Nagoya Keizai University

ABSTRACTDownarowicz and Maass [7] proposed topological ranks for all homeomorphic Cantor minimal dynamical systems using properly ordered Bratteli diagrams. In this study, we adopt this definition to the case of the essentially minimal zero-dimensional systems. We consider the cases in which topological ranks are 2 and unique minimal sets are fixed points. Akin and Kolyada [2], had shown that if the unique minimal set of an essentially minimal system is a fixed point, then the system must be proximal. The finite topological rank implies expansiveness; furthermore, in the case of proximal Cantor systems with topological rank 2, the expansiveness is always from the lowest degree. Rank 2 proximal Cantor systems are residually scrambled. We present a necessary and sufficient condition for the unique ergodicity of these systems. In addition, we show that the number of ergodic measures of the systems that are topologically mixing can be 1 and 2. Moreover, we present examples that are topologically weakly mixing, not topologically mixing, and uniquely ergodic. Finally, we show that the number of ergodic measures of the systems that are not weakly mixing can be 1 and 2.

The ventromedial hypothalamus (VMH) regulates glucose and energy metabolism in mammals. Optogenetic stimulation of VMH neurons that express steroidogenic factor 1 (SF1) induces hyperglycemia. However, leptin acting via the VMH stimulates whole-body glucose utilization and insulin sensitivity in some peripheral tissues, and this effect of leptin appears to be mediated by SF1 neurons. We examined the effects of activation of SF1 neurons with DREADD (designer receptors exclusively activated by designer drugs) technology. Activation of SF1 neurons by an intraperitoneal injection of clozapine-N-oxide (CNO), a specific hM3Dq ligand, reduced food intake and increased energy expenditure in mice expressing hM3Dq in SF1 neurons. It also increased whole-body glucose utilization and glucose uptake in red-type skeletal muscle, heart, and interscapular brown adipose tissue, as well as glucose production and glycogen phosphorylase a activity in the liver, thereby maintaining blood glucose levels. During hyperinsulinemic-euglycemic clamp, such activation of SF1 neurons increased insulin-induced glucose uptake in the same peripheral tissues and tended to enhance insulin-induced suppression of glucose production by suppressing gluconeogenic gene expression and glycogen phosphorylase a activity in the liver. DREADD technology is thus an important tool for studies of the role of the brain in the regulation of insulin sensitivity in peripheral tissues.

本論文では, 区間の境界があいまいなデータをファジィ区間データと呼び, それを用いた期待効用値と情報量の分析を考察している.ここでは, Zadehにより定義されたファジィ事象の確率概念を用いて, ファジィ区間データに基づく期待効用値と情報量を定式化している.しかしながら, ファジィ区間データのメンバシップ関数を直接的に取り扱う手法では, メンバシップ関数の形状を正確に把握する必要があるということと, 計算が非常に複雑となり効率的ではないという問題がある.この問題を解決するため, 我々はメンバシップ関数の中心値を代表値として取り扱う実用的な手法を提案する.これにより, ファジィ区間データが与えられたときでも, 通常の期待効用分析とさほど変わらない手法を示すことができる.また, 実際のファジィ区間データが与えられる状況では, 常に左右対称形のメンバシップ関数でファジィ区間データを表現できるとは限らないので, 台形型メンバシップ関数が左右非対称な場合を設定し, 数値例を実行した.その結果, 我々が提案している手法の有用性を示すことができた.