4,082 research outputs found
Stationary states of a spherical Minority Game with ergodicity breaking
Using generating functional and replica techniques, respectively, we study
the dynamics and statics of a spherical Minority Game (MG), which in contrast
with a spherical MG previously presented in J.Phys A: Math. Gen. 36 11159
(2003) displays a phase with broken ergodicity and dependence of the
macroscopic stationary state on initial conditions. The model thus bears more
similarity with the original MG. Still, all order parameters including the
volatility can computed in the ergodic phases without making any
approximations. We also study the effects of market impact correction on the
phase diagram. Finally we discuss a continuous-time version of the model as
well as the differences between on-line and batch update rules. Our analytical
results are confirmed convincingly by comparison with numerical simulations. In
an appendix we extend the analysis of the earlier spherical MG to a model with
general time-step, and compare the dynamics and statics of the two spherical
models.Comment: 26 pages, 8 figures; typo correcte
Extending the Real-Time Maude Semantics of Ptolemy to Hierarchical DE Models
This paper extends our Real-Time Maude formalization of the semantics of flat
Ptolemy II discrete-event (DE) models to hierarchical models, including modal
models. This is a challenging task that requires combining synchronous
fixed-point computations with hierarchical structure. The synthesis of a
Real-Time Maude verification model from a Ptolemy II DE model, and the formal
verification of the synthesized model in Real-Time Maude, have been integrated
into Ptolemy II, enabling a model-engineering process that combines the
convenience of Ptolemy II DE modeling and simulation with formal verification
in Real-Time Maude.Comment: In Proceedings RTRTS 2010, arXiv:1009.398
Doing-it-All with Bounded Work and Communication
We consider the Do-All problem, where cooperating processors need to
complete similar and independent tasks in an adversarial setting. Here we
deal with a synchronous message passing system with processors that are subject
to crash failures. Efficiency of algorithms in this setting is measured in
terms of work complexity (also known as total available processor steps) and
communication complexity (total number of point-to-point messages). When work
and communication are considered to be comparable resources, then the overall
efficiency is meaningfully expressed in terms of effort defined as work +
communication. We develop and analyze a constructive algorithm that has work
and a nonconstructive
algorithm that has work . The latter result is close to the
lower bound on work. The effort of each of
these algorithms is proportional to its work when the number of crashes is
bounded above by , for some positive constant . We also present a
nonconstructive algorithm that has effort
Parameterized Synthesis
We study the synthesis problem for distributed architectures with a
parametric number of finite-state components. Parameterized specifications
arise naturally in a synthesis setting, but thus far it was unclear how to
detect realizability and how to perform synthesis in a parameterized setting.
Using a classical result from verification, we show that for a class of
specifications in indexed LTL\X, parameterized synthesis in token ring networks
is equivalent to distributed synthesis in a network consisting of a few copies
of a single process. Adapting a well-known result from distributed synthesis,
we show that the latter problem is undecidable. We describe a semi-decision
procedure for the parameterized synthesis problem in token rings, based on
bounded synthesis. We extend the approach to parameterized synthesis in
token-passing networks with arbitrary topologies, and show applicability on a
simple case study. Finally, we sketch a general framework for parameterized
synthesis based on cutoffs and other parameterized verification techniques.Comment: Extended version of TACAS 2012 paper, 29 page
Asynchronous Variational Contact Mechanics
An asynchronous, variational method for simulating elastica in complex
contact and impact scenarios is developed. Asynchronous Variational Integrators
(AVIs) are extended to handle contact forces by associating different time
steps to forces instead of to spatial elements. By discretizing a barrier
potential by an infinite sum of nested quadratic potentials, these extended
AVIs are used to resolve contact while obeying momentum- and
energy-conservation laws. A series of two- and three-dimensional examples
illustrate the robustness and good energy behavior of the method
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