Wreath determinants for group-subgroup pairs

The aim of the present paper is to generalize the notion of the group determinants for finite groups. For a finite group $G$ of order $kn$ and its subgroup $H$ of order $n$, one may define an $n$ by $kn$ matrix $X=(x_{hg^{-1}})_{h\in H,g\in G}$, where $x_g$ ($g\in G$) are indeterminates indexed by the elements in $G$. Then, we define an invariant $\Theta(G,H)$ for a given pair $(G,H)$ by the $k$-wreath determinant of the matrix $X$, where $k$ is the index of $H$ in $G$. The $k$-wreath determinant of $n$ by $kn$ matrix is a relative invariant of the left action by the general linear group of order $k$ and right action by the wreath product of two symmetric groups of order $k$ and $n$. Since the definition of $\Theta(G,H)$ is ordering-sensitive, representation theory of symmetric groups are naturally involved. In this paper, we treat abelian groups with a special choice of indeterminates and give various examples of non-abelian group-subgroup pairs.Comment: 12 pages, 2 figure

Evaluating EUV mask pattern imaging with two EUV microscopes

Aerial image measurement plays a key role in the development of patterned reticles for each generation of lithography. Studying the field transmitted (reflected) from EUV masks provides detailed information about potential disruptions caused by mask defects, and the performance of defect repair strategies, without the complications of photoresist imaging. Furthermore, by measuring the continuously varying intensity distribution instead of a thresholded, binary resist image, aerial image measurement can be used as feedback to improve mask and lithography system modeling methods. Interest in EUV, at-wavelength, aerial image measurement lead to the creation of several research tools worldwide. These tools are used in advanced mask development work, and in the evaluation of the need for commercial at-wavelength inspection tools. They describe performance measurements of two such tools, inspecting the same EUV mask in a series of benchmarking tests that includes brightfield and darkfield patterns. One tool is the SEMATECH Berkeley Actinic Inspection Tool (AIT) operating on a bending magnet beamline at Lawrence Berkeley National Laboratory's Advanced Light Source. The AIT features an EUV Fresnel zoneplate microscope that emulates the numerical aperture of a 0.25-NA stepper, and projects the aerial image directly onto a CCD camera, with 700x magnification. The second tool is an EUV microscope (EUVM) operating at the NewSUBARU synchrotron in Hyogo, Japan. The NewSUBARU tool projects the aerial image using a reflective, 30x Schwarzschild objective lens, followed by a 10-200x x-ray zooming tube. The illumination conditions and the imaging etendue are different for the two tools. The benchmarking measurements were used to determine many imaging and performance properties of the tools, including resolution, modulation transfer function (MTF), aberration magnitude, aberration field-dependence (including focal-plane tilt), illumination uniformity, line-edge roughness, and flare. These measurements reveal the current state of the art in at-wavelength inspection performance, and will be a useful reference as performance improves over time

DOCK2 is involved in the host genetics and biology of severe COVID-19

「コロナ制圧タスクフォース」COVID-19疾患感受性遺伝子DOCK2の重症化機序を解明 --アジア最大のバイオレポジトリーでCOVID-19の治療標的を発見--. 京都大学プレスリリース. 2022-08-10.Identifying the host genetic factors underlying severe COVID-19 is an emerging challenge. Here we conducted a genome-wide association study (GWAS) involving 2, 393 cases of COVID-19 in a cohort of Japanese individuals collected during the initial waves of the pandemic, with 3, 289 unaffected controls. We identified a variant on chromosome 5 at 5q35 (rs60200309-A), close to the dedicator of cytokinesis 2 gene (DOCK2), which was associated with severe COVID-19 in patients less than 65 years of age. This risk allele was prevalent in East Asian individuals but rare in Europeans, highlighting the value of genome-wide association studies in non-European populations. RNA-sequencing analysis of 473 bulk peripheral blood samples identified decreased expression of DOCK2 associated with the risk allele in these younger patients. DOCK2 expression was suppressed in patients with severe cases of COVID-19. Single-cell RNA-sequencing analysis (n = 61 individuals) identified cell-type-specific downregulation of DOCK2 and a COVID-19-specific decreasing effect of the risk allele on DOCK2 expression in non-classical monocytes. Immunohistochemistry of lung specimens from patients with severe COVID-19 pneumonia showed suppressed DOCK2 expression. Moreover, inhibition of DOCK2 function with CPYPP increased the severity of pneumonia in a Syrian hamster model of SARS-CoV-2 infection, characterized by weight loss, lung oedema, enhanced viral loads, impaired macrophage recruitment and dysregulated type I interferon responses. We conclude that DOCK2 has an important role in the host immune response to SARS-CoV-2 infection and the development of severe COVID-19, and could be further explored as a potential biomarker and/or therapeutic target

Association between tumor cell in air space and treatment outcomes in early-stage lung cancer treated with stereotactic body radiation therapy

