4,475 research outputs found
Coloring random graphs
We study the graph coloring problem over random graphs of finite average
connectivity . Given a number of available colors, we find that graphs
with low connectivity admit almost always a proper coloring whereas graphs with
high connectivity are uncolorable. Depending on , we find the precise value
of the critical average connectivity . Moreover, we show that below
there exist a clustering phase in which ground states
spontaneously divide into an exponential number of clusters and where the
proliferation of metastable states is responsible for the onset of complexity
in local search algorithms.Comment: 4 pages, 1 figure, version to app. in PR
Mobile Resource Guarantees for Smart Devices
Abstract. We present the Mobile Resource Guarantees framework: a system for ensuring that downloaded programs are free from run-time violations of resource bounds. Certificates are attached to code in the form of efficiently checkable proofs of resource bounds; in contrast to cryptographic certificates of code origin, these are independent of trust networks. A novel programming language with resource constraints encoded in function types is used to streamline the generation of proofs of resource usage.
Photoemission spectroscopy and sum rules in dilute electron-phonon systems
A family of exact sum rules for the one-polaron spectral function in the
low-density limit is derived. An algorithm to calculate energy moments of
arbitrary order of the spectral function is presented. Explicit expressions are
given for the first two moments of a model with general electron-phonon
interaction, and for the first four moments of the Holstein polaron. The sum
rules are linked to experiments on momentum-resolved photoemission
spectroscopy. The bare electronic dispersion and the electron-phonon coupling
constant can be extracted from the first and second moments of spectrum. The
sum rules could serve as constraints in analytical and numerical studies of
electron-phonon models.Comment: 4 page
GParareal: A time-parallel ODE solver using Gaussian process emulation
Sequential numerical methods for integrating initial value problems (IVPs)
can be prohibitively expensive when high numerical accuracy is required over
the entire interval of integration. One remedy is to integrate in a parallel
fashion, "predicting" the solution serially using a cheap (coarse) solver and
"correcting" these values using an expensive (fine) solver that runs in
parallel on a number of temporal subintervals. In this work, we propose a
time-parallel algorithm (GParareal) that solves IVPs by modelling the
correction term, i.e. the difference between fine and coarse solutions, using a
Gaussian process emulator. This approach compares favourably with the classic
parareal algorithm and we demonstrate, on a number of IVPs, that GParareal can
converge in fewer iterations than parareal, leading to an increase in parallel
speed-up. GParareal also manages to locate solutions to certain IVPs where
parareal fails and has the additional advantage of being able to use archives
of legacy solutions, e.g. solutions from prior runs of the IVP for different
initial conditions, to further accelerate convergence of the method --
something that existing time-parallel methods do not do
Recovery of Large Angular Scale CMB Polarization for Instruments Employing Variable-delay Polarization Modulators
Variable-delay Polarization Modulators (VPMs) are currently being implemented
in experiments designed to measure the polarization of the cosmic microwave
background on large angular scales because of their capability for providing
rapid, front-end polarization modulation and control over systematic errors.
