Closing Duality Gaps of SDPs through Perturbation

Let $({\bf P},{\bf D})$ be a primal-dual pair of SDPs with a nonzero finite duality gap. Under such circumstances, ${\bf P}$ and ${\bf D}$ are weakly feasible and if we perturb the problem data to recover strong feasibility, the (common) optimal value function $v$ as a function of the perturbation is not well-defined at zero (unperturbed data) since there are ``two different optimal values'' $v({\bf P})$ and $v({\bf D})$, where $v({\bf P})$ and $v({\bf D})$ are the optimal values of ${\bf P}$ and ${\bf D}$ respectively. Thus, continuity of $v$ is lost at zero though $v$ is continuous elsewhere. Nevertheless, we show that a limiting version ${v_a}$ of $v$ is a well-defined monotone decreasing continuous bijective function connecting $v({\bf P})$ and $v({\bf D})$ with domain $[0, \pi/2]$ under the assumption that both ${\bf P}$ and ${\bf D}$ have singularity degree one. The domain $[0,\pi/2]$ corresponds to directions of perturbation defined in a certain manner. Thus, ${v_a}$ ``completely fills'' the nonzero duality gap under a mild regularity condition. Our result is tight in that there exists an instance with singularity degree two for which ${v_a}$ is not continuous.Comment: 26 pages. Comments welcom

Study on the Teaching Strategy of an Elementary School and Improving the Program for Training Students to be Teachers of University (1) : In the Case of Japanese Language, Arithmetic and Science

　本研究は，教科内容構成の考え方に基づいて小学校の授業づくりのあり方を検討するとともに，それをふまえることで大学の教員養成プログラムの授業が具体的にどのように改善されるかを明らかにしようとしたものである。教科内容構成とは，教員養成において従来から課題とされてきた教科の内容に関わる知識・技能と教科の指導法に関わる知識・技能の分離という問題を克服するために提案されたものである。教科内容構成は，教科の内容と指導法に関わる知識・技能を統合し，それらを応用して，教師が自ら「どのような内容をどのように教えるべきか」を考え，授業づくりに取り組むことができるようになるための考え方を示すものであり，本研究では教員養成プログラムにおける具体的な授業プランを提示してそれを明らかにしていく。本稿では，特に，小学校の国語科，算数科，理科を事例として論じていくことにしたい

Study on the Teaching Strategy of an Junior High School and Improving the Program for Training Students to be teachers of University (1) : In the Case of Japanese Language, Arithmetic, Science and Social Studies

　本研究は，教科内容構成の考え方に基づいて中学校の授業づくりのあり方を検討するとともに，それをふまえることで大学の教員養成プログラムの授業が具体的にどのように改善されるかを明らかにしようとしたものである。教科内容構成とは，教員養成において従来から課題とされてきた教科の内容に関わる知識・技能と教科の指導法に関わる知識・技能の分離という問題を克服するために提案されたものである。教科内容構成は，教科の内容と指導法に関わる知識・技能を統合し，それらを応用して，教師が自ら「どのような内容をどのように教えるべきか」を考え，授業づくりに取り組むことができるようになるための考え方を示すものであり，本研究では教員養成プログラムにおける具体的な授業プランを提示してそれを明らかにしていく。本稿では，特に，中学校の国語科，数学科，理科，社会科を事例として論じていくことにしたい

Maternal GABAergic and GnRH/corazonin pathway modulates egg diapause phenotype of the silkworm Bombyx mori

Diapause represents a major developmental switch in insects and is a seasonal adaptation that evolved as a specific subtype of dormancy in most insect species to ensure survival under unfavorable environmental conditions and synchronize populations. However, the hierarchical relationship of the molecular mechanisms involved in the perception of environmental signals to integration in morphological, physiological, behavioral, and reproductive responses remains unclear. In the bivoltine strain of the silkworm Bombyx mori, embryonic diapause is induced transgenerationally as a maternal effect. Progeny diapause is determined by the environmental temperature during embryonic development of the mother. Here, we show that the hierarchical pathway consists of a gamma-aminobutyric acid (GABA)ergic and corazonin signaling system modulating progeny diapause induction via diapause hormone release, which may be finely tuned by the temperature-dependent expression of plasma membrane GABA transporter. Furthermore, this signaling pathway possesses similar features to the gonadotropin-releasing hormone (GnRH) signaling system for seasonal reproductive plasticity in vertebrates.ArticleProceedings of The National Academy of Sciences of The United States of America 118(1) : e2020028118-(2021)journal articl

Disruption of diapause induction by TALEN-based gene mutagenesis in relation to a unique neuropeptide signaling pathway in Bombyx

