of gravitational radiation recoil generated during black-hole binary mergers have reopened the possibility that a merged binary can be ejected even from the nucleus of a massive host galaxy. Here we report the first systematic study of gravitational recoil of equal-mass binaries with equal, but anti-aligned, spins parallel to the orbital plane. Such an orientation of the spins is expected to maximize the recoil. We find that recoil velocity (which is perpendicular to the orbital plane) varies sinusoidally with the angle that the initial spin directions make with the initial linear momenta of each hole and scales up to a maximum of ~4000 km/s for maximally-rotating holes. Our results show that the amplitude of the recoil velocity can depend sensitively on spin orientations of the black holes prior to merger.Comment: 4 pages, 4 figs, revtex