Chromatic roots and minor-closed families of graphs

Given a minor-closed class of graphs $\mathcal{G}$, what is the infimum of the non-trivial roots of the chromatic polynomial of $G \in \mathcal{G}$? When $\mathcal{G}$ is the class of all graphs, the answer is known to be $32/27$. We answer this question exactly for three minor-closed classes of graphs. Furthermore, we conjecture precisely when the value is larger than $32/27$.Comment: 18 pages, 5 figure

Teaching and Learning Data Visualization: Ideas and Assignments

This article discusses how to make statistical graphics a more prominent element of the undergraduate statistics curricula. The focus is on several different types of assignments that exemplify how to incorporate graphics into a course in a pedagogically meaningful way. These assignments include having students deconstruct and reconstruct plots, copy masterful graphs, create one-minute visual revelations, convert tables into `pictures', and develop interactive visualizations with, e.g., the virtual earth as a plotting canvas. In addition to describing the goals and details of each assignment, we also discuss the broader topic of graphics and key concepts that we think warrant inclusion in the statistics curricula. We advocate that more attention needs to be paid to this fundamental field of statistics at all levels, from introductory undergraduate through graduate level courses. With the rapid rise of tools to visualize data, e.g., Google trends, GapMinder, ManyEyes, and Tableau, and the increased use of graphics in the media, understanding the principles of good statistical graphics, and having the ability to create informative visualizations is an ever more important aspect of statistics education

DDLSTM: Dual-Domain LSTM for Cross-Dataset Action Recognition

Domain alignment in convolutional networks aims to learn the degree of layer-specific feature alignment beneficial to the joint learning of source and target datasets. While increasingly popular in convolutional networks, there have been no previous attempts to achieve domain alignment in recurrent networks. Similar to spatial features, both source and target domains are likely to exhibit temporal dependencies that can be jointly learnt and aligned. In this paper we introduce Dual-Domain LSTM (DDLSTM), an architecture that is able to learn temporal dependencies from two domains concurrently. It performs cross-contaminated batch normalisation on both input-to-hidden and hidden-to-hidden weights, and learns the parameters for cross-contamination, for both single-layer and multi-layer LSTM architectures. We evaluate DDLSTM on frame-level action recognition using three datasets, taking a pair at a time, and report an average increase in accuracy of 3.5%. The proposed DDLSTM architecture outperforms standard, fine-tuned, and batch-normalised LSTMs.Comment: To appear in CVPR 201

Evolution in the Volumetric Type Ia Supernova Rate from the Supernova Legacy Survey

We present a measurement of the volumetric Type Ia supernova (SN Ia) rate (SNR_Ia) as a function of redshift for the first four years of data from the Canada-France-Hawaii Telescope Supernova Legacy Survey (SNLS). This analysis includes 286 spectroscopically confirmed and more than 400 additional photometrically identified SNe Ia within the redshift range 0.1 ≤ z ≤ 1.1. The volumetric SNR_Ia evolution is consistent with a rise to z ~ 1.0 that follows a power law of the form (1+z)^α, with α = 2.11 ± 0.28. This evolutionary trend in the SNLS rates is slightly shallower than that of the cosmic star formation history (SFH) over the same redshift range. We combine the SNLS rate measurements with those from other surveys that complement the SNLS redshift range, and fit various simple SN Ia delay-time distribution (DTD) models to the combined data. A simple power-law model for the DTD (i.e., ∝ t^(–β)) yields values from β = 0.98 ± 0.05 to β = 1.15 ± 0.08 depending on the parameterization of the cosmic SFH. A two-component model, where SNR_Ia is dependent on stellar mass (M_stellar) and star formation rate (SFR) as SNR_(Ia)(z) = A × M_(stellar)(z) + B × SFR(z), yields the coefficients A = (1.9 ± 0.1) × 10^(–1)4 SNe yr^(–1) M^(–1)_☉ and B = (3.3 ± 0.2) × 10^(–4) SNe yr^(–1) (M_☉ yr^(–1))^(–1). More general two-component models also fit the data well, but single Gaussian or exponential DTDs provide significantly poorer matches. Finally, we split the SNLS sample into two populations by the light-curve width (stretch), and show that the general behavior in the rates of faster-declining SNe Ia (0.8 ≤ s < 1.0) is similar, within our measurement errors, to that of the slower objects (1.0 ≤ s < 1.3) out to z ~ 0.8

Fruit over sunbed : carotenoid skin coloration is found more attractive than melanin coloration

