2023 Fiscal Year Final Research Report
A study on construction and search of cyclic difference families for communication codes
| Project/Area Number |
21K13845
|
|---|
| Research Category |
Grant-in-Aid for Early-Career Scientists
|
| Allocation Type | Multi-year Fund |
|---|
| Review Section |
Basic Section 12040:Applied mathematics and statistics-related
|
|---|
| Research Institution | Osaka Institute of Technology |
|---|
Principal Investigator |
CHISAKI Shoko 大阪工業大学, 情報科学部, 講師 (90778250)
|
|---|
| Project Period (FY) |
2021-04-01 – 2024-03-31
|
| Keywords | 組合せデザイン / 実験計画法 / 最適性 |
|---|
| Outline of Final Research Achievements |
We have studied on combinatorial designs with structures related to cyclic difference families and their applications. We proposed a new combinatorial structure related to complete bipartite graphs (called Spanning Bipartite Block Design, SBBD) and gave the construction methods using known designs such as block designs and ordered designs. We also discussed the optimality observed when SBBD is applied to experimental design, and showed the conditions for satisfying A-optimality and E-optimality. In addition, we conducted experiments on deep learning with dropout designs and evaluated the performance.
|
| Free Research Field |
組合せデザイン理論
|
| Academic Significance and Societal Importance of the Research Achievements |
実験計画法とは，要因の効果を精度良く効率的に調べる統計的方法であり，通常の実験計画では処理集合とその集まりで計画を構成する. 本研究では処理に構造を持っている場合を考えており，完全二部グラフの辺集合を処理集合としている. 与えた完全二部グラフに関連する組合せ構造は，実験計画法に適用することでA最適計画やD最適計画を与えることができる. また，ドロップアウトデザインを用いた深層学習の実験結果は，限定的な条件下ではあるが，組合せデザインを深層学習に用いたときに現行の手法と同程度の性能が得られることを確認した点においては新規性のある試みであった.
|
