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John McKay's remarkable insights unveiled a connection between the 'double covers' of the groups of regular polyhedra, known since ancient Greek times, and the exceptional Lie algebras, recognized since the late nineteenth century. The correspondence involves certain diagrams, the ADE diagrams, which can be interpreted in different ways: as quivers associated with the groups, and Dynkin diagrams of root systems of Lie algebras. The ADE diagrams arise in many areas of mathematics, including topics in relativity and string theory, spectral theory of graphs and cluster algebras. Accessible to students, this book explains these connections with exercises and examples throughout. An excellent introduction for students and researchers wishing to learn more about this unifying principle of mathematics.
Edited by
R. A. Bailey, University of St Andrews, Scotland,Peter J. Cameron, University of St Andrews, Scotland,Yaokun Wu, Shanghai Jiao Tong University, China
Edited by
R. A. Bailey, University of St Andrews, Scotland,Peter J. Cameron, University of St Andrews, Scotland,Yaokun Wu, Shanghai Jiao Tong University, China
Eigenvalues of the Laplacian matrix of a graph have been widely used in studying connectivity and expansion properties of networks, and also in analyzing random walks on a graph. Independently, statisticians introduced various optimality criteria in experimental design, the goal being to obtain more accurate estimates of quantities of interest in an experiment. It turns out that the most popular of these optimality criteria for block designs are determined by the Laplacian eigenvalues of the concurrence graph, or of the Levi graph, of the design. The most important optimality criteria, called A (average), D (determinant) and E (extreme), are related to the conductance of the graph as an electrical network, the number of spanning trees, and the isoperimetric properties of the graphs, respectively. The number of spanning trees is also an evaluation of the Tutte polynomial of the graph, and is the subject of the Merino–Welsh conjecture relating it to acyclic and totally cyclic orientations, of interest in their own right. This chapter ties these ideas together, building on the work in [4] and [5].
Edited by
R. A. Bailey, University of St Andrews, Scotland,Peter J. Cameron, University of St Andrews, Scotland,Yaokun Wu, Shanghai Jiao Tong University, China
Edited by
R. A. Bailey, University of St Andrews, Scotland,Peter J. Cameron, University of St Andrews, Scotland,Yaokun Wu, Shanghai Jiao Tong University, China
Edited by
R. A. Bailey, University of St Andrews, Scotland,Peter J. Cameron, University of St Andrews, Scotland,Yaokun Wu, Shanghai Jiao Tong University, China
Edited by
R. A. Bailey, University of St Andrews, Scotland,Peter J. Cameron, University of St Andrews, Scotland,Yaokun Wu, Shanghai Jiao Tong University, China
Edited by
R. A. Bailey, University of St Andrews, Scotland,Peter J. Cameron, University of St Andrews, Scotland,Yaokun Wu, Shanghai Jiao Tong University, China
This collection of four short courses looks at group representations, graph spectra, statistical optimality, and symbolic dynamics, highlighting their common roots in linear algebra. It leads students from the very beginnings in linear algebra to high-level applications: representations of finite groups, leading to probability models and harmonic analysis; eigenvalues of growing graphs from quantum probability techniques; statistical optimality of designs from Laplacian eigenvalues of graphs; and symbolic dynamics, applying matrix stability and K-theory. An invaluable resource for researchers and beginning Ph.D. students, this book includes copious exercises, notes, and references.
The nature of the pathway from conduct disorder (CD) in adolescence to antisocial behavior in adulthood has been debated and the role of certain mediators remains unclear. One perspective is that CD forms part of a general psychopathology dimension, playing a central role in the developmental trajectory. Impairment in reflective functioning (RF), i.e., the capacity to understand one's own and others' mental states, may relate to CD, psychopathology, and aggression. Here, we characterized the structure of psychopathology in adult male-offenders and its role, along with RF, in mediating the relationship between CD in their adolescence and current aggression.
Methods
A secondary analysis of pre-treatment data from 313 probation-supervised offenders was conducted, and measures of CD symptoms, general and specific psychopathology factors, RF, and aggression were evaluated through clinical interviews and questionnaires.
Results
Confirmatory factor analyses indicated that a bifactor model best fitted the sample's psychopathology structure, including a general psychopathology factor (p factor) and five specific factors: internalizing, disinhibition, detachment, antagonism, and psychoticism. The structure of RF was fitted to the data using a one-factor model. According to our mediation model, CD significantly predicted the p factor, which was positively linked to RF impairments, resulting in increased aggression.
Conclusions
These findings highlight the critical role of a transdiagnostic approach provided by RF and general psychopathology in explaining the link between CD and aggression. Furthermore, they underscore the potential utility of treatments focusing on RF, such as mentalization-based treatment, in mitigating aggression in offenders with diverse psychopathologies.
