Fractional quantum Hall (FQH) liquids contain extremely rich internal structures which represent a whole new kind of ordering. We discuss the characterization and classification of the new orders (which is called topological orders). We also discuss the edge excitations in FQH liquids, which form the so-called chiral Luttinger liquids. The chiral Luttinger liquids at the edges also have very ri...

The immersion relation is a partial ordering relation on graphs that is weaker than the topological minor relation in the sense that if a graph G contains a graph H as a topological minor, then it also contains it as an immersion but not vice versa. Kuratowski graphs, namely K5 and K3,3, give a precise characterization of planar graphs when excluded as topological minors. In this note we give a...

Although we can build a belief network starting from any ordering of its variables, its structure depends heavily on the ordering being selected: the topology of the network, and therefore the number of conditional independence relationships that may be explicitly represented can vary greatly from one ordering to another. We develop an algorithm for learning belief networks composed of two main...

Many applications like pointer analysis and incremental compilation require maintaining a topological ordering of the nodes of a directed acyclic graph (DAG) under dynamic updates. All known algorithms for this problem are either only analyzed for worst-case insertion sequences or only evaluated experimentally on random DAGs. We present the first average-case analysis of online topological orde...

Machining features are groupings of geometric and topological entities that have certain engineering sig-niicance. Recognizing these features from a designed parts is crucial in the automation of Computer Integrated Manufacturing (CIM). In this paper, the machining feature recognition problem is formulated as a partial constraint satisfaction problem (PCSP) where variables are the faces in the ...

Although partially observable Markov decision processes (POMDPs) have received significant attention in past years, to date, solving problems of realistic order of magnitude remains a serious challenge. In this context, techniques that accelerate fundamental algorithms have been a main focus of research. Among them prioritized solvers suggest solutions to the problem of ordering backup operatio...

AbstructThis paper presents effective algorithms for multiway partitioning. Confirming ideas originally due to Hall, we demonstrate that geometric embeddings of the circuit netlist can lead to high-quality k-way partitionings. The netlist embeddings are derived via the computation of d eigenvectors of the Laplacian for a graph representation of the netlist. As Hall did not specify how to partit...