Geometry and Topology of Escape II: Homotopic Lobe Dynamics

We continue our study of the fractal structure of escape-time plots for chaotic maps. In the preceding paper, we showed that the escape-time plot contains regular sequences of successive escape segments, called epistrophes, which converge geometrically upon each endpoint of every escape segment. In the present paper, we use topological techniques to: (1) show that there exists a minimal required set of escape segments within the escape-time plot; (2) develop an algorithm which computes this minimal set; (3) show that the minimal set eventually displays a recursive structure governed by an ``Epistrophe Start Rule'': a new epistrophe is spawned Delta = D+1 iterates after the segment to which it converges, where D is the minimum delay time of the complex.Comment: 13 pages, 8 figures, to appear in Chaos, second of two paper

Geometry and Topology of Escape I: Epistrophes

We consider a dynamical system given by an area-preserving map on a two-dimensional phase plane and consider a one-dimensional line of initial conditions within this plane. We record the number of iterates it takes a trajectory to escape from a bounded region of the plane as a function along the line of initial conditions, forming an ``escape-time plot''. For a chaotic system, this plot is in general not a smooth function, but rather has many singularities at which the escape time is infinite; these singularities form a complicated fractal set. In this article we prove the existence of regular repeated sequences, called ``epistrophes'', which occur at all levels of resolution within the escape-time plot. (The word ``epistrophe'' comes from rhetoric and means ``a repeated ending following a variable beginning''.) The epistrophes give the escape-time plot a certain self-similarity, called ``epistrophic'' self-similarity, which need not imply either strict or asymptotic self-similarity.Comment: 15 pages, 9 figures, to appear in Chaos, first of two paper

Enhancing the practical utility of risk assessments in climate change adaptation

In 2012, the Intergovernmental Panel on Climate Change (IPCC) moved from a vulnerability to a risk-based conception of climate change adaptation. However, there are few examples of work that translates this approach into climate change adaptation practice, in order to demonstrate the practical utility of following a risk-based approach to adapting to climate change. The paper explores critically the differing conceptions of vulnerability and risk across the literature relating to disaster risk management and climate change adaptation. The paper also examines a selection of spatially focused climate change vulnerability and risk assessment methodologies in this context. In doing so, we identify issues with the availability of spatial data to enable spatial risk-based climate change assessments. We argue that the concept of risk is potentially favorable in helping cities to understand the challenges posed by climate change, identify adaptation options, and build resilience to the changing climate. However, we suggest that change is needed in the way that practitioners and policymakers engage with risk-based concepts if they are to be embed into climate change adaptation activities

Including Organizational Cultural Parameters in Work Processes

Recent work in modeling decision-making work processes has focused on including the national culture of individual decision-makers in order to emphasize the differences in decision criteria between decision-makers of different nationalities. In addition to nationality, a decision-maker is also a member of an organization and brings this organizational culture to his role in the work process, where it may also affect his task performance. In order to represent the organizational impact on the work process, five organizational cultural parameters were identified and included in an algorithm for modeling and simulation of cultural difference in human decision-making. While the five modifiers are not orthogonal, each captures a unique aspect of the organizational impact. The organizational cultural parameters are Authority Distance, Interface Culture, Command Authority, Doctrine, and Hierarchical Arrangement. This allows the prediction of outcome changes for a work process when interacting decision-makers have similar national cultures but whose organizational culture is different. The effect of including these parameters was illustrated on a Public Affairs Office process that integrated U.S. and U.K. decision-makers