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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...
Dyck paths are classical Catalan objects. The peak distribution of Dyck paths is an important topic of combinatorics, and further the representation of symmetric groups.
Molecular biologists and bioengineers at the University of California, San Diego have unraveled key mechanisms behind the mysteries of aging. They isolated two distinct paths that cells trav...
Astronomers using the Atacama Large Millimeter/submillimeter Array (ALMA) have found the clearest evidence yet that giant planets have recently formed around four young stars. These new worlds, each p...
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...
The presence of ionospheric perturbations in possible association with two huge earthquakes (Noto-hanto peninsula and Niigata-chuetu-oki earthquakes) in 2007 was studied on the basis of a conventional...
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...
Traditional methods of delineating stream channel networks use gridded raster elevation data. Direct use of LiDAR point clouds, without first creating a raster or grid, could improve efficiency and ac...
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 ...
This essay is written for a particular group of Ph.D. students in oceanography, not the majority who are in the Ph.D. program to learn how to be researchers in research universities and research insti...
Tills for this study were analyzed from sites in East Antarctica (EA), West Antarctica (WA) and along a transect in the Ross Sea. Particle size, sand petrography, and detrital zircons were used to pro...
Traditional methods of delineating stream channel networks use gridded raster elevation data. Direct use of LiDAR point clouds, without first creating a raster or grid, could improve efficiency and ac...
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...
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...

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