Results 31 to 40 of about 3,648 (134)
TinyAD: Automatic Differentiation in Geometry Processing Made Simple
Computer Graphics Forum, Volume 41, Issue 5, Page 113-124, August 2022., 2022 Abstract Non‐linear optimization is essential to many areas of geometry processing research. However, when experimenting with different problem formulations or when prototyping new algorithms, a major practical obstacle is the need to figure out derivatives of objective functions, especially when second‐order derivatives are required.
P. Schmidt +4 more
wiley +1 more source
Graded Linearity of Stanley–Reisner Ring of Broken Circuit Complexes
Journal of Mathematics, Volume 2022, Issue 1, 2022., 2022 This paper introduces two new notions of graded linear resolution and graded linear quotients, which generalize the concepts of linear resolution property and linear quotient for modules over the polynomial ring A = k[x1, …, xn]. Besides, we compare graded linearity with componentwise linearity in general.
Mohammad Reza-Rahmati +2 more
wiley +1 more source
Fourientations and the Tutte polynomial [PDF]
Research in the Mathematical Sciences, 2017 A fourientation of a graph is a choice for each edge of the graph whether to orient that edge in either direction, leave it unoriented, or biorient it. Fixing a total order on the edges and a reference orientation of the graph, we investigate properties of cuts and cycles in fourientations which give trivariate generating functions that are generalized
Backman, Spencer, Hopkins, Sam
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A study about the Tutte polynomials of benzenoid chains
Topological Algebra and its Applications, 2017 The Tutte polynomials for signed graphs were introduced by Kauffman. In 2012, Fath-Tabar, Gholam-Rezaeı and Ashrafı presented a formula for computing Tutte polynomial of a benzenoid chain. From this point on, we have also calculated the Tutte polynomials
Sahin Abdulgani
doaj +1 more source
, 2022 18 pages, 6 figures. This is a draft of a chapter for the Handbook on the Tutte Polynomial. Comments are welcome!
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Topological Graph Polynomials in Colored Group Field Theory [PDF]
, 2009 In this paper we analyze the open Feynman graphs of the Colored Group Field Theory introduced in [arXiv:0907.2582]. We define the boundary graph $\cG_{\partial}$ of an open graph $\cG$ and prove it is a cellular complex.
A. Connes +37 more
core +1 more source
A generalization of weight polynomials to matroids [PDF]
, 2015 Generalizing polynomials previously studied in the context of linear codes, we define weight polynomials and an enumerator for a matroid $M$. Our main result is that these polynomials are determined by Betti numbers associated with graded minimal free ...
Johnsen, Trygve +2 more
core +2 more sources
Relations between cumulants in noncommutative probability [PDF]
, 2014 We express classical, free, Boolean and monotone cumulants in terms of each other, using combinatorics of heaps, pyramids, Tutte polynomials and permutations.
Arizmendi, Octavio +3 more
core +1 more source
, 2023 The Tutte polynomial and Derksen's $\mathcal{G}$-invariant are the universal deletion-contraction and valuative matroid and polymatroid invariants, respectively. There are only a handful of well known invariants (like the matroid Kazhdan-Lusztig polynomials) between (in terms of fineness) the Tutte polynomial and Derksen's $\mathcal{G}$-invariant.
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Bollobás–Riordan and Relative Tutte Polynomials [PDF]
Arnold Mathematical Journal, 2015 We establish a relation between the Bollobas-Riordan polynomial of a ribbon graph with the relative Tutte polynomial of a plane graph obtained from the ribbon graph using its projection to the plane in a nontrivial way. Also we give a duality formula for the relative Tutte polynomial of dual plane graphs and an expression of the Kauffman bracket of a ...
Butler, Clark, Chmutov, Sergei
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