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Irredundant bases for finite almost simple groups
Get PDFIn this thesis, we study maximum irredundant base sizes I(G, Γ) of three types of finite primitive permutation groups G, where two of the three types are almost simple. The maximum irredundant base size is equal to the length of the longest strictly descending chain of pointwise stabilisers of G on Γ, and its value has implications for the relational complexity of the permutation group.
We start against the backdrop of Kelsey and Roney-Dougal (2022) showing that that if G is not large-base, then I(G, Γ) < 5 log |Γ|. While no (log |Γ|) bounds on I(G, Γ) exist for large-base G, we give a pair of lower and upper bounds that are attained by infinitely many large-base groups.
We then turn to almost simple permutation groups and study the non-standard actions of Sₙ and Aₙ. In this case, we give best possible upper bounds on I(G, Γ) in terms of n. We also show that an (log |Γ| / log log |Γ|) bound holds and in most cases an ((log log |Γ|)²) bound holds.
The third type of primitive permutation groups is almost simple classical groups over finite fields. If such a group G is of rank r over a field of characteristic p and order pᵉ, the best known upper bound is (r⁸ + log e), shown by Gill and Liebeck (2023). We construct large explicit irredundant bases for the primitive actions of the symplectic, unitary, and orthogonal groups on sets of subspaces, complementing the construction by Kelsey and Roney-Dougal (2022) for linear groups. The lower bounds on I(G, Γ) deduced from these constructions suggest that an (r² + log e) bound, if shown to be true, would be best possible for each of the four families of classical groups.
The thesis ends with an exploration of computer-assisted formalisation of mathematics. We present the formalisation – in the programming language Lean – of a key result on wreath products used to find I(G, Γ) for some large-base groups
In balance : understanding the use of scales in Andean life
Get PDFToday, balances (scales) are used in modern highland Andean communities, a tradition that archaeological research demonstrates has pre-Hispanic roots. In this paper, we discuss how the uses of balances are embedded in perceptions of what it means for an individual and their community to be “in balance”. To do this, we unite archaeological, historical, and ethnographic research to understand the diverse uses of scales. In modern-day Andean highland communities, scales known as wipis are used to exchange goods across resource zones and to weigh wool and yarn used in weaving. Wipis are also employed as part of important ancestral traditions, where the act of weighing takes place in association with sacred objects and landscapes. Across these different historic and contemporary contexts, balance use is embedded in perceptions of fairness and sufficiency. In this sense, balances often gauge how an individual or group measures up against predetermined expectations rather than a specific standardized weight. In the ancient Andes, while it is difficult to fully reconstruct how balances were used and the social meanings they were associated with, research on craft production, administration and exchange can elucidate a variety of weight measurement practices. Pre-Hispanic balances were used by traders, artisans and leaders to determine what was sufficient in exchanges and tribute collections, and to verify that goods possessed certain qualities. Across these contexts what was deemed sufficient likely depended on agreements between the actors involved and social understandings of community and personal responsibility, rather than a standardized weight and the scale always achieving balance.Peer reviewe
Shape and spin state model of contact binary (388188) 2006 DP14 using combined radar and optical observations
Get PDFFunding: This material is based in part upon work supported by NASA under the Science Mission Directorate Research and Analysis Programs. REC, AR, CS, and AD acknowledge the support from the UK Science and Technology Facilities Council. Part of this work was carried out at the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration (80NM0018D0004). The work at Ondřejov was supported by Praemium Academiae award to PP by the Academy of Sciences of the Czech Republic. TH acknowledges funding from the Public Scholarship, Development, Disability and Maintenance Fund of the Republic of Slovenia. UGJ acknowledges funding from the Novo Nordisk Foundation Interdisciplinary Synergy Programme grant no. NNF19OC0057374. EK was supported by the National Research Foundation of Korea (2021M3F7A1082056). PL-P was partly funded by the FONDECYT Initiation Project No. 11241572. RFJ acknowledges support for this project provided by ANID’s Millennium Science Initiative through grant ICN12_009, awarded to the Millennium Institute of Astrophysics (MAS), and by ANID’s Basal project FB210003.Contact binaries are found throughout the Solar System. The recent discovery of Selam, the satellite of main-belt asteroid (152830) Dinkinesh, by the