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Verified Calculations
, 2013
"... Calculational proofs—proofs by stepwise formula manipulation—are praised for their rigor, readability, and elegance. It seems desirable to reuse this style, often employed on paper, in the context of mechanized reasoning, and in particular, program verification. This work leverages the power of SMT ..."
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Cited by 4 (1 self)
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of SMT solvers to machinecheck calculational proofs at the level of detail they are usually written by hand. It builds the support for calculations into the programming language and autoactive program verifier Dafny. The paper demonstrates that calculations integrate smoothly with other language
On the Necessary Grid Resolution for Verified Calculation
 of Premixed Laminar Flames,”Communications in Computational Physics
"... Abstract. We consider the grid resolution necessary to resolve combustion in a mixture of calorically imperfect ideal gases described by detailed kinetics and multicomponent transport. Using the steady premixed laminar flame as a paradigm, the required spatial discretization to capture all detailed ..."
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Cited by 5 (4 self)
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Abstract. We consider the grid resolution necessary to resolve combustion in a mixture of calorically imperfect ideal gases described by detailed kinetics and multicomponent transport. Using the steady premixed laminar flame as a paradigm, the required spatial discretization to capture all detailed physics in the reaction zone is found via 1) determination of the finest grid used in a standard software tool which employs adaptive mesh refinement, 2) examination of peak values of intermediate species mass fractions in the flame zone as a function of grid size, 3) a formal grid resolution study, and 4) a robust new eigenvalue analysis developed to estimate the finest length scale. Application to laminar premixed flames in hydrogenair flames reveals that the finest length scale is on the order of 10 −4 cm for combustion at atmospheric pressure. Resolution at this scale is shown to be necessary to capture detailed species mass fraction profiles; other features such as steady flame speeds and equilibrium thermochemical properties do not have such a stringent length scale requirement.
Verified calculation of the nodes and weights for Gaussian quadrature formulas
 Interval Computation
"... Using Gaussian Quadrature for the verified calculation of an integral assumes that enclosures of the nodes and weights are given. The traditional method of computing the nodes and weights is illconditioned and cannot be performed with interval arithmetic. Since the nodes and weights can be determin ..."
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Cited by 2 (0 self)
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Using Gaussian Quadrature for the verified calculation of an integral assumes that enclosures of the nodes and weights are given. The traditional method of computing the nodes and weights is illconditioned and cannot be performed with interval arithmetic. Since the nodes and weights can
Matching properties of MOS transistors
 IEEE J. SolidState Circuits
, 1989
"... AbstractThe matching properties of the threshold voltage, substrate factor, and current factor of MOS transistors have been analyzed and measured. Improvements to the existing theory are given, as well as extensions for longdistance matching and rotation of devices. Matching parameters of several ..."
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Cited by 361 (1 self)
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processes are compared. The matching results have been verified by measurements and calculations on several basic circuits. 1.
PREPARERS AND VERIFIERS
"... The objective of this calculation is to demonstrate the structural adequacy of the Advanced ..."
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The objective of this calculation is to demonstrate the structural adequacy of the Advanced
Verified hybrid controllers for automated vehicles
 IEEE Transactions on Automatic Control
, 1998
"... Abstract — The objective of an Automated Highway System (AHS) is to increase the safety and throughput of the existing highway infrastructure by introducing traffic automation. AHS is an example of a large scale, multiagent complex dynamical system and is ideally suited for a hierarchical hybrid con ..."
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Cited by 74 (23 self)
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for further verification. The calculations also provide an upper bound on the performance that can be expected in terms of throughput at various levels of centralization. Index Terms — Automated highway systems, game theory, safety. I.
Verifying monitor unit calculations for tangential breast fields
, 2005
"... An essential component of quality assurance in radiation therapy is verifying the accuracy of monitor unit calculations. Differences between sophisticated algorithms using 2.5D or 3D calculations and simpler monitor unit check algorithms or hand calculations assuming a flat water phantom must be exp ..."
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An essential component of quality assurance in radiation therapy is verifying the accuracy of monitor unit calculations. Differences between sophisticated algorithms using 2.5D or 3D calculations and simpler monitor unit check algorithms or hand calculations assuming a flat water phantom must
Coil sensitivity encoding for fast MRI. In:
 Proceedings of the ISMRM 6th Annual Meeting,
, 1998
"... New theoretical and practical concepts are presented for considerably enhancing the performance of magnetic resonance imaging (MRI) by means of arrays of multiple receiver coils. Sensitivity encoding (SENSE) is based on the fact that receiver sensitivity generally has an encoding effect complementa ..."
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Cited by 193 (3 self)
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configurations and kspace sampling patterns. Special attention is given to the currently most practical case, namely, sampling a common Cartesian grid with reduced density. For this case the feasibility of the proposed methods was verified both in vitro and in vivo. Scan time was reduced to onehalf using a two
Verifying concurrent systems with symbolic execution
 Journal of Logic and Computation (Special Issue
"... Abstract Current techniques for interactively proving temporal properties of concurrent systems translate transition systems into temporal formulas by introducing program counter variables. Proofs are not intuitive, because control flow is not explicitly considered. For sequential programs symbolic ..."
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Cited by 33 (20 self)
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and allows simple, local invariants. 1 Introduction As an example of a concurrent system, consider the parallel program Binom which is shown in Fig. 1 and has been taken from [15]. Two parallel processes calculate the binomial coefficient \Gamma n
Refinement of the AMBER Force Field for Nucleic Acids: Improving the Description of a/g Conformers
, 2007
"... ABSTRACT We present here the parmbsc0 force field, a refinement of the AMBER parm99 force field, where emphasis has been made on the correct representation of the a/g concerted rotation in nucleic acids (NAs). The modified force field corrects overpopulations of the a/g (g1,t) backbone that were se ..."
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Cited by 178 (31 self)
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seen in long (more than 10 ns) simulations with previous AMBER parameter sets (parm9499). The force field has been derived by fitting to highlevel quantum mechanical data and verified by comparison with very highlevel quantum mechanical calculations and by a very extensive comparison between
Results 1  10
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4,916