Prepotential of N=2N=2 Supersymmetric Yang-Mills Theories in the Weak Coupling Region

We show how to obtain the explicite form of the low energy quantum effective action for $N=2$ supersymmetric Yang-Mills theory in the weak coupling region from the underlying hyperelliptic Riemann surface. This is achieved by evaluating the integral representation of the fields explicitly. We calculate the leading instanton corrections for the group SU(\nc), SO(N) and $SP(2N)$ and find that the one-instanton contribution of the prepotentials for the these group coincide with the one obtained recently by using the direct instanton caluculation.Comment: 13 pages, LaTe

Fuzzy Algebrae of the General Kaehler Coset Space G/H\otimesU(1)^k

We study the fuzzy structure of the general Kaehler coset space G/S\otimes{U(1)}^k deformed by the Fedosov formalism. It is shown that the Killing potentials satisfy the fuzzy algebrae working in the Darboux coordinates.Comment: 8 pages, LaTex, no figur

Supersymmetric extension of Moyal algebra and its application to the matrix model

We construct operator representation of Moyal algebra in the presence of fermionic fields. The result is used to describe the matrix model in Moyal formalism, that treat gauge degrees of freedom and outer degrees of freedom equally.Comment: to appear in Mod.Phys.Let

Immunization of networks with community structure

In this study, an efficient method to immunize modular networks (i.e., networks with community structure) is proposed. The immunization of networks aims at fragmenting networks into small parts with a small number of removed nodes. Its applications include prevention of epidemic spreading, intentional attacks on networks, and conservation of ecosystems. Although preferential immunization of hubs is efficient, good immunization strategies for modular networks have not been established. On the basis of an immunization strategy based on the eigenvector centrality, we develop an analytical framework for immunizing modular networks. To this end, we quantify the contribution of each node to the connectivity in a coarse-grained network among modules. We verify the effectiveness of the proposed method by applying it to model and real networks with modular structure.Comment: 3 figures, 1 tabl