NASA Lucy mission has made it clear that the term ‘contact binary’ covers a variety of different types of bimodal mass distributions and formation mechanisms. Only by modelling more contact binaries can this population be properly understood. We determined a spin state and shape model for the Apollo group contact binary asteroid (388188) 2006 DP14 using ground-based optical and radar observations collected between 2014 and 2023. Radar delay-Doppler images and continuous-wave spectra were collected over 2 d in February 2014, while 16 light curves in the Cousins R and SDSS-r filters were collected in 2014, 2022, and 2023. We modelled the spin state using convex inversion before using the SHAPE modelling software to include the radar observations in modelling concavities and the distinctive neck structure connecting the two lobes. We find a spin state with a period of (5.7860 ± 0.0001) h and pole solution of λ = (180 ± 121)◦ and β = (−80 ± 7)◦ with morphology indicating a 520 m long bilobed shape. The model’s asymmetrical bimodal mass distribution resembles other small near-Earth asteroid contact binaries such as (85990) 1999 JV6 or (8567) 1996 HW1, which also feature a smaller ‘head’ attached to a larger ‘body’. The final model features a crater on the larger lobe, similar to several other modelled contact binaries. The model’s resolution is 25 m, comparable to that of the radar images used.Peer reviewe
Spatiotemporal variation in size-dependent growth rates in small isolated populations of Arctic charr (Salvelinus alpinus)
Get PDFFunding: The long term monitoring of Arctic charr in lava caves is funded by the Icelandic Research Fund, RANNÍS (research grants 120227 and 162893). E.A.M. was supported by the Icelandic Research Fund, RANNÍS (162893) & a NERC research grant awarded to M.B.M. (NE/R011109/1). M.B.M. was supported by a University Research Fellowship from the Royal Society (London). C.A.L. & B.K.K. were supported by Hólar University, Iceland.As a key life-history trait, growth rates are often used to measure individual performance and to inform parameters in demographic models. Furthermore, intraspecific trait variation generates diversity in nature. Therefore, partitioning out and understanding drivers of spatiotemporal variation in growth rate is of fundamental interest in ecology and evolution. However, this has rarely been attempted owing to the amount of individual-level data required through both time and space, and issues with missing data in important covariates. Here, we implemented a Bayesian state-space model using individual-level data from 20 populations of Arctic charr (Salvelinus alpinus) across 15 capture occasions, which allowed us to: (i) integrate over the uncertainty of missing recapture records; (ii) robustly estimate size-dependence; and (iii) include a covariate (water temperature) that contained missing data. Interestingly, although there was substantial spatial, temporal and spatiotemporal variation in growth rate, this was only weakly associated with variation in water temperature and almost entirely independent of size, suggesting that spatiotemporal variation in other environmental conditions affected individuals across sizes similarly. This fine-scale spatiotemporal variation emphasizes the importance of local conditions and highlights the potential for spatiotemporal variation in a size-dependent life-history trait, even when environmental conditions are apparently very similar.Peer reviewe
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No full textAbstract redacted"Scottish Funding Council/Global Challenges
Research Fund (grant number SMDO-XFC119) and the University of St Andrews (School of
Medicine),"--Fundin
Emergence and clonal expansion of a qacA-harbouring sequence type 45 lineage of methicillin-resistant Staphylococcus aureus
Get PDFFunding: This work is funded by a National Health and Medical Research Council (NHMRC) Investigator Grant (APP1174555).The past decade has seen an increase in the prevalence of sequence type (ST) 45 methicillin-resistant Staphylococcus aureus (MRSA), yet the underlying drivers for its emergence and spread remain unclear. To better understand the worldwide dissemination of ST45 S. aureus, we performed phylogenetic analyses of Australian isolates, supplemented with a global population of ST45 S. aureus genomes. Our analyses revealed a distinct lineage of multidrug-resistant ST45 MRSA harbouring qacA, predominantly found in Australia and Singapore. Bayesian inference predicted that the acquisition of qacA occurred in the late 1990s. qacA was integrated into a structurally variable region of the chromosome containing Tn552 (carrying blaZ) and Tn4001 (carrying aac(6')-aph(2")) transposable elements. Using mutagenesis and in vitro assays, we provide phenotypic evidence that qacA confers tolerance to chlorhexidine. These findings collectively suggest both antimicrobial resistance and the carriage of qacA may play a role in the successful establishment of ST45 MRSA.Peer reviewe
One-pot fabrication of sodium deoxycholate based supramolecular self-healing antibacterial double network hydrogels
