On Probabilistic Parallel Programs with Process Creation and Synchronisation

We initiate the study of probabilistic parallel programs with dynamic process creation and synchronisation. To this end, we introduce probabilistic split-join systems (pSJSs), a model for parallel programs, generalising both probabilistic pushdown systems (a model for sequential probabilistic procedural programs which is equivalent to recursive Markov chains) and stochastic branching processes (a classical mathematical model with applications in various areas such as biology, physics, and language processing). Our pSJS model allows for a possibly recursive spawning of parallel processes; the spawned processes can synchronise and return values. We study the basic performance measures of pSJSs, especially the distribution and expectation of space, work and time. Our results extend and improve previously known results on the subsumed models. We also show how to do performance analysis in practice, and present two case studies illustrating the modelling power of pSJSs.Comment: This is a technical report accompanying a TACAS'11 pape

A Survey of Monte Carlo Tree Search Methods

Monte Carlo tree search (MCTS) is a recently proposed search method that combines the precision of tree search with the generality of random sampling. It has received considerable interest due to its spectacular success in the difficult problem of computer Go, but has also proved beneficial in a range of other domains. This paper is a survey of the literature to date, intended to provide a snapshot of the state of the art after the first five years of MCTS research. We outline the core algorithm's derivation, impart some structure on the many variations and enhancements that have been proposed, and summarize the results from the key game and nongame domains to which MCTS methods have been applied. A number of open research questions indicate that the field is ripe for future work

Computational Complexity for Physicists

These lecture notes are an informal introduction to the theory of computational complexity and its links to quantum computing and statistical mechanics.Comment: references updated, reprint available from http://itp.nat.uni-magdeburg.de/~mertens/papers/complexity.shtm

Evaluating Innovation

In their pursuit of the public good, foundations face two competing forces -- the pressure to do something new and the pressure to do something proven. The epigraph to this paper, "Give me something new and prove that it works," is my own summary of what foundations often seek. These pressures come from within the foundations -- their staff or boards demand them, not the public. The aspiration to fund things that work can be traced to the desire to be careful, effective stewards of resources. Foundations' recognition of the growing complexity of our shared challenges drives the increased emphasis on innovation. Issues such as climate change, political corruption, and digital learning andwork environments have enticed new players into the social problem-solving sphere and have con-vinced more funders of the need to find new solutions. The seemingly mutually exclusive desires for doing something new and doing something proven are not new, but as foundations have grown in number and size the visibility of the paradox has risen accordingly.Even as foundations seek to fund innovation, they are also seeking measurements of those investments success. Many people's first response to the challenge of measuring innovation is to declare the intention oxymoronic. Innovation is by definition amorphous, full of unintended consequences, and a creative, unpredictable process -- much like art. Measurements, assessments, evaluation are -- also by most definitions -- about quantifying activities and products. There is always the danger of counting what you can count, even if what you can count doesn't matter.For all our awareness of the inherent irony of trying to measure something that we intend to be unpredictable, many foundations (and others) continue to try to evaluate their innovation efforts. They are, as John Westley, Brenda Zimmerman, and Michael Quinn Patton put it in "Getting to Maybe", grappling with "....intentionality and complexity -- (which) meet in tension." It is important to see the struggles to measure for what they are -- attempts to evaluate the success of the process of innovation, not necessarily the success of the individual innovations themselves. This is not a semantic difference.What foundations are trying to understand is how to go about funding innovation so that more of it can happenExamples in this report were chosen because they offer a look at innovation within the broader scope of a foundation's work. This paper is the fifth in a series focused on field building. In this context I am interested in where evaluation fits within an innovation strategy and where these strategies fit within a foundation's broader funding goals. I will present a typology of innovation drawn from the OECD that can be useful inother areas. I lay the decisions about evaluation made by Knight, MacArthur, and the Jewish NewMedia Innovation Funders against their program-matic goals. Finally, I consider how evaluating innovation may improve our overall use of evaluation methods in philanthropy