scholarly journals Presheaf Models for Concurrency

1996 ◽  
Vol 3 (35) ◽  
Author(s):  
Gian Luca Cattani ◽  
Glynn Winskel
Keyword(s):  
Broad Class ◽  
General Nature ◽  
General Process ◽  
Process Calculi ◽  
Event Structures ◽  
Wide Range ◽  
Concurrent Computation ◽  
Kan Extensions ◽  
Modelling Process ◽  
Open Maps

This paper studies presheaf models for concurrent computation. An aim is to harness the general machinery around presheaves for the purposes of process calculi. Traditional models like synchronisation trees and event structures have been shown to embed fully and faithfully in particular<br />presheaf models in such a way that bisimulation, expressed through the presence of a span of open maps, is conserved. As is shown in the work of Joyal and Moerdijk, presheaves are rich in constructions which preserve open<br />maps, and so bisimulation, by arguments of a very general nature. This paper contributes similar results but biased towards questions of bisimulation in process calculi. It is concerned with modelling process constructions on presheaves, showing these preserve open maps, and with transferring such<br />results to traditional models for processes. One new result here is that a wide range of left Kan extensions, between categories of presheaves, preserve open maps. As a corollary, this also implies that any colimit-preserving functor between presheaf categories preserves open maps. A particular left Kan extension is shown to coincide with a refinement operation on event structures. A broad class of presheaf models is proposed for a general process calculus. General arguments are given for why the operations of a presheaf model preserve open maps and why for specic presheaf models the operations coincide with those of traditional models.

scholarly journals Presheaf Models for CCS-like Languages

1999 ◽  
Vol 6 (36) ◽  
Author(s):  
Gian Luca Cattani ◽  
Glynn Winskel
Keyword(s):  
General Definition ◽  
General Process ◽  
Process Calculi ◽  
Event Structures ◽  
Open Map ◽  
Process Operations ◽  
Definition Of ◽  
Refinement Operator ◽  
Congruence Properties ◽  
Open Maps

The aim of this paper is to harness the mathematical machinery around<br />presheaves for the purposes of process calculi. Joyal, Nielsen and Winskel<br />proposed a general definition of bisimulation from open maps. Here we show<br />that open-map bisimulations within a range of presheaf models are congruences<br /> for a general process language, in which CCS and related languages<br />are easily encoded. The results are then transferred to traditional models<br /> for processes. By first establishing the congruence results for presheaf<br />models, abstract, general proofs of congruence properties can be provided<br />and the awkwardness caused through traditional models not always possessing<br /> the cartesian liftings, used in the break-down of process operations,<br />are side-stepped. The abstract results are applied to show that hereditary<br />history-preserving bisimulation is a congruence for CCS-like languages to<br />which is added a refinement operator on event structures as proposed by<br />van Glabbeek and Goltz.

scholarly journals An Axiomatic Approach to Reversible Computation

2020 ◽  
pp. 442-461
Author(s):  
Ivan Lanese ◽  
Iain Phillips ◽  
Irek Ulidowski
Keyword(s):  
Discrete Event ◽  
Axiomatic Approach ◽  
Transition System ◽  
Parallel Discrete Event Simulation ◽  
Event Simulation ◽  
Process Calculi ◽  
Event Structures ◽  
Concurrent Computation ◽  
Parallel Discrete Event ◽  
Labelled Transition System

AbstractUndoing computations of a concurrent system is beneficial in many situations, e.g., in reversible debugging of multi-threaded programs and in recovery from errors due to optimistic execution in parallel discrete event simulation. A number of approaches have been proposed for how to reverse formal models of concurrent computation including process calculi such as CCS, languages like Erlang, prime event structures and occurrence nets. However it has not been settled what properties a reversible system should enjoy, nor how the various properties that have been suggested, such as the parabolic lemma and the causal-consistency property, are related. We contribute to a solution to these issues by using a generic labelled transition system equipped with a relation capturing whether transitions are independent to explore the implications between these properties. In particular, we show how they are derivable from a set of axioms. Our intention is that when establishing properties of some formalism it will be easier to verify the axioms rather than proving properties such as the parabolic lemma directly. We also introduce two new notions related to causal consistent reversibility, namely causal safety and causal liveness, and show that they are derivable from our axioms.

