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Search Results (4)

Search Parameters:
Keywords = order and chain polytopes

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7 pages, 269 KiB  
Proceeding Paper
Analysis of Ecological Networks: Linear Inverse Modeling and Information Theory Tools
by Valérie Girardin, Théo Grente, Nathalie Niquil and Philippe Regnault
Phys. Sci. Forum 2023, 9(1), 24; https://doi.org/10.3390/psf2023009024 - 20 Feb 2024
Viewed by 1526
Abstract
In marine ecology, the most studied interactions are trophic and are in networks called food webs. Trophic modeling is mainly based on weighted networks, where each weighted edge corresponds to a flow of organic matter between two trophic compartments, containing individuals of similar [...] Read more.
In marine ecology, the most studied interactions are trophic and are in networks called food webs. Trophic modeling is mainly based on weighted networks, where each weighted edge corresponds to a flow of organic matter between two trophic compartments, containing individuals of similar feeding behaviors and metabolisms and with the same predators. To take into account the unknown flow values within food webs, a class of methods called Linear Inverse Modeling was developed. The total linear constraints, equations and inequations defines a multidimensional convex-bounded polyhedron, called a polytope, within which lie all realistic solutions to the problem. To describe this polytope, a possible method is to calculate a representative sample of solutions by using the Monte Carlo Markov Chain approach. In order to extract a unique solution from the simulated sample, several goal (cost) functions—also called Ecological Network Analysis indices—have been introduced in the literature as criteria of fitness to the ecosystems. These tools are all related to information theory. Here we introduce new functions that potentially provide a better fit of the estimated model to the ecosystem. Full article
(This article belongs to the Proceedings of The 42nd International Workshop on Bayesian Inference and Maximum Entropy Methods in Science and Engineering)
6 pages, 215 KiB  
Article
Faces of 2-Dimensional Simplex of Order and Chain Polytopes
by Aki Mori
Mathematics 2019, 7(9), 851; https://doi.org/10.3390/math7090851 - 14 Sep 2019
Cited by 1 | Viewed by 2421
Abstract
Each of the descriptions of vertices, edges, and facets of the order and chain polytope of a finite partially ordered set are well known. In this paper, we give an explicit description of faces of 2-dimensional simplex in terms of vertices. Namely, it [...] Read more.
Each of the descriptions of vertices, edges, and facets of the order and chain polytope of a finite partially ordered set are well known. In this paper, we give an explicit description of faces of 2-dimensional simplex in terms of vertices. Namely, it will be proved that an arbitrary triangle in 1-skeleton of the order or chain polytope forms the face of 2-dimensional simplex of each polytope. These results mean a generalization in the case of 2-faces of the characterization known in the case of edges. Full article
(This article belongs to the Special Issue Current Trends on Monomial and Binomial Ideals)
5 pages, 243 KiB  
Article
Compatible Algebras with Straightening Laws on Distributive Lattices
by Daniel Bănaru and Viviana Ene
Mathematics 2019, 7(8), 671; https://doi.org/10.3390/math7080671 - 27 Jul 2019
Viewed by 2367
Abstract
We characterize the finite distributive lattices on which there exists a unique compatible algebra with straightening laws. Full article
(This article belongs to the Special Issue Current Trends on Monomial and Binomial Ideals)
14 pages, 270 KiB  
Article
Cutting Convex Polytopes by Hyperplanes
by Takayuki Hibi and Nan Li
Mathematics 2019, 7(5), 381; https://doi.org/10.3390/math7050381 - 26 Apr 2019
Cited by 4 | Viewed by 2568
Abstract
Cutting a polytope is a very natural way to produce new classes of interesting polytopes. Moreover, it has been very enlightening to explore which algebraic and combinatorial properties of the original polytope are hereditary to its subpolytopes obtained by a cut. In this [...] Read more.
Cutting a polytope is a very natural way to produce new classes of interesting polytopes. Moreover, it has been very enlightening to explore which algebraic and combinatorial properties of the original polytope are hereditary to its subpolytopes obtained by a cut. In this work, we devote our attention to all the separating hyperplanes for some given polytope (integral and convex) and study the existence and classification of such hyperplanes. We prove the existence of separating hyperplanes for the order and chain polytopes for any finite posets that are not a single chain, and prove there are no such hyperplanes for any Birkhoff polytopes. Moreover, we give a complete separating hyperplane classification for the unit cube and its subpolytopes obtained by one cut, together with some partial classification results for order and chain polytopes. Full article
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