Stochastic Process Algebra Models of a Circadian Clock

We present stochastic process algebra models of a Circadian clock mechanism used in many biological organisms to regulate time-based behaviour. We compare modelling techniques from different modelling paradigms, PEPA and stochastic $pi$-calculus

Distributed computation of transient state distributions and passage time quantiles in large semi-Markov models

Submitted versio

Analysing distributed Internet worm attacks using continuous state-space approximation of process algebra models

AbstractInternet worms are classically described using SIR models and simulations, to capture the massive dynamics of the system. Here we are able to generate a differential equation-based model of infection based solely on the underlying process description of the infection agent model. Thus, rather than craft a differential equation model directly, we derive this representation automatically from a high-level process model expressed in the PEPA process algebra. This extends existing population infection dynamics models of Internet worms by explicitly using frequency-based spread of infection. Three types of worm attack are analysed which are differentiated by the nature of recovery from infection and vulnerability to subsequent attacks.To perform this analysis we make use of continuous state-space approximation, a recent breakthrough in the analysis of massively parallel stochastic process algebra models. Previous explicit state-representation techniques can only analyse systems of order 109 states, whereas continuous state-space approximation can allow analysis of models of 1010000 states and beyond

Superflares on Ordinary Solar-Type Stars

Short duration flares are well known to occur on cool main-sequence stars as well as on many types of `exotic' stars. Ordinary main-sequence stars are usually pictured as being static on time scales of millions or billions of years. Our sun has occasional flares involving up to $\sim 10^{31}$ ergs which produce optical brightenings too small in amplitude to be detected in disk-integrated brightness. However, we identify nine cases of superflares involving $10^{33}$ to $10^{38}$ ergs on normal solar-type stars. That is, these stars are on or near the main-sequence, are of spectral class from F8 to G8, are single (or in very wide binaries), are not rapid rotators, and are not exceedingly young in age. This class of stars includes many those recently discovered to have planets as well as our own Sun, and the consequences for any life on surrounding planets could be profound. For the case of the Sun, historical records suggest that no superflares have occurred in the last two millennia.Comment: 16 pages, accepted for publication in Ap

Cache-Oblivious Streaming B-Trees

A streaming B-tree is a dictionary that efficiently implements insertions and range queries. We present two cache-oblivious streaming B-trees, the shuttle tree, and the cache-oblivious lookahead array (COLA). For block-transfer size B and on N elements, the shuttle tree implements searches in optimal $O(log_{B+1}N)$ transfers, range queries of L successive elements in optimal $O(log_{B+1}N +L/B)$ transfers, and insertions in $O((log_{B+1}N)/B^{\Theta(1/(log log B)^2)}+(log^2N)/B)$ transfers, which is an asymptotic speedup over traditional B-trees if $B ≥ (log N)^{1+c log log log^2 N}$ for any constant c >1. A COLA implements searches in O(log N) transfers, range queries in O(log N + L/B) transfers, and insertions in amortized O((log N)/B) transfers, matching the bounds for a (cache-aware) buffered repository tree. A partially deamortized COLA matches these bounds but reduces the worst-case insertion cost to O(log N) if memory size $M = \Omega(log N)$. We also present a cache-aware version of the COLA, the lookahead array, which achieves the same bounds as Brodal and Fagerberg's (cache-aware) $B^{\epsilon}$-tree. We compare our COLA implementation to a traditional B-tree. Our COLA implementation runs 790 times faster for random insertions, 3.1 times slower for insertions of sorted data, and 3.5 times slower for searches.Engineering and Applied Science

Distributed Response Time Analysis of GSPN Models with MapReduce

widely used in the performance analysis of computer and communications systems. Response time densities and quantiles are often key outputs of such analysis. These can be extracted from a GSPN’s underlying semi-Markov process using a method based on numerical Laplace transform inversion. This method typically requires the solution of thousands of systems of complex linear equations, each of rank n, where n is the number of states in the model. For large models substantial processing power is needed and the computation must therefore be distributed. This paper describes the implementation of a Response Time Analysis module for the Platform Independent Petri net Editor (PIPE2) which interfaces with Hadoop, an open source implementation of Google’s MapReduce distributed programming environment, to provide distributed calculation of response time densities in GSPN models. The software is validated with analytically calculated results as well as simulated ones for larger models. Excellent scalability is shown. I

