Eigenvalues of the Laplacian of a graph

Let G be a finite undirected graph with no loops or multiple edges. The Laplacian matrix of G, Delta(G), is defined by Delta sub ii = degree of vertex i and Delta sub ij = -1 if there is an edge between vertex i and vertex j. The structure of the graph G is related to the eigenvalues of Delta(G); in particular, it is proved that all the eigenvalues of Delta(G) are nonnegative, less than or equal to the number of vertices, and less than or equal to twice the maximum vertex degree. Precise conditions for equality are given

Escaping the Thucydides Trap in Political Commentary

This is the author accepted manuscript. The final version is available from History & Policy via the link in this recordExecutive Summary Thucydides (c.460-404 BCE) wrote an account of the Peloponnesian War between Athens and Sparta (431-404 BCE). He is often seen as the founder of critical historiography, but also as a pioneering political theorist, since he claims his account of the past will be useful in understanding present and future events. Thucydides is currently much in vogue, cited as an authority on global developments such as US-China relations and Brexit, as well as factionalism and populism within democratic politics. However, he did not offer simple principles of political behaviour, based on a timeless and universal human nature, although this is how he is often portrayed today. Rather, he presented a detailed narrative, including reconstructions of speeches and debates, to encourage his readers to reflect on the complex and unpredictable nature of events, the limitations of democratic deliberation, and the power of political rhetoric. It is a high irony that Thucydides himself is now being deployed as a rhetorical device. The more enduring and valid policy lesson to draw from Thucydides is not that human nature is a fixed entity through time, from which secure prognostications can be made, but that democracies are vulnerable to cognitive biases of various kinds, which can be manipulated by adroit rhetoricians. In recent years, the fifth-century BCE Greek author Thucydides has been perhaps the most widely cited classical authority, appearing in a surprisingly wide range of contexts from discussions of US-China relations to Brexit. Commentators have noted his presence in the Trump White House, cited both by political advisers and military figures, and he has also become more prominent in British political discourse. In many cases, however, he appears simply as an authoritative name attached to a few quotes; the nature of his work, an account of the war between Athens and Sparta known today as the Peloponnesian War (431-404), and the long history of its reception and influence, remains concealed.History & Polic

Status as performance in Roman society

This is the author accepted manuscriptHow should we approach the study of Roman society? The traditional approach has been to focus on the different groups identified by the Romans themselves as making up their political community, defined either in legal or political terms or more informally (e.g. the army and the poor). This focus on (in anthropological terms) ‘agents’ concepts’ –which inevitably limits our perspective to that of the dominant, literate elite who produce the bulk of our sources –raises the question of what sort of groups these are in modern sociological terms. In scholarship over the last few decades this has tended to be reduced to a choice between status and class, since other modern definitions of social groups based on income or form of labour are clearly anachronistic. The long-running debates about both these terms has led many recent studies to side-step the issue, by focusing on a binary division between ‘elite’ and ‘non-elite’ (conflating wealth and power, and freea nd unfree, in a manner which neither reflects ancient categories of thought nor offers any significant analytical advantage from a modern perspective) or side-stepping the issue altogether by concentrating on the nature of social relations. This has produced some exciting and insightfulaccounts of the dynamics of Roman social interactions, but it leaves a whole other set of questions open: what were the key groups that made up Roman society, and hence shaped individuals’ behaviour and relations with one another

Thucydides and International Relations

This is the author accepted manuscript. The final version is available from the Classical Association via the link in this recordThucydides is not only famous as one of the first historians. He is also, surprisingly, seen as an authority on modern international politics. Neville Morley explores why Thucydides is regularly cited in discussions of the current relationship between the United States and China

Incidence, socioeconomic deprivation, volume-outcome and survival in adult patients with acute lymphoblastic leukaemia in England

BACKGROUND: We examined incidence and survival in relation to age, gender, socioeconomic deprivation, rurality and trends over time. We also examined the association between volume of patients treated by hospitals and survival. METHODS: Incident cases (2001-12) were identified using comprehensive National Health Service admissions data for England, with follow-up to March 2013. Socioeconomic deprivation was based on census area of residence. Volume was assessed in a three-year subset of the data with consistent hospital provider codes. RESULTS: There were 2921 adults aged 18 or more years diagnosed with acute lymphoblastic leukaemia (ALL) in the 12-year time span, giving a crude annual incidence of 0.61/100,000 population. Five-year survival was 32% (1870 deaths). Compared with patients living in least deprived areas, survival was worse for patients living in intermediate and most deprived areas, with mortality hazard ratios 21% (95% CI 8-35%) and 16% (95% CI 3-30%) higher respectively. Hospitals treating low volumes of adults with ALL were associated with poorer survival. The adjusted mortality hazard ratio in this subset of 465 patients was 33% (95% CI 3-73%) higher in low volume hospitals. There was no evidence of association between socioeconomic deprivation and incidence. Rurality did not appear to be associated with incidence or survival. Incidence was higher in men but there was no evidence of a gender difference in survival. Survival improved over time. CONCLUSION: The associations between socioeconomic deprivation and survival and between volume and outcome for adults with ALL, if confirmed, are likely to have significant implications for the organisation of services for adults with ALL

