Finite nilpotent semigroups of small coclass

The parameter coclass has been used successfully in the study of nilpotent algebraic objects of different kinds. In this paper a definition of coclass for nilpotent semigroups is introduced and semigroups of coclass 0, 1, and 2 are classified. Presentations for all such semigroups and formulae for their numbers are obtained. The classification is provided up to isomorphism as well as up to isomorphism or anti-isomorphism. Commutative and self-dual semigroups are identified within the classification.Comment: 11 page

Intra- and interprofessional practices through fresh eyes: a qualitative analysis of medical students’ early workplace experiences

Background Professional identities are influenced by experiences in the clinical workplace including socialisation processes that may be hidden from academic faculty and potentially divergent from formal curricula. With the current educational emphasis on complexity, preparedness for practice, patient safety and team-working it is necessary to evaluate and respond to what students are learning about collaborative practices during their clinical placements. Methods 394 second year medical students at a London medical school were invited to submit a short formative essay as part of their coursework describing, evaluating and reflecting on their experiences of how healthcare professionals work together. Their experiences were derived from having spent two days each week for 25 weeks in clinical contexts across primary and secondary care. We consented 311 participants and used a Consensual Qualitative Research approach to analyse these essays, creating a ‘students-eye view’ of intra- and interprofessional practices in the workplace. Results We identified four overarching themes in students’ essays: Theme 1: analyses of contextual factors driving team tensions including staff shortages, shifting teams, and infrastructural issues; Theme 2: observations of hierarchical and paternalistic attitudes and behaviours; Theme 3: respect for team members’ ability to manage and mitigate tensions and attitudes; and Theme 4: take-forward learning including enthusiasm for quality improvement and system change. Conclusions Students are being socialised into a complex, hierarchical, pressurised clinical workplace and experience wide variations in professional behaviours and practices. They articulate a need to find constructive ways forward in the interests of staff wellbeing and patient care. We present educational recommendations including providing safe reflective spaces, using students’ lived experience as raw material for systems thinking and quality improvement, and closing the feedback loop with placement sites on behalf of students

‘I was exhausted trying to figure it out’: the experiences of females receiving an autism diagnosis in middle to late adulthood

Females often receive autism spectrum condition diagnoses later than males, leaving needs misunderstood. This study aimed to explore the lived experiences of female adults diagnosed with an autism spectrum condition in middle to late adulthood. Eleven autistic females diagnosed over the age of 40 years completed semi-structured interviews, analysed using Interpretative Phenomenological Analysis. Four superordinate themes emerged: A hidden condition (pretending to be normal and fitting in; mental health and mislabelling), The process of acceptance (initial reactions and search for understanding; re-living life through a new lens), The impact of others post-diagnosis (initial reactions; stereotyped assumptions), and A new identity on the autism spectrum (negotiating relationships, connections and community; changing well-being and views of the self; the meaning of diagnosis). Findings highlight several factors not previously identified that affect late diagnosis in females, including widespread limited understandings of others. Diagnosis was experienced by several participants as facilitating transition from being self-critical to self-compassionate, coupled with an increased sense of agency. Participants experienced a change in identity that enabled greater acceptance and understanding of the self. However, this was painful to adjust to at such a late stage