scholarly journals Bisimulation from Open Maps

1994 ◽  
Vol 1 (7) ◽  
Author(s):  
André Joyal ◽  
Mogens Nielsen ◽  
Glynn Winskel
Keyword(s):  
Petri Nets ◽  
Parallel Computation ◽  
Transition Systems ◽  
New Model ◽  
Event Structures ◽  
Uniform Definition ◽  
Refinement Operators ◽  
Definition Of ◽  
Open Maps

An abstract definition of bisimulation is presented. It enables a uniform definition of bisimulation across a range of different models for parallel computation presented as categories. As examples, transition systems, synchronisation trees, transition systems with independence (an abstraction from Petri nets) and labelled event structures are considered. On transition systems the abstract definition readily specialises to Milner's strong bisimulation. On event structures it explains and leads to a revision of history-preserving bisimulation of Rabinovitch and Traktenbrot, Goltz and van Glabeek. A tie-up with open maps in a (pre)topos, as they appear in the work of Joyal and Moerdijk, brings to light a promising new model, presheaves on categories of pomsets, into which the usual category of labelled event structures embeds fully and faithfully. As an indication of its promise, this new presheaf model has ``refinement'' operators, though further work is required to justify their appropriateness and understand their relation to previous attempts. The general approach yields a logic, generalising Hennessy-Milner logic, which is characteristic for the generalised notion of bisimulation.

scholarly journals A Presheaf Semantics of Value-Passing Processes

1996 ◽  
Vol 3 (44) ◽  
Author(s):  
Glynn Winskel
Keyword(s):  
Operational Semantics ◽  
Denotational Semantics ◽  
Domain Theory ◽  
Process Calculi ◽  
Traditional Definition ◽  
Open Maps

This paper investigates presheaf models for process calculi with<br />value passing. Denotational semantics in presheaf models are shown<br />to correspond to operational semantics in that bisimulation obtained<br />from open maps is proved to coincide with bisimulation as defined<br />traditionally from the operational semantics. Both "early" and "late"<br />semantics are considered, though the more interesting "late" semantics<br />is emphasised. A presheaf model and denotational semantics is proposed<br />for a language allowing process passing, though there remains<br />the problem of relating the notion of bisimulation obtained from open<br />maps to a more traditional definition from the operational semantics.<br />A tentative beginning is made of a "domain theory" supporting<br />presheaf models.

scholarly journals Stochastic cycle selection in active flow networks

2016 ◽  
Vol 113 (29) ◽  
pp. 8200-8205 ◽  
Author(s):  
Francis G. Woodhouse ◽  
Aden Forrow ◽  
Joanna B. Fawcett ◽  
Jörn Dunkel
Keyword(s):  
Broad Class ◽  
Generic Model ◽  
Rate Theory ◽  
Flow Networks ◽  
Complex Flow ◽  
Slime Molds ◽  
Arterial Blood ◽  
Wide Range ◽  
Theoretical And Numerical Analysis ◽  
Active Flow

Active biological flow networks pervade nature and span a wide range of scales, from arterial blood vessels and bronchial mucus transport in humans to bacterial flow through porous media or plasmodial shuttle streaming in slime molds. Despite their ubiquity, little is known about the self-organization principles that govern flow statistics in such nonequilibrium networks. Here we connect concepts from lattice field theory, graph theory, and transition rate theory to understand how topology controls dynamics in a generic model for actively driven flow on a network. Our combined theoretical and numerical analysis identifies symmetry-based rules that make it possible to classify and predict the selection statistics of complex flow cycles from the network topology. The conceptual framework developed here is applicable to a broad class of biological and nonbiological far-from-equilibrium networks, including actively controlled information flows, and establishes a correspondence between active flow networks and generalized ice-type models.

scholarly journals ETHOS – an effective parametrization and classification for structure formation: the non-linear regime at z ≳ 5

