Combinatorial Markov chains on linear extensions

We consider generalizations of Schuetzenberger's promotion operator on the set L of linear extensions of a finite poset of size n. This gives rise to a strongly connected graph on L. By assigning weights to the edges of the graph in two different ways, we study two Markov chains, both of which are irreducible. The stationary state of one gives rise to the uniform distribution, whereas the weights of the stationary state of the other has a nice product formula. This generalizes results by Hendricks on the Tsetlin library, which corresponds to the case when the poset is the anti-chain and hence L=S_n is the full symmetric group. We also provide explicit eigenvalues of the transition matrix in general when the poset is a rooted forest. This is shown by proving that the associated monoid is R-trivial and then using Steinberg's extension of Brown's theory for Markov chains on left regular bands to R-trivial monoids.Comment: 35 pages, more examples of promotion, rephrased the main theorems in terms of discrete time Markov chain

Casimir Energies for 6D Supergravities Compactified on T_2/Z_N with Wilson Lines

We compute (as functions of the shape and Wilson-line moduli) the one-loop Casimir energy induced by higher-dimensional supergravities compactified from 6D to 4D on 2-tori, and on some of their Z_N orbifolds. Detailed calculations are given for a 6D scalar field having an arbitrary 6D mass m, and we show how to extend these results to higher-spin fields for supersymmetric 6D theories. Particular attention is paid to regularization issues and to the identification of the divergences of the potential, as well as the dependence of the result on m, including limits for which m^2 A> 1 where A is the volume of the internal 2 dimensions. Our calculation extends those in the literature to very general boundary conditions for fields about the various cycles of these geometries. The results have potential applications towards Supersymmetric Large Extra Dimensions (SLED) as a theory of the Dark Energy. First, they provide an explicit calculation within which to follow the dependence of the result on the mass of the bulk states which travel within the loop, and for heavy masses these results bear out the more general analysis of the UV-sensitivity obtained using heat-kernel methods. Second, because the potentials we find describe the dynamics of the classical flat directions of these compactifications, within SLED they would describe the present-day dynamics of the Dark Energy.Comment: 40 pages, 7 figure

The Sudbury Neutrino Observatory

The Sudbury Neutrino Observatory is a second generation water Cherenkov detector designed to determine whether the currently observed solar neutrino deficit is a result of neutrino oscillations. The detector is unique in its use of D2O as a detection medium, permitting it to make a solar model-independent test of the neutrino oscillation hypothesis by comparison of the charged- and neutral-current interaction rates. In this paper the physical properties, construction, and preliminary operation of the Sudbury Neutrino Observatory are described. Data and predicted operating parameters are provided whenever possible.Comment: 58 pages, 12 figures, submitted to Nucl. Inst. Meth. Uses elsart and epsf style files. For additional information about SNO see http://www.sno.phy.queensu.ca . This version has some new reference

Post-traumatic stress and future substance use outcomes: leveraging antecedent factors to stratify risk

Background: Post-traumatic stress disorder (PTSD) and substance use (tobacco, alcohol, and cannabis) are highly comorbid. Many factors affect this relationship, including sociodemographic and psychosocial characteristics, other prior traumas, and physical health. However, few prior studies have investigated this prospectively, examining new substance use and the extent to which a wide range of factors may modify the relationship to PTSD. Methods: The Advancing Understanding of RecOvery afteR traumA (AURORA) study is a prospective cohort of adults presenting at emergency departments (N = 2,943). Participants self-reported PTSD symptoms and the frequency and quantity of tobacco, alcohol, and cannabis use at six total timepoints. We assessed the associations of PTSD and future substance use, lagged by one timepoint, using the Poisson generalized estimating equations. We also stratified by incident and prevalent substance use and generated causal forests to identify the most important effect modifiers of this relationship out of 128 potential variables. Results: At baseline, 37.3% (N = 1,099) of participants reported likely PTSD. PTSD was associated with tobacco frequency (incidence rate ratio (IRR): 1.003, 95% CI: 1.00, 1.01, p = 0.02) and quantity (IRR: 1.01, 95% CI: 1.001, 1.01, p = 0.01), and alcohol frequency (IRR: 1.002, 95% CI: 1.00, 1.004, p = 0.03) and quantity (IRR: 1.003, 95% CI: 1.001, 1.01, p = 0.001), but not with cannabis use. There were slight differences in incident compared to prevalent tobacco frequency and quantity of use; prevalent tobacco frequency and quantity were associated with PTSD symptoms, while incident tobacco frequency and quantity were not. Using causal forests, lifetime worst use of cigarettes, overall self-rated physical health, and prior childhood trauma were major moderators of the relationship between PTSD symptoms and the three substances investigated. Conclusion: PTSD symptoms were highly associated with tobacco and alcohol use, while the association with prospective cannabis use is not clear. Findings suggest that understanding the different risk stratification that occurs can aid in tailoring interventions to populations at greatest risk to best mitigate the comorbidity between PTSD symptoms and future substance use outcomes. We demonstrate that this is particularly salient for tobacco use and, to some extent, alcohol use, while cannabis is less likely to be impacted by PTSD symptoms across the strata