Background and purpose: Spread-through air space (STAS) is an unfavorable factor in patients with lung cancer treated with surgery. However, the relationship between the treatment outcomes of stereotactic body radiation therapy (SBRT) for lung cancer and STAS has not been adequately investigated. This study aimed to evaluate the impact of tumor cells in the air space (TCIAS), which show a STAS burden, on treatment outcomes in patients with early-stage lung cancer treated with SBRT. Materials and methods: Data of patients who underwent SBRT for early-stage lung cancer treated with SBRT were retrospectively reviewed. The influence of the TCIAS status on local progression-free (LPF), regional failure-free (RFF), distant failure-free (DFF), progression-free survival (PFS), and overall survival (OS) rates was assessed using univariate and multivariate analyses. Results: Overall, 68 patients were included. The median follow-up time was 24.3 months. For patients positive/negative for TCIAS, the 2-year LPF, RFF, DFF, PFS, and OS rates were 81.4 %/91.1 %, 73.7 %/96.2 %, 55.9 %/75.3 %, 55.0 %/84.6 %, and 67.8 %/92.2 %, respectively. In the multivariate analysis, TCIAS-positive was a significant unfavorable factor for RFF (hazard ratio [HR]: 4.10; 95 % confidence interval [CI]: 1.04–16.16, p = 0.04), DFF (HR: 2.61, 95 % CI: 1.03–6.57, p = 0.04), and PFS (HR: 2.36; 95 % CI: 1.05–5.30, p = 0.04). By contrast, TCIAS-positive was not a significant risk factor for LPF and OS. Conclusion: TCIAS-positive is an unfavorable factor for regional and distant failure after SBRT. TCIAS status may be useful in predicting the treatment outcome of SBRT for early-stage lung cancer

Factors Affecting Survival and Local Control in Patients with Bone Metastases Treated with Radiotherapy

The aim of this study was to evaluate the expected prognosis and factors affecting local control (LC) of the bone metastatic sites treated with palliative external beam radiotherapy (RT). Between December 2010 and April 2019, 420 cases (male/female = 240/180; median age [range]: 66 [12–90] years) with predominantly osteolytic bone metastases received RT and were evaluated. LC was evaluated by follow-up computed tomography (CT) image. Median RT doses (BED10) were 39.0 Gy (range, 14.4–71.7 Gy). The 0.5-year overall survival and LC of RT sites were 71% and 84%, respectively. Local recurrence on CT images was observed in 19% (n = 80) of the RT sites, and the median recurrence time was 3.5 months (range, 1–106 months). In univariate analysis, abnormal laboratory data before RT (platelet count, serum albumin, total bilirubin, lactate dehydrogenase, or serum calcium level), high-risk primary tumor sites (colorectal, esophageal, hepatobiliary/pancreatic, renal/ureter, and non-epithelial cancers), no antineoplastic agents (ATs) administration after RT, and no bone modifying agents (BMAs) administration after RT were significantly unfavorable factors for both survival and LC of RT sites. Sex (male), performance status (≥3), and RT dose (BED10) (<39.0 Gy) were significantly unfavorable factors for only survival, and age (≥70 years) and bone cortex destruction were significantly unfavorable factors for only LC of RT sites. In multivariate analysis, only abnormal laboratory data before RT influenced both unfavorable survival and LC of RT sites. Performance status (≥3), no ATs administration after RT, RT dose (BED10) (<39.0 Gy), and sex (male) were significantly unfavorable factors for survival, and primary tumor sites and BMAs administration after RT were significantly unfavorable factors for LC of RT sites. In conclusion, laboratory data before RT was important factor both prognosis and LC of bone metastases treated with palliative RT. At least in patients with abnormal laboratory data before RT, palliative RT seemed to be focused on the only pain relief

Performance evaluation for 120 four-layer DOI block detectors of the jPET-D4

The jPET-D4 is a brain positron emission tomography (PET) scanner that we have developed to meet user demands for high sensitivity and high spatial resolution. For this scanner, we developed a four-layer depth-of-interaction (DOI) detector. The four-layer DOI detector is a key component for the jPET-D4, its performance has great influence on the overall system performance. Previously, we reported the original technique for encoding four-layer DOI. Here, we introduce the final design of the jPET-D4 detector and present the results of an investigation on uniformity in performance of the detector. The performance evaluation was done over the 120 DOI crystal blocks for the detectors, which are to be assembled into the jPET-D4 scanner. We also introduce the crystal assembly method, which is simple enough, even though each DOI crystal block is composed of 1,024 crystal elements. The jPET-D4 detector consists of four layers of 16 × 16 Gd2SiO5 (GSO) crystals and a 256-channel flat-panel position-sensitive photomultiplier tube (256ch FP-PMT). To identify scintillated crystals in the four-layer DOI detector, we use pulse shape discrimination and position discrimination on the two-dimensional (2D) position histogram. For pulse shape discrimination, two kinds of GSO crystals that show different scintillation decay time constants are used in the upper two and lower two layers, respectively. Proper reflector arrangement in the crystal block then allows the scintillated crystals to be identified in these two-layer groupings with two 2D position histograms. We produced the 120 DOI crystal blocks for the jPET-D4 system, and measured their characteristics such as the accuracy of pulse shape discrimination, energy resolution, and the pulse height of the full energy peak. The results show a satisfactory and uniform performance of the four-layer DOI crystal blocks; for example, misidentification rate in each GSO layer is <5% based on pulse shape discrimination, the averaged energy resolutions for the central four crystals of the first (farthest from the FP-PMT), second, third, and 4th layers are 15.7 ± 1.0, 15.8 ± 0.6, 17.7 ± 1.2, and 17.3 ± 1.4%, respectively, and variation in pulse height of the full energy peak among the four layers is <5% on average