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

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

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

Relationship between physical activity during the first 20 weeks of gestation and hypertension in pregnancy

چکیده: زمینه و هدف: اختلالات فشارخون بارداری از عوارض خطرناک بارداری است که علت آن شناخته نشده است. تلاش های اخیر برای کنترل و پیشگیری از آن بر روی عوامل مؤثر بر افزایش توان بدن برای مقابله با استرس اکسیداتیو بنا شده است. با توجه به اثرات آنتی اکسیدانت فعالیت فیزیکی، این تحقیق با هدف بررسی ارتباط بین مدت و شدت فعالیت فیزیکی با اختلالات فشارخون بارداری انجام گرفت. روش بررسی: این مطالعه از نوع مورد –شاهدی است که بر روی دو گروه 97 نفره زنان حامله با فشارخون بارداری و بدون فشارخون بارداری بستری در بیمارستانهای شهید بهشتی، الزهرا(س) و شهید صدوقی اصفهان انجام شد. میزان و مدت فعالیت فیزیکی بر حسب شدت و نوع فعالیت در بیست هفته اول بارداری در دو گروه با استفاده از پرسشنامه استاندارد فعالیت فیزیکی (MET) در دوران بارداری سنجیده شد. برای مقایسه متغیرهای کمی از آزمون t و برای متغیرهای کیفی آزمون من ویتنی استفاده شد. یافته ها: دو گروه از نظر سن، میانگین شاخص توده بدنی (BMI)، سطح تحصیلات، سن حاملگی و وضعیت اشتغال اختلاف معنی داری نداشتند. نتایج نشان داد که میزان فعالیت فیزیکی بر اساس پرسشنامه استاندارد فعالیت فیزیکی در زنان بدون فشارخون بارداری (89/14±38/30) به طور معنی داری بیشتر از گروه دارای فشارخون بالاتر (24/12±63/14) بود (001/0

Response variability in balanced cortical networks

We study the spike statistics of neurons in a network with dynamically balanced excitation and inhibition. Our model, intended to represent a generic cortical column, comprises randomly connected excitatory and inhibitory leaky integrate-and-fire neurons, driven by excitatory input from an external population. The high connectivity permits a mean-field description in which synaptic currents can be treated as Gaussian noise, the mean and autocorrelation function of which are calculated self-consistently from the firing statistics of single model neurons. Within this description, we find that the irregularity of spike trains is controlled mainly by the strength of the synapses relative to the difference between the firing threshold and the post-firing reset level of the membrane potential. For moderately strong synapses we find spike statistics very similar to those observed in primary visual cortex.Comment: 22 pages, 7 figures, submitted to Neural Computatio

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

A Complete Characterization of the Gap between Convexity and SOS-Convexity

Our first contribution in this paper is to prove that three natural sum of squares (sos) based sufficient conditions for convexity of polynomials, via the definition of convexity, its first order characterization, and its second order characterization, are equivalent. These three equivalent algebraic conditions, henceforth referred to as sos-convexity, can be checked by semidefinite programming whereas deciding convexity is NP-hard. If we denote the set of convex and sos-convex polynomials in $n$ variables of degree $d$ with $\tilde{C}_{n,d}$ and $\tilde{\Sigma C}_{n,d}$ respectively, then our main contribution is to prove that $\tilde{C}_{n,d}=\tilde{\Sigma C}_{n,d}$ if and only if $n=1$ or $d=2$ or $(n,d)=(2,4)$. We also present a complete characterization for forms (homogeneous polynomials) except for the case $(n,d)=(3,4)$ which is joint work with G. Blekherman and is to be published elsewhere. Our result states that the set $C_{n,d}$ of convex forms in $n$ variables of degree $d$ equals the set $\Sigma C_{n,d}$ of sos-convex forms if and only if $n=2$ or $d=2$ or $(n,d)=(3,4)$. To prove these results, we present in particular explicit examples of polynomials in $\tilde{C}_{2,6}\setminus\tilde{\Sigma C}_{2,6}$ and $\tilde{C}_{3,4}\setminus\tilde{\Sigma C}_{3,4}$ and forms in $C_{3,6}\setminus\Sigma C_{3,6}$ and $C_{4,4}\setminus\Sigma C_{4,4}$, and a general procedure for constructing forms in $C_{n,d+2}\setminus\Sigma C_{n,d+2}$ from nonnegative but not sos forms in $n$ variables and degree $d$. Although for disparate reasons, the remarkable outcome is that convex polynomials (resp. forms) are sos-convex exactly in cases where nonnegative polynomials (resp. forms) are sums of squares, as characterized by Hilbert.Comment: 25 pages; minor editorial revisions made; formal certificates for computer assisted proofs of the paper added to arXi

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

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

Entanglement as a source of black hole entropy

We review aspects of black hole thermodynamics, and show how entanglement of a quantum field between the inside and outside of a horizon can account for the area-proportionality of black hole entropy, provided the field is in its ground state. We show that the result continues to hold for Coherent States and Squeezed States, while for Excited States, the entropy scales as a power of area less than unity. We also identify location of the degrees of freedom which give rise to the above entropy.Comment: 12 pages, latex, 5 figures. Invited talk by SD at `Recent Developments in Gravity' (NEB XII), Nafplion, Greece, 30 June 2006. To appear in Journal of Physics: Conference Series; V2: References added, Minor changes to match published versio