1,337 research outputs found
Game Refinement Relations and Metrics
We consider two-player games played over finite state spaces for an infinite
number of rounds. At each state, the players simultaneously choose moves; the
moves determine a successor state. It is often advantageous for players to
choose probability distributions over moves, rather than single moves. Given a
goal, for example, reach a target state, the question of winning is thus a
probabilistic one: what is the maximal probability of winning from a given
state?
On these game structures, two fundamental notions are those of equivalences
and metrics. Given a set of winning conditions, two states are equivalent if
the players can win the same games with the same probability from both states.
Metrics provide a bound on the difference in the probabilities of winning
across states, capturing a quantitative notion of state similarity.
We introduce equivalences and metrics for two-player game structures, and we
show that they characterize the difference in probability of winning games
whose goals are expressed in the quantitative mu-calculus. The quantitative
mu-calculus can express a large set of goals, including reachability, safety,
and omega-regular properties. Thus, we claim that our relations and metrics
provide the canonical extensions to games, of the classical notion of
bisimulation for transition systems. We develop our results both for
equivalences and metrics, which generalize bisimulation, and for asymmetrical
versions, which generalize simulation
Distributed Approximation of Minimum Routing Cost Trees
We study the NP-hard problem of approximating a Minimum Routing Cost Spanning
Tree in the message passing model with limited bandwidth (CONGEST model). In
this problem one tries to find a spanning tree of a graph over nodes
that minimizes the sum of distances between all pairs of nodes. In the
considered model every node can transmit a different (but short) message to
each of its neighbors in each synchronous round. We provide a randomized
-approximation with runtime for
unweighted graphs. Here, is the diameter of . This improves over both,
the (expected) approximation factor and the runtime
of the best previously known algorithm.
Due to stating our results in a very general way, we also derive an (optimal)
runtime of when considering -approximations as done by the
best previously known algorithm. In addition we derive a deterministic
-approximation
Recommended from our members
Economic analysis of ethanol production from switchgrass using hybrid thermal/biological processing
The economics of ethanol production from switchgrass using Waterloo fast pyrolysis with a fermentation step is investigated. Standard chemical engineering methods are used to estimate capital investment and operating costs. Order of magnitude method is employed for preliminary approximation of capital investment. The azeotropic ethanol production capacity used in this case study is 189 million liters/year (50 million gallons/year). All cost figures are updated to 1997 US 142 million, while the annual operating cost is about 0.62/l (0.58/l (0.30 million/year, in order to meet the heat energy requirement of the process. Sensitivity analyses of feedstock cost and yield of sugar fermentation on the selling price of ethanol show that feedstock cost is positively related to ethanol selling price, while the yield has a negative relationship with selling price
Preparation and ferroelectric properties of (124)-oriented SrBi4Ti4O15 ferroelectric thin film on (110)-oriented LaNiO3 electrode
A (124)-oriented SrBi4Ti4O15 (SBTi) ferroelectric thin film with high volume
fraction of {\alpha}SBTi(124)=97% was obtained using a metal organic
decomposition process on SiO2/Si substrate coated by (110)-oriented LaNiO3
(LNO) thin film. The remanent polarization and coercive field for
(124)-oriented SBTi film are 12.1 {\mu}C/cm2 and 74 kV/cm, respectively. No
evident fatigue of (124)-oriented SBTi thin film can be observed after
1{\times}10e9 switching cycles. Besides, the (124)-oriented SBTi film can be
uniformly polarized over large areas using a piezoelectric-mode atomic force
microscope. Considering that the annealing temperature was 650{\deg}C and the
thickness of each deposited layer was merely 30 nm, a long-range epitaxial
relationship between SBTi(124) and LNO(110) facets was proposed. The epitaxial
relationship was demonstrated based on the crystal structures of SBTi and LNO.Comment: 11 pages, 4 figures, published in Journal of Materials Science:
Materials in Electronics (JMSE), 19 (2008), 1031-103
Prevalence of chronic kidney disease in adults in England: comparison of nationally representative cross-sectional surveys from 2003 to 2016
Objectives: To identify recent trends in chronic kidney disease (CKD) prevalence in England and explore their association with changes in sociodemographic, behavioural and clinical factors. Design: Pooled cross-sectional analysis.Setting: Health Survey for England 2003, 2009/2010 combined, and 2016.Participants: 17,663 individuals (aged 16+) living in private households.Primary and secondary outcome measures: Prevalence of estimated glomerular filtration rate (eGFR
Continuous Truth II: Reflections
Abstract. In the late 1960s, Dana Scott first showed how the Stone-Tarski topological interpretation of Heyting’s calculus could be extended to model intuitionistic analysis; in particular Brouwer’s continuity prin-ciple. In the early ’80s we and others outlined a general treatment of non-constructive objects, using sheaf models—constructions from topos theory—to model not only Brouwer’s non-classical conclusions, but also his creation of “new mathematical entities”. These categorical models are intimately related to, but more general than Scott’s topological model. The primary goal of this paper is to consider the question of iterated extensions. Can we derive new insights by repeating the second act? In Continuous Truth I, presented at Logic Colloquium ’82 in Florence, we showed that general principles of continuity, local choice and local com-pactness hold in the gros topos of sheaves over the category of separable locales equipped with the open cover topology. We touched on the question of iteration. Here we develop a more gen-eral analysis of iterated categorical extensions, that leads to a reflection schema for statements of predicative analysis. We also take the opportunity to revisit some aspects of both Continuous Truth I and Formal Spaces (Fourman & Grayson 1982), and correct two long-standing errors therein
Read-It: A Multi-modal Tangible Interface for Children Who Learn to Read
Multi-modal tabletop applications offer excellent opportunities for enriching the education of young children. Read-It is an example of an interactive game with a multi-modal tangible interface that was designed to combine the advantages of current physical games and computer exercises. It is a novel approach for supporting children who learn to read. The first experimental evaluation has demonstrated that the Read-It approach is indeed promising and meets a priori expectations
Indestructibility of Vopenka's Principle
We show that Vopenka's Principle and Vopenka cardinals are indestructible
under reverse Easton forcing iterations of increasingly directed-closed partial
orders, without the need for any preparatory forcing. As a consequence, we are
able to prove the relative consistency of these large cardinal axioms with a
variety of statements known to be independent of ZFC, such as the generalised
continuum hypothesis, the existence of a definable well-order of the universe,
and the existence of morasses at many cardinals.Comment: 15 pages, submitted to Israel Journal of Mathematic
- …