Conjugacy and centralisers in Thompson's group T

PhD ThesisThe Thompson family of groups F < T < V are well-known as interesting (counter-) examples in group theory. Working algebraically with these objects is difficult, and yet the groups are computationally tractable. For instance, T and V are infinite simple groups; despite this, both are finitely presented. This thesis studies the middle group T, using the piecewise-linear function point of view. We present a solution to the conjugacy problem in this group, adapting the approach of Kassabov and Matucci1 to 1 Kassabov and Matucci 2012. the same problem in F. Conjugacy of elements in T was shown2 to 2 Belk and Matucci 2014. be decidable by Belk and Matucci; however our approach constructs explicit conjugators (when they exist). Later, we refine the description given by Matucci3 of nontorsion elements’ centralisers in T. 3 Matucci 2008, Chapter 7. * * * The first chapter introduces the world of Thompson’s groups. The sections on cyclic order, the generalised groups PLS,G and groupoid PL2, and on the Cantor space are particularly important for readers interested in the rest of the thesis. The second chapter discusses Thompson’s groups from a dynamical point of view. We summarise how F, T and V rerrange the interval, noting the distinction between dyadic and nondyadic points. Focussing on T, we introduce the rotation number and explain what we can learn from it. Amidst all this we present a number of intermediate results, forming a toolkit for use in later chapters. The third chapter studies conjugacy in T. We narrow the search space by finding constraints that a conjugator must satisfy. Next, we break the conjugacy problem into a search for a coarse and fine conjugator, the product of which—if they exist—is a bona fide conjugator. We solve these search problems,4 and thus solve the conjugacy problem in T. 4 Lemma 3.3.2 and Algorithms 3.3.5 and 3.4.8. In the fourth chapter, we study element centralisers in T via a particular group extension. We focus on nontorsion elements, providing small details missing from Matucci’s proof which identifies the extension’s kernel.5 We explain how to find the size of the extension’s quotient, by 5 Theorem 4.2.1 and Remark 4.2.2. reducing the problem to a search for coarse conjugators.6 6 Algorithm 4.2.3. The final chapter describes the extension structure of CT(α) in more detail.7 We do so by classifying α into one of four cases. In all but 7 Section 5.2. one case, this extension splits (as a wreath or direct product); in the remaining case, we identify8 exactly when the extension splits (again as 8 See Proposition 5.2.15 and the summary in in Theorem 5.3.2. a wreath product). In each case, we describe the centraliser’s structure9 9 Proposition 5.2.17. in terms of integer parameters. We then show how to construct10 an 10 Corollaries 5.2.6, 5.2.16, 5.2.18, 5.2.23 element of T whose centraliser has a given list of parameters

Climate action and the vantage point of imagined futures: a scenario-based conversation

This paper is a structured dialogue between its four authors on the question “How might future scenarios nourish our thinking about climate action?” A scenario set for the future of European regional inequality in the year 2048, developed by the Horizon Europe funded IMAJINE programme, is used as the prism for this conversation. Each author has a distinct disciplinary and professional background, and initially approaches the question from their own angle. These individual explorations encompass: the nature of climate change and our understanding of it in each IMAJINE scenario; questions of risk and responsibility now and in times to come; the use of scenarios to identify current blind spots and stimulate creative thinking; and the possibility that scenarios might offer fresh perspectives which allow us to reevaluate our notions of the sustainable “good life” and identify vulnerabilities which are overlooked in the present day. The second part of the paper comprises reflections on these individual contributions, with the authors pairing off so that two authors comment on the inputs by the other two, and vice versa. This exemplifies the polyphonic and discursive nature of scenarios, understood as “the art of strategic conversation”. The concluding comments reflect on the wider ability of readers, writers, and researchers to use scenario processes and structured conversations like those in this paper to sustain open spaces of mutual uncertainty, exploration, and generation

