Counting intersection numbers of closed geodesics on Shimura curves

Let $\Gamma\backslash\mathbb{H}$ be a Shimura curve, where $\Gamma$ corresponds to the group of units of norm $1$ in an Eichler order $\mathrm{O}$ of an indefinite quaternion algebra over $\mathbb{Q}$. Closed geodesics on $\Gamma\backslash\mathbb{H}$ correspond to optimal embeddings of real quadratic orders into $\mathrm{O}$. The intersection numbers of pairs of these closed geodesics conjecturally relates to the work of Darmon and Vonk on a real quadratic analogue to $j(\tau_1)-j(\tau_2)$. In this paper, we study the total intersection number over all embeddings of a given pair of discriminants $D_1, D_2$. We precisely describe the arithmetic of each intersection, and produce a formula for the total intersection of $D_1, D_2$. This formula is a real quadratic analogue of the work of Gross and Zagier on factorizing $\text{nrd}(j(\tau_1)-j(\tau_2))$. The results are fairly general, allowing for a large class of non-maximal Eichler orders, and non-fundamental/non-coprime discriminants. The paper ends with some explicit examples illustrating the results of the paper.Comment: 43 pages, 1 figure, 11 table

The Local-Global Conjecture for Apollonian circle packings is false

In a primitive integral Apollonian circle packing, the curvatures that appear must fall into one of six or eight residue classes modulo 24. The local-global conjecture states that every sufficiently large integer in one of these residue classes will appear as a curvature in the packing. We prove that this conjecture is false for many packings, by proving that certain quadratic and quartic families are missed. The new obstructions are a property of the thin Apollonian group (and not its Zariski closure), and are a result of quadratic and quartic reciprocity, reminiscent of a Brauer-Manin obstruction. Based on computational evidence, we formulate a new conjectureComment: 28 pages, 4 figures. Minor changes based on feedbac

The political power of twitter

In June 2016, the British voted by 52 per cent to leave the EU, a club the UK joined in 1973. This paper examines Twitter public and political party discourse surrounding the BREXIT withdrawal agreement. In particular, we focus on tweets from four different BREXIT exit strategies known as “Norway”, “Article 50”, the “Backstop” and “No Deal” and their effect on the pound and FTSE 100 index from the period of December 10th 2018 to February 24th 2019. Our approach focuses on using a Naive Bayes classification algorithm to assess political party and public Twitter sentiment. A Granger causality analysis is then introduced to investigate the hypothesis that BREXIT public sentiment, as measured by the twitter sentiment time series, is indicative of changes in the GBP/EUR Fx and FTSE 100 Index. Our results from the Twitter public sentiment indicate that the accuracy of the “Article 50” scenario had the single biggest effect on short run dynamics on the FTSE 100 index, additionally the “Norway” BREXIT strategy has a marginal effect on the FTSE 100 index whilst there was no significant causation to the GBP/EUR Fx. The BREXIT Political party sentiment for the “No Deal” was indicative of short term dynamics on the GBP/EUR Fx at a marginal rate. Our test concluded that there was no causality on the FTSE 100

Californian Science Students' Perceptions of their Classoom Learning Environments.

This study utilised the What Is Happening In this Class (WIHIC) questionnaire to examine factors that influence Californian student perceptions of their learning environment. Data were collected from 665 USA middle school science students in 11 Californian schools. Several background variables were included in the study to investigate their effects on students’ perceptions, such as student and teacher gender, student ethnic background and socio-economic status (SES), and student age. Class and school variables, such as class ethnic composition, class size and school socioeconomic status were also collected. A hierarchical analysis of variance was conducted to investigate separate and joint effects of these variables. Results from this study indicate that some scales of the WIHIC are more inclined to measure personal or idiosyncratic features of student perceptions of their learning environment whereas other scales contain more variance at the class level. Also, it was found that different variables affect different scale scores. A variable that consistently affected students' perceptions, regardless of the element of interest in the learning environment was student gender. Generally speaking girls perceived their learning environment more positively than did boys

Hydrological research for AMMA-2050

In recent decades, West Africa has experienced some of the most extreme rainfall variability anywhere in the world. At present there is no consensus on how changes in greenhouse gases, land cover and aerosols will impact rainfall and flow regimes in the region. AMMA-2050 will investigate how the West African monsoon will change in future decades, and investigate the causes of High Impact Weather (HIW) and how they might change in the future. We will use this information to increase the understanding of future changes in floods, water resources and urban flooding

Hydrological research for AMMA-2050

In recent decades, West Africa has experienced some of the most extreme rainfall variability anywhere in the world. At present there is no consensus on how changes in greenhouse gases, land cover and aerosols will impact rainfall and flow regimes in the region. AMMA-2050 will investigate how the West African monsoon will change in future decades, and investigate the causes of High Impact Weather (HIW) and how they might change in the future. We will use this information to increase the understanding of future changes in floods, water resources and urban flooding

Human cytomegalovirus UL141 promotes efficient downregulation of the natural killer cell activating ligand CD112

Human cytomegalovirus (HCMV) UL141 induces protection against natural killer cell-mediated cytolysis by downregulating cell surface expression of CD155 (nectin-like molecule 5; poliovirus receptor), a ligand for the activating receptor DNAM-1 (CD226). However, DNAM-1 is also recognized to bind a second ligand, CD112 (nectin-2). We now show that HCMV targets CD112 for proteasome-mediated degradation by 48 h post-infection, thus removing both activating ligands for DNAM-1 from the cell surface during productive infection. Significantly, cell surface expression of both CD112 and CD155 was restored when UL141 was deleted from the HCMV genome. While gpUL141 alone is sufficient to mediate retention of CD155 in the endoplasmic reticulum, UL141 requires assistance from additional HCMV-encoded functions to suppress expression of CD112

Can national policy blockages accelerate the development of polycentric governance? Evidence from climate change policy in the United Kingdom

Many factors can conspire to limit the scope for policy development at the national level. In this paper, we consider whether blockages in national policy processes − resulting for example from austerity or small state political philosophies − might be overcome by the development of more polycentric governance arrangements. Drawing on evidence from three stakeholder workshops and fifteen interviews, we address this question by exploring the United Kingdom’s recent retrenchment in the area of climate change policy, and the ways in which its policy community have responded. We identify two broad strategies based on polycentric principles: ‘working with gatekeepers’ to unlock political capital and ‘collaborate to innovate’ to develop policy outputs. We then empirically examine the advantages that these actions bring, analysing coordination across overlapping sites of authority, such as those associated with international regimes, devolved administrations and civic and private initiatives that operate in conjunction with, and sometimes independently of, the state. Despite constraining political and economic factors, which are by no means unique to the UK, we find that a polycentric climate policy network can create opportunities for overcoming central government blockages. However, we also argue that the ambiguous role of the state in empowering but also in constraining such a network will determine whether a polycentric approach to climate policy and governance is genuinely additional and innovative, or whether it is merely a temporary ‘sticking plaster’ for the retreat of the state and policy retrenchment during austere times