5,447 research outputs found
Mass conserved elementary kinetics is sufficient for the existence of a non-equilibrium steady state concentration
Living systems are forced away from thermodynamic equilibrium by exchange of
mass and energy with their environment. In order to model a biochemical
reaction network in a non-equilibrium state one requires a mathematical
formulation to mimic this forcing. We provide a general formulation to force an
arbitrary large kinetic model in a manner that is still consistent with the
existence of a non-equilibrium steady state. We can guarantee the existence of
a non-equilibrium steady state assuming only two conditions; that every
reaction is mass balanced and that continuous kinetic reaction rate laws never
lead to a negative molecule concentration. These conditions can be verified in
polynomial time and are flexible enough to permit one to force a system away
from equilibrium. In an expository biochemical example we show how a
reversible, mass balanced perpetual reaction, with thermodynamically infeasible
kinetic parameters, can be used to perpetually force a kinetic model of
anaerobic glycolysis in a manner consistent with the existence of a steady
state. Easily testable existence conditions are foundational for efforts to
reliably compute non-equilibrium steady states in genome-scale biochemical
kinetic models.Comment: 11 pages, 2 figures (v2 is now placed in proper context of the
excellent 1962 paper by James Wei entitled "Axiomatic treatment of chemical
reaction systems". In addition, section 4, on "Utility of steady state
existence theorem" has been expanded.
MetaboTools: A comprehensive toolbox for analysis of genome-scale metabolic models
Metabolomic data sets provide a direct read-out of cellular phenotypes and
are increasingly generated to study biological questions. Our previous work
revealed the potential of analyzing extracellular metabolomic data in the
context of the metabolic model using constraint-based modeling. Through this
work, which consists of a protocol, a toolbox, and tutorials of two use cases,
we make our methods available to the broader scientific community. The protocol
describes, in a step-wise manner, the workflow of data integration and
computational analysis. The MetaboTools comprise the Matlab code required to
complete the workflow described in the protocol. Tutorials explain the
computational steps for integration of two different data sets and demonstrate
a comprehensive set of methods for the computational analysis of metabolic
models and stratification thereof into different phenotypes. The presented
workflow supports integrative analysis of multiple omics data sets.
Importantly, all analysis tools can be applied to metabolic models without
performing the entire workflow. Taken together, this protocol constitutes a
comprehensive guide to the intra-model analysis of extracellular metabolomic
data and a resource offering a broad set of computational analysis tools for a
wide biomedical and non-biomedical research community
Overeducation, gender, income and life satisfaction. Panel evidence from Korea
One reason often put forward for South Korea’s rapid economic growth has been the rising level of educational attainment of its workforce. Correspondingly, the proportion of Koreans who complete tertiary education has also rapidly increased (and is also considerably higher than the OECD average). Such increases raise the possibility of overeducation if the amount of jobs which require such education do not increase at a similar pace. Among the consequences of overeducation are reduced life satisfaction and underutilised human capital. Given that Korean females are better educated than males, and they also face more discrimination in the labour market, the consequences of overeducation are likely to differ by gender. Using Korean panel data and both a subjective and objective measure of overeducation, the results are consistent with females having lower aspirations despite their high levels of education, and indicate that a more female friendly labour market could address the country’s currently underutilised human capital, for the benefit of the females themselves, as well as males, and the Korean economy
Thin film evolution equations from (evaporating) dewetting liquid layers to epitaxial growth
In the present contribution we review basic mathematical results for three
physical systems involving self-organising solid or liquid films at solid
surfaces. The films may undergo a structuring process by dewetting,
evaporation/condensation or epitaxial growth, respectively. We highlight
similarities and differences of the three systems based on the observation that
in certain limits all of them may be described using models of similar form,
i.e., time evolution equations for the film thickness profile. Those equations
represent gradient dynamics characterized by mobility functions and an
underlying energy functional.
Two basic steps of mathematical analysis are used to compare the different
system. First, we discuss the linear stability of homogeneous steady states,
i.e., flat films; and second the systematics of non-trivial steady states,
i.e., drop/hole states for dewetting films and quantum dot states in epitaxial
growth, respectively. Our aim is to illustrate that the underlying solution
structure might be very complex as in the case of epitaxial growth but can be
better understood when comparing to the much simpler results for the dewetting
liquid film. We furthermore show that the numerical continuation techniques
employed can shed some light on this structure in a more convenient way than
time-stepping methods.
Finally we discuss that the usage of the employed general formulation does
not only relate seemingly not related physical systems mathematically, but does
as well allow to discuss model extensions in a more unified way
Conditions for duality between fluxes and concentrations in biochemical networks
Mathematical and computational modelling of biochemical networks is often
done in terms of either the concentrations of molecular species or the fluxes
of biochemical reactions. When is mathematical modelling from either
perspective equivalent to the other? Mathematical duality translates concepts,
theorems or mathematical structures into other concepts, theorems or
structures, in a one-to-one manner. We present a novel stoichiometric condition
that is necessary and sufficient for duality between unidirectional fluxes and
concentrations. Our numerical experiments, with computational models derived
from a range of genome-scale biochemical networks, suggest that this
flux-concentration duality is a pervasive property of biochemical networks. We
also provide a combinatorial characterisation that is sufficient to ensure
flux-concentration duality. That is, for every two disjoint sets of molecular
species, there is at least one reaction complex that involves species from only
one of the two sets. When unidirectional fluxes and molecular species
concentrations are dual vectors, this implies that the behaviour of the
corresponding biochemical network can be described entirely in terms of either
concentrations or unidirectional fluxes
Pointwise convergence of vector-valued Fourier series
We prove a vector-valued version of Carleson's theorem: Let Y=[X,H]_t be a
complex interpolation space between a UMD space X and a Hilbert space H. For
p\in(1,\infty) and f\in L^p(T;Y), the partial sums of the Fourier series of f
converge to f pointwise almost everywhere. Apparently, all known examples of
UMD spaces are of this intermediate form Y=[X,H]_t. In particular, we answer
affirmatively a question of Rubio de Francia on the pointwise convergence of
Fourier series of Schatten class valued functions.Comment: 26 page
Numerical Modeling and Open-Source Implementation of Variational Partition-of-Unity Localizations of Space-Time Dual-Weighted Residual Estimators for Parabolic Problems
In this work, we consider space-time goal-oriented a posteriori error estimation for parabolic problems. Temporal and spatial discretizations are based on Galerkin finite elements of continuous and discontinuous type. The main objectives are the development and analysis of space-time estimators, in which the localization is based on a weak form employing a partition-of-unity. The resulting error indicators are used for temporal and spatial adaptivity. Our developments are substantiated with several numerical examples
Driving Rydberg-Rydberg transitions from a co-planar microwave waveguide
The coherent interaction between ensembles of helium Rydberg atoms and
microwave fields in the vicinity of a solid-state co-planar waveguide is
reported. Rydberg-Rydberg transitions, at frequencies between 25 GHz and 38
GHz, have been studied for states with principal quantum numbers in the range
30 - 35 by selective electric-field ionization. An experimental apparatus
cooled to 100 K was used to reduce effects of blackbody radiation.
Inhomogeneous, stray electric fields emanating from the surface of the
waveguide have been characterized in frequency- and time-resolved measurements
and coherence times of the Rydberg atoms on the order of 250 ns have been
determined.Comment: 5 pages, 5 figure
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