Statistical Mechanics of 2+1 Gravity From Riemann Zeta Function and Alexander Polynomial:Exact Results

In the recent publication (Journal of Geometry and Physics,33(2000)23-102) we demonstrated that dynamics of 2+1 gravity can be described in terms of train tracks. Train tracks were introduced by Thurston in connection with description of dynamics of surface automorphisms. In this work we provide an example of utilization of general formalism developed earlier. The complete exact solution of the model problem describing equilibrium dynamics of train tracks on the punctured torus is obtained. Being guided by similarities between the dynamics of 2d liquid crystals and 2+1 gravity the partition function for gravity is mapped into that for the Farey spin chain. The Farey spin chain partition function, fortunately, is known exactly and has been thoroughly investigated recently. Accordingly, the transition between the pseudo-Anosov and the periodic dynamic regime (in Thurston's terminology) in the case of gravity is being reinterpreted in terms of phase transitions in the Farey spin chain whose partition function is just a ratio of two Riemann zeta functions. The mapping into the spin chain is facilitated by recognition of a special role of the Alexander polynomial for knots/links in study of dynamics of self homeomorphisms of surfaces. At the end of paper, using some facts from the theory of arithmetic hyperbolic 3-manifolds (initiated by Bianchi in 1892), we develop systematic extension of the obtained results to noncompact Riemannian surfaces of higher genus. Some of the obtained results are also useful for 3+1 gravity. In particular, using the theorem of Margulis, we provide new reasons for the black hole existence in the Universe: black holes make our Universe arithmetic. That is the discrete Lie groups of motion are arithmetic.Comment: 69 pages,11 figures. Journal of Geometry and Physics (in press

Promoting cohesion, challenging expectations: educating the teachers of tomorrow for race equality and diversity in 21st century schools

Survey evidence suggests that newly qualified teachers tend to feel relatively ill-prepared to engage with pupils of BME (Black and Minority Ethnic) heritage or to respond to potentially challenging issues related to race equality in schools. Of key concern is how the teaching work force - predominantly white, monolingual, female and middle class - can be enabled to be more effective and culturally competent in teaching an increasingly diverse pupil population in terms of ethnicity, culture, language and economics. Preparing teachers to support schools’ role in promoting social cohesion remains of vital relevance in a period of increasing austerity and social change. A research team from the University of Edinburgh and Manchester Metropolitan University interviewed 31 lecturers involved in teacher education in Scotland and England, to find out how they are dealing with race equality issues

'The People Want The Regime Brought Down': Popular Geopolitics and The 2011 Egyptian Revolution

This thesis uses popular geopolitics in order to examine the eighteen days of the 2011 Egyptian revolution. Popular outlets such as novels, films and cartoons have been identified by geopolitical scholars as legitimate sources through which to analyse political issues and define geopolitical identities. (ó’Tuathail & Dalby, 1998; Dodds, 2008; Sharp, 2000; Dittmer, 2007). In the case of Egypt, these sources carry particular importance, as past research indicates the power that Egyptian popular entertainment has on the formation of Egyptian national identity (Fahmy, 2011). Within the 2011 Egyptian revolution, popular culture sources largely contributed to the success of the revolution (El Zein & Ortiz, 2011; Macfarland, 2011). This work uses examples of popular literature from the 2011 Egyptian revolution to explore not just the expressed emotions, articulated identities, agency and experience of the Egyptian population living it. The texts of Khaled Al Khamissi’s Taxi, Tarek Shanin’s Al-Khan, Nariman Youssef’s diary of her experiences in the square and examples of the protesters’ signs and poetry are examined through a detailed discourse analysis. The thesis begins with an introduction to how the four texts and popular cultural discourses shape and challenge the geographical imagination of Egypt prior to 2011. It shows how the texts construct the geopolitical identity of the Egyptian protester in Tahrir Square, and how the Egyptian protester also utilised the popular literature to construct their own identity. With reference to the different spaces of the revolution acknowledged in the texts, it contributes to the space and geography of the revolution. Reading these texts reveals the extent of the Egyptian protesters’ grievances and their experience throughout the event. It provides a space for their voice and agency. This thesis argues the importance of focusing on popular geopolitics more regularly in analyses of major political events

An assessment of the Sister Cities International Program as an international public relations entity

Going global is the business perspective for the 21st century. Unfortunately, global perspective from American business and organization is limited. With the world shrinking at an astonishing pace, organizations need to find their communication channels to their international publics. The purpose of this study was to learn if the techniques used in the Sister Cities International Program are effective for international public relations. The findings of this study would prove helpful to international public relations professionals in planning their own programs based on the effectiveness of the Sister Cities Program. Five cities were evaluated based on their activities, public relations techniques, promotion, planning, goals, objectives and evaluation procedures. Evaluation of the cities was done through research of news articles, brochures, reports and surveys. The five cities varied in economic, social, cultural and developed backgrounds. This was necessary to prove if the program worked on all levels of community development. Based on the information found, Sister Cities International effectively uses public relations and publicity techniques to promote its organization and activities. Positive media coverage of programs and events were found in all five cities with high concentrations of commitment and sponsorship from the media in two of the five cities

Metacognition in forensic patients with schizophrenia and a history of interpersonal violence: an exploratory study

Metacognition has been shown to be impaired in people with schizophrenia, and related to poorer social functioning outcomes. To date, no research has looked at the relationship between a particularly rare – but problematic – social functioning outcome (violence) and metacognition. The present study aimed at doing this by exploring patterns of metacognition in people with schizophrenia and a history of interpersonal violence, and comparing them to a group with schizophrenia and no history of violence. Participants took part in an interview which explored stress and coping, which was subsequently coded for metacognitive ability. Results indicate that metacognitive functioning is not directly associated with violence as an outcome in schizophrenia, as metacognition did not differ significantly between the two groups. However, results revealed that metacognition has a hierarchical structure with some domains more impaired than others, which may be relevant to the observed social functioning outcomes in schizophrenia. The limitations of the study and implications for clinical practice and future research are discussed

Asymmetric synthesis of quaternary centres using organocatalysis

Quaternary carbon centres are ubiquitous in nature, typically in natural products. The task of creating an all carbon quaternary centre, bearing an alkyl moiety with differentiated functionalities and substituents is a desired key step in organic synthesis. A variety of endeavours by research groups have lead to the construction of stereogenic quaternary centres, albeit with narrow scope of substrate. Despite the repertoire of transition metals/ligands, chiral auxiliaries and reagents available at hand, efficient enantioselective and organocatalytic methodologies for the construction of all carbon quaternary centres still remains a daunting challenge for synthetic chemists. One of the most popular methods to install a quaternary centre is via a conjugate addition, the addition of a chiral tertiary enolate to an electron deficient alkene or carbonyl compound has led to high levels of synthetic accomplishment over generations. Our strategy to assemble such quaternary centres focused on an organocatalytic tandem Michael-aldol reaction, as an efficient one-pot strategy to install vicinal quaternary centres with good levels of enantioselective induction. Initial 1,4-conjugate addition of the nucleophile with α-acrolein type Michael acceptors generates the enolate, which is now set up to undergo an intramolecular aldol reaction providing the desired molecules. Molecular complexes of this class are also amenable to further catalytic transformations and synthetic elaborations.This thesis presents our investigations towards organocatalytic enantioselective strategies for the assembly of fully substituted quaternary centres