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...

We propose a method for a parallel implementation of the Self-Organizing Map (SOM) algorithm, widely used in data-mining. We call this method Hybrid in the sense that it combines the advantages of the common network-partition and data-partition approaches, and is particularly effective when dealing with large maps. Based on the fact that a global topological ordering of the map is achieved in a...

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...

Motivated by the potential of atomically thin magnets towards achieving tunable high-frequency magnonics, we detail spin-wave dispersion bilayer ${\mathrm{CrI}}_{3}$. We demonstrate that magnonic behavior strongly depends on its stacking configuration and interlayer magnetic ordering, where a topological band gap opens in caused Dzyaloshinskii-Moriya Kitaev interactions, classifying ${\mathrm{C...