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

Semi-definite programming and functional inequalities for Distributed Parameter Systems

We study one-dimensional integral inequalities, with quadratic integrands, on bounded domains. Conditions for these inequalities to hold are formulated in terms of function matrix inequalities which must hold in the domain of integration. For the case of polynomial function matrices, sufficient conditions for positivity of the matrix inequality and, therefore, for the integral inequalities are cast as semi-definite programs. The inequalities are used to study stability of linear partial differential equations.Comment: 8 pages, 5 figure

Comparison of efficacy Ephedrine and phenylephrine in Postoperative Vomiting in Cesarean section

Introduce: Postoperative nausea and vomiting (PONV) still is the most big problem event encountered in the PACU (Post Anesthesia Care Unit), despite advances in prevention and treatment. The incidence of PONV has remained high and has a major negative impact on patient satisfaction about the overall surgical experience. Method: In double-blind, clinical trial, 104 patients were undergoing cesarean section was randomizing into two groups: Group P (100μg Phenylephrine) and Group E (6μg Ephedrine). We compared the Vomiting parameters between the two groups. Result: Patients in the recovery were compared in 2 groups regarding occurrence of vomiting that no statistical difference between two group (P >0.05). The results show that vomiting was seen in ASA1, and in ASA2 no vomiting was observed. The incidence of vomiting was 2 patients in young group and 1 patient in middle-aged group. The incidence of vomiting was 2 patients in slim group, 1 in moderate group and no sign of vomiting has been seen in the obese group. Conclusion: We conclude that ephedrine is the best drug for antiemetic prophylaxis before cesarean surgery based on cost and lack of side effects

Quantum gravitational optics: the induced phase

The geometrical approximation of the extended Maxwell equation in curved spacetime incorporating interactions induced by the vacuum polarization effects is considered. Taking into account these QED interactions and employing the analogy between eikonal equation in geometrical optics and Hamilton-Jacobi equation for the particle motion, we study the phase structure of the modified theory. There is a complicated, local induced phase which is believed to be responsible for the modification of the classical picture of light ray. The main features of QGO could be obtained through the study of this induced phase. We discuss initial principles in conventional and modified geometrical optics and compare the results.Comment: 10 pages, REVTex forma

Incidence patterns and spatial analysis of the most common cancers in southeastern Iran using Geographic Information System (GIS)

Abstract: Background and aim: Cancer is the third leading cause of mortality in Iran. By use of Geographic Information System, location-based and accurate analytical and descriptive date can be given to health policy makers. The aim of this study is to identify the incidental patterns of cancers (random, scattered, cluster) and analyze them spatially. Method(s): This is a periodical descriptive and analytical study which has investigated all new recorded incidents of cancers in Chaharmahal and Bakhtiari Province in southwestern Iran from 2008 to 2011. The data were analyzed using ArcGIS9.3 and Stata12. Spatial Auto correlation coefficient and Moran I and Getis-Ord, t test, ANOVA and Chi-square were used for data analysis. Results revealed that in the age Mean and Standard deviation of the patients was 5/81 ±9/59. The mean age of the patients was meaningful according to gender and different towns (P=0.037). Standardized Incidences of Cancer in Shahrekord, Farsan, Ardal, Kiar, Koohrang, Lordegan and Borougen towns were 220/9, 154/3, 143/8, 80/9, 64/2, 61/1 and 57/2 per one hundred thousand of population, respectively. The most frequency of cancers was related to cancers of the digestive system ((2/25%, skin(2/81%)and urinary system (9/85%) and the least of them was related to cartilage(3/0%). Patterns of cancer incidence in southwestern Iran was random (P=0.13519). In Conclusions: Reports of differences in cancer incidence based on age, sex, city of residence and non-cluster cancers in the area studied can support the cancer prevention and screening programs focusing hypothesis and pave the road for decision makers and planners in the health system