Geometric and spectral properties of causal maps

We study the random planar map obtained from a critical, finite variance, Galton-Watson plane tree by adding the horizontal connections between successive vertices at each level. This random graph is closely related to the well-known causal dynamical triangulation that was introduced by Ambj{\o}rn and Loll and has been studied extensively by physicists. We prove that the horizontal distances in the graph are smaller than the vertical distances, but only by a subpolynomial factor: The diameter of the set of vertices at level $n$ is both $o(n)$ and $n^{1-o(1)}$. This enables us to prove that the spectral dimension of the infinite version of the graph is almost surely equal to 2, and consequently that the random walk is diffusive almost surely. We also initiate an investigation of the case in which the offspring distribution is critical and belongs to the domain of attraction of an $\alpha$-stable law for $\alpha \in (1,2)$, for which our understanding is much less complete.Institut Universitaire de France, ANR Graal (ANR-14-CE25-0014), ANR Liouville (ANR-15-CE40-0013), ERC GeoBrown, ISF grant 1207/15 and ERC grant 676970 RandGeom

The Alexander-Orbach conjecture holds in high dimensions

We examine the incipient infinite cluster (IIC) of critical percolation in regimes where mean-field behavior has been established, namely when the dimension d is large enough or when d>6 and the lattice is sufficiently spread out. We find that random walk on the IIC exhibits anomalous diffusion with the spectral dimension d_s=4/3, that is, p_t(x,x)= t^{-2/3+o(1)}. This establishes a conjecture of Alexander and Orbach. En route we calculate the one-arm exponent with respect to the intrinsic distance.Comment: 25 pages, 2 figures. To appear in Inventiones Mathematica

Supplier qualification for high value goods and services in Nigeria: A comparison of qualified and non-qualified suppliers

This study set out to understand the capabilities of suppliers of high value products and services in Nigeria. Supplier capability data was collected from almost 500 potential suppliers across 28 product categories. The findings indicate that only a small minority of potential suppliers achieved the required levels of performance and that very few companies have suitable operational capabilities or corporate citizenship behaviour. Furthermore, significant differences were found between service suppliers and product suppliers with regard to performance. The findings suggest that the majority of suppliers of products and services in Nigeria need to improve their operational capabilities and corporate citizenship behaviours or else risk losing their ability to compete in a changing market place with new barriers to entry

Personal values, social capital, and higher education student career decidedness: a new 'protean'-informed model

This study investigates the role of personal values as motivational antecedents for understanding HE student career decidedness among university business school (UBS) students. We propose a new ‘protean’ informed HE student career decidedness model for theorizing how both personal values and social capital mediators (student social capital; personal, social and enterprise skills; access to resources) help in the student-centric and self-directed processes of career decision-making. A mixed methods study combines a (stage 1) survey of 308 UBS students from five (UK) university business schools, with results from (stage 2) four student focus groups, and (stage 3) two staff-student interactive seminars. From an employability perspective, arguably, the ultimate responsibility for becoming a ‘protean graduate’ rests with each UBS student, whilst the obligation of HE staff is to effectively facilitate and nurture all possible personal growth and skills development opportunities

Resolving new ultrastructural features of cytokinetic abscission with soft X ray cryo tomography

Mammalian cytokinetic abscission is mediated by the ESCRT membrane fission machinery. While much has been clarified on the topology and kinetics of abscission through high resolution microscopy, key questions regarding the mechanism of abscission remain open. Here we apply cryogenic soft X ray tomography to elucidate new ultrastructural details in the intercellular membrane bridge connecting cells undergoing abscission. In particular, we resolve defined ring like structures inside the midbody dark zone that have been inaccessible to EM, and identify membrane extrusions at the abscission sites. In cells at late stages of abscission we resolve a complex array of helical spirals, extending the structural information obtained by EM. Our results highlight the advantages of soft X ray tomography and emphasize the importance of using complementary approaches for characterizing cellular structures. Notably, by providing new structural data from intact cells we present a realistic view on the topology of abscission and suggest new mechanistic models for ESCRT mediated abscissio

Interviewer: 'Are women and girls ever responsible for the domestic violence they encounter?' Student: 'No, well, unless they did something really, really bad …'

