We develop fast algorithms for computing the linking number of a simplicial complex within a filtration. We give experimental results in applying our work toward the detection of non-trivial tangling in biomolecules, modeled as alpha complexes.

In the standard Random Surfer Model, the teleportation matrix is necessary to ensure that the final PageRank vector is well-defined. The introduction of this matrix, however, results in serious problems and imposes fundamental limitations to the quality of the ranking vectors. In this work, building on the recently proposed NCDawareRank framework, we exploit the decomposition of the underlying ...

We represent chord collections by simplicial complexes. A temporal organization of the chords corresponds to a path in the complex. A set of n-note chords equivalent up to transposition and inversion is represented by a complex related by its 1-skeleton to a generalized Tonnetz. Complexes are computed with MGS, a spatial computing language, and analyzed and visualized in Hexachord, a computer-a...

A classical combinatorial fact is that the simplicial complex consisting of disjointly embedded chords in a convex planar polygon is a sphere. For any surface F with non-empty boundary, there is an analogous complex Arc(F ) consisting of suitable equivalence classes of arcs in F connecting its boundary components. The main result of this paper is the determination of those arc complexes Arc(F )...

For a simplicial complex X and a field K, let h̃i(X) = dim H̃i(X;K). It is shown that if X,Y are complexes on the same vertex set, then for k ≥ 0 h̃k−1(X ∩ Y ) ≤ ∑

By using Alexander duality on simplicial complexes we give a new and algebraic proof of Dirac’s theorem on chordal graphs.

Provan and Billera defined the notion of weak k-decomposability for pure simplicial complexes in the hopes of bounding the diameter of convex polytopes. They showed the diameter of a weakly k-decomposable simplicial complex ã is bounded above by a polynomial function of the number of k-faces in ã and its dimension. For weakly 0-decomposable complexes, this bound is linear in the number of verti...

We introduce pretty clean modules, extending the notion of clean modules by Dress, and show that pretty clean modules are sequentially CohenMacaulay. We also extend a theorem of Dress on shellable simplicial complexes to multicomplexes.