Reconstruction and simulation of neocortical microcircuitry

We present a first-draft digital reconstruction of the microcircuitry of somatosensory cortex of juvenile rat. The reconstruction uses cellular and synaptic organizing principles to algorithmically reconstruct detailed anatomy and physiology from sparse experimental data. An objective anatomical method defines a neocortical volume of 0.29 ± 0.01 mm3 containing ∼31,000 neurons, and patch-clamp studies identify 55 layer-specific morphological and 207 morpho-electrical neuron subtypes. When digitally reconstructed neurons are positioned in the volume and synapse formation is restricted to biological bouton densities and numbers of synapses per connection, their overlapping arbors form ∼8 million connections with ∼37 million synapses. Simulations reproduce an array of in vitro and in vivo experiments without parameter tuning. Additionally, we find a spectrum of network states with a sharp transition from synchronous to asynchronous activity, modulated by physiological mechanisms. The spectrum of network states, dynamically reconfigured around this transition, supports diverse information processing strategies

Parallel GMRES with a multiplicative Schwarz preconditioner

This paper presents a robust hybrid solver for linear systems that combines a Krylov subspace method as accelerator with a Schwarz-based preconditioner. This preconditioner uses an explicit formulation associated to one iteration of the multiplicative Schwarz method. The Newtonbasis GMRES, which aim at expressing a good data parallelism between subdomains is used as accelerator. In the first part of this paper, we present the pipeline parallelism that is obtained when the multiplicative Schwarz preconditioner is used to build the Krylov basis for the GMRES method. This is referred as the first level of parallelism. In the second part, we introduce a second level of parallelism inside the subdomains. For Schwarz-based preconditioners, the number of subdomains are keeped small to provide a robust solver. Therefore, the linear systems associated to subdomains are solved efficiently with this approach. Numerical experiments are performed on several problems to demonstrate the benefits of using these two levels of parallelism in the solver, mainly in terms of numerical robustness and global efficiency.Cet article présente un solveur hybride robuste pour des systèmes linéaires. Ce solveur parallèle construit un préconditionneur de type Schwarz pour accélerer une méthode basée sur les sous-espaces de Krylov. Le préconditionneur est défini à partir d’une formulation explicite correspondant à une itération de Schwarz multiplicatif. Dans le but de réduire les communications et les dépendences entre les sous-domaines, nous utilisons la version de GMRES qui dissocie la construction de la base de Krylov et son orthogonalisation. Nous présentons dans un premier temps le parallélisme qui est obtenu lorsque ce préconditionneur Schwarz multiplicatif est utilisé dans la construction de la base de Krylov. C’est le premier niveau de parallélisme. Dans la deuxième partie de ce travail, nous introduisons un deuxième niveau de parallélisme à l’intérieur de chaque sous-domaine. Pour des décompositions de domaines avec recouvrement, le nombre de sous-domaines doit rester faible pour fournir un solveur robuste. De ce fait, les systèmes linéaires associés aux sous-domaines sont résolus de manière efficace avec ce deuxième niveau de parallélisme. Plusieurs tests numériques sont présentés à la fin du document pour valider l’efficacité de cette approche

An explicit formulation of the multiplicative Schwarz preconditionner

We provide an explicit formulation of the splitting associated with the Multiplicative Schwarz iteration. We show the advantage of considering the explicit formulation, when the iteration is used as a preconditioner of a Krylov method. // A partir d'une expression explicite du splitting défini par l'itération multiplicative de Schwarz, nous étudions son utilisation comme précondtionnement d'une méthode de Krylov

Parallélisation de GMRES préconditionné par une itération de Schwarz multiplicatif

Cette thèse propose une alternative à la parallélisation de GMRES préconditionné par Schwarz multiplicatif par la technique de coloriage de graphe adjacent à la matrice. Cette parallélisation suppose que le graphe adjacent à la matrice est partitionné selon une direction. A partir de ce partionnement on peut dériver une forme explicite pour l'itération de Schwarz multiplicatif. On utilise cette forme explicite dans un pipeline pour la construction de l'espace de Krylov. On conserve les qualités du pipeline, en évitant d'inserrer les points de synchronisation comme les produits scalaires globaux dans le procédé d'Arnoldi. Pour cela, on utilise une version de GMRES qui découple la construction de l'espace de Krylov et la factorisation QR dans le procédé d'Arnoldi. Tous ces algorithmes sont implémentés sur le standard PETSc et portent le nom de GPREMS (Gmres PREconditionned by multiplicatif Schwarz). Les tests sont réalisés sur des problèmes issus de la simulation de semiconducteurs et de la mécanique des fluides. Cette validation numérique confirme les qualités parallèles de notre code, mais aussi sa compétitivité par rapport aux autres préconditionneurs du type décomposition de domaine comme Schwarz additif ou le complément de Schur.This thesis proposes an alternative to the parallelization of GMRES preconditioned by multiplicative Schwarz by the technique of coloring adjacent graph to the matrix. This parallelization implies that the adjacent graph to the matrix is partitioned according to one direction. From this partitioning we can derive an explicit form of spliting of multiplicatif Schwarz. We use this explicite form in a pipeline for the construction of Krylov subspace basis. The qualities of the pipeline are prevent by avoiding a synchronization points due to the dot product in overall process Arnoldi. For this reason, we use a version of GMRES which decouples the construction of the space Krylov and QR factorization in the process Arnoldi. All these algorithms are implemented on standard PETSc and bears the name of GPREMS (GMRES PREconditoned by multiplicative Schwarz). The tests are performed on problems arising from the simulation of semiconductors and fluid mechanics. This validation confirms the parallel qualities of our code, but also its competitiveness with other preconditioner type domain decomposition as Schwarz additive or additional Schur.RENNES1-BU Sciences Philo (352382102) / SudocRENNES-INRIA Rennes Irisa (352382340) / SudocSudocFranceF

