375 research outputs found
Formal Verification of a Geometry Algorithm: A Quest for Abstract Views and Symmetry in Coq Proofs
This extended abstract is about an effort to build a formal description of a
triangulation algorithm starting with a naive description of the algorithm
where triangles, edges, and triangulations are simply given as sets and the
most complex notions are those of boundary and separating edges. When
performing proofs about this algorithm, questions of symmetry appear and this
exposition attempts to give an account of how these symmetries can be handled.
All this work relies on formal developments made with Coq and the mathematical
components library
Mining State-Based Models from Proof Corpora
Interactive theorem provers have been used extensively to reason about
various software/hardware systems and mathematical theorems. The key challenge
when using an interactive prover is finding a suitable sequence of proof steps
that will lead to a successful proof requires a significant amount of human
intervention. This paper presents an automated technique that takes as input
examples of successful proofs and infers an Extended Finite State Machine as
output. This can in turn be used to generate proofs of new conjectures. Our
preliminary experiments show that the inferred models are generally accurate
(contain few false-positive sequences) and that representing existing proofs in
such a way can be very useful when guiding new ones.Comment: To Appear at Conferences on Intelligent Computer Mathematics 201
Bottom‐up effects of soil quality on a coffee arthropod interaction web
Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/117198/1/ecs213000721.pd
Population statistics study of radio and gamma-ray pulsars in the Galactic plane
We present results of our pulsar population synthesis of ordinary isolated
and millisecond pulsars in the Galactic plane. Over the past several years, a
program has been developed to simulate pulsar birth, evolution and emission
using Monte Carlo techniques. We have added to the program the capability to
simulate millisecond pulsars, which are old, recycled pulsars with extremely
short periods. We model the spatial distribution of the simulated pulsars by
assuming that they start with a random kick velocity and then evolve through
the Galactic potential. We use a polar cap/slot gap model for -ray
emission from both millisecond and ordinary pulsars. From our studies of radio
pulsars that have clearly identifiable core and cone components, in which we
fit the polarization sweep as well as the pulse profiles in order to constrain
the viewing geometry, we develop a model describing the ratio of radio
core-to-cone peak fluxes. In this model, short period pulsars are more
cone-dominated than in our previous studies. We present the preliminary results
of our recent study and the implications for observing these pulsars with GLAST
and AGILE.Comment: 6 pages, 3 figures, 1 table, accepted in Astrophysics and Space
Scienc
Hydrogeology, Hydraulic Properties, and Water Quality of the Surficial Aquifer: a Potential Alternative Water Source at Fort Stewart, Liberty County, Georgia
Proceedings of the 2011 Georgia Water Resources Conference, April 11, 12, and 13, 2011, Athens, Georgia.In the coastal area of Georgia, the Upper Floridan aquifer is the principal water-supply source. Restrictions have been placed on withdrawals from the aquifer because of declining water levels and saltwater contamination, which has prompted interest in the development of alternative sources of groundwater. At Fort Stewart in Liberty County, Georgia, a well was completed to test the surficial aquifer as a possible source of irrigation water for athletic fields. The U.S. Geological Survey in cooperation with the U.S. Army conducted an evaluation in 2010 of the water-bearing potential of the surficial aquifer. This evaluation included describing the depth, thickness, and lithology of the surficial aquifer and its geophysical characteristics, hydraulic properties, and water quality. Results of a 24-hour aquifer test indicate that the aquifer is capable of well yields in hundreds of gallons per minute of suitable quality for irrigation use.Sponsored by:
Georgia Environmental Protection Division
U.S. Geological Survey, Georgia Water Science Center
U.S. Department of Agriculture, Natural Resources Conservation Service
Georgia Institute of Technology, Georgia Water Resources Institute
The University of Georgia, Water Resources FacultyThis book was published by Warnell School of Forestry and Natural Resources, The University of Georgia, Athens, Georgia 30602-2152. The views and statements advanced in this publication are solely those of the authors and do not represent official views or policies of The University of Georgia, the U.S. Geological Survey, the Georgia Water Research Institute as authorized by the Water Research Institutes Authorization Act of 1990 (P.L. 101-307) or the other conference sponsors
Identifying challenges towards practical quantum advantage through resource estimation: the measurement roadblock in the variational quantum eigensolver
Recent advances in Noisy Intermediate-Scale Quantum (NISQ) devices have
brought much attention to the potential of the Variational Quantum Eigensolver
(VQE) and related techniques to provide practical quantum advantage in
computational chemistry. However, it is not yet clear whether such algorithms,
even in the absence of device error, could achieve quantum advantage for
systems of practical interest and how large such an advantage might be. To
address these questions, we have performed an exhaustive set of benchmarks to
estimate number of qubits and number of measurements required to compute the
combustion energies of small organic molecules to within chemical accuracy
using VQE as well as state-of-the-art classical algorithms. We consider several
key modifications to VQE, including the use of Frozen Natural Orbitals, various
Hamiltonian decomposition techniques, and the application of fermionic marginal
constraints. Our results indicate that although Frozen Natural Orbitals and
low-rank factorizations of the Hamiltonian significantly reduce the qubit and
measurement requirements, these techniques are not sufficient to achieve
practical quantum computational advantage in the calculation of organic
molecule combustion energies. This suggests that new approaches to estimation
leveraging quantum coherence, such as Bayesian amplitude estimation
