5,022 research outputs found
The earlier the better: a theory of timed actor interfaces
Programming embedded and cyber-physical systems requires attention not only to functional behavior and correctness, but also to non-functional aspects and specifically timing and performance constraints. A structured, compositional, model-based approach based on stepwise refinement and abstraction techniques can support the development process, increase its quality and reduce development time through automation of synthesis, analysis or verification. For this purpose, we introduce in this paper a general theory of timed actor interfaces. Our theory supports a notion of refinement that is based on the principle of worst-case design that permeates the world of performance-critical systems. This is in contrast with the classical behavioral and functional refinements based on restricting or enlarging sets of behaviors. An important feature of our refinement is that it allows time-deterministic abstractions to be made of time-non-deterministic systems, improving efficiency and reducing complexity of formal analysis. We also show how our theory relates to, and can be used to reconcile a number of existing time and performance models and how their established theories can be exploited to represent and analyze interface specifications and refinement steps.\u
Loop-erased random walk and Poisson kernel on planar graphs
Lawler, Schramm and Werner showed that the scaling limit of the loop-erased
random walk on is . We consider scaling limits
of the loop-erasure of random walks on other planar graphs (graphs embedded
into so that edges do not cross one another). We show that if the
scaling limit of the random walk is planar Brownian motion, then the scaling
limit of its loop-erasure is . Our main contribution is showing
that for such graphs, the discrete Poisson kernel can be approximated by the
continuous one. One example is the infinite component of super-critical
percolation on . Berger and Biskup showed that the scaling limit
of the random walk on this graph is planar Brownian motion. Our results imply
that the scaling limit of the loop-erased random walk on the super-critical
percolation cluster is .Comment: Published in at http://dx.doi.org/10.1214/10-AOP579 the Annals of
Probability (http://www.imstat.org/aop/) by the Institute of Mathematical
Statistics (http://www.imstat.org
The prescription in the SYK model
We introduce an prescription for the SYK model both at
finite and at zero temperature. This prescription regularizes all the naive
ultraviolet divergences of the model. As expected the prescription breaks the
conformal invariance, but the latter is restored in the limit.
We prove rigorously that the Schwinger Dyson equation of the resummed two point
function at large and low momentum is recovered in this limit. Based on
this prescription we introduce an effective field theory
Lagrangian for the infrared SYK model.Comment: Second version: the effective field theory part of the paper
(subsections 2.1 and 3.1 and discussion) adde
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