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162
Simulation of networks of spiking neurons: A review of tools and strategies
 Journal of Computational Neuroscience
, 2007
"... We review different aspects of the simulation of spiking neural networks. We start by reviewing the different types of simulation strategies and algorithms that are currently implemented. We next review the precision of those simulation strategies, in particular in cases where plasticity depends on ..."
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Cited by 108 (29 self)
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We review different aspects of the simulation of spiking neural networks. We start by reviewing the different types of simulation strategies and algorithms that are currently implemented. We next review the precision of those simulation strategies, in particular in cases where plasticity depends on the exact timing of the spikes. We overview different simulators and simulation environments presently available (restricted to those freely available, open source and documented). For each simulation tool, its advantages and pitfalls are reviewed, with an aim to allow the reader to identify which simulator is appropriate for a given task. Finally, we provide a series of benchmark simulations of different types of networks of spiking neurons, including HodgkinHuxley type, integrateandfire models, interacting with currentbased or conductancebased synapses, using clockdriven or eventdriven integration strategies. The same set of models are implemented on the different simulators, and the codes are made available. The ultimate goal of this review is to provide a resource to facilitate identifying the appropriate integration strategy and simulation tool to use for a given
Rulebased modeling of biochemical systems with BioNetGen
 IN METHODS IN MOLECULAR BIOLOGY: SYSTEMS BIOLOGY
, 2009
"... Rulebased modeling involves the representation of molecules as structured objects and molecular interactions as rules for transforming the attributes of these objects. The approach is notable in that it allows one to systematically incorporate sitespecific details about proteinprotein interactio ..."
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Cited by 43 (10 self)
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Rulebased modeling involves the representation of molecules as structured objects and molecular interactions as rules for transforming the attributes of these objects. The approach is notable in that it allows one to systematically incorporate sitespecific details about proteinprotein interactions into a model for the dynamics of a signaltransduction system, but the method has other applications as well, such as following the fates of individual carbon atoms in metabolic reactions. The consequences of proteinprotein interactions are difficult to specify and track with a conventional modeling approach because of the large number of protein phosphoforms and protein complexes that these interactions potentially generate. Here, we focus on how a rulebased model is specified in the BioNetGen language (BNGL) and how a model specification is analyzed using the BioNetGen software tool. We also discuss new developments in rulebased modeling that should enable the construction and analyses of comprehensive models for signal transduction pathways and similarly largescale models for other biochemical systems.
A fully implicit numerical method for singlefluid resistive magnetohydrodynamics
 J. Comput. Phys
"... Abstract We present a nonlinearly implicit, conservative numerical method for integration of the singlefluid resistive MHD equations. The method uses a highorder spatial discretization that preserves the solenoidal property of the magnetic field. The fully coupled PDE system is solved implicitly ..."
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Cited by 11 (3 self)
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Abstract We present a nonlinearly implicit, conservative numerical method for integration of the singlefluid resistive MHD equations. The method uses a highorder spatial discretization that preserves the solenoidal property of the magnetic field. The fully coupled PDE system is solved implicitly in time, providing for increased interaction between physical processes as well as additional stability over explicittime methods. A highorder adaptive time integration is employed, which in many cases enables time steps ranging from one to two orders of magnitude larger than those constrained by the explicit CFL condition. We apply the solution method to illustrative examples relevant to stiff magnetic fusion processes which challenge the efficiency of explicit methods. We provide computational evidence showing that for such problems the method is comparably accurate with explicittime simulations, while providing a significant runtime improvement due to its increased temporal stability.
On the Unlikeliness of MultiField Inflation
 Bounded Random Potentials and our Vacuum, JCAP 1206 (2012) 034, [arXiv:1203.3941
"... conditions and sampling for ..."
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LONGTIME SIMULATIONS ON HIGH RESOLUTION MESHES TO Model Calcium Waves In A Heart Cell
, 2008
"... A model for the flow of calcium on the scale of one heart cell is given by a system of timedependent reactiondiffusion equations coupled by nonlinear reaction terms. Calcium ions enter into the cell at release units distributed throughout the cell and then diffuse. At each release unit, the proba ..."
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Cited by 9 (8 self)
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A model for the flow of calcium on the scale of one heart cell is given by a system of timedependent reactiondiffusion equations coupled by nonlinear reaction terms. Calcium ions enter into the cell at release units distributed throughout the cell and then diffuse. At each release unit, the probability for calcium to be released increases along with the concentration of calcium, thus creating a feedback loop of waves regenerating themselves repeatedly. The validation of this model requires simulations on the time scale of several repeated waves and on the spatial scale of the entire cell. This requires longtime studies on spatial meshes that need to have a high resolution to resolve the positions of the calcium release units throughout the entire cell. We detail the development of a specialpurpose numerical method and parallel implementation for this problem. Parallel performance studies demonstrate the scalability of the implementation on a distributedmemory cluster with lowlatency interconnect. Convergence studies verify convergence to analytical expectations and confirm the appropriateness of all numerical parameters. Application studies on the desired time and length scales confirm that the model exhibits the desired feedback mechanism for calcium currents through the release units at suitable high levels, but the longtime studies demonstrate also that the current model with its present parameters leads to excessive calcium concentrations over time. This phenomenon could only be observed using a computational method able to reach laboratory scale final times for a domain on the scale of a complete cell.
