Let f(n) denote the number of conngurations of n 2 mutually non-attacking kings on a 2n 2n chessboard. We show that log f(n) grows like 2n log n 2n log 2, with an error term of O(n 4=5 log n). The result depends on an estimate for the sum of the entries of a high power of a matrix with positive entries. In chess, two kings can attack one another if their squares are horizontally, vertically, or...

This introductory article presents the special Discussion and Debate volume “From black swans to dragon-kings, is there life beyond power laws?” We summarize and put in perspective the contributions into three main themes: (i) mechanisms for dragon-kings, (ii) detection of dragon-kings and statistical tests and (iii) empirical evidence in a large variety of natural and social systems. Overall, ...

Previous studies have found broad distributions, resembling power laws for different measures of the size of rainfall events. We investigate the large-event tail of these distributions and find in one measure that tropical cyclones account for a large proportion of the very largest events outside the scaling regime, i.e., beyond the cutoff of the power law. Tropical cyclones are sufficiently ra...

always on kingdom history of the world a king without a crown is unconceivable. the persian kings were not exception of this rule. iranian ancient kings crown as one of the aspects of the monarchy and power, the image of king while makes he distinguishes from other persons is visible in various artistic works. one of the important artistic works that image of iran’s kings with their power symbo...

ALAN L. KOLATA Cities, and the larger political formations within which they are embedded, are dynamic congeries of political, economic, and social institutions that are shaped and reshaped by historical circumstance. This dynamism and mutability in the face of exogenou-s forces might suggest the impossibility of a coherent, general theory about the forms and forces of urban transformation of t...

John Paul Vargheese, Peter Travers, Jeff Pan Computing Science University of Aberdeen Kings College Aberdeen, AB24 5UA, UK [email protected] [email protected] [email protected] Kathryn Vincent, Claire Wallace, Anna Kabedeva School of Social Science University of Aberdeen Kings College Aberdeen, AB24 3QY, UK [email protected] [email protected] anna.kabedeva.11@aberdeen....