Structural controllability is studied for a system described in the form with auxiliary variable w:
F_x=A₁x+B₁u+C₁w, 0=A₂x+B₂u+C₂w,
where the nonzero entries of the coefficient matrices F, A_i, B_i, C_i (i=1, 2) are classified into two groups, one of which is the set of independent parameters and the other of which is the set of fixed elements; the structural controllability is defined as the generic controllability with respect to those independent parameters. Under a certain assumption based on physical considerations, a necessary and sufficient condition for the structural controllability is given. An efficient algorithm for testing it is also constructed with the aid of matroid-theoretic concepts.

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One of the major topics in the structural rigidity theory is the rigidity of graphs, which concerns about the rigidity or the flexibility of abstract models of linkages, truss structures, and so on. This article is an introductory survey about the combinatorial aspect of graph rigidity.

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統計学と代数学の新たな接点として, 計算代数統計 (computational algebraic statistics) が注目を集めている. 本稿ではこの分野の契機となった分割表のマルコフ基底に関する問題を解説するとともに, 関連する様々な問題にふれながらこの分野の今後の展望について述べる.

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The combinatorial zeta function is a type of zeta function defined for discrete structures, originating from the study of expressions for the Ihara zeta function of graphs. The Ihara zeta function is expressed in four forms: exponential, Euler, Hashimoto, and Ihara. However, the combinatorial zeta function supports only three of these representations, excluding the Ihara expression. This paper provides an overview of these expressions from the perspective of combinatorial zeta function. Finally, it examines the challenges associated with the Ihara representation and outlines the current progress toward achieving its anticipated conclusions.

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