Height bounds and the Siegel property

Let $G$ be a reductive group defined over $\mathbb{Q}$ and let $\mathfrak{S}$ be a Siegel set in $G(\mathbb{R})$. The Siegel property tells us that there are only finitely many $\gamma \in G(\mathbb{Q})$ of bounded determinant and denominator for which the translate $\gamma.\mathfrak{S}$ intersects $\mathfrak{S}$. We prove a bound for the height of these $\gamma$ which is polynomial with respect to the determinant and denominator. The bound generalises a result of Habegger and Pila dealing with the case of $GL_2$, and has applications to the Zilber-Pink conjecture on unlikely intersections in Shimura varieties. In addition we prove that if $H$ is a subset of $G$, then every Siegel set for $H$ is contained in a finite union of $G(\mathbb{Q})$-translates of a Siegel set for $G$.Comment: 24 pages, minor revision

Families of abelian varieties with many isogenous fibres

Let Z be a subvariety of the moduli space of principally polarised abelian varieties of dimension g over the complex numbers. Suppose that Z contains a Zariski dense set of points which correspond to abelian varieties from a single isogeny class. A generalisation of a conjecture of Andr\'e and Pink predicts that Z is a weakly special subvariety. We prove this when dim Z = 1 using the Pila--Zannier method and the Masser--W\"ustholz isogeny theorem. This generalises results of Edixhoven and Yafaev when the Hecke orbit consists of CM points and of Pink when it consists of Galois generic points.Comment: Gap in Lemma 3.3 found and corrected by Gabriel Dil

Models for online, open, flexible and technology enhanced higher education across the globe – a comparative analysis

Digital technology has become near ubiquitous in many countries today or is on a path to reach this state in the near future. Across the globe the share of internet users, for instance, has jumped in the last ten years. In Europe most countries have a share of internet users near to or above 90% in 2016 (last year available for international comparisons), in China the current share is 53%, but this has grown from just 16% in 2007, even in Ethiopia the share has grown from 0.4% to 15.4% in the same period (data from ITU). At the same time expectations of widespread adoption of digital solutions in higher education have been rising. In 2017 the New Media Consortium’s Horizon Report predicted that adaptive learning would take less than a year to be widely adopted (Adams Becker et al., 2017). And projects such as ‘Virtually Inspired’ are showcasing creative examples of how new technologies are already being harnessed to improve the quality of teaching and learning. Furthermore, discussion of the United Nations’ Sustainable Development Goals emphasise the key potentials that digital technology holds for achieving the goals for education in 2030 (UNESCO, 2017). These developments lead university and college leadership to the question of how they should position their institution. What type of digitalisation initiatives can be found practice beyond best practices and future potentials? This is the question that this study attempts to answer. It sets out to analyse how higher education providers from across the world are harnessing digitalisation to improve teaching and learning and learner support and to identify emerging types of practice. For this, it focuses on the dimensions of flexibility of provision (in terms of time, place and pace) and openness of provision (in terms of who has access to learning and support and who is involved in the design of learning provision), as both of these dimensions can significantly benefit from integration of digital solutions. The method of information collation used by the study was a global survey of higher education institutions (HEIs) covering all world continents, more than thirty countries and 69 cases. The survey found that nearly three-quarters of all HEIs have at least one strategic focus and typologies were developed based on this analysis to group HEIs with similar strategic focuses. Overall, the findings suggest that most higher education providers are just at the beginning of developing comprehensive strategies for harnessing digitalisation. For this reason, the authors of this study believe that providers can benefit from the outcomes of this study’s research, as it can be used by university and college leadership for benchmarking similarities and differences and for cooperative peer learning between institutions. The database of cases and the guidelines for reviewing current strategies, which accompany this study, aim to facilitate this learning and evaluation process

Clearing Up Some Conceptual Confusions About Conspiracy Theory Theorising

A reply to Gérald Bronner, Véronique Campion-Vincent, Sylvain Delouvée, Sebastian Dieguez, Nicolas Gauvrit, Anthony Lantian, and Pascal Wagner-Egger's piece, '“They” Respond: Comments on Basham et al.’s “Social Science’s Conspiracy-Theory Panic: Now They Want to Cure Everyone”

THE CHILD AS THE PRESENTING SYMPTOM, AND WHAT HAPPENS WHEN THINGS GO WRONG?

In this paper I wish to draw attention to Balint’s concept of ‘the Child as the presenting symptom’ and ask whether this concept is relevant to us as psychiatrists. What arises is whether this concept might illuminate situations where there is serious mental illness in the family, and whether the presentation of a child to a doctor might be indicative of mental illness in the family. If such an interpretation is possible, then there are important clinical implications, since at present, all UK government guidance, based on the analysis of many high-profile cases where children have been severely abused, is that the needs of the child are paramount, and thence it may be that, whilst quite dramatic intervention may well occur in order to protect the child, perhaps the mental health needs of the parents might be somewhat overlooked. Examples of the interplay between child and parents in the context of mental illness are given, and the present way in which children within families where there is mental illness are cared for is described, also considering the consequences for the parents

Azimuthal decorrelation of forward and backward jets at the Tevatron

We analyse the azimuthal decorrelation of Mueller-Navelet dijets produced in the collisions at Tevatron energies using a BFKL framework which incorporates dominant subleading effects. We show that these effects significantly reduce the decorrelation yet they are still insufficient to give satisfactory description of experimental data. However a good description of the data is obtained after incorporating within formalism the effective rapidity defined by Del Duca and Schmidt.Comment: 1+9 pages, 6 eps figures; the final version to appear in Phys. Lett. B; one reference added, the use of effective rapidity and the need for BFKL resummmation for small azimuthal angles better motivate

Additional Soft Jets in ttˉ{\rm t\bar{t}} Production at the Tevatron \pp Collider

A large fraction of top quark events in \pp collisions at 1.8\ \TeV will contain additional soft hadronic jets from gluon bremsstrahlung off the quarks and gluons in the hard processes \qq, gg \to \tt \to \bb \ww. These extra jets can cause complications when attempting to reconstruct $m_t$ from the invariant mass of combinations of final-state quarks and leptons. We show how such soft radiation cannot be unambiguously associated with either initial-state radiation or or with final-state radiation off the $b$ quarks. The top quarks can radiate too, and in fact the pattern of radiation has a very rich structure, which depends on the orientation of the final-state particles with respect to each other and with respect to the beam. We calculate the full radiation pattern of soft jets in the soft gluon approximation and compare with several approximate forms which are characteristic of parton shower Monte Carlos. The implications for top mass measurements are discussed.Comment: plain LaTeX, 13 pages plus 9 figures included as a separate uuencoded file (or avail. from authors); DTP/94/60, UR-136