Complex spherical codes with two inner products

A finite set $X$ in a complex sphere is called a complex spherical $2$-code if the number of inner products between two distinct vectors in $X$ is equal to $2$. In this paper, we characterize the tight complex spherical $2$-codes by doubly regular tournaments, or skew Hadamard matrices. We also give certain maximal 2-codes relating to skew-symmetric $D$-optimal designs. To prove them, we show the smallest embedding dimension of a tournament into a complex sphere by the multiplicity of the smallest or second-smallest eigenvalue of the Seidel matrix.Comment: 10 pages, to appear in European Journal of Combinatoric

Complex spherical codes with three inner products

Let $X$ be a finite set in a complex sphere of $d$ dimension. Let $D(X)$ be the set of usual inner products of two distinct vectors in $X$. A set $X$ is called a complex spherical $s$-code if the cardinality of $D(X)$ is $s$ and $D(X)$ contains an imaginary number. We would like to classify the largest possible $s$-codes for given dimension $d$. In this paper, we consider the problem for the case $s=3$. Roy and Suda (2014) gave a certain upper bound for the cardinalities of $3$-codes. A $3$-code $X$ is said to be tight if $X$ attains the bound. We show that there exists no tight $3$-code except for dimensions $1$, $2$. Moreover we make an algorithm to classify the largest $3$-codes by considering representations of oriented graphs. By this algorithm, the largest $3$-codes are classified for dimensions $1$, $2$, $3$ with a current computer.Comment: 26 pages, no figur

A characterization of skew Hadamard matrices and doubly regular tournaments

We give a new characterization of skew Hadamard matrices of size $n$ in terms of the data of the spectra of tournaments of size $n-2$.Comment: 9 page

Use of Particle Multi-Swarm Optimization for Handling Tracking Problems

As prior work, several multiple particle swarm optimizers with sensors, that is, MPSOS, MPSOIWS, MCPSOS, and HPSOS, were proposed for handling tracking problems. Due to more efficient handling of these problems, in this chapter we innovate the strategy of information sharing (IS) to these existing methods and propose four new search methods that are multiple particle swarm optimizers with sensors and information sharing (MPSOSIS), multiple particle swarm optimizers with inertia weight with sensors and information sharing (MPSOIWSIS), multiple canonical particle swarm optimizers with sensors and information sharing (MCPSOSIS), and hybrid particle swarm optimizers with sensors and information sharing (HPSOSIS). Based on the added strategy of information sharing, the search ability and performance of these methods are improved, and it is possible to track a moving target promptly. Therefore, the search framework of particle multi-swarm optimization (PMSO) is established. For investigating search ability and characteristics of the proposed methods, several computer experiments are carried out to handle the tracking problems of constant speed I type, variable speed II type, and variable speed III type, which are a set of benchmark tracking problems. Owing to analyze experimental results, we reveal the outstanding search performance and tracking ability of the proposed search methods

HNF-1β過剰発現を呈する卵巣明細胞癌においてGSK-3βは新たなシグナル伝達経路を介在する

Deubiquitinase USP28 is a target gene of the transcription factor HNF1 homeobox β (HNF-1β), which promotes the survival of ovarian clear cell carcinoma (OCCC) cell lines. However, the pharmacological inhibition of HNF-1β can cause several adverse effects as it is abundantly expressed in numerous organ systems, including the kidney, liver, pancreas and digestive tract. Therefore, small interfering RNA (siRNA) screening was performed in the current study to identify other potential downstream targets of the HNF-1β-mediated pathway. The results revealed that glycogen synthase kinase-3β (GSK-3β) may be a potential downstream target affecting cell viability. To further clarify the effects of GSK-3β, two human OCCC cell lines, TOV-21G (HNF-1β overexpressing line) and ES2 (HNF-1β negative) were transfected with siRNA targeting GSK-3β or control vectors. Loss-of-function studies using RNAi-mediated gene silencing indicated that HNF-1β facilitated GSK-3β expression, resulting in the loss of phosphorylated nuclear factor-κB (p-NFκB) and the reduction of TOV-21G cell proliferation. The cell proliferation assay also revealed that GSK-3β inhibitors rescued the effects of HNF-1β silencing on cell viability in a dose-dependent manner. Furthermore, the GSK-3β inhibitor, AR-A014418, effectively inhibited tumor cell proliferation in a xenograft mouse model. In conclusion and to the best of our knowledge, the current study was the first to determine that GSK-3β is a target gene of HNF-1β. In addition, the results of the present study revealed the novel HNF-1β-GSK-3β-p-NFκB pathway, occurring in response to DNA damage. Targeting this pathway may therefore represent a putative, novel, anticancer strategy in patients with OCCC.博士（医学）・甲第785号・令和3年3月15日Copyright: © Kawaharaet al. This is an open access article distributed under theterms of CreativeCommons Attribution License(https://creativecommons.org/licenses/by-nc-nd/4.0/)