2020 ◽  
Vol 498 (3) ◽  
pp. 3403-3419
Author(s):  
Sebastian Bohr ◽  
Jesús Zavala ◽  
Francis-Yan Cyr-Racine ◽  
Mark Vogelsberger ◽  
Torsten Bringmann ◽  
...  
Keyword(s):  
Power Spectrum ◽  
Structure Formation ◽  
Parameter Space ◽  
Broad Class ◽  
High Redshift ◽  
Acoustic Oscillations ◽  
Effective Parameters ◽  
Matter Power Spectrum ◽  
Wide Range ◽  
Non Linear

ABSTRACT We propose two effective parameters that fully characterize galactic-scale structure formation at high redshifts (z ≳ 5) for a variety of dark matter (DM) models that have a primordial cutoff in the matter power spectrum. Our description is within the recently proposed ETHOS framework and includes standard thermal warm DM (WDM) and models with dark acoustic oscillations (DAOs). To define and explore this parameter space, we use high-redshift zoom-in simulations that cover a wide range of non-linear scales from those where DM should behave as CDM (k ∼ 10 h Mpc−1), down to those characterized by the onset of galaxy formation (k ∼ 500 h Mpc−1). We show that the two physically motivated parameters hpeak and kpeak, the amplitude and scale of the first DAO peak, respectively, are sufficient to parametrize the linear matter power spectrum and classify the DM models as belonging to effective non-linear structure formation regions. These are defined by their relative departure from cold DM (kpeak → ∞) and WDM (hpeak = 0) according to the non-linear matter power spectrum and halo mass function. We identify a region where the DAOs still leave a distinct signature from WDM down to z = 5, while a large part of the DAO parameter space is shown to be degenerate with WDM. Our framework can then be used to seamlessly connect a broad class of particle DM models to their structure formation properties at high redshift without the need of additional N-body simulations.

The Two-Good Theory in Practice: From Abstract Generalization to Specific Inference

2017 ◽  
Author(s):  
T. Clifton Morgan ◽  
Glenn Palmer
Keyword(s):  
Foreign Policy ◽  
Empirical Support ◽  
The United States ◽  
Status Quo ◽  
Theoretical Development ◽  
General Nature ◽  
Good Theory ◽  
Trade Offs ◽  
Wide Range ◽  
The Status

The “two-good theory” is a theory of foreign policy that is meant to apply to all states in all situations; that is, it is general. The theory is simple and assumes that states pursue two things in theory with respect to foreign policies: change (altering aspects of the status quo that they do not like) and maintenance (protecting aspects of the status quo that they do like). It also assumes that states have finite resources. In making these assumptions, the theory focuses on the trade-offs that states face in constructing their most desired foreign policy portfolios. Further, the theory assumes that protecting realized outcomes is easier than bringing about desired changes in the status quo. The theory assumes that states pursue two goods instead of the more traditional one good; for realism, that good is “power,” and for neorealism, it is “security.” This small step in theoretical development is very fruitful and leads to more interesting hypotheses, many of which enjoy empirical support. The theory captures more of the dynamics of international relations and of foreign policy choices than more traditional approaches do. A number of empirical tests of the implications of the two-good theory have been conducted and support the theory. As the theory can speak to a variety of foreign policy behaviors, these tests appropriately cover a wide range of activities, including conflict initiation and foreign aid allocation. The theory enjoys support from the results of these tests. If the research relaxes some of the parameters of the theory, the investigator can derive a series of corollaries to it. For example, the initial variant of the theory keeps a number of parameters constant to determine the effect of changes in capability. If, however, the investigator allows preferences to vary in a systematic and justifiable manner (consistent with the theory but not established by the theory), she can see how leaders in a range of situations can be expected to behave. The research strategy proposed, in other words, is to utilize the general nature of the two-good theory to investigate a number of interesting and surprising implications. For example, what may one expect to see if the United States supplies a recipient state with military aid to counter a rebellion? Under reasonable circumstances, the two-good theory can predict that the recipient would increase its change-seeking behavior by, for instance, engaging in negotiations to lower trade barriers.

