94,640 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
Local Hidden Variable Theories for Quantum States
While all bipartite pure entangled states violate some Bell inequality, the
relationship between entanglement and non-locality for mixed quantum states is
not well understood. We introduce a simple and efficient algorithmic approach
for the problem of constructing local hidden variable theories for quantum
states. The method is based on constructing a so-called symmetric
quasi-extension of the quantum state that gives rise to a local hidden variable
model with a certain number of settings for the observers Alice and Bob.Comment: 8 pages Revtex; v2 contains substantial changes, a strengthened main
theorem and more reference
Getting Feasible Variable Estimates From Infeasible Ones: MRF Local Polytope Study
This paper proposes a method for construction of approximate feasible primal
solutions from dual ones for large-scale optimization problems possessing
certain separability properties. Whereas infeasible primal estimates can
typically be produced from (sub-)gradients of the dual function, it is often
not easy to project them to the primal feasible set, since the projection
itself has a complexity comparable to the complexity of the initial problem. We
propose an alternative efficient method to obtain feasibility and show that its
properties influencing the convergence to the optimum are similar to the
properties of the Euclidean projection. We apply our method to the local
polytope relaxation of inference problems for Markov Random Fields and
demonstrate its superiority over existing methods.Comment: 20 page, 4 figure
A Sparse Multi-Scale Algorithm for Dense Optimal Transport
Discrete optimal transport solvers do not scale well on dense large problems
since they do not explicitly exploit the geometric structure of the cost
function. In analogy to continuous optimal transport we provide a framework to
verify global optimality of a discrete transport plan locally. This allows
construction of an algorithm to solve large dense problems by considering a
sequence of sparse problems instead. The algorithm lends itself to being
combined with a hierarchical multi-scale scheme. Any existing discrete solver
can be used as internal black-box.Several cost functions, including the noisy
squared Euclidean distance, are explicitly detailed. We observe a significant
reduction of run-time and memory requirements.Comment: Published "online first" in Journal of Mathematical Imaging and
Vision, see DO
Efficient Algorithms for Asymptotic Bounds on Termination Time in VASS
Vector Addition Systems with States (VASS) provide a well-known and
fundamental model for the analysis of concurrent processes, parameterized
systems, and are also used as abstract models of programs in resource bound
analysis. In this paper we study the problem of obtaining asymptotic bounds on
the termination time of a given VASS. In particular, we focus on the
practically important case of obtaining polynomial bounds on termination time.
Our main contributions are as follows: First, we present a polynomial-time
algorithm for deciding whether a given VASS has a linear asymptotic complexity.
We also show that if the complexity of a VASS is not linear, it is at least
quadratic. Second, we classify VASS according to quantitative properties of
their cycles. We show that certain singularities in these properties are the
key reason for non-polynomial asymptotic complexity of VASS. In absence of
singularities, we show that the asymptotic complexity is always polynomial and
of the form , for some integer , where is the
dimension of the VASS. We present a polynomial-time algorithm computing the
optimal . For general VASS, the same algorithm, which is based on a complete
technique for the construction of ranking functions in VASS, produces a valid
lower bound, i.e., a such that the termination complexity is .
Our results are based on new insights into the geometry of VASS dynamics, which
hold the potential for further applicability to VASS analysis.Comment: arXiv admin note: text overlap with arXiv:1708.0925
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