Research shows the ‘gendered nature’ of domestic violence, with Women’s Aid (a UK-based charity) estimating that 1 in 4 women are affected (2014). This paper reports on a project - funded by Comic Relief, completed by Nottinghamshire Domestic Violence Forum (now known as Equation) and evaluated by Nottingham Trent University. The project adopts a Whole School Approach in seeking to prevent domestic violence. Students at three secondary schools attended between one and five blocks of work, and special events. There is evidence of positive developments - with young people showing understanding of domestic violence as well as the margins between healthy and unhealthy relationships. However, not all students could reply ‘never’ to the question of ‘are women and girls to blame for the domestic violence they experience?’, remarking that if the woman had done something ‘really, really bad’ then violence might be justified. We argue that young people’s uncertainties need to be situated within the gender-unequal socio-contexts of contemporary society, and further call for a WSA to domestic violence prevention to be a compulsory part of the UK national curriculum

Self-avoiding walks and connective constants

The connective constant $\mu(G)$ of a quasi-transitive graph $G$ is the asymptotic growth rate of the number of self-avoiding walks (SAWs) on $G$ from a given starting vertex. We survey several aspects of the relationship between the connective constant and the underlying graph $G$. $\bullet$ We present upper and lower bounds for $\mu$ in terms of the vertex-degree and girth of a transitive graph. $\bullet$ We discuss the question of whether $\mu\ge\phi$ for transitive cubic graphs (where $\phi$ denotes the golden mean), and we introduce the Fisher transformation for SAWs (that is, the replacement of vertices by triangles). $\bullet$ We present strict inequalities for the connective constants $\mu(G)$ of transitive graphs $G$, as $G$ varies. $\bullet$ As a consequence of the last, the connective constant of a Cayley graph of a finitely generated group decreases strictly when a new relator is added, and increases strictly when a non-trivial group element is declared to be a further generator. $\bullet$ We describe so-called graph height functions within an account of "bridges" for quasi-transitive graphs, and indicate that the bridge constant equals the connective constant when the graph has a unimodular graph height function. $\bullet$ A partial answer is given to the question of the locality of connective constants, based around the existence of unimodular graph height functions. $\bullet$ Examples are presented of Cayley graphs of finitely presented groups that possess graph height functions (that are, in addition, harmonic and unimodular), and that do not. $\bullet$ The review closes with a brief account of the "speed" of SAW.Comment: Accepted version. arXiv admin note: substantial text overlap with arXiv:1304.721

A generation apart? Youth and political participation in Britain

Conventional wisdom holds that young people in Britain are alienated from politics, with some claiming that this reflects a wider crisis of legitimacy that should be met by initiatives to increase citizenship. This article addresses these areas, presenting both panel survey and focus group data from first-time voters. It concludes that, contrary to the findings from many predominantly quantitative studies of political participation, young people are interested in political matters, and do support the democratic process. However they feel a sense of anti-climax having voted for the first time, and are critical of those who have been elected to positions of political power. If they are a generation apart, this is less to do with apathy, and more to do with their engaged scepticism about ‘formal’ politics in Britain

Pupil response hazard rates predict perceived gaze durations

We investigated the mechanisms for evaluating perceived gaze-shift duration. Timing relies on the accumulation of endogenous physiological signals. Here we focused on arousal, measured through pupil dilation, as a candidate timing signal. Participants timed gaze-shifts performed by face stimuli in a Standard/Probe comparison task. Pupil responses were binned according to “Longer/Shorter” judgements in trials where Standard and Probe were identical. This ensured that pupil responses reflected endogenous arousal fluctuations opposed to differences in stimulus content. We found that pupil hazard rates predicted the classification of sub-second intervals (steeper dilation =“Longer” classifications). This shows that the accumulation of endogenous arousal signals informs gaze-shift timing judgements. We also found that participants relied exclusively on the 2nd stimulus to perform the classification, providing insights into timing strategies under conditions of maximum uncertainty. We observed no dissociation in pupil responses when timing equivalent neutral spatial displacements, indicating that a stimulus-dependent timer exploits arousal to time gaze-shifts

Random walk on sparse random digraphs

International audienceA finite ergodic Markov chain exhibits cutoff if its distance to equilibrium remains close to its initial value over a certain number of iterations and then abruptly drops to near 0 on a much shorter time scale. Originally discovered in the context of card shuffling (Aldous-Diaconis, 1986), this remarkable phenomenon is now rigorously established for many reversible chains. Here we consider the non-reversible case of random walks on sparse directed graphs, for which even the equilibrium measure is far from being understood. We work under the configuration model, allowing both the in-degrees and the out-degrees to be freely specified. We establish the cutoff phenomenon, determine its precise window and prove that the cutoff profile approaches a universal shape. We also provide a detailed description of the equilibrium measure