23,138 research outputs found
Proof-irrelevant model of CC with predicative induction and judgmental equality
We present a set-theoretic, proof-irrelevant model for Calculus of
Constructions (CC) with predicative induction and judgmental equality in
Zermelo-Fraenkel set theory with an axiom for countably many inaccessible
cardinals. We use Aczel's trace encoding which is universally defined for any
function type, regardless of being impredicative. Direct and concrete
interpretations of simultaneous induction and mutually recursive functions are
also provided by extending Dybjer's interpretations on the basis of Aczel's
rule sets. Our model can be regarded as a higher-order generalization of the
truth-table methods. We provide a relatively simple consistency proof of type
theory, which can be used as the basis for a theorem prover
Case management of persons with acquired immunodeficiency syndrome in San Francisco.
The acquired immunodeficiency syndrome (AIDS) epidemic represents a growing challenge for the health care system and for case management models applied to persons with AIDS. The experience of San Francisco highlights some of the issues involved in developing a case management system appropriate to the needs of persons with AIDS, as well as providers, and payers. Dramatic growth in the size and complexity of the AIDS caseload and the involvement of public, health maintenance organization, and community providers has required the increasing formalization and centralization of case management roles. Persistent questions about the definition and goals of case management complicate development of these services
Anomalous velocity distributions in active Brownian suspensions
Large scale simulations and analytical theory have been combined to obtain
the non-equilibrium velocity distribution, , of randomly accelerated
particles in suspension. The simulations are based on an event-driven
algorithm, generalised to include friction. They reveal strongly anomalous but
largely universal distributions which are independent of volume fraction and
collision processes, which suggests a one-particle model should capture all the
essential features. We have formulated this one-particle model and solved it
analytically in the limit of strong damping, where we find that decays
as for multiple decades, eventually crossing over to a Gaussian decay for
the largest velocities. Many particle simulations and numerical solution of the
one-particle model agree for all values of the damping.Comment: 6 pages, 5 figure
Renyi Entropy and Geometry
Entanglement entropy in even dimensional conformal field theories (CFTs)
contains well-known universal terms arising from the conformal anomaly. Renyi
entropies are natural generalizations of the entanglement entropy that are much
less understood. Above two spacetime dimensions, the universal terms in the
Renyi entropies are unknown for general entangling geometries. We conjecture a
new structure in the dependence of the four-dimensional Renyi entropies on the
intrinsic and extrinsic geometry of the entangling surface. We provide evidence
for this conjecture by direct numerical computations in the free scalar and
fermion field theories. The computation involves relating the four-dimensional
free massless Renyi entropies across cylindrical entangling surfaces to
corresponding three-dimensional massive Renyi entropies across circular
entangling surfaces. Our numerical technique also allows us to directly probe
other interesting aspects of three-dimensional Renyi entropy, including the
massless renormalized Renyi entropy and calculable contributions to the
perimeter law.Comment: 16 pages, 3 figures; v2 refs added, minor improvement
Dark-Matter Harmonics Beyond Annual Modulation
The count rate at dark-matter direct-detection experiments should modulate
annually due to the motion of the Earth around the Sun. We show that
higher-frequency modulations, including daily modulation, are also present and
in some cases are nearly as strong as the annual modulation. These higher-order
modes are particularly relevant if (i) the dark matter is light, O(10) GeV,
(ii) the scattering is inelastic, or (iii) velocity substructure is present;
for these cases, the higher-frequency modes are potentially observable at
current and ton-scale detectors. We derive simple expressions for the harmonic
modes as functions of the astrophysical and geophysical parameters describing
the Earth's orbit, using an updated expression for the Earth's velocity that
corrects a common error in the literature. For an isotropic halo velocity
distribution, certain ratios of the modes are approximately constant as a
function of nuclear recoil energy. Anisotropic distributions can also leave
observable features in the harmonic spectrum. Consequently, the higher-order
harmonic modes are a powerful tool for identifying a potential signal from
interactions with the Galactic dark-matter halo.Comment: 40 pages, 10 figures; v2 refs added, minor improvements; v3 refs
added, minor improvements, JCAP versio
Distinguishing Dark Matter from Unresolved Point Sources in the Inner Galaxy with Photon Statistics
Data from the Fermi Large Area Telescope suggests that there is an extended
excess of GeV gamma-ray photons in the Inner Galaxy. Identifying potential
astrophysical sources that contribute to this excess is an important step in
verifying whether the signal originates from annihilating dark matter. In this
paper, we focus on the potential contribution of unresolved point sources, such
as millisecond pulsars (MSPs). We propose that the statistics of the
photons---in particular, the flux probability density function (PDF) of the
photon counts below the point-source detection threshold---can potentially
distinguish between the dark-matter and point-source interpretations. We
calculate the flux PDF via the method of generating functions for these two
models of the excess. Working in the framework of Bayesian model comparison, we
then demonstrate that the flux PDF can potentially provide evidence for an
unresolved MSP-like point-source population.Comment: 27 pages, 8 figures; v2, reference added and other minor change
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