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

Efficient quantum processing of ideals in finite rings

Suppose we are given black-box access to a finite ring R, and a list of generators for an ideal I in R. We show how to find an additive basis representation for I in poly(log |R|) time. This generalizes a recent quantum algorithm of Arvind et al. which finds a basis representation for R itself. We then show that our algorithm is a useful primitive allowing quantum computers to rapidly solve a wide variety of problems regarding finite rings. In particular we show how to test whether two ideals are identical, find their intersection, find their quotient, prove whether a given ring element belongs to a given ideal, prove whether a given element is a unit, and if so find its inverse, find the additive and multiplicative identities, compute the order of an ideal, solve linear equations over rings, decide whether an ideal is maximal, find annihilators, and test the injectivity and surjectivity of ring homomorphisms. These problems appear to be hard classically.Comment: 5 page

Incidence of branch block of the heart and its related factors in patients with myocardial infarction hospitalized in Hajar hospital, Shahrekord

زمینه و هدف: با وجود پیشرفت های وسیع تشخیصی و درمانی، هنوز یک سوم بیمارانی که دچار انفارکتوس حاد میوکارد می شوند، فوت می کنند.آریتمی های قلبی شایع­ترین علت مرگ در جریان انفارکتوس حاد میوکارد و بلوک­های قلبی دسته مهمی از این آریتمی ها هستند. هدف از این مطالعه، تعیین بروز بلوک های شاخه ای قلب و عوامل خطر دموگرافیک و سوابق بالینی مرتبط با آن در بیماران انفارکتوس قلبی می باشد. روش بررسی: در این مطالعه توصیفی تحلیلی مقطعی پرونده 263 بیمار مبتلا به انفارکتوس حاد میوکارد بستری شده در بخش مراقبت ویژه قلب مورد بررسی قرار گرفت و اطلاعات دموگرافیک و سوابق بالینی بیماران جمع آوری شد. اطلاعات به­دست آمده با استفاده از شاخص های مرکزی و پراکندگی و آزمون های تی مستقل، کای اسکور و آنالیز واریانس یک­طرفه در نرم­افزار STATA مورد تجزیه و تحلیل آماری قرار گرفت. یافته ها: فراوانی نسبی بروز بلوک شاخه ای کامل 97/15 (42 بیمار) بود. 23/45 بیماران بلوک شاخه راست کامل و 76/54 بلوک شاخه چپ کامل داشتند. بروز بلوک شاخه راست و چپ در کل جمعیت مورد مطالعه به­ترتیب 22/7 و 75/8 بود. بروز بلوک شاخه ای چپ و راست قلبی با متغیرهای جنسیت، سن، محل سکونت افراد، فشارخون بالا و سابقه بیماری ایسکمیک ارتباط معنی­داری نداشت (05/0<P)؛ ولی با سابقه ابتلا به دیابت رابطه معنی داری داشت (05/0>P). نتیجه گیری: در این مطالعه بروز بلوک های شاخه ای قلب در بیماران بستری گزارش شد. با توجه به بروز بالای پیامد مورد بررسی، توصیه می شود بیماران با انفارکتوس حاد میوکارد قلب به­طور جدی از­نظر عوامل مساعد کننده نظیر دیابت و آریتمی های بطنی مانند وجود اختلالات الکتریکی بررسی شوند. در نهایت اقدامات درمانی مناسب، از ایجاد آریتمی های خطرناک جلوگیری نمایند

Temperature Dependent Raman Studies and Thermal Conductivity of Few Layer MoS2

We report on the temperature dependence of in-plane E2g and out of plane A1g Raman modes in high quality few layers MoS2 (FLMS) prepared using a high temperature vapor-phase method. The materials obtained were investigated using transmission electron microscopy. The frequencies of these two phonon modes were found to vary linearly with temperature. The first order temperature coefficients for E2g and A1g modes were found to be 1.32*10-2 and 1.23*10-2 cm-1/K, respectively. The thermal conductivity of the suspended FLMS at room temperature was estimated to be about 52 W/mK

Exploring the phase space of the quantum delta kicked accelerator

We experimentally explore the underlying pseudo-classical phase space structure of the quantum delta kicked accelerator. This was achieved by exposing a Bose-Einstein condensate to the spatially corrugated potential created by pulses of an off-resonant standing light wave. For the first time quantum accelerator modes were realized in such a system. By utilizing the narrow momentum distribution of the condensate we were able to observe the discrete momentum state structure of a quantum accelerator mode and also to directly measure the size of the structures in the phase space.Comment: 4 pages, 5 figures, added 2 references and figures are modified to increase the readability, submitted to Phys. Rev. Let

Energy use and economic analysis of strawberry production in Sanandaj zone of Iran