A Physiological Role for Amyloid Beta Protein: Enhancement of Learning and Memory

Amyloid beta protein (A[beta]) is well recognized as having a significant role in the pathogenesis of Alzheimer's disease (AD). The reason for the presence of A[beta] and its physiological role in non-disease states is not clear. In these studies, low doses of A[beta] enhanced memory retention in two memory tasks and enhanced acetylcholine production in the hippocampus _in vivo_. We then tested whether endogenous A[beta] has a role in learning and memory in young, cognitively intact mice by blocking endogenous A[beta] in healthy 2-month-old CD-1 mice. Blocking A[beta] with antibody to A[beta] or DFFVG (which blocks A[beta] binding) or decreasing A[beta] expression with an antisense directed at the A[beta] precursor APP all resulted in impaired learning in T-maze foot-shock avoidance. Finally, A[beta]1-42 facilitated induction and maintenance of long term potentiation in hippocampal slices, whereas antibodies to A[beta] inhibited hippocampal LTP. These results indicate that in normal healthy young animals the presence of A[beta] is important for learning and memory

Computer-aided communication satellite system analysis and optimization

The capabilities and limitations of the various published computer programs for fixed/broadcast communication satellite system synthesis and optimization are discussed. A satellite Telecommunication analysis and Modeling Program (STAMP) for costing and sensitivity analysis work in application of communication satellites to educational development is given. The modifications made to STAMP include: extension of the six beam capability to eight; addition of generation of multiple beams from a single reflector system with an array of feeds; an improved system costing to reflect the time value of money, growth in earth terminal population with time, and to account for various measures of system reliability; inclusion of a model for scintillation at microwave frequencies in the communication link loss model; and, an updated technological environment

Expansive Learning

Chapter six explores the concept of ‘expansive learning’ taken from Fuller and Unwin’s (2003) research of apprenticeships where they identified a ‘restrictive- expansive continuum’ that classified the type of learning environment presented in the work place. Crucially, expansive learning encouraged a supportive environment for students to learn higher level skills such as dialogue, problem solving and reflexive forms of expertise. Supportive and collaborative learning environments can instil confidence in the student to develop and the supervisory role (or previously the mentor) is significant to this. The chapter theme of expansive learning is led by the goal to discover what teaching and learning processes can assist all levels of clinical staff in supporting students to move effectively, and in a well-supported way, to the expertise or ‘graduateness’ (Eden, 2014) required at registration and beyond. This was an important foundation of the recent NMC (2017) review. Chapter 2 and 3 have already demonstrated the potential educational role of unqualified staff and peer students who previously have not been officially recognised for coaching learners in practice. With focused and explicit support for their learning, students’ placement experience can be ‘supercharged’ so their learning advances quicker and with greater impact on their long term professional development (Morley, 2018). A model of coaching that emerged from the research study is also presented. Current emphasis in practice learning is placed on the assessment of measurable clinical skills rather than the students’ ability to join these skills holistically in professional practice (Morley, 2015). The ability to be able to teach this type of integration of student performance into the busy clinical practice is more akin to the fluidity of ‘coaching’ rather than ‘teaching’ and this is explored fully within the chapter

Design and development of magnetostrictive actuators and sensors for structural health monitoring

Carbon Fibre Reinforced Polymer composite (CFRP) is widely used in the aerospace industry, but is prone to delamination, which is a major causes of failure. Structural Health Monitoring (SHM) systems need to be developed to determine the damage occurring within it. Our motivation is to design cost-effective new sensors and a data acquisition system for magnetostrictive structural health monitoring of aerospace composites using a simple RLC circuit. The developed system is tested on magnetostrictive FeSiB and CoSiB actuator ribbons using a bending rig. Our results show detectable sensitivity of inductors as low as 0.6 μH for a bending rig radii between 600 to 300 mm (equivalent to 0.8 to 1.7 mStrain), which show a strain sensitivity resolution of 0.01 μStrain (surface area: ~36 mm2). This value is at the detectability limit of our fabricated system. The best resolution (1.86 μStrain) was obtained from a 70-turn copper (~64 μH) wire inductor (surface area: ~400 mm2) that was paired with a FeSiB actuator