These are notes from introductory survey lectures given at the Institute for Studies in Theoretical Physics and Mathematics (IPM), Teheran, in 2008 and 2010. We present the definition and the fundamental properties of Fomin-Zelevinsky’s cluster algebras. Then we introduce quiver representations and show how they can be used to construct cluster variables, which are the canonical generators of c...

It is proved that any cluster-tilted algebra defined in the cluster category C(H) has the same representation type as the initial hereditary algebra H . For any valued quiver (Γ,Ω), an injection from the subset PI(Ω) of the cluster category C(Ω) consisting of indecomposable preprojective objects, preinjective objects and the first shifts of indecomposable projective modules to the set of cluste...

present survey studies intensity of heavy metals pollution (ca, fe, ni, cd, pb, zn, as, hg) in the sediments of bamdezh wetland. the main objective of the study is to quantify heavy metal pollution intensity in the wetland. other objectives of the study are separation of natural and anthropogenic heavy metal pollution and identification of the origin of heavy metals. results of this study shows...

One of the most important problems in modern finance is finding efficient ways to summarize and visualize the stock market data to give individuals or institutions useful information about the market behavior for investment decisions. The enormous amount of valuable data generated by the stock market has attracted researchers to explore this problem domain using different methodologies. This pa...

In this paper, we devise an efficient algorithm for clustering market-basket data. Different from those of the traditional data, the features of market-basket data are known to be of high dimensionality, sparsity, and with massive outliers. Clustering transactions across different levels of the taxonomy is of great importance for marketing strategies as well as for the result representation of ...

Background With the development of psychiatric science the group of Personality Disorders becomes clearly defined and within the various existing classifications a well-defined group stands out, characterized mainly by the cold affect and by the lack of empathy. The historical overview of the Paranoid and the Schizoid Personality Disorders reveals extremely high historical (temporal) stability ...

We show that the quotients of the continuous cluster category Cπ and the rational subcategory X modulo the additive subcategory generated by any cluster are abelian categories and we show that they are isomorphic to categories of infinite and finite length modules, respectively, over the endomorphism ring of the cluster. These theorems extend the theorems of Caldero-ChapotonSchiffler and Buan-M...

We show that the quotients of the continuous cluster category Cπ and the rational subcategory X modulo the additive subcategory generated by any cluster are abelian categories and we show that they are isomorphic to categories of infinite and finite length modules, respectively, over the endomorphism ring of the cluster. These theorems extend the theorems of Caldero-ChapotonSchiffler and Buan-M...

We provide a graded and quantum version of the category of rooted cluster algebras introduced by Assem, Dupont and Schiffler and show that every graded quantum cluster algebra of infinite rank can be written as a colimit of graded quantum cluster algebras of finite rank. As an application, for each k we construct a graded quantum infinite Grassmannian admitting a cluster algebra structure, exte...