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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Rooted trees, Hopf algebras and rough paths
有根树 Hopf代数 粗路径
2023/11/15
In this talk, we first recall some classical Hopf algebras on rooted trees, including Connes-Kreimer Hopf algebra and Loday-Ronco Hopf algebra. Then we give a combinatorial description of the coproduc...
Bartholdi, Neuhauser and Woess proved that a family of metabelian groups including lamplighters have a striking geometric manifestation as 1-skeleta of horocyclic products of trees. The purpose of thi...
The absence of efficient dual pairs of spanning trees in planar graphs
planar graphs cells
2015/8/26
A spanning tree T in a finite planar connected graph G determines a dual spanning tree T* in the dual graph G* such that T and T* do not intersect. We show that it is not always possible to find T in ...
Groups of automorphisms of trees and their limit sets
Groups automorphisms trees limit sets
2015/8/26
Let T be a locally finite simplicial tree and let ! ⊂ Aut(T ) be a finitely generated discrete subgroup. We obtain an explicit formula for the critical exponent of the Poincare series associated...
Shrinking Trees
Shrinking Trees
2015/8/21
Tree-based models provide an alternative to linear models for classification and regression data. They are used primarily for exploratory analysis of complex data or as a diagnostic tool following a l...
Margin trees for high-dimensional classification
Maximum margin classifier supprt vector machine decision tree CART
2015/8/21
We propose a method for the classification of more than two classes, from high-dimensional features. Our approach is to build a binary decision tree in a top-down manner, using the optimal margin clas...
Majority dynamics on trees and the dynamic cavity method
Voters independent distribution random variables the initialization
2015/8/20
An elector sits on each vertex of an in nite tree of degree k, and has to decide between two alternatives.At each time step, each elector switches to the opinion of the majority of her neighbors. We a...
In this paper I will survey some recent developments in the combinatorics of Aronszajn trees. I will cover work on coherent and Lipschitz trees, the basis problem for uncountable linear orderings, sub...
The rotor-router model is a deterministic analogue of random walk. It can be used to define a deterministic growth model analogous to internal DLA. We show that the set of occupied sites for this mode...
COCOMMUTATIVE HOPF ALGEBRAS OF PERMUTATIONS AND TREES
Hopf algebr rooted tree planar binary tree symmetric group
2015/8/14
Consider the coradical filtrations of the Hopf algebras of planar binary
trees of Loday and Ronco and of permutations of Malvenuto and Reutenauer. We
give explicit isomorphisms showing that the asso...
SANDPILE GROUPS AND SPANNING TREES OF DIRECTED LINE GRAPHS
SANDPILE GROUPS SPANNING TREES DIRECTED LINE GRAPHS
2015/8/14
We generalize a theorem of Knuth relating the oriented spanning trees of a directed graph G and its directed line graph LG. The sandpile group is an abelian group associated to a directed graph, whose...
STRUCTURE OF THE LODAY-RONCO HOPF ALGEBRA OF TREES
Hopf algebra planar binary tree permutation weak order
2015/8/14
Loday and Ronco defined an interesting Hopf algebra structure on the linear
span of the set of planar binary trees. They showed that the inclusion of the Hopf algebra
of non-commutative symmetric fu...
Matchings and phylogenetic trees。
Random Walks on Trees and Matchings
Markov Chain Matchings Phylogenetic Tree Fourier analysis Zonal polynomials Coagulation-Fragmentation
2015/7/8
We give sharp rates of convergence for a natural Markov chain on the space of phylogenetic trees and dually for the natural random walk on the set of perfect matchings in the complete graph on 2n vert...
A Pre-Lie algebra is a vector space L endowed with a bilinear product * : L \times L to L satisfying the relation (x*y)*z-x*(y*z)= (x*z)*y-x*(z*y), for all x,y,z in L. We give an explicit combinatoria...