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From the nucleus, histone deacetylase 4 (HDAC4) regulates a variety of cellular processes, including growth, differentiation, and survival, by orchestrating transcriptional changes. Extracellular signals control its repressive influence mostly through regulating its nuclear-cytoplasmic shuttling. In particular, specific posttranslational modifications such(More)
The connection between Gauss quadrature rules and the algebraic eigenvalue problem for a Jacobi matrix was first exploited in the now classical paper by Golub and Welsch (Math. Comput. 23(106), 221–230, 1969). From then on many computational problems arising in the construction of (polynomial) Gauss quadrature formulas have been reduced to solving direct(More)
In this paper we study both direct and inverse eigenvalue problems for diagonal-plus-semiseparable (dpss) matrices. In particular, we show that the computation of the eigenvalues of a symmetric dpss matrix can be reduced by a congruence transformation to solving a generalized symmetric definite tridiagonal eigenproblem. Using this reduction, we devise a set(More)
The space of all proper rational functions with prescribed poles is considered. Given a set of points z i in the complex plane and the weights w i , we define the discrete inner product φ, ψ := n i=0 |w i | 2 φ(z i)ψ(z i). In this paper we derive a method to compute the coefficients of a recurrence relation generating a set of orthonormal rational basis(More)
One of the most relevant tasks in network analysis is the detection of community structures, or clustering. Most popular techniques for community detection are based on the max-imization of a quality function called modularity, which in turn is based upon particular quadratic forms associated to a real symmetric modularity matrix M , defined in terms of the(More)
Various modularity matrices appeared in the recent literature on network analysis and algebraic graph theory. Their purpose is to allow writing as quadratic forms certain combinatorial functions appearing in the framework of graph clustering problems. In this paper we put in evidence certain common traits of various modularity matrices and shed light on(More)