On Index Coding and Graph Homomorphism

In this work, we study the problem of index coding from graph homomorphism perspective. We show that the minimum broadcast rate of an index coding problem for different variations of the problem such as non-linear, scalar, and vector index code, can be upper bounded by the minimum broadcast rate of another index coding problem when there exists a homomorphism from the complement of the side information graph of the first problem to that of the second problem. As a result, we show that several upper bounds on scalar and vector index code problem are special cases of one of our main theorems. For the linear scalar index coding problem, it has been shown in [1] that the binary linear index of a graph is equal to a graph theoretical parameter called minrank of the graph. For undirected graphs, in [2] it is shown that $\mathrm{minrank}(G) = k$ if and only if there exists a homomorphism from $\bar{G}$ to a predefined graph $\bar{G}_k$. Combining these two results, it follows that for undirected graphs, all the digraphs with linear index of at most k coincide with the graphs $G$ for which there exists a homomorphism from $\bar{G}$ to $\bar{G}_k$. In this paper, we give a direct proof to this result that works for digraphs as well. We show how to use this classification result to generate lower bounds on scalar and vector index. In particular, we provide a lower bound for the scalar index of a digraph in terms of the chromatic number of its complement. Using our framework, we show that by changing the field size, linear index of a digraph can be at most increased by a factor that is independent from the number of the nodes.Comment: 5 pages, to appear in "IEEE Information Theory Workshop", 201

Subdeterminant Maximization via Nonconvex Relaxations and Anti-concentration

Several fundamental problems that arise in optimization and computer science can be cast as follows: Given vectors $v_1,\ldots,v_m \in \mathbb{R}^d$ and a constraint family ${\cal B}\subseteq 2^{[m]}$, find a set $S \in \cal{B}$ that maximizes the squared volume of the simplex spanned by the vectors in $S$. A motivating example is the data-summarization problem in machine learning where one is given a collection of vectors that represent data such as documents or images. The volume of a set of vectors is used as a measure of their diversity, and partition or matroid constraints over $[m]$ are imposed in order to ensure resource or fairness constraints. Recently, Nikolov and Singh presented a convex program and showed how it can be used to estimate the value of the most diverse set when ${\cal B}$ corresponds to a partition matroid. This result was recently extended to regular matroids in works of Straszak and Vishnoi, and Anari and Oveis Gharan. The question of whether these estimation algorithms can be converted into the more useful approximation algorithms -- that also output a set -- remained open. The main contribution of this paper is to give the first approximation algorithms for both partition and regular matroids. We present novel formulations for the subdeterminant maximization problem for these matroids; this reduces them to the problem of finding a point that maximizes the absolute value of a nonconvex function over a Cartesian product of probability simplices. The technical core of our results is a new anti-concentration inequality for dependent random variables that allows us to relate the optimal value of these nonconvex functions to their value at a random point. Unlike prior work on the constrained subdeterminant maximization problem, our proofs do not rely on real-stability or convexity and could be of independent interest both in algorithms and complexity.Comment: in FOCS 201

On the Sample Information About Parameter and Prediction

The Bayesian measure of sample information about the parameter, known as Lindley's measure, is widely used in various problems such as developing prior distributions, models for the likelihood functions and optimal designs. The predictive information is defined similarly and used for model selection and optimal designs, though to a lesser extent. The parameter and predictive information measures are proper utility functions and have been also used in combination. Yet the relationship between the two measures and the effects of conditional dependence between the observable quantities on the Bayesian information measures remain unexplored. We address both issues. The relationship between the two information measures is explored through the information provided by the sample about the parameter and prediction jointly. The role of dependence is explored along with the interplay between the information measures, prior and sampling design. For the conditionally independent sequence of observable quantities, decompositions of the joint information characterize Lindley's measure as the sample information about the parameter and prediction jointly and the predictive information as part of it. For the conditionally dependent case, the joint information about parameter and prediction exceeds Lindley's measure by an amount due to the dependence. More specific results are shown for the normal linear models and a broad subfamily of the exponential family. Conditionally independent samples provide relatively little information for prediction, and the gap between the parameter and predictive information measures grows rapidly with the sample size.Comment: Published in at http://dx.doi.org/10.1214/10-STS329 the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org

