Seminar Schedule のバックアップ(No.6)

数理工学特別セミナー / AMP PhD Seminar
2019年度秋学期 / Fall 2019 †

10月16日 / October 16 †

The first meeting of the semester.
Let us gather, greet new members to the Department, and set a plan for the semester before us.
We can play some warm-up board games to get to know each other, and hear some information on the ICT-Innovations event from experienced participants.

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10月21日 / October 21 †

Speaker: Shoya Motonaga
Dynamical Systems Group
Topic: TBA

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10月28日 / October 28 †

Speaker: Kaito Ito
Control Systems Theory Group
Topic: Stochastic dynamical models with heavy-tailed noise

In order to evaluate the effect of probabilistic uncertainty, stochastic dynamical models play an important role. In particular, a linear dynamical system driven by the Wiener process is a popular framework. Although this framework is tractable analytically, it cannot represent outliers due to the Gaussianity. On the other hand, a modeling method for uncertainty that utilizes stable processes instead of the Wiener process is proposed recently. This method can model dynamics equipped with extreme outliers, and the model has similar mathematical properties to the linear Gaussian model. Then we first explain the non-Gaussian framework and its properties. In addition, we introduce our recent work using this framework. This work provides the error analysis for linearization of nonlinear feedback systems.

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11月6日 / November 6 †

Speaker: Naveed Ahmed Azam
Discrete Mathematics Group

Topic:
Counting Tree-Like Graphs with a Given Number of Vertices and Self-loops

Graph enumeration with given constraints is an interesting problem considered to be one of the fundamental problems in graph theory, with many applications in the natural sciences and engineering, such as bio-informatics and computational chemistry. For any two integers n ≥ 1 and ∆ ≥ 0, we propose a method to count all non-isomorphic trees with n vertices, ∆ self-loops, and no multi-edges, based on dynamic programming. To achieve this goal, we count the number of non-isomorphic rooted trees with n vertices, ∆ self-loops and no multi-edges, in O(n^2(n + ∆(n + ∆ · min{n, ∆}))) time and O(n^2(∆^2 + 1)) space, since every tree can be uniquely viewed as a rooted tree by either regarding its unicentroid as the root, or in the case of bicentroid, by introducing a virtual vertex on the bicentriod and assuming the virtual vertex to be the root.

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11月18日 / November 18 †

Speaker: Shogo Yamanaka
Dynamical Systems Group
Topic: Convergent normalization and integrability of two-dimensional systems of differential equations

We consider systems of differential equations with equilibrium points. These systems are formally transformed to Poincaré-Dulac normal forms, but the normalization may not be convergent. Such an convergent normalization is a classical problem that dates back to Poincaré. Zung proved that analytically integrable systems of differential equations have convergent normalizations. In this talk, we prove thet a special class of two-dimensional systems have no convergent normalizations so that they are not integrable.

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