The <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si10.gif" display="inline" overflow="scroll"><mml:mi>k</mml:mi></mml:math>-assignment polytope

Gill, Jonna; Linusson, Svante

doi:10.1016/j.disopt.2008.10.003

Cited by 6 publications

(2 citation statements)

References 9 publications

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“…The k-assignment polytope M m,n,k was studied in [8] and is defined as the convex hull over all 0/1-matrices of size m × n with exactly k number of 1, such that no row or column has more than one 1. This polytope is a natural generalization of the Birkhoff polytope; when m = n = k then M m,n,k = B n .…”

Section: Examples Of the Rhombus Criterionmentioning

confidence: 99%

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Greedy Causal Discovery Is Geometric

Linusson¹,

Restadh²,

Solus³

2023

SIAM J. Discrete Math.

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The purpose of this paper is twofold. We investigate a simple necessary condition, called the rhombus criterion, for two vertices in a polytope not to form an edge and show that in many examples of 0/1-polytopes it is also sufficient. We explain how also when this is not the case, the criterion can give a good algorithm for determining the edges of high-dimenional polytopes.In particular we study the Chordal graph polytope, which arises in the theory of causality and is an important example of a characteristic imset polytope. We prove that, asymptotically, for almost all pairs of vertices the rhombus criterion holds. We conjecture it to hold for all pairs of vertices.

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Section: Examples Of the Rhombus Criterionmentioning

confidence: 99%

“…Then we will say that a path P is alternating (with respect to the two matchings M 1 and M 2 ) if every other edge of P lies in M 1 and the rest in M 2 . Then we can restate Theorem 13 in [8] as follows. Proof.…”

Section: Examples Of the Rhombus Criterionmentioning

confidence: 99%

Greedy Causal Discovery Is Geometric

Linusson¹,

Restadh²,

Solus³

2023

SIAM J. Discrete Math.

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Overexpressing Ugp1 promotes phosphate uptake and accumulation in rice (Oryza sativa)

Zhang,

Meng,

Liu

et al. 2023

Physiol Mol Biol Plants

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Plant responses to phosphate (Pi) starvation stress involve an array of adaptive strategies including enhanced accumulation and shoot-to-root transport of carbohydrates required for activating the plant Pi starvation signaling. However, the contribution of carbohydrate biosynthesis genes to maintaining phosphorus (P) homeostasis remains unknown, and the functional characterization of sugar metabolism genes is often impeded or compromised due to the loss of fertility of the null mutants. Here, a highly expressed gene encoding UDP-glucose pyrophosphorylase in rice (Oryza sativa), Ugp1, was functionally characterized. Ugp1 was transcriptionally induced in leaf blades by Pi starvation. As a link between sucrose (Suc) and P, we assumed that overexpression of Upg1 would alter the Suc concentration. Given that Suc is a signaling molecule, such concentration changes would affect the P deficiency signal transduction, thereby altering the homeostasis of endogenous P. The results showed that, overexpression of Ugp1 decreased plant biomass, increased sucrose content, and promoted Pi accumulation. The elevated Pi accumulation in Ugp1-OX plants was accompanied by the up-regulation of Pi-starvation-induced genes. Taken together, these results demonstrate that Ugp1 is a positive regulator of sucrose accumulation, and is required for maintaining P homeostasis in rice. Ugp1 thus represents a novel entry point to dissect the mechanisms underlying the carbon-P crosstalk.

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Computation of Fluid and Particle Motion From a Time-Sequenced Image Pair: A Global Outlier Identification Approach

Ray

2011

IEEE Trans. on Image Process.

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Fluid motion estimation from time sequenced images is a significant image analysis task. Its application is widespread in experimental fluidics research and many related areas like biomedical engineering and atmospheric sciences. In this paper, we present a novel flow computation framework to estimate the flow velocity vectors from two consecutive image frames. In an energy minimization-based flow computation, we propose a novel data fidelity term, which (1) can accommodate various measures, such as cross-correlation or sum of absolute or squared differences of pixel intensities between image patches, (2) has a global mechanism to control the adverse effect of outliers arising out of motion discontinuities, proximity of image borders, and (3) can go hand-in-hand with various spatial smoothness terms. Further the proposed data term and related regularization schemes are both applicable to dense and sparse flow vector estimations. We validate these claims by numerical experiments on benchmark flow data sets.

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The k-assignment polytope

Cited by 6 publications

References 9 publications

Greedy Causal Discovery Is Geometric

Greedy Causal Discovery Is Geometric

Overexpressing Ugp1 promotes phosphate uptake and accumulation in rice (Oryza sativa)

Computation of Fluid and Particle Motion From a Time-Sequenced Image Pair: A Global Outlier Identification Approach

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