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We formulate and implement a generalized island-dynamics model of epitaxial growth based on the level-set technique to include the effect of an additional energy barrier for the attachment and detachm...
ASB/ISB award paper Manipulating the edge of instability     Feedback  Motor control  Time-delay  Hand  Biomechanics       font style='font-size:12px;'> 2015/8/25
We investigate the integration of visual and tactile sensory input for dynamic manipulation. Our experimental data and computational modeling reveal that time-delays are as critical to task-optimal m...
Topological finiteness for edge-vertex enumeration     Topological finiteness  edge-vertex enumeration       font style='font-size:12px;'> 2015/8/25
The number of PL-homeomorphism types of combinatorial manifolds in a fixed dimension with an upper bound on g2 is finite.
This paper describes newly invented multiscale transforms known under the name of the ridgelet [6] and the curvelet transforms [9, 8]. These systems combine ideas of multiscale analysis and geometry. ...
Acyclic edge-coloring using entropy compression     Acyclic edge-coloring  entropy compression  Combinatorics       font style='font-size:12px;'> 2012/6/29
An edge-coloring of a graph G is acyclic if it is a proper edge-coloring of G and every cycle contains at least three colors. We prove that every graph with maximum degree Delta has an acyclic edge-co...
This paper considers a kind of generalized measure $\lambda_s^{(h)}$ of fault tolerance in the $(n,k)$-star graph $S_{n,k}$ for $2\leqslant k \leqslant n-1$ and $0\leqslant h \leqslant n-k$, and deter...
Acyclic edge coloring of sparse graphs     acyclic  coloring  average degree  critical       font style='font-size:12px;'> 2012/2/29
A proper edge coloring of a graph $G$ is called acyclic if there is no bichromatic cycle in $G$. The acyclic chromatic index of $G$, denoted by $\chi'_a(G)$, is the least number of colors $k$ such tha...
Edge growth in graph powers     Edge growth  graph powers       font style='font-size:12px;'> 2012/2/29
For a graph G, its rth power G^r has the same vertex set as G, and has an edge between any two vertices within distance r of each other in G. We give a lower bound for the number of edges in the rth p...
Abstract: We give a simpler proof of Seymour's Theorem on edge-coloring series-parallel multigraphs and derive a linear-time algorithm to check whether a given series-parallel multigraph can be colore...
On spanning maximum k-edge-colorable subgraphs     maximum k-edge-colorable subgraphs  Discrete Mathematics       font style='font-size:12px;'> 2011/10/9
Abstract: A subgraph $H$ of a graph $G$ is called spanning, if any vertex of $G$ is not isolated in $H$, while it is called maximum $k$-edge-colorable, if $H$ is $k$-edge-colorable and contains as man...
Edge-Removal and Non-Crossing Perfect Matchings     Edge-Removal  Non-Crossing  Matchings  Combinatorics  Probability       font style='font-size:12px;'> 2011/9/5
Abstract: We study the following problem - How many arbitrary edges can be removed from a complete geometric graph with 2n vertices such that the resulting graph always contains a perfect non-crossing...
Minimal Reductions and Cores of Edge Ideals      edge ideal  even cycles  minimal reductions  core       font style='font-size:12px;'> 2011/2/28
We study minimal reductions of edge ideals of graphs containing a unique even cycle, and determine restrictions on the coefficients of the generators of these minimal reductions.
Let C be a clutter and let I(C)  R be its edge ideal. This is a survey paper on the algebraic and combinatorial properties of R/I(C) and C, respectively. We give a criterion to estimate the regulari...
Jump Sequences of Edge Ideals      Jump Sequences  Edge Ideals        font style='font-size:12px;'> 2011/1/17
Given an edge ideal of graph G, we show that if the first nonlinear strand in the resolution of IG is zero until homological stage a1, then the next non-linear strand in the resolution is zero until h...
Let the chromatic index of a hypergraph be the smallest number of colours needed to colour the edges such that similarly-coloured edges are disjoint. Likewise, let the cover index be the maximum numb...

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