Unique protein features of SARS-CoV-2 relative to other Sarbecoviruses

Defining the unique properties of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) protein sequences has potential to explain the range of Coronavirus Disease 2019 severity. To achieve this we compared proteins encoded by all Sarbecoviruses using profile Hidden Markov Model similarities to identify protein features unique to SARS-CoV-2. Consistent with previous reports, a small set of bat- and pangolin-derived Sarbecoviruses show the greatest similarity to SARS-CoV-2 but are unlikely to be the direct source of SARS-CoV-2. Three proteins (nsp3, spike, and orf9) showed regions differing between the bat Sarbecoviruses and SARS-CoV-2 and indicate virus protein features that might have evolved to support human infection and/or transmission. Spike analysis identified all regions of the protein that have tolerated change and revealed that the current SARS-CoV-2 variants of concern have sampled only a fraction (∼31 per cent) of the possible spike domain changes which have occurred historically in Sarbecovirus evolution. This result emphasises the evolvability of these coronaviruses and the potential for further change in virus replication and transmission properties over the coming years

Face identity verification : five challenges facing practitioners

The scientific study of facial identification in Psychology is of practical relevance to security operations and police investigations in which establishing the identity of an unfamiliar person is of critical importance. At border control checkpoints, for example, officials compare the face of each traveler to their corresponding passport photograph. A key security threat in these settings is the occurrence of identity mismatches (aka "impostors"), who attempt to evade detection by using stolen or borrowed passports. Recently, impostors have also begun utilizing more sophisticated methods of hiding their identity. In this short review, we outline five of the key challenges for facial identification that are of current relevance to applied security settings, with a focus on how psychological science can be instrumental in overcoming the difficulties that accompany this task

Facial identity verification: Five challenges facing practitioners

The scientific study of facial identification in Psychology is of practical relevance to security operations and police investigations in which establishing the identity of an unfamiliar person is of critical importance. At border control checkpoints, for example, officials compare the face of each traveler to their corresponding passport photograph. A key security threat in these settings is the occurrence of identity mismatches (aka “impostors”), who attempt to evade detection by using stolen or borrowed passports. Recently, impostors have also begun utilizing more sophisticated methods of hiding their identity. In this short review, we outline five of the key challenges for facial identification that are of current relevance to applied security settings, with a focus on how psychological science can be instrumental in overcoming the difficulties that accompany this task

The Association of Participation in a Summer Prelaw Training Program and First-Year Law School Students’ Grades

This study estimates the association of participation in a nine-week online educational program to prepare students for post-graduate (juris doctorate) education and law school grades. We collected registrar data from 17 U.S. law schools for participants and non-participants from the same year and a prior year. We compared first-semester law school grades between participating and non-participating students weighted by propensity scores. Course participation was associated with improved first-semester grades in a keyed course (Contracts Law) and overall grade point average. According to pre- and post-survey responses, a substantial portion of those who completed the program reported feeling more prepared for law school

Lessons from Laparoscopic Liver Surgery: A Nine-Year Case Series

Objective. This series describes a developing experience in laparoscopic liver surgery presenting results from 40 procedures including right hemihepatectomy, left lateral lobectomy, and microwave ablation therapy. Methods. Forty patients undergoing laparoscopic liver surgery between September 1997 and November 2006 were included. The data set includes: operative procedure and duration, intraoperative blood loss, conversion to open operation rates, length of hospital stay, complications, mortality, histology of lesions/resection margins, and disease recurrence. Results. Mean age of patient: 59 years, 17/40 male, 23/40 female, 23/40 of lesions were benign, and 17/40 malignant. Operations included: laparoscopic anatomical resections n = 15, nonanatomical resections n = 11, microwave ablations n = 8 and deroofing of cysts n = 7. Median anaesthetic time: 120 minutes (range 40–240), mean blood loss 78 mL and 1/40 conversions to open. Median resection margins were 10 mm (range 1–14) and median length of stay 3 days (range 1–10). Operative and 30-day mortality were zero with no local disease recurrence. Conclusion. Laparoscopic liver surgery appears safe and effective and is associated with reduced hospital stay. Larger studies are required to confirm it is oncologically sound

Increased resolution of African swine fever virus genome patterns based on profile HMMs of protein domains.

