A rigorous analysis of the cavity equations for the minimum spanning tree

We analyze a new general representation for the Minimum Weight Steiner Tree (MST) problem which translates the topological connectivity constraint into a set of local conditions which can be analyzed by the so called cavity equations techniques. For the limit case of the Spanning tree we prove that the fixed point of the algorithm arising from the cavity equations leads to the global optimum.Comment: 5 pages, 1 figur

Density functional theory study of the {\alpha} --> {\omega} martensitic transformation in titanium induced by hydrostatic pressure

The martensitic {\alpha} --> {\omega} transition was investigated in Ti under hydrostatic pressure. The calculations were carried out using the density functional theory (DFT) framework in combination with the Birch-Murnaghan equation of state. The calculated ground-state properties of {\alpha} and {\omega} phases of Ti, their bulk moduli and pressure derivatives are in agreement with the previous experimental data. The lattice constants of {\alpha} and {\omega}-phase at 0 K were modeled as a function of pressure from 0 to 74 GPa and 0 to 119 GPa, respectively. It is shown that the lattice constants vary in a nonlinear manner upon compression. The calculated lattice parameters were used to describe the {\alpha} --> {\omega} transition and show that the phase transition can be obtained at 0 GPa and 0 K.Comment: 6 pages, 5 figure

Belief-Propagation for Weighted b-Matchings on Arbitrary Graphs and its Relation to Linear Programs with Integer Solutions

We consider the general problem of finding the minimum weight \bm-matching on arbitrary graphs. We prove that, whenever the linear programming (LP) relaxation of the problem has no fractional solutions, then the belief propagation (BP) algorithm converges to the correct solution. We also show that when the LP relaxation has a fractional solution then the BP algorithm can be used to solve the LP relaxation. Our proof is based on the notion of graph covers and extends the analysis of (Bayati-Shah-Sharma 2005 and Huang-Jebara 2007}. These results are notable in the following regards: (1) It is one of a very small number of proofs showing correctness of BP without any constraint on the graph structure. (2) Variants of the proof work for both synchronous and asynchronous BP; it is the first proof of convergence and correctness of an asynchronous BP algorithm for a combinatorial optimization problem.Comment: 28 pages, 2 figures. Submitted to SIAM journal on Discrete Mathematics on March 19, 2009; accepted for publication (in revised form) August 30, 2010; published electronically July 1, 201

Statistical Mechanics of the Hyper Vertex Cover Problem

We introduce and study a new optimization problem called Hyper Vertex Cover. This problem is a generalization of the standard vertex cover to hypergraphs: one seeks a configuration of particles with minimal density such that every hyperedge of the hypergraph contains at least one particle. It can also be used in important practical tasks, such as the Group Testing procedures where one wants to detect defective items in a large group by pool testing. Using a Statistical Mechanics approach based on the cavity method, we study the phase diagram of the HVC problem, in the case of random regualr hypergraphs. Depending on the values of the variables and tests degrees different situations can occur: The HVC problem can be either in a replica symmetric phase, or in a one-step replica symmetry breaking one. In these two cases, we give explicit results on the minimal density of particles, and the structure of the phase space. These problems are thus in some sense simpler than the original vertex cover problem, where the need for a full replica symmetry breaking has prevented the derivation of exact results so far. Finally, we show that decimation procedures based on the belief propagation and the survey propagation algorithms provide very efficient strategies to solve large individual instances of the hyper vertex cover problem.Comment: Submitted to PR

Evaluation of auditory efferent system function in children with autism

زمینه و هدف: مطالعات مختلف نشان داده اند که سیستم وابران شنیداری در توجه انتخابی نقش دارد و از این رو بررسی این سیستم در کودکان اوتیسمی بسیار ارزشمند است. هدف از این مطالعه بررسی مسیر وابران شنوایی در کودکان مبتلا به اوتیسم در مقایسه با کودکان با رشد هنجار بوده است. روش بررسی: در این مطالعه توصیفی-تحلیلی تعداد 34 کودک 11-5 ساله در قالب دو گروه هنجار (17 نفر) و مبتلا به اوتیسم (17 نفر) مورد بررسی قرار گرفتند. کلیه کودکان در آزمون های ادیومتری تون خالص (Pure-tone audionetry)، ادیومتری گفتاری (Speech audiometery)، تمپانومتری (Tympanometry) و گسیل های صوتی گوشی گذرا (otoacoustic emissions=TEOAE-evoked Transient)دارای نتایج طبیعی بودند. عملکرد سیستم وابران از طریق ثبت پاسخ های TEOAE در دو حالت ارائه نویز دگر طرفی و بدون ارائه نویز بررسی گردید. جهت آنالیز نتایج از از نرم افزار آماری SPSS و آزمون های تی مستقل و تی زوجی استفاده شد. یافته ها: نتایج این پژوهش نشان داد که تفاوت قابل ملاحظه ای بین میانگین میزان مهار در دو گروه وجود دارد (001/0=P). میانگین دامنه TEOAE در حالت بدون نویز دگر طرفی در گروه هنجار (09/4 ± 63/17) و در گروه اوتیسم (78/3 ± 40/17) به دست آمد که از لحاظ آماری نشان دهنده تفاوت معنی داری نبود (83/0=P). نتیجه گیری: یافته های کسب شده در مطالعه حاضر نشان دهنده کاهش فعالیت سیستم وابران شنوایی در کودکان مبتلا به اوتیسم نسبت به کودکان با رشد هنجار بود. با توجه به اینکه آزمون مورد استفاده در این مطالعه، مهار گسیل های صوتی گوشی گذرا (TEOAE suppression) است، می توان نتیجه گرفت این آزمون ابزار بالینی حساس، غیر تهاجمی، عینی و مناسب برای بررسی عملکرد سیستم وابران در کودکان مبتلا به اوتیسم است