The insect neuropeptide family FXPRLa, which carries the Phe-Xaa-Pro-Arg-Leu-NH2 sequence at the C-terminus, is involved in many physiological processes. Although ligand–receptor interactions in FXPRLa signaling have been examined using in vitro assays, the correlation between these interactions and in vivo physiological function is unclear. Diapause in the silkworm, Bombyx mori, is thought to be elicited by diapause hormone (DH, an FXPRLa) signaling, which consists of interactions between DH and DH receptor (DHR). Here, we performed transcription activator-like effector nuclease (TALEN)-based mutagenesis of the Bombyx DH-PBAN and DHR genes and isolated the null mutants of these genes in a bivoltine strain. All mutant silkworms were fully viable and showed no abnormalities in the developmental timing of ecdysis or metamorphosis. However, female adults oviposited non-diapause eggs despite diapause-inducing temperature and photoperiod conditions. Therefore, we conclude that DH signaling is essential for diapause induction and consists of highly sensitive and specific interactions between DH and DHR selected during ligand–receptor coevolution in Bombyx mori.ArticleSCIENTIFIC REPORTS. 5:15566 (2015)journal articl

A Study on “Subject Contents Organization (SCO)” for Teacher Training Program in the Faculty of Education, Okayama University : Practice and Assessment of SCO in Elementary School and Junior High School Teacher Training Curriculum

　岡山大学教育学部・教師教育開発センターは，平成23 ～ 27年度「教員の資質向上に寄与する『大学と学校・教育委員会の協働』の実現−学校教育改善との連動で教員養成教育を進化させる−(先進的教員養成プロジェクト)」に取り組んだ。その中の教科構成学開発事業では，本学部で独自に構築・実施しているコア・カリキュラムの中での教科内容構成のあり方について，２つのプロセスから研究を行った。本稿では，平成26年度に学部教育全体で取り組んだ「教科内容構成要素に関するシラバス記述」と，部会員が平成26・27年度に授業を実践した小・中学校の教職および教科に関する科目（数学・理科・家庭科・国語科）の受講生に対して実施した「教科内容構成力」に関するアンケート調査の分析から，本学部の教科内容構成研究の特徴と課題について検討した

Impact of functional studies on exome sequence variant interpretation in early-onset cardiac conduction system diseases

Aims The genetic cause of cardiac conduction system disease (CCSD) has not been fully elucidated. Whole-exome sequencing (WES) can detect various genetic variants; however, the identification of pathogenic variants remains a challenge. We aimed to identify pathogenic or likely pathogenic variants in CCSD patients by using WES and 2015 American College of Medical Genetics and Genomics (ACMG) standards and guidelines as well as evaluating the usefulness of functional studies for determining them. Methods and Results We performed WES of 23 probands diagnosed with early-onset (<65 years) CCSD and analyzed 117 genes linked to arrhythmogenic diseases or cardiomyopathies. We focused on rare variants (minor allele frequency < 0.1%) that were absent from population databases. Five probands had protein truncating variants in EMD and LMNA which were classified as “pathogenic” by 2015 ACMG standards and guidelines. To evaluate the functional changes brought about by these variants, we generated a knock-out zebrafish with CRISPR-mediated insertions or deletions of the EMD or LMNA homologs in zebrafish. The mean heart rate and conduction velocities in the CRISPR/Cas9-injected embryos and F2 generation embryos with homozygous deletions were significantly decreased. Twenty-one variants of uncertain significance were identified in 11 probands. Cellular electrophysiological study and in vivo zebrafish cardiac assay showed that 2 variants in KCNH2 and SCN5A, 4 variants in SCN10A, and 1 variant in MYH6 damaged each gene, which resulted in the change of the clinical significance of them from “Uncertain significance” to “Likely pathogenic” in 6 probands. Conclusions Of 23 CCSD probands, we successfully identified pathogenic or likely pathogenic variants in 11 probands (48%). Functional analyses of a cellular electrophysiological study and in vivo zebrafish cardiac assay might be useful for determining the pathogenicity of rare variants in patients with CCSD. SCN10A may be one of the major genes responsible for CCSD. Translational Perspective Whole-exome sequencing (WES) may be helpful in determining the causes of cardiac conduction system disease (CCSD), however, the identification of pathogenic variants remains a challenge. We performed WES of 23 probands diagnosed with early-onset CCSD, and identified 12 pathogenic or likely pathogenic variants in 11 of these probands (48%) according to the 2015 ACMG standards and guidelines. In this context, functional analyses of a cellular electrophysiological study and in vivo zebrafish cardiac assay might be useful for determining the pathogenicity of rare variants, and SCN10A may be one of the major development factors in CCSD