Dimensional Reduction of Seiberg-Witten Monopole Equations, N=2 Noncommutative Supersymmetric Field Theories and Young Diagrams

We investigate the Seiberg-Witten monopole equations on noncommutative(N.C.) R^4 at the large N.C. parameter limit, in terms of the equivariant cohomology. In other words, N}=2 supersymmetric U(1) gauge theories with hypermultiplet on N.C. R}^4 are studied. It is known that after topological twisting partition functions of N}>1 supersymmetric theories on N.C. R^2D are invariant under N.C.parameter shift, then the partition functions can be calculated by its dimensional reduction. At the large N.C. parameter limit, the Seiberg-Witten monopole equations are reduced to ADHM equations with the Dirac equation reduced to 0 dimension. The equations are equivalent to the dimensional reduction of non-Abelian U(N) Seiberg-Witten monopole equations in N -> \infty. The solutions of the equations are also interpreted as a configuration of brane anti-brane system. The theory has global symmetries under torus actions originated in space rotations and gauge symmetries. We investigate the Seiberg-Witten monopole equations reduced to 0 dimension and the fixed point equations of the torus actions. We show that the Dirac equation reduced to 0 dimension is trivial when the fixed point equations and the ADHM equations are satisfied. For finite N, it is known that the fixed points of the ADHM data are isolated and are classified by the Young diagrams. We give a new proof of this statement by solving the ADHM equations and the fixed point equations concretely and by giving graphical interpretations of the field components and these equations.Comment: v2: 28+1 pages, 13 figures, appendix for convention added, references added, some descriptions improved, v3: eq.(113),(117) corrected, v4: 29+1 pages, minor correction

BPS Analysis of the Charged Soliton Solutions of D-brane Worldvolume Theory from the Viewpoint of Target-space Supersymmetry

We investigate BPS properties of the charged soliton solutions of D-brane worldvolume theory, which is described by the supersymmetric Dirac-Born-Infeld action, by means of the N=2 target-space supersymmetry algebra. Our results agree with those obtained previously. We also extend our BPS analysis to the case where axion background exists.Comment: 11 pages, LaTeX, 3 eps figures, v2: references corrected, a note added, minor changes, v3: references corrected, notes added, equations added, discussions adde

Comparison Table of Jiguge Version of Shuowen Jiezi and Its Derived Versions

「四庫全書本『説文解字繫傳』に見える小篆異体字」[1]では、清初に出版された汲古閣本説文解字1と四庫全書薈要の小篆を全数比較し、大徐本説文解字を四庫全書に収めるにあたり、少なくとも小篆字形に関しては意図的な改変は殆ど無いとした。 その後、董婧宸氏との議論の結果、この評価には修正が必要であることが明らかとなった。本資料は、この議論の材料と、議論の中で見つかった注意点を整理する。In the article “Investigation of the Seal Variants Specific to Siku Quanshu Version of Shuowen Jiezi Xizhuan” [1], all heading Seal characters in the Jiguge version (汲古閣本) of Shuowen Jiezi (説文解字) and those of Siku Quanshu Huiyao (四庫全書薈要) are compared and concluded that Siku Quanshu project had applied few intentional modifications to include DaXu book (大徐本) of Shuowen Jiezi in its collection. In later, during the discussion with Professor Dong Jingchen (董婧宸), this conclusion needs to be cross-checked with other materials and should be updated. In this document, the points to be updated are summarized.大徐本説文解字の汲古閣本の系列の変化を見る為、汲古閣本(早稲田大学所蔵)、汲古閣重刊本(京都大学所蔵)、四庫全書薈要摛藻堂本、四庫全書文淵閣本、四庫全書文津閣本の小篆を全て切り出し、対照表とした。「東洋学へのコンピュータ利用」第32回研究セミナー(2020/03/06)での発表資料に対し、早大所蔵本の画像を所蔵機関の許可を得た上で追加した(早稲田大学図書館　許可19-410号)。 本資料の作成にあたり科研費課題番号16K004600A, 19K12716 の補助を受けました

New Constructions for Query-Efficient Locally Decodable Codes of Subexponential Length

