On the zero set of G-equivariant maps

Let $G$ be a finite group acting on vector spaces $V$ and $W$ and consider a smooth $G$-equivariant mapping $f:V\to W$. This paper addresses the question of the zero set near a zero $x$ of $f$ with isotropy subgroup $G$. It is known from results of Bierstone and Field on $G$-transversality theory that the zero set in a neighborhood of $x$ is a stratified set. The purpose of this paper is to partially determine the structure of the stratified set near $x$ using only information from the representations $V$ and $W$. We define an index $s(\Sigma)$ for isotropy subgroups $\Sigma$ of $G$ which is the difference of the dimension of the fixed point subspace of $\Sigma$ in $V$ and $W$. Our main result states that if $V$ contains a subspace $G$-isomorphic to $W$, then for every maximal isotropy subgroup $\Sigma$ satisfying $s(\Sigma)>s(G)$, the zero set of $f$ near $x$ contains a smooth manifold of zeros with isotropy subgroup $\Sigma$ of dimension $s(\Sigma)$. We also present a systematic method to study the zero sets for group representations $V$ and $W$ which do not satisfy the conditions of our main theorem. The paper contains many examples and raises several questions concerning the computation of zero sets of equivariant maps. These results have application to the bifurcation theory of $G$-reversible equivariant vector fields

Peripheral vasoconstriction influences thenar oxygen saturation as measured by near-infrared spectroscopy

Purpose: Near-infrared spectroscopy has been used as a noninvasive monitoring tool for tissue oxygen saturation (StO2) in acutely ill patients. This study aimed to investigate whether local vasoconstriction induced by body surface cooling significantly influences thenar StO2 as measured by InSpectra model 650. Methods: Eight healthy individuals (age 26 ± 6 years) participated in the study. Using a cooling blanket, we aimed to cool the entire body surface to induce vasoconstriction in the skin without any changes in central temperature. Thenar StO2 was noninvasively measured during a 3-min vascular occlusion test using InSpectra model 650 with a 15-mm probe. Measurements were analyzed for resting StO2 values, rate of StO2 desaturation (RdecStO2, %/min), and rate of StO2 recovery (RincStO2, %/s) before, during, and after skin cooling. Measurements also included heart rate (HR), mean arterial pressure (MAP), cardiac output (CO), stroke volume (SV), capillary refill time (CRT), forearm-to-fingertip skintemperature gradient (Tskin-diff), perfusion index (PI), and tissue hemoglobin index (THI). Results: In all subjects MAP, CO, SV, and core temperature did not change during the procedure. Skin cooling resulted in a significant decrease in StO2 from 82% (80-87) to 72% (70-77) (P\0.05) and in RincStO2 from 3.0%/s (2.8-3.3) to 1.7%/s (1.1-2.0) (P\0.05). Similar changes in CRT, Tskin-diff, and PI were also observed: from 2.5 s (2.0-3.0) to 8.5 s (7.2-11.0) (P\0.05), from 1.0 (-1.6-1.8) to 3.1 (P\0.05), and from 10.0% (9.1-11.7) to 2.5

Results from a combined test of an electromagnetic liquid argon calorimeter with a hadronic scintillating-tile calorimeter

The first combined test of an electromagnetic liquid argon accordion calorimeter and a hadronic scintillating-tile calorimeter was carried out at the CERN SPS. These devices are prototypes of the barrel calorimeter of the future ATLAS experiment at the LHC. The energy resolution of pions in the energy range from 20 to 300~GeV at an incident angle $\theta$ of about 11$^\circ$ is well-described by the expression \sigma/E = ((46.5 \pm 6.0)\%/\sqrt{E} +(1.2 \pm 0.3)\%) \oplus (3.2 \pm 0.4)~\mbox{GeV}/E. Shower profiles, shower leakage, and the angular resolution of hadronic showers were also studied

Sub-genic intolerance, ClinVar, and the epilepsies: A whole-exome sequencing study of 29,165 individuals

Both mild and severe epilepsies are influenced by variants in the same genes, yet an explanation for the resulting phenotypic variation is unknown. As part of the ongoing Epi25 Collaboration, we performed a whole-exome sequencing analysis of 13,487 epilepsy-affected individuals and 15,678 control individuals. While prior Epi25 studies focused on gene-based collapsing analyses, we asked how the pattern of variation within genes differs by epilepsy type. Specifically, we compared the genetic architectures of severe developmental and epileptic encephalopathies (DEEs) and two generally less severe epilepsies, genetic generalized epilepsy and non-acquired focal epilepsy (NAFE). Our gene-based rare variant collapsing analysis used geographic ancestry-based clustering that included broader ancestries than previously possible and revealed novel associations. Using the missense intolerance ratio (MTR), we found that variants in DEE-affected individuals are in significantly more intolerant genic sub-regions than those in NAFE-affected individuals. Only previously reported pathogenic variants absent in available genomic datasets showed a significant burden in epilepsy-affected individuals compared with control individuals, and the ultra-rare pathogenic variants associated with DEE were located in more intolerant genic sub-regions than variants associated with non-DEE epilepsies. MTR filtering improved the yield of ultra-rare pathogenic variants in affected individuals compared with control individuals. Finally, analysis of variants in genes without a disease association revealed a significant burden of loss-of-function variants in the genes most intolerant to such variation, indicating additional epilepsy-risk genes yet to be discovered. Taken together, our study suggests that genic and sub-genic intolerance are critical characteristics for interpreting the effects of variation in genes that influence epilepsy