Specification and Data Presentation in Linear Control Systems-Part Two

This is the second part of a 2 volume report on the specification and data presentation in linear control systems. This volume deals with Sample Data Systems, Linear Time Variable Parameter Systems, and Performance Indices, which are respectively Chapter II, III, and IV of the volume. Since these subjects are somewhat unrelated, a separate abstract is given at the beginning of each chapter, with the exception of the introductory Chapter I. The separate chapter abstracts are repeated here for the convenience of the reader. Abstract - Linear Sampled Data Control Systems The specifications recommended, for use with sampled data control systems are those recommended for linear, continuous systems [1]. These specifications must be supplemented, as is dictated by the requirements of a particular system, by compatibility considerations that are detailed in the following sections. Abstract - The Specification of Linear Time Variable Parameter Systems Linear time variable parameter (LTVP) systems are defined and subdivided into those systems with fast or slow variations and/or large or small variations. The methods of analysis of such systems are reviewed, and the following recommendations are made. Specifications 1) Time Domain Specifications (a) LTVP systems with fast variation of parameters. Simulated unfrozen system step function responses should all lie within a prescribed envelope. Whenever possible, the actual system response should be obtained. (b) LTVP systems with slow variation of parameters. Simulated or actual frozen or unfrozen system step function responses should all lie within a prescribed envelope. 2) Frequency Domain Specifications (a) LTVP system with fast variation of parameters. Frequency domain specifications are not recommended. (b) LTFP system with slow variation of parameters. The family of frequency response curves of the system frozen at different instants should all lie within a predetermined envelope. Data Presentation It is recommended that the region of variation of closed loop poles of the frozen system be exhibited on the complex plane. Thus, for example, if the only varying parameter is an open loop gain, then the region of variation of the closed loop poles will correspond to the root loci over the total range of variation of gain. It is also recommended that a family of Nyquist diagrams corresponding to the system frozen at different instants be displayed in the case of system with slow variations of parameters. Abstract - Performance Index This study was undertaken to determine whether or not Performance Indices should be used to evaluate and specify control systems* It is recommended that they not be used at this time by the Air Force for the stated purpose. A performance index is defined and detailed discussions are presented for the various performance indices. Analytical methods for evaluating performance indices are presented

Stability of Nonlinear Control Systems by the Second Method of Liapunov

This report investigates the stability of autonomous closed-loop control systems containing nonlinear elements. An n-th order nonlinear autonomous system is described by a set of n first order differential equations of the type dxi/dt=xi(x1, x2, …xn) i=1,2,…n. Liapunov\u27s second (direct) method is used in the stability analysis of such systems. This method enables one to prove that a system is stable (or unstable) if a function V=V (x1, x2, … xn) can be found which, together with its time derivative, satisfies the requirements of Liapunov\u27s stability (or instability) theorems. At the present time, there are no generally applicable straight forward procedures available for constructing these Liapunov\u27s functions. Several Liapunov\u27s functions, applicable to systems described in the canonic form of differential equations, have been reported in the literature. In this report, it is shown that any autonomous closed-loop system containing a single nonlinear element can be described by canonic differential equations. The stability criteria derived from the Liapunov\u27s functions for canonic systems give sufficient and not necessary conditions for stability. It is known that these criteria reject many systems which are actually stable. The reasons why stable systems are sometimes rejected by these simplified stability criteria are investigated in the report. It is found that a closed-loop system will always be rejected by these simplified stabi1ity criteria if the root locus of the transfer function G(s), representing the linear portion of the system, is not confined to the left-half of the s-plane for all positive values of the loop gain. A pole-shifting technique and a zero-shifting technique, extending -the applicability of the simplified stability criteria to systems that are stable for sufficiently high and/or sufficiently low values of the loop gain, are proposed in this report. New simplified stability criteria have been developed which incorporate the changes in the canonic form of differential equations caused by the application of the zero-shifting technique. Other methods of constructing Liapunov\u27s functions for nonlinear control systems are presented in Chapter III, These include the work of Pliss, Aizerman and Krasovski. Numerous other procedures, which have been reported in literature, apply to only very special cases of automatic control systems. No attempt has been made to account for all of these special cases and the presentation of methods of constructing Liapunov’s functions is limited to only those which are more generally applicable. A pseudo-canonic transformation has been developed which enables one to find stability criteria of canonic systems without the use of complex variables. The results of this research indicate that the second method of Liapunov is a very powerfuI tool of exact stability analysis of nonlinear systems. Additional research, especially in the direction of the methods of construction of Liapunov’s functions, will not only yield new analysis and synthesis procedures, but also will aid in arriving at a set of meaningful performance specifications for nonlinear control systems