Statistical Mechanics of Steiner trees

The Minimum Weight Steiner Tree (MST) is an important combinatorial optimization problem over networks that has applications in a wide range of fields. Here we discuss a general technique to translate the imposed global connectivity constrain into many local ones that can be analyzed with cavity equation techniques. This approach leads to a new optimization algorithm for MST and allows to analyze the statistical mechanics properties of MST on random graphs of various types

Full scale monitoring of the twin chimneys of the rovinari power plant

The presented paper deals with the structural identification and monitoring of two twin chimneys in very close arrangement. Due to twin arrangement, important interference effects are expected to modify the chimney response to wind action, causing vortex shedding and state-dependent excitation associated to the oscillatory motion of the leeward chimney, in and out of the windward chimney wake. The complexity of the physics of this problem is increased by the dependency of the aerodynamics of circular cylinders on Reynolds number; however, there is a weakness of literature about cylinders behaviour at critical and super-critical range of Reynolds number, due to experimental limitations. Also the International Committee on Industrial Chimneys (CICIND) does not provide, at present, any specific technical guideline about twin chimneys whose interaxis distance is less or equal two times the diameter, as in this case. For this reason a Tuned Mass Damper (TMD) has been installed in order to increase the damping of the chimney, as merely suggested. This work aims at assessing the effectiveness of the installed TMD and characterizing the tower dynamic behaviour itself due to the wind excitation, as well as providing full scale measurements for twin cylinders configuration at high Reynolds numbers

Statistical mechanics of budget-constrained auctions

Finding the optimal assignment in budget-constrained auctions is a combinatorial optimization problem with many important applications, a notable example being the sale of advertisement space by search engines (in this context the problem is often referred to as the off-line AdWords problem). Based on the cavity method of statistical mechanics, we introduce a message passing algorithm that is capable of solving efficiently random instances of the problem extracted from a natural distribution, and we derive from its properties the phase diagram of the problem. As the control parameter (average value of the budgets) is varied, we find two phase transitions delimiting a region in which long-range correlations arise.Comment: Minor revisio

Norms of anthropometric, body composition measures and prevalence of overweight and obesity in urban populations of Iran

زمینه و هدف: تدوین هنجارهای ملی برای اندازه‌های پیکری و ترکیب بدنی و نیز تعیین شیوع اضافه وزن و چاقی به دلیل ارتباط آن با بیماری‌های مزمن از ضروریات جوامع امروزی است. این پژوهش با هدف تهیه‌ی این هنجارها در جمعیت‌های شهری ایران طراحی و اجرا شد. روش بررسی: در این پژوهش مقطعی که از نوع توصیفی – تحلیلی بود، 991 نفر مرد و 1188 نفر زن با دامنه سنی 15 تا 64 سال به شیوه در دسترس از شهرهای اردبیل، اصفهان، اهواز، تهران، رشت، کرمان و مشهد فراخوان شدند. شاخص توده‌ی بدن (BMI)، دور کمر (WC)، نسبت دور کمر به لگن (WHR)، نسبت دور کمر به قد (WHtR) و درصد چربی بدن آزمودنی‌ها اندازه‌گیری شد. داده ها با استفاده از آزمون های t مستقل، ضریب همبستگی جزیی تعدیل شده و تحلیل واریانس یک طرفه در نرم افزار SPSS تجزیه و تحلیل شدند. یافته‌ها: با توجه به اندازه‌های BMI، 49 مردان و 53 زنان دارای اضافه وزن یا چاقی بودند که 2/10 مردان و 6/18 زنان چاق بودند. در هر گروه سنی، مردان درصد چربی کمتری نسبت به زنان داشتند (001/0>P). در هر دوی مردان و زنان شیوع اضافه وزن در میان رده‌ی سنی 49-40 سال و شیوع چاقی در رده‌ی سنی بالای 50 سال بیشتر از سنین دیگر بود. نتیجه‌گیری: یافته‌های پژوهش حاضر ضمن ارایه‌ی هنجارهای ملی، شیوع بالای اضافه وزن و چاقی عمومی و شکمی را در هر دو جنسیت در جمعیت‌های شهری ایران نشان داد که بیانگر لزوم ارزیابی‌های مستمر و ارایه‌ی برنامه‌های مداخله‌ای در جهت کنترل و پیشگیری از اختلال‌های مرتبط با چاقی مانند دیابت می‌باش

Fermions and Loops on Graphs. II. Monomer-Dimer Model as Series of Determinants

We continue the discussion of the fermion models on graphs that started in the first paper of the series. Here we introduce a Graphical Gauge Model (GGM) and show that : (a) it can be stated as an average/sum of a determinant defined on the graph over $\mathbb{Z}_{2}$ (binary) gauge field; (b) it is equivalent to the Monomer-Dimer (MD) model on the graph; (c) the partition function of the model allows an explicit expression in terms of a series over disjoint directed cycles, where each term is a product of local contributions along the cycle and the determinant of a matrix defined on the remainder of the graph (excluding the cycle). We also establish a relation between the MD model on the graph and the determinant series, discussed in the first paper, however, considered using simple non-Belief-Propagation choice of the gauge. We conclude with a discussion of possible analytic and algorithmic consequences of these results, as well as related questions and challenges.Comment: 11 pages, 2 figures; misprints correcte