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Bioinformatics High Performance Parallel Computer Architectures Embedded Multi Core Systems
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This approach requires sophisticate techniques and it is not always applicable. The general idea is to decompose an IVP into sub-problems that can be solved with different methods and different step-size strategies. Waveform relaxation is a well-known class of decomposition techniques, where a continuous problem is split and the corresponding interactions a la Picard is defined.
Bioinformatics: High Performance Parallel Computer Architectures (Embedded Multi Core Systems)
These methodologies require a stringent synchronisation of the computations in order to assure the consistency of the results. A different method exploits parallelism by performing concurrently several integration steps with a given interaction method, leading to the class of techniques of parallelism across the steps. These techniques may be theoretically employed with a large number of processors, but intrinsic poor convergence behaviour could lead to robustness problems.
However, this parallelisation method is receiving great attention because of its potential in scaling up the size of the problem that can be managed e. These are the main approaches to the parallelisation of numerical methods for ODE. For a deeper introduction, we refer to the good monograph [ 8 ] and to the special issue [ 16 ]. As in the case of parallel linear algebra, many libraries that can be included in general purpose softwares have been developed. These libraries are then used within complex tools such as, for example, the Systems Biology Workbench [ 20 ], a tool which offers design, simulation and analysis instruments.
Behind the use of libraries within specific simulation and analysis tools, new research lines specifically tailored on biological pathways deserve a separate discussion. The on-chip solver computes concentration of substances for each time step by integrating rate law functions. Often biologists use cluster computers to launch many simulations of the same model with different parameters at the same time. ReCSiP is particularly suited for this kind of job offering a speed about to fold compared with modern microprocessors, and it is cheaper than the cluster solution.
Both linear algebra applications and ODE solvers are actively studied, but actually specific works on pathway-related problems are not available. A new and fruitful research line can be opened. Another interesting proposal is to parallelise algorithms that are specific to the analysis of biological pathways, as opposed to general ODE methods.
For instance, extreme pathways [ 23 ] are an algorithm for the analysis of metabolic networks. A solution of the IVP describes a particular metabolic phenotype, while extreme pathways analysis aims at finding the cone of solutions corresponding to the theoretical capabilities of a metabolic genotype. Extreme pathways algorithm shows combinatorial complexity, but its parallel version [ 24 ] exhibits super-linear scalability, which means that the execution time decreases faster than the rate of increase in the number of processors. Stochastic simulation algorithms are computer programs that generate a trajectory i.
The SSA is referred to biochemical systems consisting of a well-stirred mix of molecular species that chemically interact, through so-called reaction channels, inside some fixed volume and at a constant temperature. Based on the CME, a propensity function is defined for each reaction j , giving the probability that a reaction j will occur in the next infinitesimal interval. Then, relying on standard Monte Carlo method reactions are stochastically selected and executed forming in that a way a simulated trajectory in the discrete state-space corresponding to the CME.
Several variants of the SSA exist, but all of them are based on the following common template: The different instances of the SSA vary in how the next reaction is selected and in the data structures used to store chemical species and reactions. In particular, the Next Reaction Method [ 28 ] is based on the so-called dependency graph, a direct graph whose nodes represent reactions, and whose arcs denote dependencies between reactions i.
Another research direction aims at integrating SSA with spatial information [ 29 ]. The Next-Subvolume Method NSM [ 30 ] simulates both reaction events and diffusion of molecules within a given volume; the algorithm partitions the volume into cubical sub-volumes that represent well-stirred systems. Stochastic simulation approaches, such as the one implemented by the SSA, are not new in systems biology; however only in relatively recent times they have received much attention, as an increasing number of studies revealed a fundamental characteristic of many biological systems.
It has been observed, in fact, that most key reactant molecules are present only in a small amount in living systems e. This renewed attention also showed the main limit of SSA: The resource requirements of SSA could be reduced either by using approximate algorithms or through parallelisation. The latter research line is a really recent one, but some interesting proposals are emerging. A first improvement can be achieved by considering that many independent running of SSA are needed to compute statistics about a discrete and stochastic model.
It is straightforward to run different simulations on different processes, but much attention has to be paid to the generation of random numbers [ 33 ]. This kind of parallelism is called parallelism across the simulation. The use of GRID architectures to run many independent simulations is promising because of inherent scalability [ 34 ]. Parallelism across the simulation is an effective technique when many simulations are needed, but there are instances where a single simulation of a large system think for example to a colony of cells is required.
In this case, the researches are only at the very beginning.
