2,300 research outputs found
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
Extra-Large Remnant Recoil Velocities and Spins from Near-Extremal-Bowen-York-Spin Black-Hole Binaries
We evolve equal-mass, equal-spin black-hole binaries with specific spins of
a/mH 0.925, the highest spins simulated thus far and nearly the largest
possible for Bowen-York black holes, in a set of configurations with the spins
counter-aligned and pointing in the orbital plane, which maximizes the recoil
velocities of the merger remnant, as well as a configuration where the two
spins point in the same direction as the orbital angular momentum, which
maximizes the orbital hang-up effect and remnant spin. The coordinate radii of
the individual apparent horizons in these cases are very small and the
simulations require very high central resolutions (h ~ M/320). We find that
these highly spinning holes reach a maximum recoil velocity of ~3300 km/s (the
largest simulated so far) and, for the hangup configuration, a remnant spin of
a/mH 0.922. These results are consistent with our previous predictions for the
maximum recoil velocity of ~4000 km/s and remnant spin; the latter reinforcing
the prediction that cosmic censorship is not violated by merging
highly-spinning black-hole binaries. We also numerically solve the initial data
for, and evolve, a single maximal-Bowen-York-spin black hole, and confirm that
the 3-metric has an O(1/r^2) singularity at the puncture, rather than the usual
O(1/r^4) singularity seen for non-maximal spins.Comment: 11 pages, 10 figures. To appear in PR
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
Study of Conformally Flat Initial Data for Highly Spinning Black Holes and their Early Evolutions
We study conformally-flat initial data for an arbitrary number of spinning
black holes with exact analytic solutions to the momentum constraints
constructed from a linear combination of the classical Bowen-York and conformal
Kerr extrinsic curvatures. The solution leading to the largest intrinsic spin,
relative to the ADM mass of the spacetime epsilon_S=S/M^2_{ADM}, is a
superposition with relative weights of Lambda=0.783 for conformal Kerr and
(1-Lambda)=0.217 for Bowen-York. In addition, we measure the spin relative to
the initial horizon mass M_{H_0}, and find that the quantity chi=S/M_{H_0}^2
reaches a maximum of \chi^{max}=0.9856 for Lambda=0.753. After equilibration,
the final black-hole spin should lie in the interval 0.9324<chi_{final}<0.9856.
We perform full numerical evolutions to compute the energy radiated and the
final horizon mass and spin. We find that the black hole settles to a final
spin of chi_{final}^{max}=0.935 when Lambda=0.783. We also study the evolution
of the apparent horizon structure of this "maximal" black hole in detail.Comment: 9 pages, 8 figure
On the accuracy of solving confluent Prony systems
In this paper we consider several nonlinear systems of algebraic equations
which can be called "Prony-type". These systems arise in various reconstruction
problems in several branches of theoretical and applied mathematics, such as
frequency estimation and nonlinear Fourier inversion. Consequently, the
question of stability of solution with respect to errors in the right-hand side
becomes critical for the success of any particular application. We investigate
the question of "maximal possible accuracy" of solving Prony-type systems,
putting stress on the "local" behavior which approximates situations with low
absolute measurement error. The accuracy estimates are formulated in very
simple geometric terms, shedding some light on the structure of the problem.
Numerical tests suggest that "global" solution techniques such as Prony's
algorithm and ESPRIT method are suboptimal when compared to this theoretical
"best local" behavior
RANCANG BANGUN PROTOTIPE MODEM FREQUENCY SHIFT KEYING (FSK) DENGAN ADAPTASI EXTERNAL RESISTOR & CAPASITOR UNTUK POWER LINE COMMUNICATION
Sistem komunikasi data melalui jala-jala listrik atau lebih dikenal dengan Power Line Communication (PLC) merupakan sistem komunikasi antara pengirim dan penerima dengan jala-jala listrik sebagai media pengiriman datanya. Sistem ini sudah dikenal dan masih terus menjadi bahan penelitian. PLC dapat menggunakan berbagai macam metode pengiriman, berbagai metode yang berbeda itu ditujukan untuk mengatasi noise pada jala-jala listrik dan peningkatan baud rate pengiriman data. Metode yang digunakan termasuk konvensional dan dengan baud rate yang rendah. Makalah ini merupakan resume penelitian yang telah dilakukan. Penelitian yang dilakukan menggunakan rangkaian Modem Frequency Shift Keying (FSK) sebagai interface alat pengirim dan penerima, juga menggunakan rangkaian kopling transformator dan rangkaian bandpass filter. Penelitian ini menggunakan komponen utama Modem yaitu Integrated Circuit (IC) XR2206 sebagai Modulator dan IC XR2211 sebagai Demodulator, serta menggunakan filter pasif yang berfungsi untuk meloloskan frekuensi yang telah ditentukan yaitu 75 KHz – 90 KHz. Nilai output yang ditargetkan dicapai dengan melakukan adaptasi perhitungan nilai Kapasitor dan resistor external. Hasil perhitungan pada tahap perancangan modulator, dengan nilai C=10nF diperoleh nilai R1=1333Ω, R2= 1111 Ω. Modem FSK diujicoba menggunakan aplikasi Hyper Terminal. Hasil dari pengujian, Modulator dapat mengirimkan sinyal data melalui kabel listrik dengan panjang kabel listrik maksimal 17 meter ke Demodulator dengan hasil baik pada kecepatan 110 dan 300 baud. Dikatakan baik karena tidak terdapat teks yang cacat/terbaca oleh Personal Computer (PC) penerima
Sub-Riemannian Fast Marching in SE(2)
We propose a Fast Marching based implementation for computing sub-Riemanninan
(SR) geodesics in the roto-translation group SE(2), with a metric depending on
a cost induced by the image data. The key ingredient is a Riemannian
approximation of the SR-metric. Then, a state of the art Fast Marching solver
that is able to deal with extreme anisotropies is used to compute a SR-distance
map as the solution of a corresponding eikonal equation. Subsequent
backtracking on the distance map gives the geodesics. To validate the method,
we consider the uniform cost case in which exact formulas for SR-geodesics are
known and we show remarkable accuracy of the numerically computed SR-spheres.
We also show a dramatic decrease in computational time with respect to a
previous PDE-based iterative approach. Regarding image analysis applications,
we show the potential of considering these data adaptive geodesics for a fully
automated retinal vessel tree segmentation.Comment: CIARP 201
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