Joint Spectral Radius and Path-Complete Graph Lyapunov Functions

We introduce the framework of path-complete graph Lyapunov functions for approximation of the joint spectral radius. The approach is based on the analysis of the underlying switched system via inequalities imposed among multiple Lyapunov functions associated to a labeled directed graph. Inspired by concepts in automata theory and symbolic dynamics, we define a class of graphs called path-complete graphs, and show that any such graph gives rise to a method for proving stability of the switched system. This enables us to derive several asymptotically tight hierarchies of semidefinite programming relaxations that unify and generalize many existing techniques such as common quadratic, common sum of squares, and maximum/minimum-of-quadratics Lyapunov functions. We compare the quality of approximation obtained by certain classes of path-complete graphs including a family of dual graphs and all path-complete graphs with two nodes on an alphabet of two matrices. We provide approximation guarantees for several families of path-complete graphs, such as the De Bruijn graphs, establishing as a byproduct a constructive converse Lyapunov theorem for maximum/minimum-of-quadratics Lyapunov functions.Comment: To appear in SIAM Journal on Control and Optimization. Version 2 has gone through two major rounds of revision. In particular, a section on the performance of our algorithm on application-motivated problems has been added and a more comprehensive literature review is presente

The use of pulse oximetry in evaluation of pulp vitality in immature permanent teeth

Background and aim: The current methods of pulp vitality assessment, either electric or thermal, are of limited use in children. Recently, traumatized and immature teeth may not respond to such methods and because such methods require subjective responses, it may not provide accurate results particularly in children. Pulse oximetry, an atraumatic approach, is used to measure oxygen saturation in vascular system. The aim of this study was to investigate the use of pulse oximetry to evaluate pulp vitality status in immature permanent teeth. Methods and materials: The study was conducted on 329 maxillary central and lateral incisors in children. The negative control group consisted of 10 root filled teeth. Systemic oxygen saturation was first measured on the thumb of the individual using a custom-made sensor. Oxygen saturation values of the teeth were then evaluated. The correlation between oxygen saturation measurement obtained from finger and tooth, and the correlation between oxygen saturation values and stage of root development were analyzed. A further comparison was made between the teeth with open and closed apex. Results: Mean oxygen values recorded in the patient's finger were 97.17, and mean oxygen values in the maxillary central and lateral incisors were 86.77 and 83/92, respectively. There was no significant correlation between blood oxygen levels in the finger and in the teeth. (P > 0.05) There was a significant negative correlation between the stage of root development and the blood oxygen levels in the patients' teeth. (P < 0.05) Mean oxygen values in the teeth with open apex were significantly higher than the teeth with closed apex. (P < 0.001). Conclusion: Vital teeth provided consistent oxygen saturation readings, and non-vital teeth recorded no oxygen saturation values. During tooth development, the oxygen saturation values decreased. These findings confirm that the pulse oximetry is capable of detecting the pulpal blood flow and oxygen saturation. © 2016 John Wiley & Sons A/S. Published by John Wiley & Sons Ltd

Is There a Negative Thermal Expansion in Supported Metal Nanoparticles? An In-Situ X-ray Absorption Study Coupled with Neural Network Analysis

Interactions with their support, adsorbates and unique structural motifs are responsible for the many intriguing properties and potential applications of supported metal nanoparticles (NPs). At the same time, they complicate the interpretation of experimental data. In fact, the methods and approaches that work well for the ex situ analysis of bulk materials may be inaccurate or introduce artifacts in the in situ analysis of nanomaterials. Here we revisit the controversial topic of negative thermal expansion and anomalies in the Debye temperature reported for oxide-supported metal NPs. In situ X-ray absorption experimental data collected for Pt NPs in ultrahigh vacuum and an advanced data analysis approach based on an artificial neural network demonstrate that Pt NPs do not exhibit intrinsic negative thermal expansion. Similarly as for bulk materials, in the absence of adsorbates the bond lengths in metal NPs increase with temperature. The previously reported anomalies in particle size-dependent Debye temperatures can also be linked to the artifacts in the interpretation of conventional X-ray absorption data of disordered materials such as NPs