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Many algorithms have been developed for NP-hard problems on graphs with small treewidth k . For example, all problems that are expressible in linear extended monadic second order can be solved in linear time on graphs of bounded treewidth. It turns out that the bottleneck of many algorithms for NP-hard problems is the computation of a tree decomposition of width O ( k ) . In particular, by the bidimensional theory, there are many linear extended monadic second order problems that can be solved on n -vertex planar graphs with treewidth k in a time linear in n and subexponential in k if a tree decomposition of width O ( k ) can be found in such a time. We present the first algorithm that, on n -vertex planar graphs with treewidth k , finds a tree decomposition of width O ( k ) in such a time. In more detail, our algorithm has a running time of O ( n k 2 log ⁡ k ) . We show the result as a special case of a result concerning so-called weighted treewidth of weighted graphs. [ABSTRACT FROM AUTHOR]

Abstract: The status of the first invested object at the beginning of psychic life is a complex, scientific, philosophical as well as human enigma. The authors have a vision that is both personal and inspired by the broad metapsychological field and this field has usually been used for a descriptive or even explanatory support for inquiry. The support of their vision is based on a three-part concept, which brings together pictographic representation processes in the sense of “containing”, the reflecting role of the external object and bidimensionality. Their modeling describes the primary object in the form of a psychological experience of nondifferentiation between the constantly evolving subject and his environment, initiated with an originating framework at the beginning of life, which then gradually becomes, and in a way that varies with the individual, the ultimate primary trace. [Copyright &y& Elsevier]

A series of hybrid electrode materials, poly(3,4-ethylenedioxythiophene)/V2O5, has been synthesized using an oxidative insertion and polymerization reaction. FTIR, X-ray diffraction and transmission electron microscopy studies have shown that the incorporation of polymer between V2O5 slabs leads to an enhanced bidimensionality. The electrochemical lithium capacity has been increased up to ∼330 mAh/g at the second discharge in the range of 2.0–4.4 V vs. Li. This improvement of electrochemical performance compared to pristine V2O5 is attributed to the higher electric conductivity and enhanced bidimensionality. [Copyright &y& Elsevier]