Deligne's duality for de Rham realizations of 1-motives

We show that the pairing on de Rham realizations of 1-motives in "Theorie di Hodge III", IHES 44, can be defined over any base scheme and we prove that it gives rise to a perfect duality if one is working with a 1-motive and its Cartier dual. Furthermore we study universal extensions of 1-motives and their relation with $\natural$-extensions.Comment: 21 pages. Last section rewritten. New proof

Frontier at your fingertips

Between the nano- and micrometre scales, the collective behaviour of matter can give rise to startling emergent properties that hint at the nexus between biology and physics.Comment: Archival copy of Nature Connections Articl

A detailed analysis of the brachistochrone problem

If A and B are two points in the plane, with B lower and to the right of A, then we may consider the trajectory of an object travelling from A to B under the influence of gravity. The search for the trajectory minimising the time taken by the object gives rise to a mathematical optimisation problem involving an indefinite integral. Although the solution of this problem is known, a full detailed handling of the problem does not seem to be available. The aim of this article is to provide such a detailed study

Phil Anderson's Magnetic Ideas in Science

In Philip W. Anderson's research, magnetism has always played a special role, providing a prism through which other more complex forms of collective behavior and broken symmetry could be examined. I discuss his work on magnetism from the 1950s, where his early work on antiferromagnetism led to the pseudospin treatment of superconductivity - to the 70s and 80s, highlighting his contribution to the physics of local magnetic moments. Phil's interest in the mechanism of moment formation, and screening evolved into the modern theory of the Kondo effect and heavy fermions.Comment: References fully hypertexed with live links to historic papers. "PWA90: A Lifetime of Emergence", editors P. Chandra, P. Coleman, G. Kotliar, P. Ong, D. Stein and C. Yu, pp 187-213, World Scientific (2016

What are your “odds-of-success”? Reflecting on the role of adaptive leadership in Leicester City’s (2015/16) English Football Premier League Title win

Purpose: This article utilizes the concept of adaptive leadership to explore how Leicester City, a small, provincial football club, defied odds of 5000-1 to became only the sixth winners of the English Premier League. It examines two research questions: 1. can adaptive leadership be used to explain how the club developed the conditions for the team’s success? and; 2. what practical lessons can be learned from this? Design/methodology/approach: This case study utilizes secondary material, published from 2011-2019, including interviews with players and staff, recordings of press conferences, club announcements, match programmes, books, magazine and newspaper articles, television reports, and social media coverage. Findings: Adaptive leadership provides a mechanism for understanding the organizational change necessary for Leicester City’s title victory. Three core elements of adaptive leadership are identified: 1. the “change leader’s” deliberate decision to engage others across the organization in a process of “intelligent reflection,” to identify the required approach to address an identified organizational objective; 2. an organization-wide focus on building leadership capacity, to promote continuous improvement through personal and organizational learning; 3. a long term commitment by the most senior organizational leader to elements of the change process, thereby ensuring new ways of working became normalized over the longer term. Originality/value: While theoretically well-developed, the practice of adaptive leadership remains under-researched (Yukl and Mahsud, 2010). Leicester City’s Premier League victory illustrates several key aspects of adaptive leadership in action, in a way that many people can easily relate to. The efficacious and team learning aspects of Leicester City’s success story are important for organizational development scholars and practitioners alike. In summary, the key findings and lessons within this article can be metaphorically transferred to other team-based learning organization, i.e. including and beyond the world of sport!.</p

The Problem of Doping

In this Essay, we examine Professor Michael J. Sandel and Judge Richard A. Posner\u27s thoughts on how to draw the line between substances and techniques that are fair game and those that constitute doping; whether there is a difference between sport and spectacle; and the nature of the public’s interest in sport as an institution and in doping as a practice that risks its integrity. Although we do not agree with all of their conclusions, they have made serious contributions to the ongoing discussion of these issues. Their linedrawing work in particular deserves considered attention from WADA and other stakeholders as they continue to work toward a useful and defensible definition of the spirit of sport