Fluid flows in a librating cylinder
 Phys. Fluids
, 2012
"... The flow in a cylinder driven by time harmonic oscillations of the rotation rate, called longitudinal librations, is investigated. Using a theoretical approach and axisymmetric numerical simulations, we study two distinct phenomena appearing in this librating flow. First, we investigate the occurre ..."
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Cited by 8 (7 self)
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The flow in a cylinder driven by time harmonic oscillations of the rotation rate, called longitudinal librations, is investigated. Using a theoretical approach and axisymmetric numerical simulations, we study two distinct phenomena appearing in this librating flow. First, we investigate the occurrence of a centrifugal instability near the oscillating boundary, leading to the socalled TaylorGörtler vortices. A viscous stability criterion is derived and compared to numerical results obtained for various libration frequencies and Ekman numbers. The strongly nonlinear regime well above the instability threshold is also documented. We show that a new mechanism of spontaneous generation of inertial waves in the bulk could exist when the sidewall boundary layer becomes turbulent. Then, we analyse the librating flow below the instability threshold and characterize the mean zonal flow correction induced by the nonlinear interaction of the boundary layer flow with itself. In the frequency regime where inertial modes are not excited, we show that the mean flow correction in the bulk is a uniform rotation, independent of the Ekman number and cylinder aspect ratio, in perfect agreement with the analytical results of Wang [J. Fluid. Mech., 41, pp. 581 592, 1970]. When inertial modes are resonantly excited, the mean flow correction is found to have a more complex structure. Its amplitude still scales as the square of the libration amplitude but now depends on the Ekman number.
A systematic numerical study of the tidal instability in a rotating triaxial ellipsoid
, 2010
"... ..."
Divide and recycle: types and compilation for a hybrid synchronous language
 In ACM SIGPLAN/SIGBED Languages, Compilers, Tools & Theory for Embedded Systems (LCTES
, 2011
"... Hybrid modelers such as SIMULINK have become corner stones of embedded systems development. They allow both discrete controllers and their continuous environments to be expressed in a single language. Despite the availability of such tools, there remain a number of issues related to the lack of repr ..."
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Cited by 7 (2 self)
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Hybrid modelers such as SIMULINK have become corner stones of embedded systems development. They allow both discrete controllers and their continuous environments to be expressed in a single language. Despite the availability of such tools, there remain a number of issues related to the lack of reproducibility of simulations and to the separation of the continuous part, which has to be exercised by a numerical solver, from the discrete part, which must be guaranteed not to evolve during a step. Starting from a minimal, yet fullfeatured, LUSTRElike synchronous language, this paper presents a conservative extension where dataflow equations can be mixed with ordinary differential equations (ODEs) with possible reset. A type system is proposed to statically distinguish discrete computations from continuous ones and to ensure that signals are used in their proper domains. We
Experimental Design for Parameter Estimation of Gene Regulatory Networks
"... Systems biology aims for building quantitative models to address unresolved issues in molecular biology. In order to describe the behavior of biological cells adequately, gene regulatory networks (GRNs) are intensively investigated. As the validity of models built for GRNs depends crucially on the k ..."
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Cited by 7 (0 self)
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Systems biology aims for building quantitative models to address unresolved issues in molecular biology. In order to describe the behavior of biological cells adequately, gene regulatory networks (GRNs) are intensively investigated. As the validity of models built for GRNs depends crucially on the kinetic rates, various methods have been developed to estimate these parameters from experimental data. For this purpose, it is favorable to choose the experimental conditions yielding maximal information. However, existing experimental design principles often rely on unfulfilled mathematical assumptions or become computationally demanding with growing model complexity. To solve this problem, we combined advanced methods for parameter and uncertainty estimation with experimental design considerations. As a showcase, we optimized three simulated GRNs in one of the challenges from the Dialogue for Reverse Engineering Assessment and Methods (DREAM). This article presents our approach, which was awarded the best performing procedure at the DREAM6 Estimation of Model Parameters challenge. For fast and reliable parameter estimation, local deterministic optimization of the likelihood was applied. We analyzed identifiability and precision of the estimates by calculating the profile likelihood. Furthermore, the profiles provided a way to uncover a selection of most informative experiments, from which the optimal one was chosen using additional criteria at every step of the design process. In conclusion, we provide a strategy for optimal experimental design and show its successful application on three highly nonlinear dynamic models. Although presented in the context of