Making Almost Commuting Matrices Commute

Suppose two Hermitian matrices $A,B$ almost commute ($\Vert [A,B] \Vert \leq \delta$). Are they close to a commuting pair of Hermitian matrices, $A',B'$, with $\Vert A-A' \Vert,\Vert B-B'\Vert \leq \epsilon$? A theorem of H. Lin shows that this is uniformly true, in that for every $\epsilon>0$ there exists a $\delta>0$, independent of the size $N$ of the matrices, for which almost commuting implies being close to a commuting pair. However, this theorem does not specify how $\delta$ depends on $\epsilon$. We give uniform bounds relating $\delta$ and $\epsilon$. We provide tighter bounds in the case of block tridiagonal and tridiagonal matrices and a fully constructive method in that case. Within the context of quantum measurement, this implies an algorithm to construct a basis in which we can make a {\it projective} measurement that approximately measures two approximately commuting operators simultaneously. Finally, we comment briefly on the case of approximately measuring three or more approximately commuting operators using POVMs (positive operator-valued measures) instead of projective measurements.Comment: 22 pages; tighter bounds; Note: fixed mistake in proof pointed out by Filonov and Kachkovski

Informatics Enhanced SNP Microarray Analysis of 30 Miscarriage Samples Compared to Routine Cytogenetics

Purpose: The metaphase karyotype is often used as a diagnostic tool in the setting of early miscarriage; however this technique has several limitations. We evaluate a new technique for karyotyping that uses single nucleotide polymorphism microarrays (SNP). This technique was compared in a blinded, prospective fashion, to the traditional metaphase karyotype. Methods: Patients undergoing dilation and curettage for first trimester miscarriage between February and August 2010 were enrolled. Samples of chorionic villi were equally divided and sent for microarray testing in parallel with routine cytogenetic testing. Results: Thirty samples were analyzed, with only four discordant results. Discordant results occurred when the entire genome was duplicated or when a balanced rearrangement was present. Cytogenetic karyotyping took an average of 29 days while microarray-based karytoyping took an average of 12 days. Conclusions: Molecular karyotyping of POC after missed abortion using SNP microarray analysis allows for the ability to detect maternal cell contamination and provides rapid results with good concordance to standard cytogenetic analysis

Validation of a Single-Nucleotide Polymorphism-Based Non-Invasive Prenatal Test in Twin Gestations : Determination of Zygosity, Individual Fetal Sex, and Fetal Aneuploidy

We analyzed maternal plasma cell-free DNA samples from twin pregnancies in a prospective blinded study to validate a single-nucleotide polymorphism (SNP)-based non-invasive prenatal test (NIPT) for zygosity, fetal sex, and aneuploidy. Zygosity was evaluated by looking for either one or two fetal genome complements, fetal sex was evaluated by evaluating Y-chromosome loci, and aneuploidy was assessed through SNP ratios. Zygosity was correctly predicted in 100% of cases (93/93; 95% confidence interval (CI) 96.1%-100%). Individual fetal sex for both twins was also called with 100% accuracy (102/102; 95% weighted CI 95.2%-100%). All cases with copy number truth were also correctly identified. The dizygotic aneuploidy sensitivity was 100% (10/10; 95% CI 69.2%-100%), and overall specificity was 100% (96/96; 95% weighted CI, 94.8%-100%). The mean fetal fraction (FF) of monozygotic twins (n = 43) was 13.0% (standard deviation (SD), 4.5%); for dizygotic twins (n = 79), the mean lower FF was 6.5% (SD, 3.1%) and the mean higher FF was 8.1% (SD, 3.5%). We conclude SNP-based NIPT for zygosity is of value when chorionicity is uncertain or anomalies are identified. Zygosity, fetal sex, and aneuploidy are complementary evaluations that can be carried out on the same specimen as early as 9 weeks' gestation

Communications Biophysics

Contains research objectives, summary of research and reports on three research projects.National Institutes of Health (Grant 5 PO1 GM14940-04)National Institutes of Health (Grant 5 TOl GM01555-04)National Aeronautics and Space Administration (Grant NGL 22-009-304

Communications Biophysics

Contains research objectives, summary of research and reports on four research projects.National Institutes of Health (Grant 5 P01 GM14940-05)National Institutes of Health (Grant 5 TOl GM01555-05)National Aeronautics and Space Administration (Grant NGL 22-009-304)B-D ElectrodyneBoston City Hospital Purchase Order 1065

Heritability and Phenotypic Variation of Canine Hip Dysplasia Radiographic Traits in a Cohort of Australian German Shepherd Dogs

