Models Development for Single-Row Networks from Connected Graphs

In this paper, we present a collection of models for connected graphs mapping into single–row networks. The collection involves three specific models for perfect binary trees, trees and partially dense graphs, and three general models for connected graphs. These models are compared in terms of their structures, energy values, congestion and number of doglegs in the single–row transformation. The numerical experiments are run by each respective developed program. The transformation is necessary in applications such as in the assignment of telephone channels to caller–receiver pairs roaming in cells in a cellular network on real–time basis

Graphical description of the action of Clifford operators on stabilizer states

We introduce a graphical representation of stabilizer states and translate the action of Clifford operators on stabilizer states into graph operations on the corresponding stabilizer-state graphs. Our stabilizer graphs are constructed of solid and hollow nodes, with (undirected) edges between nodes and with loops and signs attached to individual nodes. We find that local Clifford transformations are completely described in terms of local complementation on nodes and along edges, loop complementation, and change of node type or sign. Additionally, we show that a small set of equivalence rules generates all graphs corresponding to a given stabilizer state; we do this by constructing an efficient procedure for testing the equality of any two stabilizer graphs.Comment: 14 pages, 8 figures. Version 2 contains significant changes. Submitted to PR

Inferring Chemical Reaction Patterns Using Rule Composition in Graph Grammars

Modeling molecules as undirected graphs and chemical reactions as graph rewriting operations is a natural and convenient approach tom odeling chemistry. Graph grammar rules are most naturally employed to model elementary reactions like merging, splitting, and isomerisation of molecules. It is often convenient, in particular in the analysis of larger systems, to summarize several subsequent reactions into a single composite chemical reaction. We use a generic approach for composing graph grammar rules to define a chemically useful rule compositions. We iteratively apply these rule compositions to elementary transformations in order to automatically infer complex transformation patterns. This is useful for instance to understand the net effect of complex catalytic cycles such as the Formose reaction. The automatically inferred graph grammar rule is a generic representative that also covers the overall reaction pattern of the Formose cycle, namely two carbonyl groups that can react with a bound glycolaldehyde to a second glycolaldehyde. Rule composition also can be used to study polymerization reactions as well as more complicated iterative reaction schemes. Terpenes and the polyketides, for instance, form two naturally occurring classes of compounds of utmost pharmaceutical interest that can be understood as "generalized polymers" consisting of five-carbon (isoprene) and two-carbon units, respectively

Non-rigid Reconstruction with a Single Moving RGB-D Camera

We present a novel non-rigid reconstruction method using a moving RGB-D camera. Current approaches use only non-rigid part of the scene and completely ignore the rigid background. Non-rigid parts often lack sufficient geometric and photometric information for tracking large frame-to-frame motion. Our approach uses camera pose estimated from the rigid background for foreground tracking. This enables robust foreground tracking in situations where large frame-to-frame motion occurs. Moreover, we are proposing a multi-scale deformation graph which improves non-rigid tracking without compromising the quality of the reconstruction. We are also contributing a synthetic dataset which is made publically available for evaluating non-rigid reconstruction methods. The dataset provides frame-by-frame ground truth geometry of the scene, the camera trajectory, and masks for background foreground. Experimental results show that our approach is more robust in handling larger frame-to-frame motions and provides better reconstruction compared to state-of-the-art approaches.Comment: Accepted in International Conference on Pattern Recognition (ICPR 2018

Minimal dilatation in Penner's construction

For all orientable closed surfaces, we determine the minimal dilatation among mapping classes arising from Penner's construction. We also discuss generalisations to surfaces with punctures.Comment: 11 pages, 6 figure