Recursive Method for Nekrasov partition function for classical Lie groups

Nekrasov partition function for the supersymmetric gauge theories with general Lie groups is not so far known in a closed form while there is a definition in terms of the integral. In this paper, as an intermediate step to derive it, we give a recursion formula among partition functions, which can be derived from the integral. We apply the method to a toy model which reflects the basic structure of partition functions for BCD type Lie groups and obtained a closed expression for the factor associated with the generalized Young diagram.Comment: 21 pages;v2 comments and references adde

SHc^c Realization of Minimal Model CFT: Triality, Poset and Burge Condition

Recently an orthogonal basis of $\mathcal{W}_N$-algebra (AFLT basis) labeled by $N$-tuple Young diagrams was found in the context of 4D/2D duality. Recursion relations among the basis are summarized in the form of an algebra SH$^c$ which is universal for any $N$. We show that it has an $\mathfrak{S}_3$ automorphism which is referred to as triality. We study the level-rank duality between minimal models, which is a special example of the automorphism. It is shown that the nonvanishing states in both systems are described by $N$ or $M$ Young diagrams with the rows of boxes appropriately shuffled. The reshuffling of rows implies there exists partial ordering of the set which labels them. For the simplest example, one can compute the partition functions for the partially ordered set (poset) explicitly, which reproduces the Rogers-Ramanujan identities. We also study the description of minimal models by SH$^c$. Simple analysis reproduces some known properties of minimal models, the structure of singular vectors and the $N$-Burge condition in the Hilbert space.Comment: 1+38 pages and 12 figures. v2: typos corrected + comments adde

The first Japanese familial sotos syndrome with a novel mutation of the NSD1 gene

Sotos syndrome is caused by the haploinsufficiency of the NSD1 gene located in5q35. More than 70% of the Japanese cases carry microdeletions encompassing ofthis gene, while point mutations are common in Caucasians. Only 15 familial cases ofSotos syndrome have been reported and all cases shown to have not microdeletions butpoint mutations. We identified the first Japanese familial case (mother and 3children). They carry the same mutation at splice donor site of intron 13(IVS13+1G>A), which results in the in-frame skipping of exon 13. This is also the firstfamilial case caused by the mutation of the splice donor site. Each member of thisfamily showed variable phenotypes and mental development. The present report willcontribute to further understanding of genotype-phenotype correlation in Sotossyndrome

Effectiveness of the Gaze Direction Recognition Task for Chronic Neck Pain and Cervical Range of Motion: A Randomized Controlled Pilot Study

We developed a mental task with gaze direction recognition (GDR) by which subjects observed neck rotation of another individual from behind and attempted to recognize the direction of gaze. A randomized controlled trial was performed in test (n = 9) and control (n = 8) groups of subjects with chronic neck pain undergoing physical therapy either with or without the GDR task carried out over 12 sessions during a three-week period. Primary outcome measures were defined as the active range of motion and pain on rotation of the neck. Secondary outcome measures were reaction time (RT) and response accuracy in the GDR task group. ANOVA indicated a main effect for task session and group, and interaction of session. Post hoc testing showed that the GDR task group exhibited a significant simple main effect upon session, and significant sequential improvement of neck motion and relief of neck pain. Rapid effectiveness was significant in both groups. The GDR task group had a significant session-to-session reduction of RTs in correct responses. In conclusion, the GDR task we developed provides a promising rehabilitation measure for chronic neck pain

A Study of the Pattern of Recurrence Using Flow Cytometric DNA Analysis and PCNA/AgNOR Sequential Staining in Non-Small Cell Lung Cancer

Summary: Flow cytometric DNA analysis and PCNA/AgNOR sequential staining were performed to examine the pattern of recurrence in non-small cell lung cancer. The DNA ploidy was aneuploidy in 80.6% and diploidy in 19.4%. The mean DNA index (DI) was 1.63 for the total population, 1.62 in non-recurrent cases, and 1.64 in recurrent cases. The differences were not statistically significant, but the distribution pattern of DIs was somewhat at odds between non-recurrent cases and recurrent cases. In the analysis of recurrence in Stage I and II, the lung metastasises or the local recurrences were concentrated in the lower DI range, and the brain or the bone metastasises in the higher DI range. Thus, cases with DIs under 1.3 showed the lung metastasises or the local recurrences, and those over 1.9 were in the brain or the bone, but the cases with DI from 1.3 to 1.9 had all types of recurrences. The AgNOR scores obtained by sequential staining with PCNA provided more accurate information on recurrences. The cases with any DI and lower AgNOR scores (under about 3.0) in PCNA-negative cells showed rare recurrences. In the DI range of 1.3 to 1.9, many cases with AgNOR scores from 3.0 to 4.1 in PCNA-negative cells had the lung metastasises or the local recurrences, and those with AgNOR scores over 4.1 had those in the brain or the bone. The above information is considered valuable for the follow-up and postoperative management of Stage I and II non-small cell lung carcinoma