Equiangular lines in Euclidean spaces

We obtain several new results contributing to the theory of real equiangular line systems. Among other things, we present a new general lower bound on the maximum number of equiangular lines in d dimensional Euclidean space; we describe the two-graphs on 12 vertices; and we investigate Seidel matrices with exactly three distinct eigenvalues. As a result, we improve on two long-standing upper bounds regarding the maximum number of equiangular lines in dimensions d=14, and d=16. Additionally, we prove the nonexistence of certain regular graphs with four eigenvalues, and correct some tables from the literature.Comment: 24 pages, to appear in JCTA. Corrected an entry in Table

Preface

金沢大学理工研究域数物科学

Exotic complex Hadamard matrices, and their equivalence

In this paper we use a design theoretical approach to construct new, previously unknown complex Hadamard matrices. Our methods generalize and extend the earlier results of de la Harpe--Jones and Munemasa--Watatani and offer a theoretical explanation for the existence of some sporadic examples of complex Hadamard matrices in the existing literature. As it is increasingly difficult to distinguish inequivalent matrices from each other, we propose a new invariant, the fingerprint of complex Hadamard matrices. As a side result, we refute a conjecture of Koukouvinos et al. on (n-8)x(n-8) minors of real Hadamard matrices.Comment: 10 pages. To appear in Cryptography and Communications: Discrete Structures, Boolean Functions and Sequence

Residue codes of extremal Type II Z_4-codes and the moonshine vertex operator algebra

In this paper, we study the residue codes of extremal Type II Z_4-codes of length 24 and their relations to the famous moonshine vertex operator algebra. The main result is a complete classification of all residue codes of extremal Type II Z_4-codes of length 24. Some corresponding results associated to the moonshine vertex operator algebra are also discussed.Comment: 21 pages, shortened from v

The Erd\H{o}s-Ko-Rado theorem for twisted Grassmann graphs

We present a "modern" approach to the Erd\H{o}s-Ko-Rado theorem for Q-polynomial distance-regular graphs and apply it to the twisted Grassmann graphs discovered in 2005 by van Dam and Koolen.Comment: 5 page

The Neuronal EGF-Related Gene Nell2 Interacts with Macf1 and Supports Survival of Retinal Ganglion Cells after Optic Nerve Injury

Nell2 is a neuron-specific protein containing six epidermal growth factor-like domains. We have identified Nell2 as a retinal ganglion cell (RGC)-expressed gene by comparing mRNA profiles of control and RGC-deficient rat retinas. The aim of this study was to analyze Nell2 expression in wild-type and optic nerve axotomized retinas and evaluate its potential role in RGCs. Nell2-positive in situ and immunohistochemical signals were localized to irregularly shaped cells in the ganglion cell layer (GCL) and colocalized with retrogradely-labeled RGCs. No Nell2-positive cells were detected in 2 weeks optic nerve transected (ONT) retinas characterized with approximately 90% RGC loss. RT-PCR analysis showed a dramatic decrease in the Nell2 mRNA level after ONT compared to the controls. Immunoblot analysis of the Nell2 expression in the retina revealed the presence of two proteins with approximate MW of 140 and 90 kDa representing glycosylated and non-glycosylated Nell2, respectively. Both products were almost undetectable in retinal protein extracts two weeks after ONT. Proteome analysis of Nell2-interacting proteins carried out with MALDI-TOF MS (MS) identified microtubule-actin crosslinking factor 1 (Macf1), known to be critical in CNS development. Strong Macf1 expression was observed in the inner plexiform layer and GCL where it was colocalizied with Thy-1 staining. Since Nell2 has been reported to increase neuronal survival of the hippocampus and cerebral cortex, we evaluated the effect of Nell2 overexpression on RGC survival. RGCs in the nasal retina were consistently more efficiently transfected than in other areas (49% vs. 13%; n = 5, p<0.05). In non-transfected or pEGFP-transfected ONT retinas, the loss of RGCs was approximately 90% compared to the untreated control. In the nasal region, Nell2 transfection led to the preservation of approximately 58% more cells damaged by axotomy compared to non-transfected (n = 5, p<0.01) or pEGFP-transfected controls (n = 5, p<0.01)

Nel positively regulates the genesis of retinal ganglion cells by promoting their differentiation and survival during development

Peer reviewedPublisher PD

Cytoplasmic E2f4 forms organizing centres for initiation of centriole amplification during multiciliogenesis

Abnormal development of multiciliated cells is a hallmark of a variety of human conditions associated with chronic airway diseases, hydrocephalus and infertility. Multiciliogenesis requires both activation of a specialized transcriptional program and assembly of cytoplasmic structures for large-scale centriole amplification that generates basal bodies. It remains unclear, however, what mechanism initiates formation of these multiprotein complexes in epithelial progenitors. Here we show that this is triggered by nucleocytoplasmic translocation of the transcription factor E2f4. After inducing a transcriptional program of centriole biogenesis, E2f4 forms apical cytoplasmic organizing centres for assembly and nucleation of deuterosomes. Using genetically altered mice and E2F4 mutant proteins we demonstrate that centriole amplification is crucially dependent on these organizing centres and that, without cytoplasmic E2f4, deuterosomes are not assembled, halting multiciliogenesis. Thus, E2f4 integrates nuclear and previously unsuspected cytoplasmic events of centriole amplification, providing new perspectives for the understanding of normal ciliogenesis, ciliopathies and cancer