70 citations
11 papers
On the shape of a tridiagonal pair
Kazumasa Nomura, Paul Terwilliger
Let denote a field and let denote a vector space over with finite positive dimension. We consider a pair of linear transformations and that sa…
Self-organization of feedforward structure and entrainment in excitatory neural networks with spike-timing-dependent plasticity
Yuko K. Takahashi, Hiroshi Kori, Naoki Masuda
Spike-timing dependent plasticity (STDP) is an organizing principle of biological neural networks. While synchronous firing of neurons is considered to be an important functional b…
The structure of a tridiagonal pair
Kazumasa Nomura, Paul Terwilliger
Let denote a field and let denote a vector space over with finite positive dimension. We consider a pair of linear transformations and that sa…
Towards a classification of the tridiagonal pairs
Kazumasa Nomura, Paul Terwilliger
Let denote a field and let denote a vector space over with finite positive dimension. Let denote the -algebra consisting of all -linear transformations f…
Sharp tridiagonal pairs
Kazumasa Nomura, Paul Terwilliger
Let denote a field and let denote a vector space over with finite positive dimension. We consider a pair of -linear transformations and tha…
Transition maps between the 24 bases for a Leonard pair
Kazumasa Nomura, Paul Terwilliger
Let denote a vector space with finite positive dimension. We consider a pair of linear transformations and that satisfy (i) and (ii) below: (i) Th…