Novel genetic loci associated with hippocampal volume

The hippocampal formation is a brain structure integrally involved in episodic memory, spatial navigation, cognition and stress responsiveness. Structural abnormalities in hippocampal volume and shape are found in several common neuropsychiatric disorders. To identify the genetic underpinnings of hippocampal structure here we perform a genome-wide association study (GWAS) of 33,536 individuals and discover six independent loci significantly associated with hippocampal volume, four of them novel. Of the novel loci, three lie within genes (ASTN2, DPP4 and MAST4) and one is found 200 kb upstream of SHH. A hippocampal subfield analysis shows that a locus within the MSRB3 gene shows evidence of a localized effect along the dentate gyrus, subiculum, CA1 and fissure. Further, we show that genetic variants associated with decreased hippocampal volume are also associated with increased risk for Alzheimer's disease (rg =-0.155). Our findings suggest novel biological pathways through which human genetic variation influences hippocampal volume and risk for neuropsychiatric illness

Effect of priming interval on reactogenicity, peak immunological response, and waning after homologous and heterologous COVID-19 vaccine schedules: exploratory analyses of Com-COV, a randomised control trial

Background: Priming COVID-19 vaccine schedules have been deployed at variable intervals globally, which might influence immune persistence and the relative importance of third-dose booster programmes. Here, we report exploratory analyses from the Com-COV trial, assessing the effect of 4-week versus 12-week priming intervals on reactogenicity and the persistence of immune response up to 6 months after homologous and heterologous priming schedules using the vaccines BNT162b2 (tozinameran, Pfizer/BioNTech) and ChAdOx1 nCoV-19 (AstraZeneca). Methods: Com-COV was a participant-masked, randomised immunogenicity trial. For these exploratory analyses, we used the trial's general cohort, in which adults aged 50 years or older were randomly assigned to four homologous and four heterologous vaccine schedules using BNT162b2 and ChAdOx1 nCoV-19 with 4-week or 12-week priming intervals (eight groups in total). Immunogenicity analyses were done on the intention-to-treat (ITT) population, comprising participants with no evidence of SARS-CoV-2 infection at baseline or for the trial duration, to assess the effect of priming interval on humoral and cellular immune response 28 days and 6 months post-second dose, in addition to the effects on reactogenicity and safety. The Com-COV trial is registered with the ISRCTN registry, 69254139 (EudraCT 2020–005085–33). Findings: Between Feb 11 and 26, 2021, 730 participants were randomly assigned in the general cohort, with 77–89 per group in the ITT analysis. At 28 days and 6 months post-second dose, the geometric mean concentration of anti-SARS-CoV-2 spike IgG was significantly higher in the 12-week interval groups than in the 4-week groups for homologous schedules. In heterologous schedule groups, we observed a significant difference between intervals only for the BNT162b2–ChAdOx1 nCoV-19 group at 28 days. Pseudotyped virus neutralisation titres were significantly higher in all 12-week interval groups versus 4-week groups, 28 days post-second dose, with geometric mean ratios of 1·4 (95% CI 1·1–1·8) for homologous BNT162b2, 1·5 (1·2–1·9) for ChAdOx1 nCoV-19–BNT162b2, 1·6 (1·3–2·1) for BNT162b2–ChAdOx1 nCoV-19, and 2·4 (1·7–3·2) for homologous ChAdOx1 nCoV-19. At 6 months post-second dose, anti-spike IgG geometric mean concentrations fell to 0·17–0·24 of the 28-day post-second dose value across all eight study groups, with only homologous BNT162b2 showing a slightly slower decay for the 12-week versus 4-week interval in the adjusted analysis. The rank order of schedules by humoral response was unaffected by interval, with homologous BNT162b2 remaining the most immunogenic by antibody response. T-cell responses were reduced in all 12-week priming intervals compared with their 4-week counterparts. 12-week schedules for homologous BNT162b2 and ChAdOx1 nCoV-19–BNT162b2 were up to 80% less reactogenic than 4-week schedules. Interpretation: These data support flexibility in priming interval in all studied COVID-19 vaccine schedules. Longer priming intervals might result in lower reactogenicity in schedules with BNT162b2 as a second dose and higher humoral immunogenicity in homologous schedules, but overall lower T-cell responses across all schedules. Future vaccines using these novel platforms might benefit from schedules with long intervals. Funding: UK Vaccine Taskforce and National Institute for Health and Care Research

Whole-genome sequencing of chronic lymphocytic leukemia identifies subgroups with distinct biological and clinical features

The value of genome-wide over targeted driver analyses for predicting clinical outcomes of cancer patients is debated. Here, we report the whole-genome sequencing of 485 chronic lymphocytic leukemia patients enrolled in clinical trials as part of the United Kingdom’s 100,000 Genomes Project. We identify an extended catalog of recurrent coding and noncoding genetic mutations that represents a source for future studies and provide the most complete high-resolution map of structural variants, copy number changes and global genome features including telomere length, mutational signatures and genomic complexity. We demonstrate the relationship of these features with clinical outcome and show that integration of 186 distinct recurrent genomic alterations defines five genomic subgroups that associate with response to therapy, refining conventional outcome prediction. While requiring independent validation, our findings highlight the potential of whole-genome sequencing to inform future risk stratification in chronic lymphocytic leukemia