1,957 research outputs found
Money and Goldstone modes
Why is ``worthless'' fiat money generally accepted as payment for goods and
services? In equilibrium theory, the value of money is generally not
determined: the number of equations is one less than the number of unknowns, so
only relative prices are determined. In the language of mathematics, the
equations are ``homogeneous of order one''. Using the language of physics, this
represents a continuous ``Goldstone'' symmetry. However, the continuous
symmetry is often broken by the dynamics of the system, thus fixing the value
of the otherwise undetermined variable. In economics, the value of money is a
strategic variable which each agent must determine at each transaction by
estimating the effect of future interactions with other agents. This idea is
illustrated by a simple network model of monopolistic vendors and buyers, with
bounded rationality. We submit that dynamical, spontaneous symmetry breaking is
the fundamental principle for fixing the value of money. Perhaps the continuous
symmetry representing the lack of restoring force is also the fundamental
reason for large fluctuations in stock markets.Comment: 7 pages, 3 figure
Communicating Processes with Data for Supervisory Coordination
We employ supervisory controllers to safely coordinate high-level
discrete(-event) behavior of distributed components of complex systems.
Supervisory controllers observe discrete-event system behavior, make a decision
on allowed activities, and communicate the control signals to the involved
parties. Models of the supervisory controllers can be automatically synthesized
based on formal models of the system components and a formalization of the safe
coordination (control) requirements. Based on the obtained models, code
generation can be used to implement the supervisory controllers in software, on
a PLC, or an embedded (micro)processor. In this article, we develop a process
theory with data that supports a model-based systems engineering framework for
supervisory coordination. We employ communication to distinguish between the
different flows of information, i.e., observation and supervision, whereas we
employ data to specify the coordination requirements more compactly, and to
increase the expressivity of the framework. To illustrate the framework, we
remodel an industrial case study involving coordination of maintenance
procedures of a printing process of a high-tech Oce printer.Comment: In Proceedings FOCLASA 2012, arXiv:1208.432
On the Executability of Interactive Computation
The model of interactive Turing machines (ITMs) has been proposed to
characterise which stream translations are interactively computable; the model
of reactive Turing machines (RTMs) has been proposed to characterise which
behaviours are reactively executable. In this article we provide a comparison
of the two models. We show, on the one hand, that the behaviour exhibited by
ITMs is reactively executable, and, on the other hand, that the stream
translations naturally associated with RTMs are interactively computable. We
conclude from these results that the theory of reactive executability subsumes
the theory of interactive computability. Inspired by the existing model of ITMs
with advice, which provides a model of evolving computation, we also consider
RTMs with advice and we establish that a facility of advice considerably
upgrades the behavioural expressiveness of RTMs: every countable transition
system can be simulated by some RTM with advice up to a fine notion of
behavioural equivalence.Comment: 15 pages, 0 figure
Expressiveness modulo Bisimilarity of Regular Expressions with Parallel Composition (Extended Abstract)
The languages accepted by finite automata are precisely the languages denoted
by regular expressions. In contrast, finite automata may exhibit behaviours
that cannot be described by regular expressions up to bisimilarity. In this
paper, we consider extensions of the theory of regular expressions with various
forms of parallel composition and study the effect on expressiveness. First we
prove that adding pure interleaving to the theory of regular expressions
strictly increases its expressiveness up to bisimilarity. Then, we prove that
replacing the operation for pure interleaving by ACP-style parallel composition
gives a further increase in expressiveness. Finally, we prove that the theory
of regular expressions with ACP-style parallel composition and encapsulation is
expressive enough to express all finite automata up to bisimilarity. Our
results extend the expressiveness results obtained by Bergstra, Bethke and
Ponse for process algebras with (the binary variant of) Kleene's star
operation.Comment: In Proceedings EXPRESS'10, arXiv:1011.601
Dynamic plantar loading index detects altered foot function in individuals with rheumatoid arthritis but not changes due to orthotic use
Background Altered foot function is common in individuals with rheumatoid arthritis. Plantar pressure distributions during gait are regularly assessed in this patient group; however, the association between frequently reported magnitude-based pressure variables and clinical outcomes has not been clearly established. Recently, a novel approach to the analysis of plantar pressure distributions throughout stance phase, the dynamic plantar loading index, has been proposed. This study aimed to assess the utility of this index for measuring foot function in individuals with rheumatoid arthritis.Methods Barefoot plantar pressures during gait were measured in 63 patients with rheumatoid arthritis and 51 matched controls. Additionally, 15 individuals with rheumatoid arthritis had in-shoe plantar pressures measured whilst walking in standardized footwear for two conditions: shoes-only; and shoes with prescribed custom foot orthoses. The dynamic plantar loading index was determined for all participants and conditions. Patient and control groups were compared for significant differences as were the shod and orthosis conditions.Findings The patient group was found to have a mean index of 0.19, significantly lower than the control group's index of 0.32 (p > 0.001, 95% CI [0.054, 0.197]). No significant differences were found between the shoe-only and shoe plus orthosis conditions. The loading index was found to correlate with clinical measures of structural deformity.Interpretation The dynamic plantar loading index may be a useful tool for researchers and clinicians looking to objectively assess dynamic foot function in patients with rheumatoid arthritis; however, it may be unresponsive to changes caused by orthotic interventions in this patient group.</p
A Process Algebra for Supervisory Coordination
A supervisory controller controls and coordinates the behavior of different
components of a complex machine by observing their discrete behaviour.