Despite the advantages provided by the VPM, it is important to identify and
mitigate any time-varying effects that leak into the synchronously modulated
component of the signal. In this paper, the effect of emission from a K
VPM on the system performance is considered and addressed. Though instrument
design can greatly reduce the influence of modulated VPM emission, some
residual modulated signal is expected. VPM emission is treated in the presence
of rotational misalignments and temperature variation. Simulations of
time-ordered data are used to evaluate the effect of these residual errors on
the power spectrum. The analysis and modeling in this paper guides
experimentalists on the critical aspects of observations using VPMs as
front-end modulators. By implementing the characterizations and controls as
described, front-end VPM modulation can be very powerful for mitigating
noise in large angular scale polarimetric surveys. None of the systematic
errors studied fundamentally limit the detection and characterization of
B-modes on large scales for a tensor-to-scalar ratio of . Indeed,
is achievable with commensurately improved characterizations and
controls.Comment: 13 pages, 13 figures, 1 table, matches published versio
Evaluation of Extent and Bioavailability of Chromium Contamination Near an Abandoned Strip Mine
Chromium is a potentially toxic element to plants and animals commonly associated with serpentine and anthropogenic sources. An abandoned Cr strip-mine at US National Guard Camp SLO, CA containing serpentinitic parent material was tested for total and bioavailable Cr in the soil and overlying vegetation via US EPA Methods 3050a (Total Cr) and 1311 (Total Characteristic Leaching Procedure, TCLP) (US EPA, 1995), respectively. The analysis of total and bioavailable Cr was used to assess the risk of nearby surface and groundwater contamination and to evaluate the site’s need for remediation. In addition, trends in soil Cr levels with respect to slope position and sampling transect were identified. Total and most bioavailable Cr concentrations in plants were below the method detection limits (TotalMDL = 0.12 mg L-1; TCLPMDL = 0.04 mg L-1), suggesting the Cr was immobile and not bioavailable. The average total Cr level was 403.5 +/- 177.6 mg kg-1, significantly below the background total Cr level of 829.4 +/- 213.6 mg kg-1. Based on Chromium’s immobility, and its low levels in the site relative to background concentrations, remediation practices were not recommended. No significant trends were observed in total soil Cr levels along any transect or between sampled slope positions. The information gained from this was used by Camp SLO officers to assess the threat of Cr mobility and bioavailability in the soils at this site, as well as in nearby waterways and ground water
NMR and NQR Fluctuation Effects in Layered Superconductors
We study the effect of thermal fluctuations of the s-wave order parameter of
a quasi two dimensional superconductor on the nuclear spin relaxation rate near
the transition temperature Tc. We consider both the effects of the amplitude
fluctuations and the Berezinskii-Kosterlitz-Thouless (BKT) phase fluctuations
in weakly coupled layered superconductors. In the treatment of the amplitude
fluctuations we employ the Gaussian approximation and evaluate the longitudinal
relaxation rate 1/T1 for a clean s-wave superconductor, with and without pair
breaking effects, using the static pair fluctuation propagator D. The increase
in 1/T1 due to pair breaking in D is overcompensated by the decrease arising
from the single particle Green's functions. The result is a strong effect on
1/T1 for even a small amount of pair breaking. The phase fluctuations are
described in terms of dynamical BKT excitations in the form of pancake
vortex-antivortex (VA) pairs. We calculate the effect of the magnetic field
fluctuations caused by the translational motion of VA excitations on 1/T1 and
on the transverse relaxation rate 1/T2 on both sides of the BKT transitation
temperature T(BKT)<Tc. The results for the NQR relaxation rates depend strongly
on the diffusion constant that governs the motion of free and bound vortices as
well as the annihilation of VA pairs. We discuss the relaxation rates for real
multilayer systems where the diffusion constant can be small and thus increase
the lifetime of a VA pair, leading to an enhancement of the rates. We also
discuss in some detail the experimental feasibility of observing the effects of
amplitude fluctuations in layered s-wave superconductors such as the
dichalcogenides and the effects of phase fluctuations in s- or d-wave
superconductors such as the layered cuprates.Comment: 38 pages, 12 figure
Functional Big-step Semantics
When doing an interactive proof about a piece of software, it is important that the underlying programming language’s semantics does not make the proof unnecessarily difficult or unwieldy. Both smallstep and big-step semantics are commonly used, and the latter is typically given by an inductively defined relation. In this paper, we consider an alternative: using a recursive function akin to an interpreter for the language. The advantages include a better induction theorem, less duplication, accessibility to ordinary functional programmers, and the ease of doing symbolic simulation in proofs via rewriting. We believe that this style of semantics is well suited for compiler verification, including proofs of divergence preservation. We do not claim the invention of this style of semantics: our contribution here is to clarify its value, and to explain how it supports several language features that might appear to require a relational or small-step approach. We illustrate the technique on a simple imperative language with C-like for-loops and a break statement, and compare it to a variety of other approaches. We also provide ML and lambda-calculus based examples to illustrate its generality
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