African swine fever virus (ASFV), belonging to the Asfarviridae family, was originally described in Africa almost 100?years ago and is now spreading uncontrolled across Europe and Asia and threatening to destroy the domestic pork industry. Neither effective antiviral drugs nor protective vaccines are currently available. Efforts to understand the basis for viral pathogenicity and the development of attenuated potential vaccine strains are complicated by the large and complex nature of the ASFV genome. We report here a novel alignment-free method of documenting viral diversity based on profile hidden Markov model domains on a genome scale. The method can be used to infer genomic relationships independent of genome alignments and also reveal ASFV genome sequence differences that determine the presence and characteristics of functional protein domains in the virus. We show that the method can quickly identify differences and shared patterns between virulent and attenuated ASFV strains and will be a useful tool for developing much-needed vaccines and antiviral agents to help control this virus. The tool is rapid to run and easy to implement, readily available as a simple Docker image

Antimicrobial octapeptin C4 analogues active against Cryptococcus species

Resistance to antimicrobials is a growing problem in both developed and developing countries. In nations where AIDS is most prevalent, the human fungal pathogen Cryptococcus neoformans is a significant contributor to mortality, and its growing resistance to current antifungals an ever-expanding threat. We investigated octapeptin C4, from the cationic cyclic lipopeptide class of antimicrobials, as a potential new antifungal. Octapeptin C4 was a potent, selective inhibitor of this fungal pathogen with minimum inhibitory concentration of 1.56 μg/mL. Further testing of octapeptin C4 against 40 clinical isolates of C. neoformans var. grubii or neoformans showed MIC 1.56-3.13 μg/mL while 20 clinical isolates of C. neoformans var. gattii had MIC 0.78-12.5 μg/mL. In each case MIC values for octapeptin C4 were equivalent to, or better than, current antifungal drugs fluconazole and amphotericin B. The negatively charged polysaccharide capsule of C. neoformans influences the pathogens sensitivity to octapeptin C4 while degree of melanisation had little effect. Testing synthetic octapeptin C4 derivatives provided insight into the structure activity relationships, revealing that the lipophilic amino acid moieties are more important to the activity than the cationic diaminobutyric acid groups. Octapeptins have promising potential for development as anticryptococcal therapeutic agents

The CASSOWARY spectroscopy survey: a new sample of gravitationally lensed galaxies in SDSS

Bright gravitationally lensed galaxies provide our most detailed view of galaxies at high redshift. The very brightest (r < 21) systems enable high spatial and spectral resolution measurements, offering unique constraints on the outflow energetics, metallicity gradients and stellar populations in high-redshift galaxies. Yet as a result of the small number of ultrabright z ≃ 2 lensed systems with confirmed redshifts, most detailed spectroscopic studies have been limited in their scope. With the goal of increasing the number of bright lensed galaxies available for detailed follow-up, we have undertaken a spectroscopic campaign targeting wide separation (≳3 arcsec) galaxy–galaxy lens candidates within the Sloan Digital Sky Survey (SDSS). Building on the earlier efforts of our Cambridge and Sloan Survey Of Wide Arcs in Thesky survey, we target a large sample of candidate galaxy–galaxy lens systems in SDSS using a well-established search algorithm which identifies blue arc-like structures situated around luminous red galaxies. In this paper, we present a new redshift catalogue containing 29 lensed sources in SDSS confirmed through spectroscopic follow-up of candidate galaxy–galaxy lens systems. Included in this new sample are two of the brightest galaxies (r = 19.6 and 19.7) known at z ≃ 2, a low metallicity (12 + log (O/H) ≃ 8.0) extreme nebular line emitting galaxy at z = 1.43, and numerous systems for which detailed follow-up will be possible. The source redshifts span 0.9 < z < 2.5 (median redshift of 1.9), and their optical magnitudes are in the range 19.6 ≲ r ≲ 22.3. We present a brief source-by-source discussion of the spectroscopic properties extracted from our confirmatory spectra and discuss some initial science results. Preliminary lens modelling reveals average source magnifications of 5–10 times. With more than 50 gravitationally lensed z ≳ 1 galaxies now confirmed within SDSS, it will soon be possible for the first time to develop generalized conclusions from detailed spectroscopic studies of the brightest lensed systems at high redshift