Exact Volume Computation for Polytopes: A Practical Study

Büeler, Benno; Enge, Andreas; Fukuda, Komei

doi:10.1007/978-3-0348-8438-9_6

Cited by 167 publications

(197 citation statements)

References 18 publications

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“…In particular, we do not use any biological objective function or external sources of knowledge such as gene expression. The goal is to find a set of k fluxes that, if measured, will reduce as much as possible the search space obtained from constraints (1) and (2). To the best of our knowledge, this is the first time such a problem is tackled in the context of metabolic networks analysis.…”

Section: Related Workmentioning

confidence: 99%

“…The number of alternative flux distributions can be expressed as the hypervolume of this polytope. Computing the exact volume of a convex polytope is a NP-hard problem and has been shown to be infeasible for dimensions bigger than 10 [2]. Since we don't need the exact volume but the smallest volume resulting when measuring a flux, we only need to estimate a relative volume.…”

Section: Research Problemmentioning

confidence: 99%

“…b n for the range of each flux. Next, it generates a set of points from the solution space of the mass-balance (see (1)) and thermodynamic (see (2)) constraints, by means of a uniform sampling procedure. Specifically, we use an implementation of the ACHR sampler algorithm [10,21] to generate such a set of sampled solutions.…”

Section: Rmev-g: Reaction Minimizing Expected Volume Greedymentioning

confidence: 99%

“…Each edge has a weight, equal to the probability of the parent node (flux) to be in the bin corresponding to that edge given the bins that have been selected in the path from the root to that edge (for instance, the probability that the flux in Fig. 1a is in bin [1,2] is 0.3).…”

Section: Rmev-g: Reaction Minimizing Expected Volume Greedymentioning

confidence: 99%

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Flux Measurement Selection in Metabolic Networks

Megchelenbrink

Huynen

Marchiori

2011

Pattern Recognition in Bioinformatics

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Abstract. Genome-scale metabolic networks can be reconstructed using a constraint-based modeling approach. The stoichiometry of the network and the physiochemical laws still enable organisms to achieve certain objectives -such as biomass composition-through many various pathways. This means that the system is underdetermined and many alternative solutions exist. A known method used to reduce the number of alternative pathways is Flux Balance Analysis (FBA), which tries to optimize a given biological objective function. FBA does not always find a correct solution and for many networks the biological objective function is simply unknown. This leaves researchers no other choice than to measure certain fluxes. In this article we propose a method that combines a sampling approach with a greedy algorithm for finding a subset of k fluxes that, if measured, are expected to reduce as much as possible the solution space towards the 'true' flux distribution. The parameter k is given by the user. Application of the proposed method to a toy example and two real-life metabolic networks indicate its effectiveness. The method achieves significantly more reduction of the solution space than when k fluxes are selected either at random or by a faster simple heuristic procedure. It can be used for guiding the biologists to perform experimental analysis of metabolic networks.

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Section: Related Workmentioning

confidence: 99%

Section: Research Problemmentioning

confidence: 99%

Section: Rmev-g: Reaction Minimizing Expected Volume Greedymentioning

confidence: 99%

Section: Rmev-g: Reaction Minimizing Expected Volume Greedymentioning

confidence: 99%

See 2 more Smart Citations

Flux Measurement Selection in Metabolic Networks

Megchelenbrink

Huynen

Marchiori

2011

Pattern Recognition in Bioinformatics

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“…2 2 We briefly note that the syntax presented here is -for the sake of space constraints -simpler than that in [16]. In particular, variable annotations, and function symbols over the annotation domain are eliminated.…”

Section: Definition 3 a Probabilistic Logic Program (Plp) Is A Finitementioning

confidence: 99%

Using Histograms to Better Answer Queries to Probabilistic Logic Programs

2009

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Probabilistic logic programs (PLPs) define a set of probability distribution functions (PDFs) over the set of all Herbrand interpretations of the underlying logical language. When answering a query Q, a lower and upper bound on Q is obtained by optimizing (min and max) an objective function subject to a set of linear constraints whose solutions are the PDFs mentioned above. A common critique not only of PLPs but many probabilistic logics is that the difference between the upper bound and lower bound is large, thus often providing very little useful information in the query answer. In this paper, we provide a new method to answer probabilistic queries that tries to come up with a histogram that "maps" the probability that the objective function will have a value in a given interval, subject to the above linear constraints. This allows the system to return to the user a histogram where he can directly "see" what the most likely probability range for his query will be. We prove that computing these histograms is #P -hard, and show that computing these histograms is closely related to polyhedral volume computation. We show how existing randomized algorithms for volume computation can be adapted to the computation of such histograms. A prototype experimental implementation is discussed.

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Identification and interpretation of nonnormality in atmospheric time series

Proistosescu

Rhines

Huybers

2016

Geophysical Research Letters

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Nonnormal characteristics of geophysical time series are important determinants of extreme events and may provide insight into the underlying dynamics of a system. The structure of nonnormality in winter temperature is examined through the use of linear filtering of radiosonde temperature time series. Filtering either low or high frequencies generally suppresses what is otherwise statistically significant nonnormal variability in temperature. The structure of nonnormality is partly attributable to geometric relations between filtering and the appearance of skewness, kurtosis, and higher order moments in time series data, and partly attributable to the presence of nonnormal temperature variations at the highest resolved frequencies in the presence of atmospheric memory. A nonnormal autoregressive model and a multiplicative noise model are both consistent with the observed frequency structure of nonnormality. These results suggest that the generating mechanism for nonnormal variations does not necessarily act at the frequencies at which greatest nonnormality is observed.

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Exact Volume Computation for Polytopes: A Practical Study

Cited by 167 publications

References 18 publications

Flux Measurement Selection in Metabolic Networks

Flux Measurement Selection in Metabolic Networks

Using Histograms to Better Answer Queries to Probabilistic Logic Programs

Identification and interpretation of nonnormality in atmospheric time series

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