Recent disasters emphasize the need for disaster risk mitigation in the health sector. A lack of standardized tools to assess hospital disaster preparedness hinders the improvement of emergency/disaster preparedness in hospitals. There is very limited research on evaluation of hospital disaster preparedness tools.
Objective:
This study aimed to determine the presence and availability of hospital preparedness tools across the world, and to identify the important components of those study instruments.
Method:
A systematic review was performed using three databases, namely Ovid Medline, Embase, and CINAHL, as well as available grey literature sourced by Google, relevant websites, and also from the reference lists of selected articles. The studies published on hospital disaster preparedness across the world from 2011-2020, written in English language, were selected by two independent reviewers. The global distribution of studies was analyzed according to the World Health Organization’s (WHO) six geographical regions, and also according to the four categories of the United Nations Human Development Index (UNHDI). The preparedness themes were identified and categorized according to the 4S conceptual framework: space, stuff, staff, and systems.
Result:
From a total of 1,568 articles, 53 met inclusion criteria and were selected for data extraction and synthesis. Few published studies had used a study instrument to assess hospital disaster preparedness. The Eastern Mediterranean region recorded the highest number of such publications. The countries with a low UNHDI were found to have a smaller number of publications. Developing countries had more focus on preparedness for natural disasters and less focus on chemical, biological, radiological, and nuclear (CBRN) preparedness. Infrastructure, logistics, capacity building, and communication were the priority themes under the space, stuff, staff, and system domains of the 4S framework, respectively. The majority of studies had neglected some crucial aspects of hospital disaster preparedness, such as transport, back-up power, morgue facilities and dead body handling, vaccination, rewards/incentive, and volunteers.
Conclusion:
Important preparedness themes were identified under each domain of the 4S framework. The neglected aspects should be properly addressed in order to ensure adequate preparedness of hospitals. The results of this review can be used for planning a comprehensive disaster preparedness tool.
The capture and analysis of diverse data is widely recognized as being vital to the design of new products and services across the digital economy. We focus on its use to inspire the co-design of visitor experiences in museums as a distinctive case that reveals opportunities and challenges for the use of personal data. We present a portfolio of data-inspired visiting experiences that emerged from a 3-year Research Through Design process. These include the overlay of virtual models on physical exhibits, a smartphone app for creating personalized tours as gifts, visualizations of emotional responses to exhibits, and the data-driven use of ideation cards. We reflect across our portfolio to articulate the diverse ways in which data can inspire design through the use of ambiguity, visualization, and inter-personalization; how data inspire co-design through the process of co-ideation, co-creation, and co-interpretation; and how its use must negotiate the challenges of privacy, ownership, and transparency. By adopting a human perspective on data, we are able to chart out the complex and rich information that can inform design activities and contribute to datasets that can drive creativity support systems.
Debate about the nature of climate and the magnitude of ecological change across Australia during the last glacial maximum (LGM; 26.5–19 ka) persists despite considerable research into the late Pleistocene. This is partly due to a lack of detailed paleoenvironmental records and reliable chronological frameworks. Geochemical and geochronological analyses of a 60 ka sedimentary record from Brown Lake, subtropical Queensland, are presented and considered in the context of climate-controlled environmental change. Optically stimulated luminescence dating of dune crests adjacent to prominent wetlands across North Stradbroke Island (Minjerribah) returned a mean age of 119.9 ± 10.6 ka; indicating relative dune stability soon after formation in Marine Isotope Stage 5. Synthesis of wetland sediment geochemistry across the island was used to identify dust accumulation and applied as an aridification proxy over the last glacial-interglacial cycle. A positive trend of dust deposition from ca. 50 ka was found with highest influx occurring leading into the LGM. Complexities of comparing sedimentary records and the need for robust age models are highlighted with local variation influencing the accumulation of exogenic material. An inter-site comparison suggests enhanced moisture stress regionally during the last glaciation and throughout the LGM, returning to a more positive moisture balance ca. 8 ka.
