The Witten index for one-dimensional split-step quantum walks under the non-Fredholm condition

Split-step quantum walks possess chiral symmetry. From a supercharge, that is the imaginary part of the time evolution operator, the Witten index can be naturally defined and it gives the lower bound of the dimension of eigenspaces of $1$ or $-1$. The first three authors studied the Witten index as a Fredholm index under the condition that the supercharge satisfies the Fredholm condition. In this paper, we establish the Witten index formula under the non-Fredholm condition. To derive it, we employ the spectral shift function induced by the fourth-order difference operator with a rank one perturbation on the half-line. Under two-phase limit conditions and trace conditions, the Witten index only depends on parameters of two-side limits. Especially, half-integer indices appear.Comment: 26 pages, 1 figure

Acute Cerebral Revascularization : Correlation among Preoperative CBF, Collateral Flow and Surgical Outcome

Twenty-two,patients,of,acute,cerebral,revascularization,were,analyzed,in,order,to,evaluate,various,predictors related to surgical effectiveness and outcome. These patients presented sudden neurological symptoms following occlusion of the middle cerebral artery (MCA). The left MCA was involved in 8 patients, and the right in 14 patients. Prior to surgical intervention, CT scan, serial angiography, and measurement of cerebral blood flow (CBF) were performed. STA-MCA anastomosis was completed in 21 patients, and left MCA embolectomy was performed on one patient. In the 14 patients of the effective group, the time elapsed from onset of stroke to revascularization was an average of 19.5 hours (6-72 hours). Of these patients,7 cases has a residual CBF of 24.8±1.2m1/100g/min (45% of normal CBF). Collateral flow, as judged from the preoperative angiograms, was good in 4 cases, and fair in 10 cases. In the 8 cases of the non-effective group, the time elapsed prior to the restoration of flow was an average of 8.2 hours (6-16 hours). Three cases had a residual CBF of 19.5 ±1.1m//100g/min. Collateral flow was fair in 5 cases, and poor in 3 cases. These results suggest that good preoperative collateral flow and residual CBF constitute the most accurate favorable predictors for the estimation of surgical effectiveness and outcome, and the time limits for acute cerebral revascularization is variable according to the degree of residual CBF supplied by collateral flow patterns

Mitochondrial DNA Haplogroup D4a Is a Marker for Extreme Longevity in Japan

We report results from the analysis of complete mitochondrial DNA (mtDNA) sequences from 112 Japanese semi-supercentenarians (aged above 105 years) combined with previously published data from 96 patients in each of three non-disease phenotypes: centenarians (99–105 years of age), healthy non-obese males, obese young males and four disease phenotypes, diabetics with and without angiopathy, and Alzheimer's and Parkinson's disease patients. We analyze the correlation between mitochondrial polymorphisms and the longevity phenotype using two different methods. We first use an exhaustive algorithm to identify all maximal patterns of polymorphisms shared by at least five individuals and define a significance score for enrichment of the patterns in each phenotype relative to healthy normals. Our study confirms the correlations observed in a previous study showing enrichment of a hierarchy of haplogroups in the D clade for longevity. For the extreme longevity phenotype we see a single statistically significant signal: a progressive enrichment of certain “beneficial” patterns in centenarians and semi-supercentenarians in the D4a haplogroup. We then use Principal Component Spectral Analysis of the SNP-SNP Covariance Matrix to compare the measured eigenvalues to a Null distribution of eigenvalues on Gaussian datasets to determine whether the correlations in the data (due to longevity) arises from some property of the mutations themselves or whether they are due to population structure. The conclusion is that the correlations are entirely due to population structure (phylogenetic tree). We find no signal for a functional mtDNA SNP correlated with longevity. The fact that the correlations are from the population structure suggests that hitch-hiking on autosomal events is a possible explanation for the observed correlations

Curated genome annotation of Oryza sativa ssp. japonica and comparative genome analysis with Arabidopsis thaliana

We present here the annotation of the complete genome of rice Oryza sativa L. ssp. japonica cultivar Nipponbare. All functional annotations for proteins and non-protein-coding RNA (npRNA) candidates were manually curated. Functions were identified or inferred in 19,969 (70%) of the proteins, and 131 possible npRNAs (including 58 antisense transcripts) were found. Almost 5000 annotated protein-coding genes were found to be disrupted in insertional mutant lines, which will accelerate future experimental validation of the annotations. The rice loci were determined by using cDNA sequences obtained from rice and other representative cereals. Our conservative estimate based on these loci and an extrapolation suggested that the gene number of rice is ~32,000, which is smaller than previous estimates. We conducted comparative analyses between rice and Arabidopsis thaliana and found that both genomes possessed several lineage-specific genes, which might account for the observed differences between these species, while they had similar sets of predicted functional domains among the protein sequences. A system to control translational efficiency seems to be conserved across large evolutionary distances. Moreover, the evolutionary process of protein-coding genes was examined. Our results suggest that natural selection may have played a role for duplicated genes in both species, so that duplication was suppressed or favored in a manner that depended on the function of a gene