Elastic properties of small-world spring networks

We construct small-world spring networks based on a one dimensional chain and study its static and quasistatic behavior with respect to external forces. Regular bonds and shortcuts are assigned linear springs of constant $k$ and $k'$, respectively. In our models, shortcuts can only stand extensions less than $\delta_c$ beyond which they are removed from the network. First we consider the simple cases of a hierarchical small-world network and a complete network. In the main part of this paper we study random small-world networks (RSWN) in which each pair of nodes is connected by a shortcut with probability $p$. We obtain a scaling relation for the effective stiffness of RSWN when $k=k'$. In this case the extension distribution of shortcuts is scale free with the exponent -2. There is a strong positive correlation between the extension of shortcuts and their betweenness. We find that the chemical end-to-end distance (CEED) could change either abruptly or continuously with respect to the external force. In the former case, the critical force is determined by the average number of shortcuts emanating from a node. In the latter case, the distribution of changes in CEED obeys power laws of the exponent $-\alpha$ with $\alpha \le 3/2$.Comment: 16 pages, 14 figures, 1 table, published versio

Phytoplankton as bio-indicator of water quality in Sefid Rud River, Iran (South of Caspian Sea)

Phytoplankton are the first bio- indicators of pollution in aquatic ecosystems. Phytoplankton assemblage and aquatic ecosystems are always influenced by environmental factors therefore these environmental changes and threats must be understood in any ecosystem. Phytoplanktons are inexpensive and readily available bio- indicators. In the present study, phytoplankton were used to study the Sefid Rud River (the south Caspian Sea), in Iran. Three sampling sites were selected up to 25- 30 km from the River estuary. Samplings were carried out from June through September 2009. Phytoplankton samples were collected by phytoplankton sampler net with mesh size of 25µm. Water parameters including transparency, temperature, water velocity and pH were measured during the survey. Mean water temperature was 26.9 ± 7.7 ºc, velocity 0.13 ± 0.01 m/s, Secchi disk transparency and pH were 45cm and 7.4, respectively. Phytoplankton assemblage comprised Bacillariophyceae (61.2٪), Chlorophyceae (31.6%), Euglenophyceae (5.0%) and Cyanophyceae (2.23٪). Significant differences were observed in diversity and abundance of four main groups of phytoplankton between sampling stages. Significant positive correlations were detected between transparency and abundance of Chlorophyta, while negative correlations were found between transparency and Euglenophyceae abundances. The highest abundance of Euglena and Phacus (Euglenophyceae) occurred at high turbidity while maximum abundance of Pediastrum and Scenedesmus (Chlorophyceae) correlated with high water transparencies. Genus Oscillatoria (Cyanophyceae) was observed (abundance 18%) only in station 2 and influenced by agricultural activities. The study showed those phytoplankton are suitable bio- indicators of environmental changes which may threaten the Sefid Rud River and the Caspian Sea

First record of Ebria tripartita (Schumann) Lemmermann, 1899 from south of the Caspian Sea

Ebria tripartita (Schumann) Lemmermann, 1899, a non-photosynthetic flagellate algae was identified from the southern coast of the Caspian Sea in December 2012. Water temperature at the sampling time was 10 ºC The average concentration of nitrate, phosphate and silicate were 0.7, 0.1 and 1.8 mg.l -1 respectively at the time when species was observed. Total observed phytoplankton cells was 3 × 106 cells.l -1, of which E. tripartita constitute 2×10 3 cells.l -1 representing only 0.75% of phytoplankton community

Banishayban in the Islamic era

Genealogists have related BaniShayban origin from Mosni-bin HarithaShaybani to prophet’s 19th ancestor called Nazar. Mosni-bin HarithaShaybani was a significant character who played a basic role in the events of early Islam. He managemd to earn reputation among Arabs due to his victory over the army of Iran in Zuqar battle, so that the first and second caliphs let him attack Iranian borders with other Islamic commanders.In addition to Zuqar battle under commandment of Mosni-bin HarithaShaybani, BaniShayban tribe had several battles with Shahrbaraz, Iranian self-styled king, including battle of chains and battle of Ullais during 11 to 14 A.H years. They participated in battle of the bridge with Abu Obadiah, another commander of the Muslim Arabs. They were also present at the battle of Boveib. The commander of Shaybanis attended the battle of al-Qādisiyyah with several injuries on his body and wished to participate in the battle of Jalula, but his life came to its end before that.In the days of Imam Ali, Shaybanis helped him and were his commanders, particularly in the  battle of Siffin, because of being allied with the descendants of Abu Talib. Although some of them stood against Imam Ali, some others lost their lives guilty of friendship with him. They acquired high positions at the time of Umayyad and Bani Abbas and were even appointed in Armenia.The most important question is whether Shaybanis had any relationships with caliphs in early Islam; what role did they play in early Muslim conquests; and what positions were they assigned in the early centuries of Islam? The present study investigates the role of Shaybanis in Islamic era, particularly during early Islam as well as Umayyad and Bani Abbas reign.Keywords: BaniShayban, Mosni-bin Haritha, Iranian army, Umayyad, Bani Abba

Spanning Trees in Random Satisfiability Problems

Working with tree graphs is always easier than with loopy ones and spanning trees are the closest tree-like structures to a given graph. We find a correspondence between the solutions of random K-satisfiability problem and those of spanning trees in the associated factor graph. We introduce a modified survey propagation algorithm which returns null edges of the factor graph and helps us to find satisfiable spanning trees. This allows us to study organization of satisfiable spanning trees in the space spanned by spanning trees.Comment: 12 pages, 5 figures, published versio

Simplifying Random Satisfiability Problem by Removing Frustrating Interactions

How can we remove some interactions in a constraint satisfaction problem (CSP) such that it still remains satisfiable? In this paper we study a modified survey propagation algorithm that enables us to address this question for a prototypical CSP, i.e. random K-satisfiability problem. The average number of removed interactions is controlled by a tuning parameter in the algorithm. If the original problem is satisfiable then we are able to construct satisfiable subproblems ranging from the original one to a minimal one with minimum possible number of interactions. The minimal satisfiable subproblems will provide directly the solutions of the original problem.Comment: 21 pages, 16 figure

Module homomorphisms and multipliers on locally compact quantum groups

For a Banach algebra $A$ with a bounded approximate identity, we investigate the $A$-module homomorphisms of certain introverted subspaces of $A^*$, and show that all $A$-module homomorphisms of $A^*$ are normal if and only if $A$ is an ideal of $A^{**}$. We obtain some characterizations of compactness and discreteness for a locally compact quantum group \G. Furthermore, in the co-amenable case we prove that the multiplier algebra of \LL can be identified with \MG. As a consequence, we prove that \G is compact if and only if \LUC={\rm WAP}(\G) and \MG\cong\mathcal{Z}({\rm LUC}(\G)^*); which partially answer a problem raised by Volker Runde.Comment: The detailed proof of Lemma 4.1 is added in addendum. 11 pages, To appear in J. Math. Anal. App

Intermittent exploration on a scale-free network

We study an intermittent random walk on a random network of scale-free degree distribution. The walk is a combination of simple random walks of duration $t_w$ and random long-range jumps. While the time the walker needs to cover all the nodes increases with $t_w$, the corresponding time for the edges displays a non monotonic behavior with a minimum for some nontrivial value of $t_w$. This is a heterogeneity-induced effect that is not observed in homogeneous small-world networks. The optimal $t_w$ increases with the degree of assortativity in the network. Depending on the nature of degree correlations and the elapsed time the walker finds an over/under-estimate of the degree distribution exponent.Comment: 12 pages, 3 figures, 1 table, published versio

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