9,451 research outputs found
Order Statistics and Benford's Law
Fix a base B and let zeta have the standard exponential distribution; the
distribution of digits of zeta base B is known to be very close to Benford's
Law. If there exists a C such that the distribution of digits of C times the
elements of some set is the same as that of zeta, we say that set exhibits
shifted exponential behavior base B (with a shift of log_B C \bmod 1). Let X_1,
>..., X_N be independent identically distributed random variables. If the X_i's
are drawn from the uniform distribution on [0,L], then as N\to\infty the
distribution of the digits of the differences between adjacent order statistics
converges to shifted exponential behavior (with a shift of \log_B L/N \bmod 1).
By differentiating the cumulative distribution function of the logarithms
modulo 1, applying Poisson Summation and then integrating the resulting
expression, we derive rapidly converging explicit formulas measuring the
deviations from Benford's Law. Fix a delta in (0,1) and choose N independent
random variables from any compactly supported distribution with uniformly
bounded first and second derivatives and a second order Taylor series expansion
at each point. The distribution of digits of any N^\delta consecutive
differences \emph{and} all N-1 normalized differences of the order statistics
exhibit shifted exponential behavior. We derive conditions on the probability
density which determine whether or not the distribution of the digits of all
the un-normalized differences converges to Benford's Law, shifted exponential
behavior, or oscillates between the two, and show that the Pareto distribution
leads to oscillating behavior.Comment: 14 pages, 2 figures, version 4: Version 3: most of the numerical
simulations on shifted exponential behavior have been suppressed (though are
available from the authors upon request). Version 4: a referee pointed out
that we need epsilon > 1/3 - delta/2 in the proof of Theorem 1.5; this has
now been adde
Structural trends in clusters of quadrupolar spheres
The influence of quadrupolar interactions on the structure of small clusters
is investigated by adding a point quadrupole of variable strength to the
Lennard-Jones potential. Competition arises between sheet-like arrangements of
the particles, favoured by the quadrupoles, and compact structures, favoured by
the isotropic Lennard-Jones attraction. Putative global potential energy minima
are obtained for clusters of up to 25 particles using the basin-hopping
algorithm. A number of structural motifs and growth sequences emerge, including
star-like structures, tubes, shells and sheets. The results are discussed in
the context of colloidal self-assembly.Comment: 8 pages, 6 figure
Industrial Policy and the Rights of Labor: The Case of Foreign Workers in the French Automobile Assemble Industry
The foreign labor which made possible Western Europe\u27s postwar economic growth has become a permanent, if belatedly recognized, component of the region\u27s labor markets. Technological change and new industrial policies stressing efficiency, skilled labor, and rationalization threaten foreign workers, raising complex and important issues of law and social policy in the debate over labor\u27s role in industrial policy. These changes already have resulted in grave problems which make agreement and clarification of the rights of foreign workers in national and international law a matter of considerable urgency
Structural relaxation in Morse clusters: Energy landscapes
We perform a comprehensive survey of the potential energy landscapes of
13-atom Morse clusters, and describe how they can be characterized and
visualized. Our aim is to detail how the global features of the funnel-like
surface change with the range of the potential, and to relate these changes to
the dynamics of structural relaxation. We find that the landscape becomes
rougher and less steep as the range of the potential decreases, and that
relaxation paths to the global minimum become more complicated.Comment: 21 pages, 3 tables, 5 figure
On the relation between the Deuteron Form Factor at High Momentum Transfer and the High Energy Neutron-Proton Scattering Amplitude
A non-relativistic potential-model version of the factorization assumption,
used in perturbative QCD calculations of hadronic form factors, is used, along
with the Born approximation valid at high energies, to derive a remarkably
simple relationship between the impulse approximation contribution to the
deuteron form factor at high momentum transfer and the high energy
neutron-proton scattering amplitude. The relation states that the form factor
at a given value of is proportional to the scattering amplitude at a
specific energy and scattering angle. This suggests that an accurate
computation of the form factors at large requires a simultaneous
description of the phase-shifts at a related energy, a statement that seems
reasonable regardless of any derivation. Our form factor-scattering amplitude
relation is shown to be accurate for some examples. However, if the potential
consists of a strong short distance repulsive term and a strong longer ranged
attractive term, as typically occurs in many realistic potentials, the relation
is found to be accurate only for ridiculously large values of . More general
arguments, using only the Schroedinger equation, suggest a strong, but
complicated, relationship between the form factor and scattering amplitude.
Furthermore, the use of recently obtained soft potentials, along with an
appropriate current operator, may allow calculations of form factors that are
consistent with the necessary phase shifts.Comment: 14 pages, 4 figures, The discussion has been extended by including
numerical examples and general argument
Vocal learning promotes patterned inhibitory connectivity.
Skill learning is instantiated by changes to functional connectivity within premotor circuits, but whether the specificity of learning depends on structured changes to inhibitory circuitry remains unclear. We used slice electrophysiology to measure connectivity changes associated with song learning in the avian analog of primary motor cortex (robust nucleus of the arcopallium, RA) in Bengalese Finches. Before song learning, fast-spiking interneurons (FSIs) densely innervated glutamatergic projection neurons (PNs) with apparently random connectivity. After learning, there was a profound reduction in the overall strength and number of inhibitory connections, but this was accompanied by a more than two-fold enrichment in reciprocal FSI-PN connections. Moreover, in singing birds, we found that pharmacological manipulations of RA's inhibitory circuitry drove large shifts in learned vocal features, such as pitch and amplitude, without grossly disrupting the song. Our results indicate that skill learning establishes nonrandom inhibitory connectivity, and implicates this patterning in encoding specific features of learned movements
A Rapidly Spinning Black Hole Powers the Einstein Cross
Observations over the past 20 years have revealed a strong relationship
between the properties of the supermassive black hole (SMBH) lying at the
center of a galaxy and the host galaxy itself. The magnitude of the spin of the
black hole will play a key role in determining the nature of this relationship.
To date, direct estimates of black hole spin have been restricted to the local
Universe. Herein, we present the results of an analysis of 0.5 Ms of
archival Chandra observations of the gravitationally lensed quasar Q 2237+305
(aka the "Einstein-cross"), lying at a redshift of z = 1.695. The boost in flux
provided by the gravitational lens allows constraints to be placed on the spin
of a black hole at such high redshift for the first time. Utilizing state of
the art relativistic disk reflection models, the black hole is found to have a
spin of at the 90% confidence level. Placing a
lower limit on the spin, we find (4). The high value of
the spin for the black hole in Q 2237+305 lends
further support to the coherent accretion scenario for black hole growth. This
is the most distant black hole for which the spin has been directly constrained
to date.Comment: 5 pages, 3 figures, 1 table, formatted using emulateapj.cls. Accepted
for publication in ApJ
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