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 $\gamma$-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