On the Recognition of Fuzzy Circular Interval Graphs

Fuzzy circular interval graphs are a generalization of proper circular arc graphs and have been recently introduced by Chudnovsky and Seymour as a fundamental subclass of claw-free graphs. In this paper, we provide a polynomial-time algorithm for recognizing such graphs, and more importantly for building a suitable representation.Comment: 12 pages, 2 figure

From large deviations to semidistances of transport and mixing: coherence analysis for finite Lagrangian data

One way to analyze complicated non-autonomous flows is through trying to understand their transport behavior. In a quantitative, set-oriented approach to transport and mixing, finite time coherent sets play an important role. These are time-parametrized families of sets with unlikely transport to and from their surroundings under small or vanishing random perturbations of the dynamics. Here we propose, as a measure of transport and mixing for purely advective (i.e., deterministic) flows, (semi)distances that arise under vanishing perturbations in the sense of large deviations. Analogously, for given finite Lagrangian trajectory data we derive a discrete-time and space semidistance that comes from the "best" approximation of the randomly perturbed process conditioned on this limited information of the deterministic flow. It can be computed as shortest path in a graph with time-dependent weights. Furthermore, we argue that coherent sets are regions of maximal farness in terms of transport and mixing, hence they occur as extremal regions on a spanning structure of the state space under this semidistance---in fact, under any distance measure arising from the physical notion of transport. Based on this notion we develop a tool to analyze the state space (or the finite trajectory data at hand) and identify coherent regions. We validate our approach on idealized prototypical examples and well-studied standard cases.Comment: J Nonlinear Sci, 201

Introduction to Gestural Similarity in Music. An Application of Category Theory to the Orchestra

Mathematics, and more generally computational sciences, intervene in several aspects of music. Mathematics describes the acoustics of the sounds giving formal tools to physics, and the matter of music itself in terms of compositional structures and strategies. Mathematics can also be applied to the entire making of music, from the score to the performance, connecting compositional structures to acoustical reality of sounds. Moreover, the precise concept of gesture has a decisive role in understanding musical performance. In this paper, we apply some concepts of category theory to compare gestures of orchestral musicians, and to investigate the relationship between orchestra and conductor, as well as between listeners and conductor/orchestra. To this aim, we will introduce the concept of gestural similarity. The mathematical tools used can be applied to gesture classification, and to interdisciplinary comparisons between music and visual arts.Comment: The final version of this paper has been published by the Journal of Mathematics and Musi

Application of Kalman Filtering to Real-time Flight Regime Recognition Algorithms in a Helicopter Health and Usage Monitoring System

The purpose of this study is the application of Kalman filters to real-time Flight Regime Recognition (FRR) algorithms to identify the regime flown and observe transitions between flight regimes. Rotor fault identification, a technique that is somewhat similar to flight regime recognition, successfully used Kalman filters to determine fault types and damage locations. Recently developed FRR algorithms successfully applied Hidden Markov Models, which are similar to Kalman filters. The selected regime set for this study derives from a study performed by Bell Helicopter Textron, Inc. The selected parameter set for this study is modified from the Schweizer 300 Flight Test Program performed by Embry-Riddle Aeronautical University. The FRR algorithms developed will use the recorded flight parameters to identify a flight regime. A graphical interface allows the user to observe the real-time FRR and transitions between regimes. This research aims to bridge the gap between the application of mathematical models for damage identification and regime recognition. Multiple mathematical models developed for rotor blade fault and damage identification include neural networks, fuzzy logic systems, and Kalman filters. Recent research indicates that only the neural network approach has been applied to FRR algorithms, and that a Hidden Markov Model (HMM) approach outperformed the neural network. Additionally, public domain regime recognition research focuses on post processing algorithms rather than real-time regime recognition. The post processing codes appear to use discrete algorithms, which do not clearly identify transitions between regimes