8,051 research outputs found
Well structured program equivalence is highly undecidable
We show that strict deterministic propositional dynamic logic with
intersection is highly undecidable, solving a problem in the Stanford
Encyclopedia of Philosophy. In fact we show something quite a bit stronger. We
introduce the construction of program equivalence, which returns the value
precisely when two given programs are equivalent on halting
computations. We show that virtually any variant of propositional dynamic logic
has -hard validity problem if it can express even just the equivalence
of well-structured programs with the empty program \texttt{skip}. We also show,
in these cases, that the set of propositional statements valid over finite
models is not recursively enumerable, so there is not even an axiomatisation
for finitely valid propositions.Comment: 8 page
Electrostatic solvation free energies of charged hard spheres using molecular dynamics with density functional theory interactions
Determining the solvation free energies of single ions in water is one of the
most fundamental problems in physical chemistry and yet many unresolved
questions remain. In particular, the ability to decompose the solvation free
energy into simple and intuitive contributions will have important implications
for models of electrolyte solution. Here, we provide definitions of the various
types of single ion solvation free energies based on different simulation
protocols. We calculate solvation free energies of charged hard spheres using
density functional theory interaction potentials with molecular dynamics
simulation (DFT-MD) and isolate the effects of charge and cavitation, comparing
to the Born (linear response) model. We show that using uncorrected Ewald
summation leads to unphysical values for the single ion solvation free energy
and that charging free energies for cations are approximately linear as a
function of charge but that there is a small non-linearity for small anions.
The charge hydration asymmetry (CHA) for hard spheres, determined with quantum
mechanics, is much larger than for the analogous real ions. This suggests that
real ions, particularly anions, are significantly more complex than simple
charged hard spheres, a commonly employed representation.Comment: 28 pages, 5 figure
Effects of hemodialysis on circulating adrenomedullin concentrations in patients with end-stage renal disease
To characterize the determinants of circulating levels of adrenomedullin (AM), the plasma levels of this peptide were measured in 58 patients with end-stage renal disease on hemodialysis, Predialysis plasma levels of AM were more than twice as high in patients on hemodialysis as compared to controls. In hemodialysis patients with heart failure (NYHA classes II-IV) or hypertensive HD patients plasma levels of AM were significantly higher than in patients with end-stage renal disease only. Plasma levels of AM were clot altered immediately by hemodialysis but decreased significantly 14-20 h after hemodialysis, AM plasma levels before hemodialysis and 14-20 h after hemodialysis were correlated with the corresponding mean arterial pressure
Real single ion solvation free energies with quantum mechanical simulation
Single ion solvation free energies are one of the most important properties
of electrolyte solutions and yet there is ongoing debate about what these
values are. Only the values for neutral ion pairs are known. Here, we use DFT
interaction potentials with molecular dynamics simulation (DFT-MD) combined
with a modified version of the quasi-chemical theory (QCT) to calculate these
energies for the lithium and fluoride ions. A method to correct for the error
in the DFT functional is developed and very good agreement with the
experimental value for the lithium fluoride pair is obtained. Moreover, this
method partitions the energies into physically intuitive terms such as surface
potential, cavity and charging energies which are amenable to descriptions with
reduced models. Our research suggests that lithium's solvation free energy is
dominated by the free energetics of a charged hard sphere, whereas fluoride
exhibits significant quantum mechanical behavior that cannot be simply
described with a reduced model.Comment: 13 pages, 4 figure
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