Basically, there are two approaches to distribute computation to the processing units: The Distributed-based Stochastic Simulation Algorithm or DSSA [ 35 ] is developed on the intuition that the main computational requirement of any SSA variants comes from Steps 2 and 3, namely the random selection and the execution of the next reaction. The DSSA relies on cluster architecture to tackle the complexity of these steps.
In particular, a cluster processing unit, termed server, coordinates the activities of the other processing units or clients in the cluster, resulting in the following workflow: The partitioning algorithm employed in Step 1 uses the dependency graph as a weighted graph to minimise communications between the server and the clients; in particular, not all the clients need to be updated after a reaction is selected by the server. The authors outline some experimental and performance analysis showing that the performance improvement with respect to SSA is linearly dependent on the number of client nodes.
Another approach that is receiving great attention is based on geometric clustering. A pioneer work is [ 36 ], but the algorithm reached a good maturation only with the recent efforts in integrating SSA with space information. In particular, in [ 37 ] the NSM is parallelised by using a geometric clustering algorithm to map set of sub-volumes to processing units. The algorithm scales well on a cluster architecture, where the main limit is the linear relation between the diffusion coefficient and the number of messages exchanged among the processing units.
The authors also test a promising GRID version of the algorithm, but the overhead due to the synchronisation among processing units requires more investigations. Finally, we refer a couple of applications of non-standard parallel hardware to speed up stochastic simulation [ 38 ]. Another work [ 40 ] exploits the high parallel structure of modern GPUs to obtain parallelism across the simulation without the costs of a computer cluster. These applications are really promising, but they require on the road testing. It was initially targeted to the verification of computer hardware designs, but it soon spread to several areas such as software verification, communication protocols verification, reliability analysis, game theory and, in recent years, it has been applied to life sciences as well.
Model checking is based on a fairly simple principle: What makes model checking so appealing is that the verification procedure is automatic and the produced result is exact up to the exactness with which the model represents the behaviour of the considered system as it is obtained through an exhaustive search of the state space of the model.
Model-checking approaches can be classified according to the type of model considered and the associated formal language used for formulating properties. Linear temporal logic LTL and computational tree logic CTL are languages used to state properties of qualitative models. CTL model checking has been considered for the verification of properties of biological systems [ 43 ].
It should be noted that application of model-checking verification to a continuous and deterministic model of a biological system entails a discretisation procedure by means of which the original model is turned into a discrete-state one. For instance, the BIOCHAM tool [ 44 ] supports CTL model checking on the qualitative model obtained from a discretisation of a system which is originally expressed as a set of reaction-rate equations the discretisation being obtained by conversion of molecules concentrations into amounts and by disregarding kinetic rates of the chemical equations.
CTL formulae are then used to express patterns characterising relevant trends for the modelled species e. In the s, the idea of model checking was extended to quantitative models. Markov chain models can be thought of as state graphs with stochastic information attached to the arcs.
Verification of properties against a Markov chain model is quantitative in two respects: Recently, effort has been put in the application of probabilistic model checking to the verification of relevant biological case studies e. The main issue with the model-checking approach is given by the explosion of the model's dimension.
The number of states in a model can easily reach a level which goes well beyond the storage capability of currently available computational resources. This is even truer with modelling of biology where systems often consist of complex networks of signals and large populations and, as a consequence, model-checking verification, in many cases, is simply not applicable.
Several techniques aimed to tackle the state-space explosion problem have been developed over the last decades. Partial order reduction techniques allow for a reduction of the state space dimension based on exploitation of the commutativity of concurrently executed transitions [ 54 ].
Bioinformatics: High Performance Parallel Computer Architectures (Embedded Multi Core Systems)
They have been extensively studied yielding so-called symbolic model-checking algorithms most popular model-checking tools, such as nuSMV [ 55 ] and PRISM [ 56 ], to mention a couple, are based on symbolic approaches. Despite the advances given by techniques for the efficient representation of large models, the state space explosion remains a major limiting factor to the application of model-checking verification to complex systems.
A promising path of research is that of parallel model-checking approaches. Classical model-checking algorithms establish the truth of a formula through exploration of the model's state space a process often referred to as reachability analysis.
Parallelisation of such algorithms is about looking at ways for distributing the reachability-based verification of a formula over a multi-processor architecture. In practice, however, model-checking algorithms differ with respect to the type of logic they are referred to, thus the parallelisation problem is different with respect to different type of model checking. This, in turn, is proved to be equivalent to finding a cycle containing an accepting state in the graph corresponding to the automaton, see [ 57 ].
Hence LTL model checking boils down to cycle detection, a well-studied subject in graph theory. There are a plethora of algorithms for cycle detection mostly based on a depth-first search DFS exploration of the graph.