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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...
MULTIFRACTAL PROPERTIES OF THE SETS OF ZEROES OF BROWNIAN PATHS
independent random variables Brownian motion local time Hausdor
2015/9/29
In this paper we study Brownian zeroes in the neighborhood of which one can observe non-typical growth
rate of Brownian excursions. We interprete the multifractal curve for the Brownian zeroes calcul...
Regularization Paths for Cox’s Proportional Hazards Model via Coordinate Descent
survival Cox model lasso elastic net
2015/8/21
We introduce a pathwise algorithm for the Cox proportional hazards model, regularized by convex combinations of `1 and `2 penalties (elastic net). Our algorithm fits via cyclical coordinate descent, a...
HOW TO DECOMPOSE A PERMUTATION INTO A PAIR OF LABELED DYCK PATHS BY PLAYING A GAME
PERMUTATION LABELED DYCK PATHS PLAYING A GAME
2015/8/14
We give a bijection between permutations of 1, . . . , 2n and certain pairs of Dyck paths with labels on the down steps. The bijection arises from a game in which two players alternate selecting from ...
Iteration theory of Maslov-type index associated with a Lagrangian subspace for symplectic paths and Multiplicity of brake orbits in bounded convex symmetric domains
Iteration theory Maslov-type index Lagrangian subspace symplectic paths and Multiplicity brake orbits in bounded convex symmetric domains
2015/4/3
Iteration theory of Maslov-type index associated with a Lagrangian subspace for symplectic paths and Multiplicity of brake orbits in bounded convex symmetric domains.
A Greedy Algorithm for Feedrate Planning of CNC Machines along Curved Tool Paths with Conned Jerk
Feedrate optimization parametric tool path conned jerk velocity limit surface analytical solutions for feedrate function
2013/9/9
In this paper, the problem of optimal feedrate planning along a curved tool path for 3-axis CNC machines with the acceleration and jerk limits for each axis and the tangential velocity bound is addres...
On the length of one-dimensional reactive paths
one-dimensional reactive paths Probability
2012/6/21
Motivated by some numerical observations on molecular dynamics simulations, we analyze metastable trajectories in a very simplecsetting, namely paths generated by a one-dimensional overdamped Langevin...
The set of Dyck paths of length $2n$ inherits a lattice structure from a bijection with the set of noncrossing partitions with the usual partial order. In this paper, we study the joint distribution o...
Noncrossing Linked Partitions and Large (3, 2)-Motzkin Paths
Noncrossing linked partition Schroder path large (3 2)-Motzkin path (3 2)-Motzkin path Schrö der number
2014/6/3
Noncrossing linked partitions arise in the study of certain transforms in free probability theory. We explore the connection between noncrossing linked partitions and (3, 2)-Motzkin paths, where a (3,...
Semi-infinite paths of the 2d-Radial Spanning Tree
stochastic geometry random tree semi-infinite path asymptotic direction competition interface
2012/6/9
We study semi-infinite paths of the radial spanning tree (RST) of a Poisson point process in the plane. We first show that the expectation of the number of intersection points between semi-infinite pa...
Matrix algorithm for determination of the elementary paths and elementary circuits using exotic semirings
idempotent semiring semiring of distinguished languages elementary path
2012/4/18
We propose a new method for determining the elementary paths and elementary circuits in a directed graph. Also, the Hamiltonian paths and Hamiltonian circuits are enumerated.
On the existence of paths between points in high level excursion sets of Gaussian random fields
Gaussian process excursion set large deviations exceedence probabilities connected component optimal path
2012/4/17
The structure of Gaussian random fields over high levels is a well researched and well understood area, particularly if the field is smooth. However, the question as to whether or not two or more poin...
Notes on area operator, geometric 2-rough paths and Young integral when p^-1+q^-1=1
Notes area operator geometric 2-rough paths Young integral
2012/4/17
1.When equipped with 2-rough norm and restricted to continuous paths with bounded variation, the area operator is a closable unbounded operator. 2.The area defined through Riemann-Stieltjes integral i...
A note on the minimum skew rank of powers of paths
minimum skew rank path (strict) power of a graph Combinatorics
2011/9/5
Abstract: The real minimum skew rank of a simple graph G is the smallest possible rank among all real skew symmetric matrices, whose (i,j)-entry (for i not equal to j) is nonzero whenever {i, j} is an...
Optimal paths for symmetric actions in the unitary group
geodesic segment Lagrangian optimal path unitarily invariant norm unitary group Grassmann manifold angular metric
2011/9/5
Abstract: Given a positive and unitarily invariant Lagrangian L defined in the algebra of Hermitian matrices, and a fixed interval $[a,b]\subset\mathbb R$, we study the action defined in the Lie group...