Get PDFFunding: S. Das and P. Saha acknowledges Amity University Kolkata for financial and infrastructural facilities. P Saha acknowledges DST INSPIRE Fellowship [IF230096] for the financial support.Double network (DN) hydrogels have emerged as a significant technology for enhancement of mechanical strength of weak supramolecular gels. In the present study, we report the one-pot route for design of a low molecular weight gelator based DN hydrogel wherein sodium deoxycholate (NaDC) forms the primary network entangled with agar matrix. Various compositions of the reported agar-NaDC hydrogels were examined through FTIR, sol-gel transition temperature (Tsg), XRD, circular dichroism (CD), scanning electron microscopy (SEM), hydrophobicity probe studies, Zeta potential studies and rheology measurements. Analysis of all studies together reveal that 1 mg/ml agar-NaDC DN hydrogel is the optimum composition that exhibits dense networking with primarily β-sheet like structure, highest mechanical strength as well as self-healing characteristics with reversed optical activity and highest Tsg. Antibacterial activity studied using inhibition zone method suggests that 1 mg/ml agar-NaDC gel demonstrates significant bactericidal effect unlike the pure gel with an inhibition zone of ∼25 mm against E.coli after 24 h and ∼32 mm after 48 h incubation. The antibacterial activity was unique for this composition of the DN hydrogel which is attributed to its reversal in optical activity exhibiting positive cotton effect resulting in stronger interaction with the bacterial cell wall. Additionally, nearly 2 times reduced water absorption capacity of the 1 mg/ml agar-NaDC DN hydrogel compared to pure NaDC hydrogel ensures the retention of its mechanical strength as well as other properties in high moisture containing environment. Hence, the 1 mg/ml agar-NaDC DN hydrogel holds appreciable potential as a novel strong supramolecular self-healing antibacterial hydrogel with sustained release characteristics primarily important for biomedical applications.Peer reviewe
Characterising HIV-1 transmission in Victoria, Australia : a molecular epidemiological study
Get PDFFunding: National Health and Medical Research Council, Australian Research Council.Background: In Australia the incidence of HIV has declined steadily, yet sustained reduction of HIV transmission in this setting requires improved public health responses. As enhanced public health responses and prioritisation of resources may be guided by molecular epidemiological data, here we aimed to assess the applicability of these approaches in Victoria, Australia. Methods: A comprehensive collection of HIV-1 pol sequences from individuals diagnosed with HIV in Victoria, Australia, between January 1st 2000 and December 31st 2020 were deidentified and used as the basis of our assessment. These sequences were subtyped and surveillance drug resistance mutations (SDRMs) identified, before definition of transmission groups was performed using HIV-TRACE (0.4.4). Phylodynamic methods were applied using BEAST (2.6.6), assessing effective reproductive numbers for large groups, and additional demographic data were integrated to provide a high resolution view of HIV transmission in Victoria on a decadal time scale. Findings: Based on standard settings for HIV-TRACE, 70% (2438/3507) of analysed HIV-1 pol sequences were readily assigned to a transmission group. Individuals in transmission groups were more commonly males (aOR 1.50), those born in Australia (aOR 2.13), those with probable place of acquisition as Victoria (aOR 6.73), and/or those reporting injectable drug use (aOR 2.13). SDRMs were identified in 375 patients (10.7%), with sustained transmission of these limited to a subset of smaller groups. Informative patterns of epidemic growth, stabilisation, and decline were observed; many transmission groups showed effective reproductive numbers (R e ) values reaching greater than 4.0, representing considerable epidemic growth, while others maintained low R e values. Interpretation: This study provides a high resolution view of HIV transmission in Victoria, Australia, and highlights the potential of molecular epidemiology to guide and enhance public health responses in this setting. This informs ongoing discussions with community groups on the acceptability and place of molecular epidemiological approaches in Australia.Peer reviewe
CHEOPS in-flight performance : a comprehensive look at the first 3.5 years of operations
