1,151 research outputs found

    Propositional Proof Complexity and Cellular Automata

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    The sharp threshold for the Duarte model

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    The class of critical bootstrap percolation models in two dimensions was recently introduced by Bollob\'as, Smith and Uzzell, and the critical threshold for percolation was determined up to a constant factor for all such models by the authors of this paper. Here we develop and refine the techniques introduced in that paper in order to determine a sharp threshold for the Duarte model. This resolves a question of Mountford from 1995, and is the first result of its type for a model with drift.Comment: 47 pages, 7 figures. To appear, Annals of Probabilit

    The Fundamental Theorems of Welfare Economics, DSGE and the Theory of Policy - Computable & Constructive Foundations

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    The genesis and the path towards what has come to be called the DSGE model is traced, from its origins in the Arrow-Debreu General Equilibrium model (ADGE), via Scarf's Computable General Equilibrium model (CGE) and its applied version as Applied Computable General Equilibrium model (ACGE), to its ostensible dynamization as a Recursive Competitive Equilibrium (RCE). It is shown that these transformations of the ADGE - including the fountainhead - are computably and constructively untenable. The policy implications of these (negative) results, via the Fundamental Theorems of Welfare Economics in particular, and against the backdrop of the mathematical theory of economic policy in general, are also discussed (again from computable and constructive points of view). Suggestions for going 'beyond DSGE' are, then, outlined on the basis of a framework that is underpinned - from the outset - by computability and constructivity considerationsComputable General Equilibrium, Dynamic Stochastic General Equilibrium, Computability, Constructivity, Fundamental Theorems of Welfare Economics, Theory of Policy, Coupled Nonlinear Dynamic

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

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    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

    Merging the Natural with the Artificial: The Nature of a Machine and the Collapse of Cybernetics

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    This thesis is concerned with the rise and fall of cybernetics, understood as an inquiry regarding the nature of a machine. The collapse of this scientific movement, usually explained by external factors such as lack of funding, will be addressed from a philosophical standpoint. Delving deeper into the theoretical core of cybernetics, one could find that the contributions of William Ross Ashby and John von Neumann shed light onto the particular ways in which cybernetics understood the nature and behavior of a machine. Ross Ashby offered an account of the nature of a machine and then extended the scope of “the mechanical”. This extension would encompass areas that will later be shown to be problematic for mechanization, such as learning and adaptation. The way in which a machine-ontology was applied would trigger effects seemingly contrary to cybernetics’ own distinctive features. Von Neumann, on the other hand, tinkered with a mechanical model of the brain, realizing grave limitations that prompted him to look for an alternative for cybernetics to work on. The proposal that came out of this resulted in a serious blow against the theoretical core of cybernetics. Why did cybernetics collapse? The contributions coming from both thinkers, in their own ways, spelled out the main tenets of the cybernetic proposal. But these very contributions led to cybernetics’ own demise. The whole story can be framed under the rubric of a serious inquiry into the metaphysical underpinnings of a machine. The rise and fall of cybernetics could thus help us better understand what a machine is from a philosophical standpoint. Although a historical component is present, my emphasis relies on a philosophical consideration of the cybernetic phenomenon. This metaphysical dissection will attempt to clarify how a machine-based ontology remained at the core of cybernetics. An emerging link will hopefully lead towards establishing a tri-partite correlation between cybernetics’ own evolution, its theoretical core, and its collapse. It will hopefully show how cybernetic inquiries into the nature of a machine might have proved fatal to the very enterprise at large, due to unsolvable theoretical tensions
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