Supervisory control theory studies automated synthesis of controller models,
known as supervisors, based on formal models of the machine components and a
formalization of the requirements. Subsequently, code generation can be used to
implement this supervisor in software, on a PLC, or embedded microprocessor. In
this article, we take a closer look at the control loop that couples the
supervisory controller and the machine. We model both event-based and
state-based observations using process algebra and bisimulation-based
semantics. The main application area of supervisory control that we consider is
coordination, referred to as supervisory coordination, and we give an academic
and an industrial example, discussing the process-theoretic concepts employed.Comment: In Proceedings PACO 2011, arXiv:1108.145
Synovial histopathology of psoriatic arthritis, both oligo- and polyarticular, resembles spondyloarthropathy more than it does rheumatoid arthritis
First-Order Logic Theorem Proving and Model Building via Approximation and Instantiation
In this paper we consider first-order logic theorem proving and model
building via approximation and instantiation. Given a clause set we propose its
approximation into a simplified clause set where satisfiability is decidable.
The approximation extends the signature and preserves unsatisfiability: if the
simplified clause set is satisfiable in some model, so is the original clause
set in the same model interpreted in the original signature. A refutation
generated by a decision procedure on the simplified clause set can then either
be lifted to a refutation in the original clause set, or it guides a refinement
excluding the previously found unliftable refutation. This way the approach is
refutationally complete. We do not step-wise lift refutations but conflicting
cores, finite unsatisfiable clause sets representing at least one refutation.
The approach is dual to many existing approaches in the literature because our
approximation preserves unsatisfiability
Towards a concurrency theory for supervisory control
In this paper we propose a process-theoretic concurrency model to express supervisory control properties. In light of the present importance of reliable control software, the current work ow of direct conversion from informal specication documents to control software implementations can be improved. A separate modeling step in terms of controllable and uncontrollable behavior of the device under control is desired. We consider the control loop as a feedback model for supervisory control, in terms of the three distinct components of plant, requirements and supervisor. With respect to the control ow, we consider event-based models as well as state-based ones. We study the process theory TCP as a convenient modeling formalism that includes parallelism, iteration, communication features and non-determinism. Via structural operational semantics, we relate the terms in TCP to labeled transition systems. We consider the partial bisimulation preorder to express controllability that is better suited to handle non-determinism, compared to bisimulation-based models. It is shown how precongruence of partial bisimulation can be derived from the format of the deduction rules. The theory of TCP is studied under nite axiomatization for which soundness and ground-completeness (modulo iteration) is proved with respect to partial bisimulation. Language-based controllability, as the neccesary condition for event-based supervisory control is expressed in terms of partial bisimulation and we discuss several drawbacks of the strict event-based approach. Statebased control is considered under partial bisimulation as a dependable solution to address non-determinism. An appropriate renaming operator is introduced to address an issue in parallel communication. A case for automated guided vehicles (AGV) is modeled using the theory TCP. The latter theory is henceforth extended to include state-based valuations for which partial bisimulation and an axiomatization are dened. We consider an extended case on industrial printers to show the modeling abilities of this extended theory. In our concluding remarks, we sketch a future research path in terms of a new formal language for concurrent control modeling
Reconciling real and stochastic time: The need for probabilistic refinement
We conservatively extend anACP-style discrete-time process theorywith discrete stochastic delays. The semantics of the timed delays relies on time additivity and time determinism, which are properties that enable us to merge subsequent timed delays and to impose their synchronous expiration. Stochastic delays, however, interact with respect to a so-called race condition that determines the set of delays that expire first, which is guided by an (implicit) probabilistic choice. The race condition precludes the property of time additivity as the merger of stochastic delays alters this probabilistic behavior. To this end, we resolve the race condition using conditionally- distributed unit delays. We give a sound and ground-complete axiomatization of the process theory comprising the standard set of ACP-style operators. In this generalized setting, the alternative composition is no longer associative, so we have to resort to special normal forms that explicitly resolve the underlying race condition. Our treatment succeeds in the initial challenge to conservatively extend standard time with stochastic time. However, the 'dissection' of the stochastic delays to conditionally-distributed unit delays comes at a price, as we can no longer relate the resolved race condition to the original stochastic delays. We seek a solution in the field of probabilistic refinements that enable the interchange of probabilistic and non deterministic choices.Fil: Markovski, J.. Technische Universiteit Eindhoven; Países BajosFil: D'argenio, Pedro Ruben. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Baeten, J. C. M.. Technische Universiteit Eindhoven; Países Bajos. Centrum Wiskunde & Informatica; Países BajosFil: De Vink, E. P.. Technische Universiteit Eindhoven; Países Bajos. Centrum Wiskunde & Informatica; Países Bajo
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