Vulnerability modeling and monadic dynamical systems
Cezar Ionescu · Universitätsbibliothek der FU Berlin Hochschulschriftenstelle u. Dokumentenserver · 2009
The present work aims to use insights from functional programming and the underlying mathematics in order to achieve a better understanding of the concept of vulnerability as used in the interdisciplinary world of Climate Impact Research, especially in the context of computational vulnerability assessments. We examine a number of definitions of vulnerability used in the fields of Development Studies and Climate Change, attempting to leverage, in particular, the work of synthesis done by Calvo and Dercon (2005) and the Intergovernmental Panel on Climate Change (2007). The common theme of all these definitions is that vulnerability represents a measure of the harm that might occur in possible future evolutions. In order to unify the various definitions of vulnerability, we have used elementary concepts of Category Theory, representing the ``possible future evolutions'' as functorially constructed structures of evolutions. Computing the harm along these evolutions is done by ``mapping'' the function that evaluates the impacts on the structure of evolutions, while vulnerability represents a measurement on the entire structure of impact values. We were able to formulate precisely the natural condition of consistency between the impact or harm evaluations and the vulnerability measure: ceteris paribus, if all impacts in the structure increase, then the vulnerability measure should not decrease. Similarly, we have also formulated compatibility conditions for vulnerability measures defined on structures of different kinds (for example on sets of impact values versus probability distributions over such values). We have also formalized the derived concepts of sensitivity and adaptive capacity, and gave precise conditions for their usage. Moving further towards an operational definition of vulnerability, we have refined the representation of possible evolutions to trajectories of a dynamical system. This conforms to the usage in computational vulnerability assessments, where the systems considered are interacting models of the physical, social, or economical world. The attempt to compute generically the trajectories of systems of different types led to an investigation of the various definitions of dynamical system available in the literature. The result of this investigation is the definition of the class of monadic dynamical systems, and is one of the main results of this work. This class includes all the types of systems commonly found in practice: deterministic, stochastic, non-deterministic, both discrete and continuous, both with or without input. We have shown how to construct monadic dynamical systems from simpler representations, such as transition functions in the case of discrete systems, and how to combine monadic dynamical systems to yield new ones. For all the systems in this class, the same generic function can be used to compute the trajectories, in a uniform fashion. Once the monadic dynamical system combinators were in place, we were able to implement the various components of our model of vulnerability, and translate the various requirements such as monotonicity or compatibility into tests which could then be automatically performed using a tool such as QuickCheck. As a final proof of concept, we conducted a ``toy vulnerability assessment'', where we encountered all the problems of realistic cases in laboratory conditions: combined systems of different types, conflicting definitions of ``harm'', partial ordering of vulnerability measurements, etc., thus enabling us to conclude, with a certain degree of confidence, that the model proposed and the attendant software infrastructure are adequate for the purposes of computational vulnerability assessments in the context of climate change.