363 research outputs found
Reply to Comment on "Dynamical corrections to the DFT-LDA electron conductance in nanoscale systems"
We reply to the comment by Jung, Bokes, and Godby (arXiv:0706.0140) on our
paper Phys. Rev. Lett. 94, 186810 (2005). We show that the results in their
comment should not be taken as an indication that the viscosity corrections to
the conductance of real nanoscale structures are small. A more accurate
treatment of the density and current density distribution and of the electronic
correlations may yield much larger corrections in realistic systems.Comment: Reply to the comment by Jung et al (arXiv:0706.0140). 1 page, no
figures, to appear in PR
Globally Optimized Parameters for a Model of Mitotic Control in Frog Egg Extracts
DNA synthesis and nuclear division in the developing frog egg are controlled by fluctuations in the activity of M-phase promoting factor (MPF). The biochemical mechanism of MPF regulation is most easily studied in cytoplasmic extracts of frog eggs, for which careful experimental studies of the kinetics of phosphorylation and dephosphorylation of MPF and its regulators have been made. In 1998 Marlovits et al. used these data sets to estimate the kinetic rate constants in a mathematical model of the control system originally proposed by Novak and Tyson. In a recent publication, we showed that a gradient-based optimization algorithm finds a locally optimal parameter set quite close to the Marlovits estimates. In this paper, we combine global and local optimization strategies to show that the refined Marlovits parameter set, with one minor but significant modification to the Novak-Tyson equations, is the unique, best-fitting solution to the parameter estimation problem
Simulating adiabatic evolution of gapped spin systems
We show that adiabatic evolution of a low-dimensional lattice of quantum
spins with a spectral gap can be simulated efficiently. In particular, we show
that as long as the spectral gap \Delta E between the ground state and the
first excited state is any constant independent of n, the total number of
spins, then the ground-state expectation values of local operators, such as
correlation functions, can be computed using polynomial space and time
resources. Our results also imply that the local ground-state properties of any
two spin models in the same quantum phase can be efficiently obtained from each
other. A consequence of these results is that adiabatic quantum algorithms can
be simulated efficiently if the spectral gap doesn't scale with n. The
simulation method we describe takes place in the Heisenberg picture and does
not make use of the finitely correlated state/matrix product state formalism.Comment: 13 pages, 2 figures, minor change
The ground state of a class of noncritical 1D quantum spin systems can be approximated efficiently
We study families H_n of 1D quantum spin systems, where n is the number of
spins, which have a spectral gap \Delta E between the ground-state and
first-excited state energy that scales, asymptotically, as a constant in n. We
show that if the ground state |\Omega_m> of the hamiltonian H_m on m spins,
where m is an O(1) constant, is locally the same as the ground state
|\Omega_n>, for arbitrarily large n, then an arbitrarily good approximation to
the ground state of H_n can be stored efficiently for all n. We formulate a
conjecture that, if true, would imply our result applies to all noncritical 1D
spin systems. We also include an appendix on quasi-adiabatic evolutions.Comment: 9 pages, 1 eps figure, minor change
Finite representations of continuum environments
Understanding dissipative and decohering processes is fundamental to the
study of quantum systems. An accurate and generic method for investigating
these processes is to simulate both the system and environment, which, however,
is computationally very demanding. We develop a novel approach to constructing
finite representations of the environment based on the influence of different
frequency scales on the system's dynamics. As an illustration, we analyze a
solvable model of an optical mode decaying into a reservoir. The influence of
the environment modes is constant for small frequencies, but drops off rapidly
for large frequencies, allowing for a very sparse representation at high
frequencies that gives a significant computational speedup in simulating the
environment. This approach provides a general framework for simulating open
quantum systems.Comment: 4 pages, 3 figures, updated to fix font
Dehydration and ionic conductance quantization in nanopores
There has been tremendous experimental progress in the last decade in
identifying the structure and function of biological pores (ion channels) and
fabricating synthetic pores. Despite this progress, many questions still remain
about the mechanisms and universal features of ionic transport in these
systems. In this paper, we examine the use of nanopores to probe ion transport
and to construct functional nanoscale devices. Specifically, we focus on the
newly predicted phenomenon of quantized ionic conductance in nanopores as a
function of the effective pore radius - a prediction that yields a particularly
transparent way to probe the contribution of dehydration to ionic transport. We
study the role of ionic species in the formation of hydration layers inside and
outside of pores. We find that the ion type plays only a minor role in the
radial positions of the predicted steps in the ion conductance. However, ions
with higher valency form stronger hydration shells, and thus, provide even more
pronounced, and therefore, more easily detected, drops in the ionic current.
Measuring this phenomenon directly, or from the resulting noise, with synthetic
nanopores would provide evidence of the deviation from macroscopic (continuum)
dielectric behavior due to microscopic features at the nanoscale and may shed
light on the behavior of ions in more complex biological channels.Comment: 13 pages, 10 figure
Quantized ionic conductance in nanopores
Ionic transport in nanopores is a fundamentally and technologically important
problem in view of its occurrence in biological processes and its impact on
novel DNA sequencing applications. Using microscopic calculations, here we show
that ion transport may exhibit strong nonlinearities as a function of the pore
radius reminiscent of the conductance quantization steps as a function of the
transverse cross section of quantum point contacts. In the present case,
however, conductance steps originate from the break up of the hydration layers
that form around ions in aqueous solution. Once in the pore, the water
molecules form wavelike structures due to multiple scattering at the surface of
the pore walls and interference with the radial waves around the ion. We
discuss these effects as well as the conditions under which the step-like
features in the ionic conductance should be experimentally observable.Comment: 6 pages, 3 figures, updated to fix font
When the optimal is not the best: parameter estimation in complex biological models
Background: The vast computational resources that became available during the
past decade enabled the development and simulation of increasingly complex
mathematical models of cancer growth. These models typically involve many free
parameters whose determination is a substantial obstacle to model development.
Direct measurement of biochemical parameters in vivo is often difficult and
sometimes impracticable, while fitting them under data-poor conditions may
result in biologically implausible values.
Results: We discuss different methodological approaches to estimate
parameters in complex biological models. We make use of the high computational
power of the Blue Gene technology to perform an extensive study of the
parameter space in a model of avascular tumor growth. We explicitly show that
the landscape of the cost function used to optimize the model to the data has a
very rugged surface in parameter space. This cost function has many local
minima with unrealistic solutions, including the global minimum corresponding
to the best fit.
Conclusions: The case studied in this paper shows one example in which model
parameters that optimally fit the data are not necessarily the best ones from a
biological point of view. To avoid force-fitting a model to a dataset, we
propose that the best model parameters should be found by choosing, among
suboptimal parameters, those that match criteria other than the ones used to
fit the model. We also conclude that the model, data and optimization approach
form a new complex system, and point to the need of a theory that addresses
this problem more generally
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