Get PDFFunding: TWi and ACCa acknowledge support from STFC consolidated grant numbers ST/R000824/1 and ST/V000861/1, and UKSA grant number ST/R003203/1. PM acknowledges support from STFC research grant number ST/R000638/1. This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (project FOUR ACES grant agreement No 724427). CHe acknowledges support from the European Union H2020-MSCA-ITN-2019 under Grant Agreement no. 860470 (CHAMELEON). NCSa acknowledges funding by the European Union (ERC, FIERCE, 101052347). V.V.G. is an F.R.S-FNRS Research Associate. NAW acknowledges UKSA grant ST/R004838/1.Context. Since the discovery of the first exoplanet almost three decades ago, the number of known exoplanets has increased dramatically. By beginning of the 2000s it was clear that dedicated facilities to advance our studies in this field were needed. The CHaracterising ExOPlanet Satellite (CHEOPS) is a space telescope specifically designed to monitor transiting exoplanets orbiting bright stars. In September 2023, CHEOPS completed its nominal mission duration of 3.5 yr and remains in excellent operational conditions. As a testament to this, the mission has been extended until the end of 2026. Aims. Scientific and instrumental data have been collected throughout in-orbit commissioning and nominal operations, enabling a comprehensive analysis of the mission’s performance. In this article, we present the results of this analysis with a twofold goal. First, we aim to inform the scientific community about the present status of the mission and what can be expected as the instrument ages. Secondly, we intend for this publication to serve as a legacy document for future missions, providing insights and lessons learned from the successful operation of CHEOPS. Methods. To evaluate the instrument performance in flight, we developed a comprehensive monitoring and characterisation (M&C) programme. It consists of dedicated observations that allow us to characterise the instrument’s response and continuously monitor its behaviour. In addition to the standard collection of nominal science and housekeeping data, these observations provide valuable input for detecting, modelling, and correcting instrument systematics, discovering and addressing anomalies, and comparing the instrument’s actual performance with expectations. Results. The precision of the CHEOPS measurements has enabled the mission objectives to be met and exceeded. The satellite’s performance remains stable and reliable, ensuring accurate data collection throughout its operational life. Careful modelling of the instrumental systematics allows the data quality to be significantly improved during the light curve analysis phase, resulting in more precise scientific measurements. Conclusions. CHEOPS is compliant with the driving scientific requirements of the mission. Although visible, the ageing of the instrument has not affected the mission’s performance. The satellite’s capabilities remain robust, and we are confident that we will continue to acquire high-quality data during the mission extension.Peer reviewe
Evolutionary growth of molecular clouds as traced by their infrared bright fraction
Get PDFFunding: EJW acknowledges funding from the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) – Project-ID 138713538 – SFB 881 (“The Milky Way System”, subproject P1). EJW and KK gratefully acknowledges funding from the DFG in the form of an Emmy Noether Research Group (grant number KR4598/2-1, PI Kreckel) and the European Research Council’s starting grant ERC StG-101077573 (“ISM-METALS"). EJW also acknowledges the support of STFC consolidated grant number ST/X001229/1. AJR acknowledges postdoctoral support from the University of Leeds. NP and AJR acknowledges the support of STFC consolidated grant number ST/N000706/1 and ST/S00033X/1. GAF gratefully acknowledges the Collaborative Research Center 1601 (SFB 1601 sub-project A2) funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) – 500700252. GAF also acknowledges support from the University of Cologne and its Global Faculty programme.Understanding how stars form, evolve and impact molecular clouds is key to understanding why star formation is such an inefficient process globally. In this paper, we use the infrared bright fraction, fIRB (the fraction of a given molecular cloud that appears bright against the 8 μm Milky Way background) as a proxy for time evolution to test how cloud properties change as star formation evolves. We apply this metric to 12,000 high-mass star-forming molecular clouds we identify using the Herschel–Hi-GAL survey between |ℓ| < 70○ on the Milky Way plane. We find clouds are not static while forming stars. Instead, molecular clouds continuously gain mass while star formation progresses. By performing principal component analysis on the cloud properties, we find that they evolve down two paths distinguished by their mass gain. Most clouds (80 %) gain four times more mass as a function of fIRB. The remaining 20% experience an extreme period of growth, growing in mass by a factor of 150 on average and during this period, they initially gain mass fast enough to outpace their star formation. For all clouds, it is only after half their area becomes star forming that mass loss occurs. We expect stellar feedback and potentially galactic shear is responsible. By analysing cloud positions, we suggest that the rate of mass growth may be linked to the larger galactic environment. Altogether, these results have strong implications on how we assess star forming ability on cloud scales when assuming molecular cloud masses are fixed in time.Peer reviewe
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