Simplicial Complexes
Centralities in simplicial complexes. Applications to protein interaction networks
... The above two definitions for two k-simplices to be adjacent leads us to the problem that there are now four possible notions we can use to define a general adjacency matrix for simplicial complexes. The ...
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Co-occurrence simplicial complexes in mathematics: identifying the holes of knowledge
... of complexes are usually studied on a filtration of the com- plex, that is a sequence of simplicial complexes starting at the empty complex and ending with the full complex, so that the complex at ...
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Local properties of simplicial complexes
... Retractable, collapsable, and recursively contractible complexes are examined in this article. Two leader election algorithms are presented. The Nowakowski and Rival theorem on the fixed edge property in an ...
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Sano
... The notion of matroids was introduced by H. Whitney [10] in 1935 as an abstraction of the notion of linear independence in a vector space. Many researchers have studied and extended the theory of matroids (cf. [2, 4, 5, ...
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The construction of simplicial groups in digital images
... and simplicial complexes in digital images due to adjacency ...the simplicial set and conclude that the simplicial identities are satisfied in digital ...the simplicial groups in digital ...
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beyondgraphs-netscicom11.pdf
... the simplicial complex on three friends A, B, and C in two possible behaviors: in one, they can only talk pairwise on the phone (left), and in the other, they can both talk pairwise and as a group ...with ...
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The Betti numbers of forests
... The simplicial complexes ∆(G) do not have an explicit description even for moderately complex graphs G and as a result, Hochster’s formula can not be applied easily to concrete ...of simplicial ...
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Lefschetz fixed point theorem for digital images
... The Lefschetz fixed point theorem is a formula that counts fixed points of a continuous mapping from a compact topological space X to itself by means of traces of the induced mappings on the homology groups of X. In , ...
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McCullough
... abstract simplicial complex ∆, one can define the reduced chain complex of ∆ with coefficients in K , which naturally defines the cycles, boundaries and homology of ...one-dimensional simplicial complex, ∆ ...
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Some Problems in Geometric Combinatorics and Mathematical Phylogenetics.
... and simplicial topology begins in many ways with the work of ...and simplicial complexes has persisted as the fields in which these objects are frequently used have ...for simplicial ...
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Cocharacter-closure and spherical buildings
... We spend much of the paper recalling relevant results from geometric invariant theory and the theory of buildings. Although the basic ideas are familiar, we need to extend many of them: for instance, the material on ...
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Discrete, circulation preserving, and stable simplicial fluids
... Abstract Simplicial Complex This structure encodes all the relationships between vertices, edges, triangles, and ...abstract simplicial complex is a set of subsets of the integers 0 ≤ i < n, such that if ...
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Axioms for the Lefschetz number as a lattice valuation
... abstract simplicial complexes, we show that the Lefschetz number is unique with respect to a valuation axiom and an axiom specifying the value on a ...
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Complex Networks: New Models and Distributed Algorithms
... using simplicial complexes, which are objects of study in algebraic topology, as generalizations of graphs to higher ...how simplicial complexes serve as more faithful models of the network ...
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Collapsing along monotone poset maps
... We recall that the notion of nonevasive simplicial complexes was introduced in [9], and was initially motivated by the complexity-theoretic considerations. For further con- nections to topology and more ...
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Completely bounded mappings and simplicial complex structure in the primitive ideal space of a C* algebra
... finite) simplicial complex we understand a collection C of subsets of { 1, 2, ...All complexes we deal with will be connected (given two vertices i, j, 1 ≤ i, j ≤ N , there is a sequence i 0 = i, i 1 , ...
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Chordal- (k,ℓ)and strongly chordal- (k,ℓ)graph sandwich problems
... ders, to the foot and to all active knees (true or false). Active knees form a clique as well as true shoulders and the foot sees every knee and every true shoulder. More- over, true shoulders are adjacent to all knees. ...
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On the stability of finding approximate fixed points by simplicial methods
... a simplicial algorithm is in order, we must face approximate fixed points as the grid size ...using simplicial methods under the perturbation of the corresponding functions and ...vector-valued ...
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Simplicial homology and Hochschild cohomology of Banach semilattice algebras
... to simplicial homology. Under certain conditions, the simplicial homology of a commutative Banach algebra gives us information on Hochschild cohomology with symmetric ...
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Refinements in Boundary Complexes of Polytopes
... An important special class of d-polytopes is the class of simplicial d-polytopes, consisting of those d-polytopes all of whose facets are .simpl ices... Combinatoria[r] ...
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