Parallel GMRES with a multiplicative Schwarz preconditioner

International audienceThis paper presents a robust hybrid solver for linear systems that combines a Krylov subspace method as accelerator with a Schwarz-based preconditioner. This preconditioner uses an explicit formulation associated to one iteration of the multiplicative Schwarz method. The Newtonbasis GMRES, which aim at expressing a good data parallelism between subdomains is used as accelerator. In the first part of this paper, we present the pipeline parallelism that is obtained when the multiplicative Schwarz preconditioner is used to build the Krylov basis for the GMRES method. This is referred as the first level of parallelism. In the second part, we introduce a second level of parallelism inside the subdomains. For Schwarz-based preconditioners, the number of subdomains are keeped small to provide a robust solver. Therefore, the linear systems associated to subdomains are solved efficiently with this approach. Numerical experiments are performed on several problems to demonstrate the benefits of using these two levels of parallelism in the solver, mainly in terms of numerical robustness and global efficiency.Cet article présente un solveur hybride robuste pour des systèmes linéaires. Ce solveur parallèle construit un préconditionneur de type Schwarz pour accélerer une méthode basée sur les sous-espaces de Krylov. Le préconditionneur est défini à partir d’une formulation explicite correspondant à une itération de Schwarz multiplicatif. Dans le but de réduire les communications et les dépendences entre les sous-domaines, nous utilisons la version de GMRES qui dissocie la construction de la base de Krylov et son orthogonalisation. Nous présentons dans un premier temps le parallélisme qui est obtenu lorsque ce préconditionneur Schwarz multiplicatif est utilisé dans la construction de la base de Krylov. C’est le premier niveau de parallélisme. Dans la deuxième partie de ce travail, nous introduisons un deuxième niveau de parallélisme à l’intérieur de chaque sous-domaine. Pour des décompositions de domaines avec recouvrement, le nombre de sous-domaines doit rester faible pour fournir un solveur robuste. De ce fait, les systèmes linéaires associés aux sous-domaines sont résolus de manière efficace avec ce deuxième niveau de parallélisme. Plusieurs tests numériques sont présentés à la fin du document pour valider l’efficacité de cette approche

Framework for efficient synthesis of spatially embedded morphologies

Many problems in science and engineering require the ability to grow tubular or polymeric structures up to large volume fractions within a bounded region of three-dimensional space. Examples range from the construction of fibrous materials and biological cells such as neurons, to the creation of initial configurations for molecular simulations. A common feature of these problems is the need for the growing structures to wind throughout space without intersecting. At any time, the growth of a morphology depends on the current state of all the others, as well as the environment it is growing in, which makes the problem computationally intensive. Neuron synthesis has the additional constraint that the morphologies should reliably resemble biological cells, which possess nonlocal structural correlations, exhibit high packing fractions, and whose growth responds to anatomical boundaries in the synthesis volume. We present a spatial framework for simultaneous growth of an arbitrary number of nonintersecting morphologies that presents the growing structures with information on anisotropic and inhomogeneous properties of the space. The framework is computationally efficient because intersection detection is linear in the mass of growing elements up to high volume fractions and versatile because it provides functionality for environmental growth cues to be accessed by the growing morphologies. We demonstrate the framework by growing morphologies of various complexity

A comparative study of some distributed linear solvers on systems arising from fluid dynamics simulations

International audienc

A Partitioning Algorithm for Block-Diagonal Matrices with Overlap

We present a graph partitioning algorithm that aims at partitioning a sparse matrix into a block-diagonal form, such that any two consecutive blocks overlap. We denote this form of the matrix as the overlapped block-diagonal matrix. The partitioned matrix is suitable for applying the explicit formulation of Multiplicative Schwarz preconditioner (EFMS) described in [3]. The graph partitioning algorithm partitions the graph of the input matrix into K partitions, such that every partition Ωi has at most two neighbors Ωi−1 and Ωi+1. First, an ordering algorithm, such as the reverse Cuthill-McKee algorithm, that reduces the matrix profile is performed. An initial overlapped block-diagonal partition is obtained from the profile of the matrix. An iterative strategy is then used to further refine the partitioning by allowing nodes to be transfered between neighboring partitions. Experiments are performed on matrices arising from real-world applications to show the feasibility and usefulness of this approach. Problem Consider the sparse matrix A ∈ R n×n. The pattern of A is the set P = {(k, l) | akl � = 0} which is the set of edges of the graph G = (W, P), where W is the set of nodes and P is a set of edges. A two-neighboring graph partitioning of graph G into K partitions is defined by the sets o