54,781 research outputs found
Two-Dimensional Lattice Gravity as a Spin System
Quantum gravity is studied in the path integral formulation applying the
Regge calculus. Restricting the quadratic link lengths of the originally
triangular lattice the path integral can be transformed to the partition
function of a spin system with higher couplings on a Kagome lattice. Various
measures acting as external field are considered. Extensions to matter fields
and higher dimensions are discussed.Comment: 3 pages, uuencoded postscript file; Proceedings of the 2nd IMACS
Conference on Computational Physics, St. Louis, Oct. 199
Fully Polynomial Time Approximation Schemes for Stochastic Dynamic Programs
We present a framework for obtaining fully polynomial time approximation schemes (FPTASs) for stochastic univariate dynamic programs with either convex or monotone single-period cost functions. This framework is developed through the establishment of two sets of computational rules, namely, the calculus of K-approximation functions and the calculus of K-approximation sets. Using our framework, we provide the first FPTASs for several NP-hard problems in various fields of research such as knapsack models, logistics, operations management, economics, and mathematical finance. Extensions of our framework via the use of the newly established computational rules are also discussed
CR-Tractors and the Fefferman Space
We develop the natural tractor calculi associated to conformal and
CR structures as a fundamental tool for the study of Fefferman's construction
of a canonical conformal class on the total space of a circle bundle over a
non--degenerate CR manifold of hypersurface type. In particular we construct
and treat the basic objects that relate the natural bundles and natural
operators on the two spaces. This is illustrated with several applications: We
prove that a number of conformally invariant overdetermined systems admit
non--trivial solutions on any Fefferman space. We show that the space of
conformal Killing fields on a Fefferman space naturally decomposes into a
direct sum of subspaces, which admit an interpretaion as solutions of certain
CR invariant PDE's. Finally we explicitly analyze the relation between tractor
calculus on a CR manifold and the complexified conformal tractor calculus on
its Fefferman space, thus obtaining a powerful computational tool for working
with the Fefferman construction.Comment: AMSLaTeX, 46 pages, v3: added link
http://www.iumj.indiana.edu/IUMJ/fulltext.php?year=2008&volume=57&artid=3359
to published version, which has different numbering of statement
Asynchronous Distributed Execution of Fixpoint-Based Computational Fields
Coordination is essential for dynamic distributed systems whose components exhibit interactive and autonomous behaviors. Spatially distributed, locally interacting, propagating computational fields are particularly appealing for allowing components to join and leave with little or no overhead. Computational fields are a key ingredient of aggregate programming, a promising software engineering methodology particularly relevant for the Internet of Things. In our approach, space topology is represented by a fixed graph-shaped field, namely a network with attributes on both nodes and arcs, where arcs represent interaction capabilities between nodes. We propose a SMuC calculus where mu-calculus- like modal formulas represent how the values stored in neighbor nodes should be combined to update the present node. Fixpoint operations can be understood globally as recursive definitions, or locally as asynchronous converging propagation processes. We present a distributed implementation of our calculus. The translation is first done mapping SMuC programs into normal form, purely iterative programs and then into distributed programs. Some key results are presented that show convergence of fixpoint computations under fair asynchrony and under reinitialization of nodes. The first result allows nodes to proceed at different speeds, while the second one provides robustness against certain kinds of failure. We illustrate our approach with a case study based on a disaster recovery scenario, implemented in a prototype simulator that we use to evaluate the performance of a recovery strategy
Engineering Resilient Collective Adaptive Systems by Self-Stabilisation
Collective adaptive systems are an emerging class of networked computational
systems, particularly suited in application domains such as smart cities,
complex sensor networks, and the Internet of Things. These systems tend to
feature large scale, heterogeneity of communication model (including
opportunistic peer-to-peer wireless interaction), and require inherent
self-adaptiveness properties to address unforeseen changes in operating
conditions. In this context, it is extremely difficult (if not seemingly
intractable) to engineer reusable pieces of distributed behaviour so as to make
them provably correct and smoothly composable.
Building on the field calculus, a computational model (and associated
toolchain) capturing the notion of aggregate network-level computation, we
address this problem with an engineering methodology coupling formal theory and
computer simulation. On the one hand, functional properties are addressed by
identifying the largest-to-date field calculus fragment generating
self-stabilising behaviour, guaranteed to eventually attain a correct and
stable final state despite any transient perturbation in state or topology, and
including highly reusable building blocks for information spreading,
aggregation, and time evolution. On the other hand, dynamical properties are
addressed by simulation, empirically evaluating the different performances that
can be obtained by switching between implementations of building blocks with
provably equivalent functional properties. Overall, our methodology sheds light
on how to identify core building blocks of collective behaviour, and how to
select implementations that improve system performance while leaving overall
system function and resiliency properties unchanged.Comment: To appear on ACM Transactions on Modeling and Computer Simulatio
Map Calculus in GIS: a proposal and demonstration
This paper provides a new representation for fields (continuous surfaces) in Geographical Information Systems (GIS), based on the notion of spatial functions and their combinations. Following Tomlin's (1990) Map Algebra, the term 'Map Calculus' is used for this new representation. In Map Calculus, GIS layers are stored as functions, and new layers can be created by combinations of other functions. This paper explains the principles of Map Calculus and demonstrates the creation of function-based layers and their supporting management mechanism. The proposal is based on Church's (1941) Lambda Calculus and elements of functional computer languages (such as Lisp or Scheme)
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