Canine Hip Dysplasia (CHD) is a common, painful and debilitating orthopaedic disorder of dogs with a partly genetic, multifactorial aetiology. Worldwide, potential breeding dogs are evaluated for CHD using radiographically based screening schemes such as the nine ordinally-scored British Veterinary Association Hip Traits (BVAHTs). The effectiveness of selective breeding based on screening results requires that a significant proportion of the phenotypic variation is caused by the presence of favourable alleles segregating in the population. This proportion, heritability, was measured in a cohort of 13,124 Australian German Shepherd Dogs born between 1976 and 2005, displaying phenotypic variation for BVAHTs, using ordinal, linear and binary mixed models fitted by a Restricted Maximum Likelihood method. Heritability estimates for the nine BVAHTs ranged from 0.14–0.24 (ordinal models), 0.14–0.25 (linear models) and 0.12–0.40 (binary models). Heritability for the summed BVAHT phenotype was 0.30±0.02. The presence of heritable variation demonstrates that selection based on BVAHTs has the potential to improve BVAHT scores in the population. Assuming a genetic correlation between BVAHT scores and CHD-related pain and dysfunction, the welfare of Australian German Shepherds can be improved by continuing to consider BVAHT scores in the selection of breeding dogs, but that as heritability values are only moderate in magnitude the accuracy, and effectiveness, of selection could be improved by the use of Estimated Breeding Values in preference to solely phenotype based selection of breeding animals

Impact of high-risk prenatal screening results for 22q11.2 deletion syndrome on obstetric and neonatal management: Secondary analysis from the SMART study

Objective One goal of prenatal genetic screening is to optimize perinatal care and improve infant outcomes. We sought to determine whether high-risk cfDNA screening for 22q11.2 deletion syndrome (22q11.2DS) affected prenatal or neonatal management. Methods This was a secondary analysis from the SMART study. Patients with high-risk cfDNA results for 22q11.2DS were compared with the low-risk cohort for pregnancy characteristics and obstetrical management. To assess differences in neonatal care, we compared high-risk neonates without prenatal genetic confirmation with a 1:1 matched low-risk cohort. Results Of 18,020 eligible participants enrolled between 2015 and 2019, 38 (0.21%) were high-risk and 17,982 (99.79%) were low-risk for 22q11.2DS by cfDNA screening. High-risk participants had more prenatal diagnostic testing (55.3%; 21/38 vs. 2.0%; 352/17,982, p < 0.001) and fetal echocardiography (76.9%; 10/13 vs. 19.6%; 10/51, p < 0.001). High-risk newborns without prenatal diagnostic testing had higher rates of neonatal genetic testing (46.2%; 6/13 vs. 0%; 0/51, P < 0.001), echocardiography (30.8%; 4/13 vs. 4.0%; 2/50, p = 0.013), evaluation of calcium levels (46.2%; 6/13 vs. 4.1%; 2/49, P < 0.001) and lymphocyte count (53.8%; 7/13 vs. 15.7%; 8/51, p = 0.008). Conclusions High-risk screening results for 22q11.2DS were associated with higher rates of prenatal and neonatal diagnostic genetic testing and other 22q11.2DS-specific evaluations. However, these interventions were not universally performed, and >50% of high-risk infants were discharged without genetic testing, representing possible missed opportunities to improve outcomes for affected individuals

Performance of prenatal cfDNA screening for sex chromosomes.

PURPOSE: The aim of this study was to assess the performance of cell-free DNA (cfDNA) screening to detect sex chromosome aneuploidies (SCAs) in an unselected obstetrical population with genetic confirmation. METHODS: This was a planned secondary analysis of the multicenter, prospective SNP-based Microdeletion and Aneuploidy RegisTry (SMART) study. Patients receiving cfDNA results for autosomal aneuploidies and who had confirmatory genetic results for the relevant sex chromosomal aneuploidies were included. Screening performance for SCAs, including monosomy X (MX) and the sex chromosome trisomies (SCT: 47,XXX; 47,XXY; 47,XYY) was determined. Fetal sex concordance between cfDNA and genetic screening was also evaluated in euploid pregnancies. RESULTS: A total of 17,538 cases met inclusion criteria. Performance of cfDNA for MX, SCTs, and fetal sex was determined in 17,297, 10,333, and 14,486 pregnancies, respectively. Sensitivity, specificity, and positive predictive value (PPV) of cfDNA were 83.3%, 99.9%, and 22.7% for MX and 70.4%, 99.9%, and 82.6%, respectively, for the combined SCTs. The accuracy of fetal sex prediction by cfDNA was 100%. CONCLUSION: Screening performance of cfDNA for SCAs is comparable to that reported in other studies. The PPV for the SCTs was similar to the autosomal trisomies, whereas the PPV for MX was substantially lower. No discordance in fetal sex was observed between cfDNA and postnatal genetic screening in euploid pregnancies. These data will assist interpretation and counseling for cfDNA results for sex chromosomes

