Solving Factored MDPs with Hybrid State and Action Variables

Efficient representations and solutions for large decision problems with continuous and discrete variables are among the most important challenges faced by the designers of automated decision support systems. In this paper, we describe a novel hybrid factored Markov decision process (MDP) model that allows for a compact representation of these problems, and a new hybrid approximate linear programming (HALP) framework that permits their efficient solutions. The central idea of HALP is to approximate the optimal value function by a linear combination of basis functions and optimize its weights by linear programming. We analyze both theoretical and computational aspects of this approach, and demonstrate its scale-up potential on several hybrid optimization problems

Mechanized semantics

The goal of this lecture is to show how modern theorem provers---in this case, the Coq proof assistant---can be used to mechanize the specification of programming languages and their semantics, and to reason over individual programs and over generic program transformations, as typically found in compilers. The topics covered include: operational semantics (small-step, big-step, definitional interpreters); a simple form of denotational semantics; axiomatic semantics and Hoare logic; generation of verification conditions, with application to program proof; compilation to virtual machine code and its proof of correctness; an example of an optimizing program transformation (dead code elimination) and its proof of correctness

AMaχoS—Abstract Machine for Xcerpt

Web query languages promise convenient and efficient access to Web data such as XML, RDF, or Topic Maps. Xcerpt is one such Web query language with strong emphasis on novel high-level constructs for effective and convenient query authoring, particularly tailored to versatile access to data in different Web formats such as XML or RDF. However, so far it lacks an efficient implementation to supplement the convenient language features. AMaχoS is an abstract machine implementation for Xcerpt that aims at efficiency and ease of deployment. It strictly separates compilation and execution of queries: Queries are compiled once to abstract machine code that consists in (1) a code segment with instructions for evaluating each rule and (2) a hint segment that provides the abstract machine with optimization hints derived by the query compilation. This article summarizes the motivation and principles behind AMaχoS and discusses how its current architecture realizes these principles

Spatio-temporal structure of cell distribution in cortical Bone Multicellular Units: a mathematical model

Bone remodelling maintains the functionality of skeletal tissue by locally coordinating bone-resorbing cells (osteoclasts) and bone-forming cells (osteoblasts) in the form of Bone Multicellular Units (BMUs). Understanding the emergence of such structured units out of the complex network of biochemical interactions between bone cells is essential to extend our fundamental knowledge of normal bone physiology and its disorders. To this end, we propose a spatio-temporal continuum model that integrates some of the most important interaction pathways currently known to exist between cells of the osteoblastic and osteoclastic lineage. This mathematical model allows us to test the significance and completeness of these pathways based on their ability to reproduce the spatio-temporal dynamics of individual BMUs. We show that under suitable conditions, the experimentally-observed structured cell distribution of cortical BMUs is retrieved. The proposed model admits travelling-wave-like solutions for the cell densities with tightly organised profiles, corresponding to the progression of a single remodelling BMU. The shapes of these spatial profiles within the travelling structure can be linked to the intrinsic parameters of the model such as differentiation and apoptosis rates for bone cells. In addition to the cell distribution, the spatial distribution of regulatory factors can also be calculated. This provides new insights on how different regulatory factors exert their action on bone cells leading to cellular spatial and temporal segregation, and functional coordination.Comment: 14 pages, 5 figures; v2: Completed model description after Eq. (16), clarified discussion/description after Eq. (23), between Eqs. (29)-(31), and in 2nd bullet point in conclusion