A $(k,\delta,\epsilon)$-locally decodable code $C: F_{q}^{n} \to F_{q}^{N}$ is an error-correcting code that encodes each message $\vec{x}=(x_{1},x_{2},...,x_{n}) \in F_{q}^{n}$ to $C(\vec{x}) \in F_{q}^{N}$ and has the following property: For any $\vec{y} \in {\bf F}_{q}^{N}$ such that $d(\vec{y},C(\vec{x})) \leq \delta N$ and each $1 \leq i \leq n$, the symbol $x_{i}$ of $\vec{x}$ can be recovered with probability at least $1-\epsilon$ by a randomized decoding algorithm looking only at $k$ coordinates of $\vec{y}$. The efficiency of a $(k,\delta,\epsilon)$-locally decodable code $C: F_{q}^{n} \to F_{q}^{N}$ is measured by the code length $N$ and the number $k$ of queries. For any $k$-query locally decodable code $C: F_{q}^{n} \to F_{q}^{N}$, the code length $N$ is conjectured to be exponential of $n$, however, this was disproved. Yekhanin [In Proc. of STOC, 2007] showed that there exists a 3-query locally decodable code $C: F_{2}^{n} \to F_{2}^{N}$ such that $N=\exp(n^{(1/\log \log n)})$ assuming that the number of Mersenne primes is infinite. For a 3-query locally decodable code $C: F_{q}^{n} \to F_{q}^{N}$, Efremenko [ECCC Report No.69, 2008] reduced the code length further to $N=\exp(n^{O((\log \log n/ \log n)^{1/2})})$, and also showed that for any integer $r>1$, there exists a $k$-query locally decodable code $C: F_{q}^{n} \to F_{q}^{N}$ such that $k \leq 2^{r}$ and $N=\exp(n^{O((\log \log n/ \log n)^{1-1/r})})$. In this paper, we present a query-efficient locally decodable code and show that for any integer $r>1$, there exists a $k$-query locally decodable code $C: F_{q}^{n} \to F_{q}^{N}$ such that $k \leq 3 \cdot 2^{r-2}$ and $N=\exp(n^{O((\log \log n/ \log n)^{1-1/r})})$.Comment: 13 pages, 1 figure, 2 table

Partition functions of Supersymmetric Gauge Theories in Noncommutative R^{2D} and their Unified Perspective

We investigate cohomological gauge theories in noncommutative R^{2D}. We show that vacuum expectation values of the theories do not depend on noncommutative parameters, and the large noncommutative parameter limit is equivalent to the dimensional reduction. As a result of these facts, we show that a partition function of a cohomological theory defined in noncommutative R^{2D} and a partition function of a cohomological field theory in R^{2D+2} are equivalent if they are connected through dimensional reduction. Therefore, we find several partition functions of supersymmetric gauge theories in various dimensions are equivalent. Using this technique, we determine the partition function of the N=4 U(1) gauge theory in noncommutative R^4, where its action does not include a topological term. The result is common among (8-dim, N=2), (6-dim, N=2), (2-dim, N=8) and the IKKT matrix model given by their dimensional reduction to 0-dim.Comment: 45 pages, no figures, Appendices B and C are added, changes in the text, references are adde

Paradise Lost: The relationships between neurological and psychological changes in nicotine-dependent patients

The neural reward circuit and cognitive distortion play an important role in addiction; however, the relationship between the two has not yet been addressed. In this article, we review recent findings on nicotine dependence and propose a novel hypothesis. Previous research using functional magnetic resonance imaging (fMRI) has shown that while activation of the reward circuit (ventral striatum) appears in response to tobacco-related rewards in nicotine dependence, responses to rewards other than tobacco (e.g. food and money) are reduced. Moreover, this change is observed at the very early stages of smoking, even when a person has smoked fewer than 10 cigarettes in his/her lifetime. Thus, we propose the following hypothesis, called the Paradise Lost theory: given addicts’ lower ventral striatal responses to non-tobacco rewards, nicotine addiction disables smokers from sensing the pleasures of ordinary life (the Paradise Lost state). However, since smokers do not notice this, they produce an overestimation of tobacco (cognitive distortion), such that they do not have many pastimes other than smoking or feel that quitting smoking would reduce the happiness and pleasure and increase the difficulty of life. Cognitive distortion thus makes it difficult for smokers to take the initiative to quit smoking and even causes relapse after smoking cessation. This theory furthers our understanding of addiction and could improve our approach to the prevention and treatment of addiction

説文解字篆韻譜 - 説文解字繫傳 小篆対照表

本資料は、『説文解字篆韻譜』の 10 巻本(馮桂芬翻刻本)、5 巻本(種善堂本・徐之昌旧蔵、四部叢刊影印)と、『説文解字繫傳』(いわゆる小徐本)の述古堂本・祁寯藻本、宋本『説文解字』(いわゆる大徐本)の岩崎本の見出し字の対照表である。「東洋学へのコンピュータ利用」第 29 回研究セミナー(2018/03/09)での発表資料に対し、部分的な画像差し替えと若干の加筆を加えている。 本資料の作成にあたり、科研費課題番号 16K004600A の補助を受けています