Skin coloration appears to play a pivotal part in facial attractiveness. Skin yellowness contributes to an attractive appearance and is influenced both by dietary carotenoids and by melanin. While both increased carotenoid coloration and increased melanin coloration enhance apparent health in Caucasian faces by increasing skin yellowness, it remains unclear firstly, whether both pigments contribute to attractiveness judgements, secondly, whether one pigment is clearly preferred over the other, and thirdly, whether these effects depend on the sex of the face. Here, in three studies, we examine these questions using controlled facial stimuli transformed to be either high or low in (a) carotenoid coloration, or (b) melanin coloration. We show, firstly, that both increased carotenoid coloration and increased melanin coloration are found attractive compared to lower levels of these pigments. Secondly, we show that carotenoid coloration is consistently preferred over melanin coloration when levels of coloration are matched. In addition, we find an effect of the sex of stimuli with stronger preferences for carotenoids over melanin in female compared to male faces, irrespective of the sex of the observer. These results are interpreted as reflecting preferences for sex-typical skin coloration: men have darker skin than women and high melanisation in male faces may further enhance this masculine trait, thus carotenoid coloration is not less desirable, but melanin coloration is relatively more desirable in males compared to females. Taken together, our findings provide further support for a carotenoid-linked health-signalling system that is highly important in mate choice.PostprintPeer reviewe

Colouring Graphs with Sparse Neighbourhoods: Bounds and Applications

Let $G$ be a graph with chromatic number $\chi$, maximum degree $\Delta$ and clique number $\omega$. Reed's conjecture states that $\chi \leq \lceil (1-\varepsilon)(\Delta + 1) + \varepsilon\omega \rceil$ for all $\varepsilon \leq 1/2$. It was shown by King and Reed that, provided $\Delta$ is large enough, the conjecture holds for $\varepsilon \leq 1/130,000$. In this article, we show that the same statement holds for $\varepsilon \leq 1/26$, thus making a significant step towards Reed's conjecture. We derive this result from a general technique to bound the chromatic number of a graph where no vertex has many edges in its neighbourhood. Our improvements to this method also lead to improved bounds on the strong chromatic index of general graphs. We prove that $\chi'_s(G)\leq 1.835 \Delta(G)^2$ provided $\Delta(G)$ is large enough.Comment: Submitted for publication in July 201

Social transmission of leadership preference:knowledge of group membership and partisan media reporting moderates perceptions of leadership ability from facial cues to competence and dominance

While first impressions of dominance and competence can influence leadership preference, social transmission of leadership preference has received little attention. The capacity to transmit, store and compute information has increased greatly over recent history, and the new media environment may encourage partisanship (i.e. ‘echo chambers’), misinformation and rumour spreading to support political and social causes and be conducive both to emotive writing and emotional contagion, which may shape voting behaviour. In our pre-registered experiment, we examined whether implicit associations between facial cues to dominance and competence (intelligence) and leadership ability are strengthened by partisan media and knowledge that leaders support or oppose us on a socio-political issue of personal importance. Social information, in general, reduced well-established implicit associations between facial cues and leadership ability. However, as predicted, social knowledge of group membership reduced preferences for facial cues to high dominance and intelligence in out-group leaders. In the opposite-direction to our original prediction, this ‘in-group bias’ was greater under less partisan versus partisan media, with partisan writing eliciting greater state anxiety across the sample. Partisanship also altered the salience of women’s facial appearance (i.e., cues to high dominance and intelligence) in out-group versus in-group leaders. Independent of the media environment, men and women displayed an in-group bias toward facial cues of dominance in same-sex leaders. Our findings reveal effects of minimal social information (facial appearance, group membership, media reporting) on leadership judgements, which may have implications for patterns of voting or socio-political behaviour at the local or national level

A zero-free interval for chromatic polynomials of graphs with 3-leaf spanning trees

It is proved that if $G$ is a graph containing a spanning tree with at most three leaves, then the chromatic polynomial of $G$ has no roots in the interval $(1,t_1]$, where $t_1 \approx 1.2904$ is the smallest real root of the polynomial $(t-2)^6 +4(t-1)^2(t-2)^3 -(t-1)^4$. We also construct a family of graphs containing such spanning trees with chromatic roots converging to $t_1$ from above. We employ the Whitney $2$-switch operation to manage the analysis of an infinite class of chromatic polynomials.Comment: 16 pages, 5 figure

Teacher Development Through Action Research : a Case Study in Focused Action Research.

\u27Focused action research\u27 was employed in a teacher inservice program which sought to develop a fusion between trainer-centred input and teacher-centred action research. The areas of input to teachers were learning strategies, thinking skills, questioning skills and the teaching of study skills. During the four months of this action research project of the teacher educators, teachers experienced two cycles of action research, one investigating their students\u27 learning strategies and the second implementing a plan to improve some aspect of their students\u27 learning - such as summary writing, remedial reading, hotseating, introducing group work, vocabulary-learning techniques - and wrote reports on their work. Although there was no evidence that the gains made transferred into the following school year the teachers both displayed and reported an increase in reflection during the project and immediately after it. Issues of sustaining transfer need to be addressed