The Eating Assessment in Toddlers FFQ (EAT FFQ) has been shown to have good reliability and comparative validity for ranking nutrient intakes in young children. With the addition of food items (n 4), we aimed to re-assess the validity of the EAT FFQ and estimate calibration factors in a sub-sample of children (n 97) participating in the Growing Up Milk – Lite (GUMLi) randomised control trial (2015–2017). Participants completed the ninety-nine-item GUMLi EAT FFQ and record-assisted 24-h recalls (24HR) on two occasions. Energy and nutrient intakes were assessed at months 9 and 12 post-randomisation and calibration factors calculated to determine predicted estimates from the GUMLi EAT FFQ. Validity was assessed using Pearson correlation coefficients, weighted kappa (κ) and exact quartile categorisation. Calibration was calculated using linear regression models on 24HR, adjusted for sex and treatment group. Nutrient intakes were significantly correlated between the GUMLi EAT FFQ and 24HR at both time points. Energy-adjusted, de-attenuated Pearson correlations ranged from 0·3 (fibre) to 0·8 (Fe) at 9 months and from 0·3 (Ca) to 0·7 (Fe) at 12 months. Weighted κ for the quartiles ranged from 0·2 (Zn) to 0·6 (Fe) at 9 months and from 0·1 (total fat) to 0·5 (Fe) at 12 months. Exact agreement ranged from 30 to 74 %. Calibration factors predicted up to 56 % of the variation in the 24HR at 9 months and 44 % at 12 months. The GUMLi EAT FFQ remained a useful tool for ranking nutrient intakes with similar estimated validity compared with other FFQ used in children under 2 years.
We describe an ultra-wide-bandwidth, low-frequency receiver recently installed on the Parkes radio telescope. The receiver system provides continuous frequency coverage from 704 to 4032 MHz. For much of the band (
${\sim}60\%$
), the system temperature is approximately 22 K and the receiver system remains in a linear regime even in the presence of strong mobile phone transmissions. We discuss the scientific and technical aspects of the new receiver, including its astronomical objectives, as well as the feed, receiver, digitiser, and signal processor design. We describe the pipeline routines that form the archive-ready data products and how those data files can be accessed from the archives. The system performance is quantified, including the system noise and linearity, beam shape, antenna efficiency, polarisation calibration, and timing stability.
We know little about the retirement plans of adults with chronic diseases. This research recruited Canadian workers 50–67 years of age from a national panel of 80,000 individuals (arthritis, n = 631; diabetes, n = 286; both arthritis and diabetes, n = 111; no chronic disabling conditions, n = 538). A cross-sectional survey asked participants about their expected age of retirement, future work plans, whether they were retiring sooner than planned, and bridged retirement. Chi-square analyses, analyses of variance, and regression analyses examined expectations and factors associated with them. Despite health difficulties, workers with arthritis and diabetes had retirement plans similar to those of healthy controls and consistent with normative expectations of working to a traditional retirement age. However, more respondents with arthritis or diabetes reported bridged retirement than healthy controls. Contrary to predictions, health factors accounted for less of the variance in retirement expectations than other factors. These findings point to the complexity surrounding retirement expectations and highlight person–job fit rather than disease factors alone.
The second year of life is a period of nutritional vulnerability. We aimed to investigate the dietary patterns and nutrient intakes from 1 to 2 years of age during the 12-month follow-up period of the Growing Up Milk – Lite (GUMLi) trial. The GUMLi trial was a multi-centre, double-blinded, randomised controlled trial of 160 healthy 1-year-old children in Auckland, New Zealand and Brisbane, Australia. Dietary intakes were collected at baseline, 3, 6, 9 and 12 months post-randomisation, using a validated FFQ. Dietary patterns were identified using principal component analysis of the frequency of food item consumption per d. The effect of the intervention on dietary patterns and intake of eleven nutrients over the duration of the trial were investigated using random effects mixed models. A total of three dietary patterns were identified at baseline: ‘junk/snack foods’, ‘healthy/guideline foods’ and ‘breast milk/formula’. A significant group difference was observed in ‘breast milk/formula’ dietary pattern z scores at 12 months post-randomisation, where those in the GUMLi group loaded more positively on this pattern, suggesting more frequent consumption of breast milk. No difference was seen in the other two dietary patterns. Significant intervention effects were seen on nutrient intake between the GUMLi (intervention) and cows’ milk (control) groups, with lower protein and vitamin B12, and higher Fe, vitamin D, vitamin C and Zn intake in the GUMLi (intervention) group. The consumption of GUMLi did not affect dietary patterns, however, GUMLi participants had lower protein intake and higher Fe, vitamins D and C and Zn intake at 2 years of age.
Combinatorics is a subject of increasing importance, owing to its links with computer science, statistics and algebra. This is a textbook aimed at second-year undergraduates to beginning graduates. It stresses common techniques (such as generating functions and recursive construction) which underlie the great variety of subject matter and also stresses the fact that a constructive or algorithmic proof is more valuable than an existence proof. The book is divided into two parts, the second at a higher level and with a wider range than the first. Historical notes are included which give a wider perspective on the subject. More advanced topics are given as projects and there are a number of exercises, some with solutions given.