Exponential renormalization

Moving beyond the classical additive and multiplicative approaches, we present an "exponential" method for perturbative renormalization. Using Dyson's identity for Green's functions as well as the link between the Faa di Bruno Hopf algebra and the Hopf algebras of Feynman graphs, its relation to the composition of formal power series is analyzed. Eventually, we argue that the new method has several attractive features and encompasses the BPHZ method. The latter can be seen as a special case of the new procedure for renormalization scheme maps with the Rota-Baxter property. To our best knowledge, although very natural from group-theoretical and physical points of view, several ideas introduced in the present paper seem to be new (besides the exponential method, let us mention the notions of counterfactors and of order n bare coupling constants).Comment: revised version; accepted for publication in Annales Henri Poincar

A case of intestinal myiasis due to Sarcophaga hemmoroidalis from Chaharmahal va Bakhtiari province

چکیده: این گزارش مربوط به پسر بچه 13 ساله‌ای است که ساکن روستای سید صالح کوتاه از توابع شهرستان کوهرنگ در استان چهارمحال و بختیاری می باشد. بیمار در شرح حال خود دردهای شکمی در قسمت راست تحتانی، احساس پری شکم، دفع مدفوع شل دو تا سه بار در شبانه روز، کاهش اشتها و کاهش وزن در چند ماه گذشته و همچنین مشاهده کرم های کوچک سفید رنگ متحرک را در مدفوع خود بیان می کرد در هنگام آزمایشات اولیه تعدادی لارو متحرک از مدفوع بیمار جدا و در محلول فرمالین 10 نگهداری شد. سپس با استفاده از کلیدهای تشخیصی و مشاهده خصوصیات مرفولوژی لارو سارکوفاگا هموروئیدالیس (Sarcophaga haemorrhoidalis) تشخیص داده شد

Numerical simulation of laminar plasma dynamos in a cylindrical von K\'arm\'an flow

The results of a numerical study of the magnetic dynamo effect in cylindrical von K\'arm\'an plasma flow are presented with parameters relevant to the Madison Plasma Couette Experiment. This experiment is designed to investigate a broad class of phenomena in flowing plasmas. In a plasma, the magnetic Prandtl number Pm can be of order unity (i.e., the fluid Reynolds number Re is comparable to the magnetic Reynolds number Rm). This is in contrast to liquid metal experiments, where Pm is small (so, Re>>Rm) and the flows are always turbulent. We explore dynamo action through simulations using the extended magnetohydrodynamic NIMROD code for an isothermal and compressible plasma model.We also study two-fluid effects in simulations by including the Hall term in Ohm's law. We find that the counter-rotating von K\'arm\'an flow results in sustained dynamo action and the self-generation of magnetic field when the magnetic Reynolds number exceeds a critical value. For the plasma parameters of the experiment, this field saturates at an amplitude corresponding to a new stable equilibrium (a laminar dynamo). We show that compressibility in the plasma results in an increase of the critical magnetic Reynolds number, while inclusion of the Hall term in Ohm's law changes the amplitude of the saturated dynamo field but not the critical value for the onset of dynamo action.Comment: Published in Physics of Plasmas, http://link.aip.org/link/?PHP/18/03211

Glass Transition Temperature of Cross-Linked Epoxy Polymers: a Molecular Dynamics Study

Recently, epoxy polymers have been used in different applications and research fields due to their superior properties. In this study, the classical molecular dynamics (MD) was used to simulate formation of the epoxy polymer from cross linking of the EPON 828 with DETA curing agent, and calculate the glass transition temperature (Tg) of the material. A series of MD simulations were independently carried out on the cross-linked epoxy polymer in a range of temperatures from 600 K down to 250 K, and the density of the materials was calculated at the end of each run. Through the linear fitting between temperature and density above and below the glass transition temperature, Tg was estimated. The glass transition temperature of the pure DGEBA were also estimated through the same procedure and compared with those of the cross-linked polymer. Molecular simulations revealed significant increase in Tg of the cross-linked epoxy polymer as a result of newly created covalent bonds between individual chains. When you are citing the document, use the following link http://essuir.sumdu.edu.ua/handle/123456789/3510