Constructing composition factors for a linear group in polynomial time

We present a Las Vegas polynomial-time algorithm that takes as input a subgroup of and, subject to the existence of certain oracles, determines its composition factors, provided that none of those factors is isomorphic to one of , , , or , for any k

E-cadherin can limit the transforming properties of activating β-catenin mutations

Wnt pathway deregulation is a common characteristic of many cancers. But only Colorectal Cancer predominantly harbours mutations in APC, whereas other cancer types (hepatocellular carcinoma, solid pseudopapillary tumours of pancreas) have activating mutations in β-catenin (CTNNB1). We have compared the dynamics and the potency of β-catenin mutations in vivo. Within the murine small intestine (SI), an activating mutation of β-catenin took much longer to achieve a Wnt deregulation and acquire a crypt-progenitor-cell (CPC) phenotype than Apc or Gsk3 loss. Within the colon, a single activating mutation of β-catenin was unable to drive Wnt deregulation or induce the CPC phenotype. This ability of β-catenin mutation to differentially transform the SI versus the colon correlated with significantly higher expression of the β-catenin binding partner E-cadherin. This increased expression is associated with a higher number of E-cadherin:β-catenin complexes at the membrane. Reduction of E-cadherin synergised with an activating mutation of β-catenin so there was now a rapid CPC phenotype within the colon and SI. Thus there is a threshold of β-catenin that is required to drive transformation and E-cadherin can act as a buffer to prevent β-catenin accumulation

Writing projective representations over subfields

Let G=〈X〉be an absolutely irreducible subgroup of GL(d, K), and let F be a proper subfield of the finite field K. We present a practical algorithm to decide constructively whether or not G is conjugate to a subgroup of GL(d, F).K×, where K× denotes the centre of GL(d, K). If the derived group of G also acts absolutely irreducibly, then the algorithm is Las Vegas and costs O(|X|d3+d2log|F|) arithmetic operations in K. This work forms part of a recognition project based on Aschbacher’s classification of maximal subgroups of GL(d, K)

Individual crypt genetic heterogeneity and the origin of metaplastic glandular epithelium in human Barrett’s oesophagus

OBJECTIVES: Current models of clonal expansion in human Barrett's oesophagus are based upon heterogenous, flow-purified biopsy analysis taken at multiple segment levels. Detection of identical mutation fingerprints from these biopsy samples led to the proposal that a mutated clone with a selective advantage can clonally expand to fill an entire Barrett's segment at the expense of competing clones (selective sweep to fixation model). We aimed to assess clonality at a much higher resolution by microdissecting and genetically analysing individual crypts. The histogenesis of Barrett's metaplasia and neo-squamous islands has never been demonstrated. We investigated the oesophageal gland squamous ducts as the source of both epithelial sub-types. METHODS: Individual crypts across Barrett's biopsy and oesophagectomy blocks were dissected. Determination of tumour suppressor gene loss of heterozygosity patterns, p16 and p53 point mutations were carried out on a crypt-by-crypt basis. Cases of contiguous neo-squamous islands and columnar metaplasia with oesophageal squamous ducts were identified. Tissues were isolated by laser capture microdissection and genetically analysed. RESULTS: Individual crypt dissection revealed mutation patterns that were masked in whole biopsy analysis. Dissection across oesophagectomy specimens demonstrated marked clonal heterogeneity, with multiple independent clones present. We identified a p16 point mutation arising in the squamous epithelium of the oesophageal gland duct, which was also present in a contiguous metaplastic crypt, whereas neo-squamous islands arising from squamous ducts were wild-type with respect to surrounding Barrett's dysplasia. CONCLUSIONS: By studying clonality at the crypt level we demonstrate that Barrett's heterogeneity arises from multiple independent clones, in contrast to the selective sweep to fixation model of clonal expansion previously described. We suggest that the squamous gland ducts situated throughout the oesophagus are the source of a progenitor cell that may be susceptible to gene mutation resulting in conversion to Barrett's metaplastic epithelium. Additionally, these data suggest that wild-type ducts may be the source of neo-squamous islands