A fluid analysis framework for a Markovian process algebra

Markovian process algebras, such as PEPA and stochastic π-calculus, bring a powerful compositional approach to the performance modelling of complex systems. However, the models generated by process algebras, as with other interleaving formalisms, are susceptible to the state space explosion problem. Models with only a modest number of process algebra terms can easily generate so many states that they are all but intractable to traditional solution techniques. Previous work aimed at addressing this problem has presented a fluid-flow approximation allowing the analysis of systems which would otherwise be inaccessible. To achieve this, systems of ordinary differential equations describing the fluid flow of the stochastic process algebra model are generated informally. In this paper, we show formally that for a large class of models, this fluid-flow analysis can be directly derived from the stochastic process algebra model as an approximation to the mean number of component types within the model. The nature of the fluid approximation is derived and characterised by direct comparison with the Chapman–Kolmogorov equations underlying the Markov model. Furthermore, we compare the fluid approximation with the exact solution using stochastic simulation and we are able to demonstrate that it is a very accurate approximation in many cases. For the first time, we also show how to extend these techniques naturally to generate systems of differential equations approximating higher order moments of model component counts. These are important performance characteristics for estimating, for instance, the variance of the component counts. This is very necessary if we are to understand how precise the fluid-flow calculation is, in a given modelling situation

CGHScan: finding variable regions using high-density microarray comparative genomic hybridization data

BACKGROUND: Comparative genomic hybridization can rapidly identify chromosomal regions that vary between organisms and tissues. This technique has been applied to detecting differences between normal and cancerous tissues in eukaryotes as well as genomic variability in microbial strains and species. The density of oligonucleotide probes available on current microarray platforms is particularly well-suited for comparisons of organisms with smaller genomes like bacteria and yeast where an entire genome can be assayed on a single microarray with high resolution. Available methods for analyzing these experiments typically confine analyses to data from pre-defined annotated genome features, such as entire genes. Many of these methods are ill suited for datasets with the number of measurements typical of high-density microarrays. RESULTS: We present an algorithm for analyzing microarray hybridization data to aid identification of regions that vary between an unsequenced genome and a sequenced reference genome. The program, CGHScan, uses an iterative random walk approach integrating multi-layered significance testing to detect these regions from comparative genomic hybridization data. The algorithm tolerates a high level of noise in measurements of individual probe intensities and is relatively insensitive to the choice of method for normalizing probe intensity values and identifying probes that differ between samples. When applied to comparative genomic hybridization data from a published experiment, CGHScan identified eight of nine known deletions in a Brucella ovis strain as compared to Brucella melitensis. The same result was obtained using two different normalization methods and two different scores to classify data for individual probes as representing conserved or variable genomic regions. The undetected region is a small (58 base pair) deletion that is below the resolution of CGHScan given the array design employed in the study. CONCLUSION: CGHScan is an effective tool for analyzing comparative genomic hybridization data from high-density microarrays. The algorithm is capable of accurately identifying known variable regions and is tolerant of high noise and varying methods of data preprocessing. Statistical analysis is used to define each variable region providing a robust and reliable method for rapid identification of genomic differences independent of annotated gene boundaries

Stochastic Simulation Methods Applied to a Secure Electronic Voting Model

We demonstrate a novel simulation technique for analysing large stochastic process algebra models, applying this to a secure electronic voting system example. By approximating the discrete state space of a PEPA model by a continuous equivalent, we can draw on rate equation simulation techniques from both chemical and biological modelling to avoid having to directly enumerate the huge state spaces involved. We use stochastic simulation techniques to provide traces of course-of-values time series representing the number of components in a particular state. Using such a technique we can get simulation results for models exceeding 10 10000 states within only a few seconds