3,035 research outputs found
Finding symmetry in models of concurrent systems by static channel diagram analysis
Over the last decade there has been much interest in exploiting symmetry to combat the state explosion problem in model checking. Although symmetry in a model often arises as a result of symmetry in the topology of the system being modelled, most model checkers which exploit structural symmetry are limited to topologies which exhibit total symmetries, such as stars and cliques. We define the static channel diagram of a concurrent, message passing program, and show that under certain restrictions there is a correspondence between symmetries of the static channel diagram of a program and symmetries of the Kripke structure associated with the program. This allows the detection, and potential exploitation, of structural symmetry in systems with arbitrary topologies. Our method of symmetry detection can handle mobile systems where channel references are passed on channels, resulting in a dynamic communication structure. We illustrate our results with an example using the Promela modelling language
Trend-based analysis of a population model of the AKAP scaffold protein
We formalise a continuous-time Markov chain with multi-dimensional discrete state space model of the AKAP scaffold protein as a crosstalk mediator between two biochemical signalling pathways. The analysis by temporal properties of the AKAP model requires reasoning about whether the counts of individuals of the same type (species) are increasing or decreasing. For this purpose we propose the concept of stochastic trends based on formulating the probabilities of transitions that increase (resp. decrease) the counts of individuals of the same type, and express these probabilities as formulae such that the state space of the model is not altered. We define a number of stochastic trend formulae (e.g. weakly increasing, strictly increasing, weakly decreasing, etc.) and use them to extend the set of state formulae of Continuous Stochastic Logic. We show how stochastic trends can be implemented in a guarded-command style specification language for transition systems. We illustrate the application of stochastic trends with numerous small examples and then we analyse the AKAP model in order to characterise and show causality and pulsating behaviours in this biochemical system
Evaluating Systematic Dependencies of Type Ia Supernovae: The Influence of Deflagration to Detonation Density
We explore the effects of the deflagration to detonation transition (DDT)
density on the production of Ni-56 in thermonuclear supernova explosions (type
Ia supernovae). Within the DDT paradigm, the transition density sets the amount
of expansion during the deflagration phase of the explosion and therefore the
amount of nuclear statistical equilibrium (NSE) material produced. We employ a
theoretical framework for a well-controlled statistical study of
two-dimensional simulations of thermonuclear supernovae with randomized initial
conditions that can, with a particular choice of transition density, produce a
similar average and range of Ni-56 masses to those inferred from observations.
Within this framework, we utilize a more realistic "simmered" white dwarf
progenitor model with a flame model and energetics scheme to calculate the
amount of Ni-56 and NSE material synthesized for a suite of simulated
explosions in which the transition density is varied in the range 1-3x10^7
g/cc. We find a quadratic dependence of the NSE yield on the log of the
transition density, which is determined by the competition between plume rise
and stellar expansion. By considering the effect of metallicity on the
transition density, we find the NSE yield decreases by 0.055 +/- 0.004 solar
masses for a 1 solar metallicity increase evaluated about solar metallicity.
For the same change in metallicity, this result translates to a 0.067 +/- 0.004
solar mass decrease in the Ni-56 yield, slightly stronger than that due to the
variation in electron fraction from the initial composition. Observations
testing the dependence of the yield on metallicity remain somewhat ambiguous,
but the dependence we find is comparable to that inferred from some studies.Comment: 15 pages, 13 figures, accepted to ApJ on July 6, 201
On variations of the brightness of type Ia supernovae with the age of the host stellar population
Recent observational studies of type Ia supernovae (SNeIa) suggest
correlations between the peak brightness of an event and the age of the
progenitor stellar population. This trend likely follows from properties of the
progenitor white dwarf (WD), such as central density, that follow from
properties of the host stellar population. We present a statistically
well-controlled, systematic study utilizing a suite of multi-dimensional SNeIa
simulations investigating the influence of central density of the progenitor WD
on the production of Fe-group material, particularly radioactive Ni-56, which
powers the light curve. We find that on average, as the progenitor's central
density increases, production of Fe-group material does not change but
production of Ni-56 decreases. We attribute this result to a higher rate of
neutronization at higher density. The central density of the progenitor is
determined by the mass of the WD and the cooling time prior to the onset of
mass transfer from the companion, as well as the subsequent accretion heating
and neutrino losses. The dependence of this density on cooling time, combined
with the result of our central density study, offers an explanation for the
observed age-luminosity correlation: a longer cooling time raises the central
density at ignition thereby producing less Ni-56 and thus a dimmer event. While
our ensemble of results demonstrates a significant trend, we find considerable
variation between realizations, indicating the necessity for averaging over an
ensemble of simulations to demonstrate a statistically significant result.Comment: 5 pages, 4 figures, 1 table, accepted to ApJ
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