Diversity and ethics in trauma and acute care surgery teams: results from an international survey

Background Investigating the context of trauma and acute care surgery, the article aims at understanding the factors that can enhance some ethical aspects, namely the importance of patient consent, the perceptiveness of the ethical role of the trauma leader, and the perceived importance of ethics as an educational subject. Methods The article employs an international questionnaire promoted by the World Society of Emergency Surgery. Results Through the analysis of 402 fully filled questionnaires by surgeons from 72 different countries, the three main ethical topics are investigated through the lens of gender, membership of an academic or non-academic institution, an official trauma team, and a diverse group. In general terms, results highlight greater attention paid by surgeons belonging to academic institutions, official trauma teams, and diverse groups. Conclusions Our results underline that some organizational factors (e.g., the fact that the team belongs to a university context or is more diverse) might lead to the development of a higher sensibility on ethical matters. Embracing cultural diversity forces trauma teams to deal with different mindsets. Organizations should, therefore, consider those elements in defining their organizational procedures. Level of evidence Trauma and acute care teams work under tremendous pressure and complex circumstances, with their members needing to make ethical decisions quickly. The international survey allowed to shed light on how team assembly decisions might represent an opportunity to coordinate team member actions and increase performance

Les droits disciplinaires des fonctions publiques : « unification », « harmonisation » ou « distanciation ». A propos de la loi du 26 avril 2016 relative à la déontologie et aux droits et obligations des fonctionnaires

The production of tt‾ , W+bb‾ and W+cc‾ is studied in the forward region of proton–proton collisions collected at a centre-of-mass energy of 8 TeV by the LHCb experiment, corresponding to an integrated luminosity of 1.98±0.02 fb−1 . The W bosons are reconstructed in the decays W→ℓν , where ℓ denotes muon or electron, while the b and c quarks are reconstructed as jets. All measured cross-sections are in agreement with next-to-leading-order Standard Model predictions.The production of $t\overline{t}$, $W+b\overline{b}$ and $W+c\overline{c}$ is studied in the forward region of proton-proton collisions collected at a centre-of-mass energy of 8 TeV by the LHCb experiment, corresponding to an integrated luminosity of 1.98 $\pm$ 0.02 \mbox{fb}^{-1}. The $W$ bosons are reconstructed in the decays $W\rightarrow\ell\nu$, where $\ell$ denotes muon or electron, while the $b$ and $c$ quarks are reconstructed as jets. All measured cross-sections are in agreement with next-to-leading-order Standard Model predictions

Analysis of shared heritability in common disorders of the brain

ience, this issue p. eaap8757 Structured Abstract INTRODUCTION Brain disorders may exhibit shared symptoms and substantial epidemiological comorbidity, inciting debate about their etiologic overlap. However, detailed study of phenotypes with different ages of onset, severity, and presentation poses a considerable challenge. Recently developed heritability methods allow us to accurately measure correlation of genome-wide common variant risk between two phenotypes from pools of different individuals and assess how connected they, or at least their genetic risks, are on the genomic level. We used genome-wide association data for 265,218 patients and 784,643 control participants, as well as 17 phenotypes from a total of 1,191,588 individuals, to quantify the degree of overlap for genetic risk factors of 25 common brain disorders. RATIONALE Over the past century, the classification of brain disorders has evolved to reflect the medical and scientific communities' assessments of the presumed root causes of clinical phenomena such as behavioral change, loss of motor function, or alterations of consciousness. Directly observable phenomena (such as the presence of emboli, protein tangles, or unusual electrical activity patterns) generally define and separate neurological disorders from psychiatric disorders. Understanding the genetic underpinnings and categorical distinctions for brain disorders and related phenotypes may inform the search for their biological mechanisms. RESULTS Common variant risk for psychiatric disorders was shown to correlate significantly, especially among attention deficit hyperactivity disorder (ADHD), bipolar disorder, major depressive disorder (MDD), and schizophrenia. By contrast, neurological disorders appear more distinct from one another and from the psychiatric disorders, except for migraine, which was significantly correlated to ADHD, MDD, and Tourette syndrome. We demonstrate that, in the general population, the personality trait neuroticism is significantly correlated with almost every psychiatric disorder and migraine. We also identify significant genetic sharing between disorders and early life cognitive measures (e.g., years of education and college attainment) in the general population, demonstrating positive correlation with several psychiatric disorders (e.g., anorexia nervosa and bipolar disorder) and negative correlation with several neurological phenotypes (e.g., Alzheimer's disease and ischemic stroke), even though the latter are considered to result from specific processes that occur later in life. Extensive simulations were also performed to inform how statistical power, diagnostic misclassification, and phenotypic heterogeneity influence genetic correlations. CONCLUSION The high degree of genetic correlation among many of the psychiatric disorders adds further evidence that their current clinical boundaries do not reflect distinct underlying pathogenic processes, at least on the genetic level. This suggests a deeply interconnected nature for psychiatric disorders, in contrast to neurological disorders, and underscores the need to refine psychiatric diagnostics. Genetically informed analyses may provide important "scaffolding" to support such restructuring of psychiatric nosology, which likely requires incorporating many levels of information. By contrast, we find limited evidence for widespread common genetic risk sharing among neurological disorders or across neurological and psychiatric disorders. We show that both psychiatric and neurological disorders have robust correlations with cognitive and personality measures. Further study is needed to evaluate whether overlapping genetic contributions to psychiatric pathology may influence treatment choices. Ultimately, such developments may pave the way toward reduced heterogeneity and improved diagnosis and treatment of psychiatric disorders

