11,063 research outputs found
An improved multi-parametric programming algorithm for flux balance analysis of metabolic networks
Flux balance analysis has proven an effective tool for analyzing metabolic
networks. In flux balance analysis, reaction rates and optimal pathways are
ascertained by solving a linear program, in which the growth rate is maximized
subject to mass-balance constraints. A variety of cell functions in response to
environmental stimuli can be quantified using flux balance analysis by
parameterizing the linear program with respect to extracellular conditions.
However, for most large, genome-scale metabolic networks of practical interest,
the resulting parametric problem has multiple and highly degenerate optimal
solutions, which are computationally challenging to handle. An improved
multi-parametric programming algorithm based on active-set methods is
introduced in this paper to overcome these computational difficulties.
Degeneracy and multiplicity are handled, respectively, by introducing
generalized inverses and auxiliary objective functions into the formulation of
the optimality conditions. These improvements are especially effective for
metabolic networks because their stoichiometry matrices are generally sparse;
thus, fast and efficient algorithms from sparse linear algebra can be leveraged
to compute generalized inverses and null-space bases. We illustrate the
application of our algorithm to flux balance analysis of metabolic networks by
studying a reduced metabolic model of Corynebacterium glutamicum and a
genome-scale model of Escherichia coli. We then demonstrate how the critical
regions resulting from these studies can be associated with optimal metabolic
modes and discuss the physical relevance of optimal pathways arising from
various auxiliary objective functions. Achieving more than five-fold
improvement in computational speed over existing multi-parametric programming
tools, the proposed algorithm proves promising in handling genome-scale
metabolic models.Comment: Accepted in J. Optim. Theory Appl. First draft was submitted on
August 4th, 201
Inhomogeneous Neutrino Degeneracy and Big Bang Nucleosynthesis
We examine Big Bang nucleosynthesis (BBN) in the case of inhomogenous
neutrino degeneracy, in the limit where the fluctuations are sufficiently small
on large length scales that the present-day element abundances are homogeneous.
We consider two representive cases: degeneracy of the electron neutrino alone,
and equal chemical potentials for all three neutrinos. We use a linear
programming method to constrain an arbitrary distribution of the chemical
potentials. For the current set of (highly-restrictive) limits on the
primordial element abundances, homogeneous neutrino degeneracy barely changes
the allowed range of the baryon-to-photon ratio. Inhomogeneous degeneracy
allows for little change in the lower bound on the baryon-to-photon ratio, but
the upper bound in this case can be as large as 1.1 \times 10^{-8} (only
electron neutrino degeneracy) or 1.0 \times 10^{-9} (equal degeneracies for all
three neutrinos). For the case of inhomogeneous neutrino degeneracy, we show
that there is no BBN upper bound on the neutrino energy density, which is
bounded in this case only by limits from structure formation and the cosmic
microwave background.Comment: 6 pages, no figure
Phase Transitions of the Typical Algorithmic Complexity of the Random Satisfiability Problem Studied with Linear Programming
Here we study the NP-complete -SAT problem. Although the worst-case
complexity of NP-complete problems is conjectured to be exponential, there
exist parametrized random ensembles of problems where solutions can typically
be found in polynomial time for suitable ranges of the parameter. In fact,
random -SAT, with as control parameter, can be solved quickly
for small enough values of . It shows a phase transition between a
satisfiable phase and an unsatisfiable phase. For branch and bound algorithms,
which operate in the space of feasible Boolean configurations, the empirically
hardest problems are located only close to this phase transition. Here we study
-SAT () and the related optimization problem MAX-SAT by a linear
programming approach, which is widely used for practical problems and allows
for polynomial run time. In contrast to branch and bound it operates outside
the space of feasible configurations. On the other hand, finding a solution
within polynomial time is not guaranteed. We investigated several variants like
including artificial objective functions, so called cutting-plane approaches,
and a mapping to the NP-complete vertex-cover problem. We observed several
easy-hard transitions, from where the problems are typically solvable (in
polynomial time) using the given algorithms, respectively, to where they are
not solvable in polynomial time. For the related vertex-cover problem on random
graphs these easy-hard transitions can be identified with structural properties
of the graphs, like percolation transitions. For the present random -SAT
problem we have investigated numerous structural properties also exhibiting
clear transitions, but they appear not be correlated to the here observed
easy-hard transitions. This renders the behaviour of random -SAT more
complex than, e.g., the vertex-cover problem.Comment: 11 pages, 5 figure
Partial Identification in Matching Models for the Marriage Market
We study partial identification of the preference parameters in models of
one-to-one matching with perfectly transferable utilities, without imposing
parametric distributional restrictions on the unobserved heterogeneity and with
data on one large market. We provide a tractable characterisation of the
identified set, under various classes of nonparametric distributional
assumptions on the unobserved heterogeneity. Using our methodology, we
re-examine some of the relevant questions in the empirical literature on the
marriage market which have been previously studied under the Multinomial Logit
assumption
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