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Tool path planning is a crucial factor of computer-aided design and manufacturing (CAD/CAM). To generate suitable tool paths, the previous methods often transform the problem into local or global opti...
In this paper we give a combinatorial characterization of projections ofgeodesics in Euclidean buildings to Weyl chambers. We apply these results to the representation theory of complex reductive Lie ...
SAMPLE PATH PROPERIES OF RANDOM TRANSFORMATIONS     TRANSFORMATIONS  SAMPLE PATH PROPERIES       font style='font-size:12px;'> 2015/9/29
In other words where is the boundary between truly random and almost deterministic behavior? I believe that very little randomness is needed. For example consider the following model. Let f1 : : : f...
In the early 1990’s, Kim and Roush developed path methods for establishing strong shift equivalence (SSE) of positive matrices over a dense subring U of R. This paper gives a detailed, unified and gen...
SAMPLE PATH PROPERTIES OF THE STOCHASTIC FLOWS     STOCHASTIC FLOWS  PATH PROPERTIES       font style='font-size:12px;'> 2015/9/29
We consider a stochastic flow driven by a finite-dimensional Brownian motion. We show that almost every realization of such a flow exhibits strong statistical properties such as th...
Multicorns are not path connected     Multicorns  not path connected       font style='font-size:12px;'> 2015/8/26
The tricorn is the connectedness locus in the space of antiholomorphic quadratic polynomials z 7! z2 + c. We prove that the tricorn is not locally connected and not even pathwise connected, confirming...
In this paper we study boosting methods from a new perspective. We build on recent work by Efron et al. to show that boosting approximately (and in some cases exactly) minimizes its loss criterion wit...
In this paper we argue that the choice of the SVM cost parameter can be critical. We then derive an algorithm that can fit the entire path of SVM solutions for every value of the cost parameter, with ...
We introduce a path following algorithm for L1-regularized generalized linear models. The L 1-regularization procedure is useful especially because it, in effect, selects variables according to the am...
We consider a random walk on a path with n nodes, with symmetric transition probabilities, i.e., the probability of making a transition between node i and node i+1 is the same as making a transition f...
Fastest mixing Markov chain on a path     Distribution probability  the edge  markov chain  random walk       font style='font-size:12px;'> 2015/7/8
We consider the problem of assigning transition probabilities to the edges of a path, so the resulting Markov chain or random walk mixes as rapidly as possible. In this note we prove that fastest mixi...
Local Coordinates on Formal Path     Local Coordinates  Formal Path       font style='font-size:12px;'> 2015/4/3
Local Coordinates on Formal Path.
Potential outcome counterfactuals represent variation in the outcome of interest after a hypothetical treatment or intervention is performed. Causal graphical models are a concise, intuitive way of re...
Aiming at reducing the CNC machining vibration and increasing machining quality, an interpolation method for parametric tool paths with confined jounce, jerk, acceleration, and speed is proposed. An a...
We prove the triviality of the first L2 cohomology class of based path spaces of Riemannian manifolds furnished with Brownian motion measure, and the consequent vanishing of L2 harmonic one-forms. We ...

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