Computational Coevolution of Antiviral Drug Resistance

1998 ◽  
Vol 4 (1) ◽  
pp. 41-59 ◽  
Author(s):  
Christopher D. Rosin ◽  
Richard K. Belew ◽  
Garrett M. Morris ◽  
Arthur J. Olson ◽  
David S. Goodsell
Keyword(s):  
Drug Resistance ◽  
Broad Class ◽  
Antiviral Drug ◽  
Resistant Mutant ◽  
Approximate Model ◽  
Cross Resistance ◽  
Resistance Mutations ◽  
Wide Range ◽  
Antiviral Drug Resistance ◽  
Mutant Forms

An understanding of antiviral drug resistance is important in the design of effective drugs. Comprehensive features of the interaction between drug designs and resistance mutations are difficult to study experimentally because of the very large numbers of drugs and mutants involved. We describe a computational framework for studying antiviral drug resistance. Data on HIV-1 protease are used to derive an approximate model that predicts interaction of a wide range of mutant forms of the protease with a broad class of protease inhibitors. An algorithm based on competitive coevolution is used to find highly resistant mutant forms of the protease, and effective inhibitors against such mutants, in the context of the model. We use this method to characterize general features of inhibitors that are effective in overcoming resistance, and to study related issues of selection pathways, cross-resistance, and combination therapies.

Elementary structures in process theory (1): Sets with renaming

2000 ◽  
Vol 10 (5) ◽  
pp. 617-663 ◽  
Author(s):  
KOHEI HONDA
Keyword(s):  
Relational Theory ◽  
Process Theory ◽  
Process Calculi ◽  
Formal Equivalence ◽  
Wide Range ◽  
Algebraic Framework ◽  
Proof Nets ◽  
Formal Status ◽  
Effective Description

We study a general algebraic framework that underlies a wide range of computational formalisms that use the notion of names, notably process calculi. The algebraic framework gives a rigorous basis for describing and reasoning about processes semantically, as well as offering new insights into existing constructions. The formal status of the theory is elucidated by introducing its alternative presentation, which is geometric in nature and is based on explicit manipulation of connections among nameless processes. Nameless processes and their relational theory form a coherent universe in their own right, which underlies existing graphical formalisms such as proof nets. We establish the formal equivalence between these two presentations, and illustrate how they can be used complementarily for the precise and effective description of diverse algebras and the dynamics of processes through examples.

Spatially amplifying modes of the Charney baroclinic-instability problem

1986 ◽  
Vol 170 ◽  
pp. 293-317 ◽  
Author(s):  
R. T. Pierrehumbert
Keyword(s):  
Broad Class ◽  
Baroclinic Instability ◽  
Surface Wind ◽  
Stationary Wave ◽  
Vertical Shear ◽  
Coriolis Parameter ◽  
Spatial Instability ◽  
Wide Range ◽  
Amplification Rate ◽  
Zero Frequency

We determine the circumstances under which baroclinic instability in the Charney model subjected to localized time-periodic forcing manifests itself as a wavetrain that oscillates at the source frequency and amplifies in space with distance from the source; analytical and numerical results describing the salient characteristics of such waves are presented. The spatially amplifying disturbance is a hitherto unsuspected part of the response to a pulsating source, and coexists with the more familiar neutral Rossby wavetrains; it is likely to play a role in a wide range of atmospheric and oceanic phenomena.The central results rely on a careful application of a causality criterion due to Briggs. These results illustrate a practical means of attacking spatial instability problems, which can be applied to a broad class of systems besides the one at hand. We have found that the Charney problem with positive vertical shear is not absolutely unstable, so long as the wind at the ground is non-negative. This implies that spatial instability and forced stationary-wave problems are well posed in an open domain under typical atmospheric circumstances.The amplifying waves appear on the downstream side of the source, have eastward (downstream) phase propagation and have wavelengths that increase monotonically with decreasing frequency, becoming infinite at zero frequency. When the surface wind is not too large, the spatial amplification rate has a single maximum near the frequency ωm= (f/N)Uz, wherefis the Coriolis parameter,Nis the stability frequency andUzis the vertical shear; the rate approaches zero at zero frequency and asymptotes algebraically to zero at large frequency for any positive surface wind. Distinct Charney and Green modes do not appear until the surface wind is made very large. The amplification rate at ωmbecomes infinite as surface wind approaches zero, suggesting a mechanism for the concentration of eddy activity.We also discuss the relationship of these results to the structure of low- and high-frequency atmospheric variability.

Sign in / Sign up

Export Citation Format

Share Document