Содержание катепсина S в плазме крови при бронхиальной астме тяжелого течения

The aim. To determine the level of cathepsin S and to identify its possible relationships with clinical, functional and laboratory indicators in patients with severe bronchial asthma.Methods. 114 patients with severe bronchial asthma were examined. 96 women (84.2%) and 18 (15.8%) men were divided into 2 groups: allergic and non-allergic severe bronchial asthma. The external respiration function was assessed with whole-body plethysmography (“Erich Jaeger”, Germany). The plasma concentration of cytokines IL-4, IL-5, IL-13, periostin, cathepsin S, TGF-β was estimated with ELISA (“eBioscience”, USA).Results. Fixed obstruction is reported in 48% and 50% of cases of allergic and non-allergic severe asthma, respectively. Peripheral blood eosinophilia occurs in 41.5% of cases with allergic and in 25% of cases with non-allergic asthma. IL-5, IL-13, and cathepsin S levels were increased in both groups. An increase in IL-4 and TGF-β levels was revealed in non-allergic asthma. Periostin levels were increased in patients with allergic asthma as compared with the control and the second group. Positive correlation between cathepsin S and concentration of IL-4, IL-5 was established in both groups. We identified weak positive correlation between cathepsin S levels and clinical symptoms of the disease, such as frequency of SABA use and asphyxiation attacks, only in the allergic asthma group. A positive correlation between cathepsin S and TGF-β was established in both groups.Conclusion. A positive correlation between serum cathepsin S and TGF-β was established in both allergic and non-allergic severe bronchial asthma. The found moderate relationship may indirectly indicate the involvement of cathepsin S in airway remodeling processes regardless of the disease type. Целью исследования явилось выявление возможной связи уровня катепсина S с клинико-функциональными и лабораторными показателями у пациентов с тяжелой бронхиальной астмой (ТБА).Материалы и методы. Обследованы пациенты с ТБА (n = 114: 96 (84,2 %) женщин и 18 (15,8 %) мужчин), которые были разделены на 2 группы: 1-я – больные аллергической ТБА, 2-я – больные неаллергической ТБА. Параметры функции внешнего дыхания регистрировали на аппарате общей плетизмографии (Erich Jaeger, Германия). Определение концентрации цитокинов интерлейкинов (IL)-4, -5 и -13, периостина, катепсина S, трансформирующего фактора роста-β (TGF-β) в плазме крови проводилось методом твердофазного иммуноферментного анализа (eBioscience, США).Результаты. Фиксированная обструкция регистрировалась в 48 и 50 % случаев, а эозинофилия периферической крови – в 41,5 и 25 % случаев в 1-й и 2-й группе соответственно. Повышение содержания IL-5, IL-13 и катепсина S в плазме крови наблюдалось в обеих группах. При неаллергической ТБА выявлено повышение уровня IL-4 и TGF-β. При аллергической ТБА отмечалось повышение содержания периостина в плазме крови в сравнении с контролем и показателями больных 2-й группы. Статистически значимая корреляционная связь между содержанием катепсина S и концентрацией IL-4, -5 в плазме крови установлена в обеих группах. Слабая корреляционная связь между уровнем катепсина S в плазме крови и клиническими симптомами заболевания, такими как частота использования КДБА и приступы удушья, выявлена только в 1-й группе. В обеих группах зафиксирована значимая корреляционная связь между уровнем катепсина S и TGF-β.Заключение. В обеих группах пациентов с ТБА установлена значимая корреляционная связь между уровнем катепсина S и TGF-β в сыворотке крови, что может косвенно свидетельствовать об участии катепсина S в процессах ремоделирования дыхательных путей независимо от формы заболевания.

Revised Lithostratigraphy of the Sonsela Member (Chinle Formation, Upper Triassic) in the Southern Part of Petrified Forest National Park, Arizona

BACKGROUND: Recent revisions to the Sonsela Member of the Chinle Formation in Petrified Forest National Park have presented a three-part lithostratigraphic model based on unconventional correlations of sandstone beds. As a vertebrate faunal transition is recorded within this stratigraphic interval, these correlations, and the purported existence of a depositional hiatus (the Tr-4 unconformity) at about the same level, must be carefully re-examined. METHODOLOGY/PRINCIPAL FINDINGS: Our investigations demonstrate the neglected necessity of walking out contacts and mapping when constructing lithostratigraphic models, and providing UTM coordinates and labeled photographs for all measured sections. We correct correlation errors within the Sonsela Member, demonstrate that there are multiple Flattops One sandstones, all of which are higher than the traditional Sonsela sandstone bed, that the Sonsela sandstone bed and Rainbow Forest Bed are equivalent, that the Rainbow Forest Bed is higher than the sandstones at the base of Blue Mesa and Agate Mesa, that strata formerly assigned to the Jim Camp Wash beds occur at two stratigraphic levels, and that there are multiple persistent silcrete horizons within the Sonsela Member. CONCLUSIONS/SIGNIFICANCE: We present a revised five-part model for the Sonsela Member. The units from lowest to highest are: the Camp Butte beds, Lot's Wife beds, Jasper Forest bed (the Sonsela sandstone)/Rainbow Forest Bed, Jim Camp Wash beds, and Martha's Butte beds (including the Flattops One sandstones). Although there are numerous degradational/aggradational cycles within the Chinle Formation, a single unconformable horizon within or at the base of the Sonsela Member that can be traced across the entire western United States (the "Tr-4 unconformity") probably does not exist. The shift from relatively humid and poorly-drained to arid and well-drained climatic conditions began during deposition of the Sonsela Member (low in the Jim Camp Wash beds), well after the Carnian-Norian transition