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The use of retrograde fluorescence double-labeling method has revealed that the internal (GPi) and external (GPe) segments of globus pallidus in squirrel monkey receive projections from different cell populations in striatum and subthalamic nucleus. Striatal neurons projecting either to GPi or GPe formed wide and nonoverlapping cell bands oriented obliquely(More)
We recall that the calculation of homology with integer coefficients of a simplicial complex reduces to the calculation of the Smith Normal Form of the boundary matrices which in general are sparse. We provide a review of several algorithms for the calculation of Smith Normal Form of sparse matrices and compare their running times for actual boundary(More)
The FFLAS project has established that exact matrix multiplication over finite fields can be performed at the speed of the highly optimized numerical BLAS routines. Since many algorithms have been reduced to use matrix multiplication in order to be able to prove an optimal theoretical complexity, this paper shows that those optimal complexity algorithms,(More)
In the past two decades, some major efforts have been made to reduce exact (e.g. integer, rational, polynomial) linear algebra problems to matrix multiplication in order to provide algorithms with optimal asymptotic complexity. To provide efficient implementations of such algorithms one need to be careful with the underlying arithmetic. It is well known(More)
We deal with the computation of the characteristic polynomial of dense matrices over word size finite fields and over the integers. We first present two algorithms for finite fields: one is based on Krylov iterates and Gaussian elimination. We compare it to an improvement of the second algorithm of Keller-Gehrig. Then we show that a generalization of(More)
We want to achieve efficient exact computations, such as the rank, of sparse matrices over finite fields. We therefore compare the practical behaviors, on a wide range of sparse matrices of the deterministic Gaussian elimination technique, using reordering heuristics, with the probabilistic, blackbox, Wiedemann algorithm. Indeed, we prove here that the(More)
To maximize efficiency in time and space, allocations and dealloca-tions, in the exact linear algebra library LinBox, must always occur in the founding scope. This provides a simple lightweight allocation model. We present this model and its usage for the rebinding of matrices between different coefficient domains. We also present automatic tools to(More)
A new block algorithm for triangularization of regular or singular matrices with dimension <i>m</i> &#215; <i>n</i> is proposed. Taking benefit of fast block multiplication algorithms, it achieves the best known sequential complexity <i>&Ogr;</i>(<i>m</i><sup><i>w</i>-1</sup><i>n</i>) for any sizes and any rank. Moreover, the block strategy enables to(More)
We present a new algorithm to compute the Integer Smith normal form of large sparse matrices. We reduce the computation of the Smith form to independent, and therefore parallel, computations modulo powers of word-size primes. Consequently, the algorithm does not suffer from coefficient growth. We have implemented several variants of this algorithm(More)