Multidifferential study of identified charged hadron distributions in ZZ-tagged jets in proton-proton collisions at s=\sqrt{s}=13 TeV

Jet fragmentation functions are measured for the first time in proton-proton collisions for charged pions, kaons, and protons within jets recoiling against a $Z$ boson. The charged-hadron distributions are studied longitudinally and transversely to the jet direction for jets with transverse momentum 20 $< p_{\textrm{T}} < 100$ GeV and in the pseudorapidity range $2.5 < \eta < 4$. The data sample was collected with the LHCb experiment at a center-of-mass energy of 13 TeV, corresponding to an integrated luminosity of 1.64 fb$^{-1}$. Triple differential distributions as a function of the hadron longitudinal momentum fraction, hadron transverse momentum, and jet transverse momentum are also measured for the first time. This helps constrain transverse-momentum-dependent fragmentation functions. Differences in the shapes and magnitudes of the measured distributions for the different hadron species provide insights into the hadronization process for jets predominantly initiated by light quarks.Comment: All figures and tables, along with machine-readable versions and any supplementary material and additional information, are available at https://cern.ch/lhcbproject/Publications/p/LHCb-PAPER-2022-013.html (LHCb public pages

Study of the B−→Λc+Λˉc−K−B^{-} \to \Lambda_{c}^{+} \bar{\Lambda}_{c}^{-} K^{-} decay

The decay $B^{-} \to \Lambda_{c}^{+} \bar{\Lambda}_{c}^{-} K^{-}$ is studied in proton-proton collisions at a center-of-mass energy of $\sqrt{s}=13$ TeV using data corresponding to an integrated luminosity of 5 $\mathrm{fb}^{-1}$ collected by the LHCb experiment. In the $\Lambda_{c}^+ K^{-}$ system, the $\Xi_{c}(2930)^{0}$ state observed at the BaBar and Belle experiments is resolved into two narrower states, $\Xi_{c}(2923)^{0}$ and $\Xi_{c}(2939)^{0}$, whose masses and widths are measured to be $$m(\Xi_{c}(2923)^{0}) = 2924.5 \pm 0.4 \pm 1.1 \,\mathrm{MeV}, \\ m(\Xi_{c}(2939)^{0}) = 2938.5 \pm 0.9 \pm 2.3 \,\mathrm{MeV}, \\ \Gamma(\Xi_{c}(2923)^{0}) = \phantom{000}4.8 \pm 0.9 \pm 1.5 \,\mathrm{MeV},\\ \Gamma(\Xi_{c}(2939)^{0}) = \phantom{00}11.0 \pm 1.9 \pm 7.5 \,\mathrm{MeV},$$ where the first uncertainties are statistical and the second systematic. The results are consistent with a previous LHCb measurement using a prompt $\Lambda_{c}^{+} K^{-}$ sample. Evidence of a new $\Xi_{c}(2880)^{0}$ state is found with a local significance of $3.8\,\sigma$, whose mass and width are measured to be $2881.8 \pm 3.1 \pm 8.5\,\mathrm{MeV}$ and $12.4 \pm 5.3 \pm 5.8 \,\mathrm{MeV}$, respectively. In addition, evidence of a new decay mode $\Xi_{c}(2790)^{0} \to \Lambda_{c}^{+} K^{-}$ is found with a significance of $3.7\,\sigma$. The relative branching fraction of $B^{-} \to \Lambda_{c}^{+} \bar{\Lambda}_{c}^{-} K^{-}$ with respect to the $B^{-} \to D^{+} D^{-} K^{-}$ decay is measured to be $2.36 \pm 0.11 \pm 0.22 \pm 0.25$, where the first uncertainty is statistical, the second systematic and the third originates from the branching fractions of charm hadron decays.Comment: All figures and tables, along with any supplementary material and additional information, are available at https://cern.ch/lhcbproject/Publications/p/LHCb-PAPER-2022-028.html (LHCb public pages