The aim of this study was to determine the energy consumption and economic analysis for strawberry production. The data were collected from 60 farmers growing strawberry in the Sanandaj zone of Iran by using a face-to-face questionnaire in August-September 2009. The plowing operation at the study area was done by two methods; manually plow (P1) and machinery plow (P2). Also the irrigation operation was done by two methods; pumping irrigation (P) and non pumping irrigation (NP). Univariate analysis of variance was used for finding the differences among the total energy used for production and profitability of this crop in the different methods at the 5% and 1% level. Total energy used in various farm operations during strawberry production was 53,605 MJ.ha-1. Total energy output was 17,338 MJ.ha-1, and the average annual yield of strawberry farms was 9,125 kg.ha-1. Energy efficiency was 0.32, and energy productivity calculated as 0.17 kg.MJ-1. This means a production of 0.17 kg per unit energy. The difference between total input energy in the different irrigation types (NP and P) is significant at 1% level. There is not any significant difference between different plow types at the 5% level. The interaction of irrigation types and plow types is significant at 5% level. The profit-cost ratio, productivity, and net profit in the strawberry production are 1.2, 0.99, and 1,825 $.ha-1, respectively. The difference between net return in the different irrigation types (NP and P) is significant at 5% level. The difference between net return in the different plow types (P1 and P2) is significant at 1% level

Dimension Reduction via Colour Refinement

Colour refinement is a basic algorithmic routine for graph isomorphism testing, appearing as a subroutine in almost all practical isomorphism solvers. It partitions the vertices of a graph into "colour classes" in such a way that all vertices in the same colour class have the same number of neighbours in every colour class. Tinhofer (Disc. App. Math., 1991), Ramana, Scheinerman, and Ullman (Disc. Math., 1994) and Godsil (Lin. Alg. and its App., 1997) established a tight correspondence between colour refinement and fractional isomorphisms of graphs, which are solutions to the LP relaxation of a natural ILP formulation of graph isomorphism. We introduce a version of colour refinement for matrices and extend existing quasilinear algorithms for computing the colour classes. Then we generalise the correspondence between colour refinement and fractional automorphisms and develop a theory of fractional automorphisms and isomorphisms of matrices. We apply our results to reduce the dimensions of systems of linear equations and linear programs. Specifically, we show that any given LP L can efficiently be transformed into a (potentially) smaller LP L' whose number of variables and constraints is the number of colour classes of the colour refinement algorithm, applied to a matrix associated with the LP. The transformation is such that we can easily (by a linear mapping) map both feasible and optimal solutions back and forth between the two LPs. We demonstrate empirically that colour refinement can indeed greatly reduce the cost of solving linear programs

Experimental investigation of optical atom traps with a frequency jump

We study the evolution of a trapped atomic cloud subject to a trapping frequency jump for two cases: stationary and moving center of mass. In the first case, the frequency jump initiates oscillations in the cloud's momentum and size. At certain times we find the temperature is significantly reduced. When the oscillation amplitude becomes large enough, local density increases induced by the anharmonicity of the trapping potential are observed. In the second case, the oscillations are coupled to the center of mass motion through the anharmonicity of the potential. This induces oscillations with even larger amplitudes, enhancing the temperature reduction effects and leading to nonisotropic expansion rates while expanding freely.Comment: 8 figures, Journal of Physics B: At. Mol. Op. Phy

Fermat's principle in quantum gravitational optics

Interactions incorporating the vacuum polarization effects in curved backgrounds modify the null cone structure in such a way that the photon trajectories would not be the space-time geodesics anymore. The gravitational birefringence introduced as a direct consequence of these effects, will allow shifts in the photon velocities leading to polarization dependent superluminal propagation. Taking these effects into account we study Fermat's principle in the context of the 1+3 (threading) formulation of the space-time decomposition. We find an expression for the modified spacetime refractive index and show it is proportional to the light cone correction to the first order. Consequences of this modification on polarization sum rules and spatial light paths are considered.Comment: 13 Pages, REVTex format, section on gravitomagnetic monopoles is removed along with its references, new references adde

Shear flow induced isotropic to nematic transition in a suspension of active filaments

We study the effects of externally applied shear flow on a model of suspensions of motors and filaments, via the equations of active hydrodynamics [PRL {\bf 89} (2002) 058101; {\bf 92} (2004) 118101]. In the absence of shear, the orientationally ordered phase of {\it both} polar and apolar active particles is always unstable at zero-wavenumber. An imposed steady shear large enough to overcome the active stresses stabilises both apolar and moving polar phases. Our work is relevant to {\it in vitro} studies of active filaments, the reorientation of endothelial cells subject to shear flow and shear-induced motility of attached cells.Comment: 8 pages, 4 figures submitted to Europhysics Letter