[arxiv:2006.09350, arxiv:2006.09349], may be required in order to achieve
practical quantum advantage with near-term devices. Our work also highlights
the crucial role that resource and performance assessments of quantum
algorithms play in identifying quantum advantage and guiding quantum algorithm
design.Comment: 27 pages, 18 figure
Isolated pulsar spin evolution on the P-Pdot Diagram
We look at two contrasting spin-down models for isolated radio pulsars and,
accounting for selection effects, synthesize observable populations. While our
goal is to reproduce all of the observable characteristics, in this paper we
pay particular attention to the form of the spin period vs. period derivative
(P-Pdot) diagram and its dependence on various pulsar properties. We analyse
the initial spin period, the braking index, the magnetic field, various beaming
models, as well as the pulsar's luminosity. In addition to considering the
standard magnetic dipole model for pulsar spin-down, we also consider the
recent hybrid model proposed by Contopoulos & Spitkovsky. The magnetic dipole
model, however, does a better job of reproducing the observed pulsar
population. We conclude that random alignment angles and period dependent
luminosity distributions are essential to reproduce the observed P-Pdot
diagram. We also consider the time decay of alignment angles, and attempt to
reconcile various models currently being studied. We conclude that, in order to
account for recent evidence for the alignment found by Weltevrede & Johnston,
the braking torque on a neutron star should not depend strongly on the
inclination. Our simulation code is publically available and includes a
web-based interface to examine the results and make predictions for yields of
current and future surveys.Comment: 9 pages, 4 figure
Spin-Dependent Cyclotron Decay Rates in Strong Magnetic Fields
Cyclotron decay and absorption rates have been well studied in the
literature, focusing primarily on spectral, angular and polarization
dependence. Astrophysical applications usually do not require retention of
information on the electron spin state, and these are normally averaged in
obtaining the requisite rates. In magnetic fields, higher order quantum
processes such as Compton scattering become resonant at the cyclotron frequency
and its harmonics, with the resonances being formally divergent. Such
divergences are usually eliminated by accounting for the finite lifetimes of
excited Landau states. This practice requires the use of spin-dependent
cyclotron rates in order to obtain accurate determinations of process rates
very near cyclotronic resonances, the phase space domain most relevant for
certain applications to pulsar models. This paper develops previous results in
the literature to obtain compact analytic expressions for cyclotron decay
rates/widths in terms of a series of Legendre functions of the second kind;
these expressions can be expediently used in astrophysical models. The rates
are derived using two popular eigenstate formalisms, namely that due to Sokolov
and Ternov, and that due to Johnson and Lippmann. These constitute two sets of
eigenfunctions of the Dirac equation that diagonalize different operators, and
accordingly yield different spin-dependent cyclotron rates. This paper
illustrates the attractive Lorentz transformation characteristics of the
Sokolov and Ternov formulation, which is another reason why it is preferable
when electron spin information must be explicitly retained.Comment: 11 pages, 2 embedded figures, apjgalley format, To appear in The
Astrophysical Journal, Vol 630, September 1, 2005 issu
Rapid cognitive decline, one-year institutional admission and one-year mortality: Analysis of the ability to predict and inter-tool agreement of four validated clinical frailty indexes in the safes cohort
Objectives: To evaluate the predictive ability of four clinical frailty indexes as regards one-year rapid cognitive decline (RCD — defined as the loss of at least 3 points on the MMSE score), and one-year institutional admission (IA) and mortality respectively; and to measure their agreement for identifying groups at risk of these severe outcomes. Design: One-year follow-up and multicentre study of old patients participating in the SAFEs cohort study. Setting: Nine university hospitals in France. Participants: 1,306 patients aged 75 or older (mean age 85±6 years; 65% female) hospitalized in medical divisions through an Emergency department. Measurements: Four frailty indexes (Winograd; Rockwood; Donini; and Schoevaerdts) reflecting the multidimensionality of the frailty concept, using an ordinal scoring system able to discriminate different grades of frailty, and constructed based on the accumulation of identified deficits after comprehensive geriatric assessment conducted during the first week of hospital stay, were used to categorize participants into three different grades of frailty: Gl — not frail; G2 — moderately frail; and G3 — severely frail. Comparisons between groups were performed using Fisher's exact test. Agreement between indexes was evaluated using Cohen's Kappa coefficient. Results: All patients were classified as frail by at least one of the four indexes. The Winograd and Rockwood indexes mainly classified subjects as G2 (85% and 96%), and the Donini and Schoevaerdts indexes mainly as G3 (71% and 67%). Among the SAFEs cohort population, 250, 1047 and 1,306 subjects were eligible for analyses of predictability for RCD, 1-year IA and 1-year mortality respectively. At 1 year, 84 subjects (34%) experienced RCD, 377 (36%) were admitted into an institutional setting, and 445 (34%) had died With the Rockwood index, all subjects who expenenced RCD were classified in G2; and in G2 and G3 when the Donini and Schoevaerdts indexes were used No significant difference was found between frailty grade and RCD, whereas frailty grade was significantly associated with an increased risk of IA and death, whatever the frailty index considered. Agreement between the different indexes of frailty was poor with Kappa coefficients ranging from −0.02 to 0.15. Conclusion: These findings confirm the poor clinimetric properties of these current indexes to measure frailty, underlining the fact that further work is needed to develop a better and more widely-accepted definition of frailty and therefore a better understanding of its pathophysiolog
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