934 research outputs found
The Stackelberg equilibrium as a consistent conjectural equilibrium
We consider a static game with conjectural variations where some firms make conjectures while others do not. Two propositions are proved. We first show that there exists a continuum of conjectural variations such that the conjectural equilibrium locally coincides with the Stackelberg equilibrium (Proposition 1). Second, we define the conditions under which a conjectural equilibrium is a locally consistent equilibrium (i.e. such that conjectures are fulfilled). The concept of (local) consistency is restricted to firms making conjectures. Two conditions on consistency are featured: consistency within a cohort and consistency among cohorts. The Stackelberg equilibrium fulfills only the latter condition (Proposition 2). An example is provided.Consistent conjectural variations, reaction functions, Stackelberg competition
Auxiliary-field quantum Monte Carlo study of first- and second-row post-d elements
A series of calculations for the first- and second-row post-d elements (Ga-Br
and In-I) are presented using the phaseless auxiliary-field quantum Monte Carlo
(AF QMC) method. This method is formulated in a Hilbert space defined by any
chosen one-particle basis, and maps the many-body problem into a linear
combination of independent-particle solutions with external auxiliary fields.
The phase/sign problem is handled approximately by the phaseless formalism
using a trial wave function, which in our calculations was chosen to be the
Hartree-Fock solution. We used the consistent correlated basis sets of Peterson
and coworkers, which employ a small core relativistic pseudopotential. The AF
QMC results are compared with experiment and with those from density-functional
(GGA and B3LYP) and coupled-cluster CCSD(T) calculations. The AF QMC total
energies agree with CCSD(T) to within a few milli-hartrees across the systems
and over several basis sets. The calculated atomic electron affinities,
ionization energies, and spectroscopic properties of dimers are, at large basis
sets, in excellent agreement with experiment.Comment: 10 pages, 2 figures. To be published in Journal of Chemical Physic
Fixed-node diffusion Monte Carlo study of the structures of m-benzyne
Diffusion Monte Carlo (DMC) calculations are performed on the monocyclic and
bicyclic forms of m-benzyne, which are the equilibrium structures at the
CCSD(T) and CCSD levels of coupled cluster theory. We employed
multi-configuration self-consistent field trial wave functions which are
constructed from a carefully selected 8-electrons-in-8-orbitals complete active
space [CAS(8,8)], with CSF coefficients that are reoptimized in the presence of
a Jastrow factor. The DMC calculations show that the monocyclic structure is
lower in energy than the bicyclic structure by 1.9(2) kcal/mole, in excellent
agreement with the best coupled cluster results.Comment: 5 pages, 2 figures. to be published in JC
Bond breaking with auxiliary-field quantum Monte Carlo
Bond stretching mimics different levels of electron correlation and provides
a challenging testbed for approximate many-body computational methods. Using
the recently developed phaseless auxiliary-field quantum Monte Carlo (AF QMC)
method, we examine bond stretching in the well-studied molecules BH and N,
and in the H chain. To control the sign/phase problem, the phaseless AF
QMC method constrains the paths in the auxiliary-field path integrals with an
approximate phase condition that depends on a trial wave function. With single
Slater determinants from unrestricted Hartree-Fock (UHF) as trial wave
function, the phaseless AF QMC method generally gives better overall accuracy
and a more uniform behavior than the coupled cluster CCSD(T) method in mapping
the potential-energy curve. In both BH and N, we also study the use of
multiple-determinant trial wave functions from multi-configuration
self-consistent-field (MCSCF) calculations. The increase in computational cost
versus the gain in statistical and systematic accuracy are examined. With such
trial wave functions, excellent results are obtained across the entire region
between equilibrium and the dissociation limit.Comment: 8 pages, 3 figures and 3 tables. Submitted to JC
Eliminating spin contamination in auxiliary-field quantum Monte Carlo: realistic potential energy curve of F2
The use of an approximate reference state wave function |Phi_r> in electronic
many-body methods can break the spin symmetry of Born-Oppenheimer
spin-independent Hamiltonians. This can result in significant errors,
especially when bonds are stretched or broken. A simple spin-projection method
is introduced for auxiliary-field quantum Monte Carlo (AFQMC) calculations,
which yields spin-contamination-free results, even with a spin-contaminated
|Phi_r>. The method is applied to the difficult F2 molecule, which is unbound
within unrestricted Hartree-Fock (UHF). With a UHF |Phi_r>, spin contamination
causes large systematic errors and long equilibration times in AFQMC in the
intermediate, bond-breaking region. The spin-projection method eliminates these
problems, and delivers an accurate potential energy curve from equilibrium to
the dissociation limit using the UHF |Phi_r>. Realistic potential energy curves
are obtained with a cc-pVQZ basis. The calculated spectroscopic constants are
in excellent agreement with experiment.Comment: 8 pages, 6 figures, submitted to J. Chem. Phy
Auxiliary-field quantum Monte Carlo calculations of molecular systems with a Gaussian basis
We extend the recently introduced phaseless auxiliary-field quantum Monte
Carlo (QMC) approach to any single-particle basis, and apply it to molecular
systems with Gaussian basis sets. QMC methods in general scale favorably with
system size, as a low power. A QMC approach with auxiliary fields in principle
allows an exact solution of the Schrodinger equation in the chosen basis.
However, the well-known sign/phase problem causes the statistical noise to
increase exponentially. The phaseless method controls this problem by
constraining the paths in the auxiliary-field path integrals with an
approximate phase condition that depends on a trial wave function. In the
present calculations, the trial wave function is a single Slater determinant
from a Hartree-Fock calculation. The calculated all-electron total energies
show typical systematic errors of no more than a few milli-Hartrees compared to
exact results. At equilibrium geometries in the molecules we studied, this
accuracy is roughly comparable to that of coupled-cluster with single and
double excitations and with non-iterative triples, CCSD(T). For stretched bonds
in HO, our method exhibits better overall accuracy and a more uniform
behavior than CCSD(T).Comment: 11 pages, 5 figures. submitted to JC
Does a Structured Data Collection Form Improve The Accuracy of Diagnosis of Acute Abdomen in an Urban Private Hospital?
Background: Accuracy of initial assessment of acute abdominal pain (AAP) is confounded by subjectivity and multiple etiologies for similar presentation. Standardized forms may harmonize the initial assessment, improve accuracy of diagnosis and enhance outcomes.Objectives: To determine the extent to which use of a structured data collection form (SDCF) affected the diagnostic accuracy of AAP.Methodology: A before and after study carried out from October 2011 to March 2012 of patients aged 13 years and older presenting with AAP in the emergency department (ED) of Aga Khan University Hospital, Nairobi (AKUH,N). Patients clerked by ED physicians using conventional history taking and examination between October and December 2011 were compared to a second group clerked after the introduction and use of a SDCF (January – March 2012) for proportion of correct diagnosis at initial encounter. This influence of age, gender and disease type on the impact of the form was evaluated as was the impact of the introduction of the structured forms on time to ED disposition, hospital stay, number and cost of investigations. Data were compiled in MS-Excel spreadsheets and analyzed using SPSS v16. P value of <0.05 was significantResults: 125 participants were included, 60 in Period 1 and 65 in Period 2. The overall mean age for males was 28 and 34 for females. Patients with surgical abdominal conditions were 21% and 49% for medical conditions. The diagnostic accuracy was 58% and 43% before and after the introduction of the SDCF respectively (p=0.088). For surgical patients, diagnostic accuracy was 77% before and 31% after the introduction of the form (p=0.018).Conclusions: The structured form did not improve the accuracy of diagnosing the causes of acute abdomen. It had a negative impact on the surgical diagnoses
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