408 research outputs found
Tensor Network alternating linear scheme for MIMO Volterra system identification
This article introduces two Tensor Network-based iterative algorithms for the
identification of high-order discrete-time nonlinear multiple-input
multiple-output (MIMO) Volterra systems. The system identification problem is
rewritten in terms of a Volterra tensor, which is never explicitly constructed,
thus avoiding the curse of dimensionality. It is shown how each iteration of
the two identification algorithms involves solving a linear system of low
computational complexity. The proposed algorithms are guaranteed to
monotonically converge and numerical stability is ensured through the use of
orthogonal matrix factorizations. The performance and accuracy of the two
identification algorithms are illustrated by numerical experiments, where
accurate degree-10 MIMO Volterra models are identified in about 1 second in
Matlab on a standard desktop pc
Randomized methods for matrix computations
The purpose of this text is to provide an accessible introduction to a set of
recently developed algorithms for factorizing matrices. These new algorithms
attain high practical speed by reducing the dimensionality of intermediate
computations using randomized projections. The algorithms are particularly
powerful for computing low-rank approximations to very large matrices, but they
can also be used to accelerate algorithms for computing full factorizations of
matrices. A key competitive advantage of the algorithms described is that they
require less communication than traditional deterministic methods
An efficient null space inexact Newton method for hydraulic simulation of water distribution networks
Null space Newton algorithms are efficient in solving the nonlinear equations
arising in hydraulic analysis of water distribution networks. In this article,
we propose and evaluate an inexact Newton method that relies on partial updates
of the network pipes' frictional headloss computations to solve the linear
systems more efficiently and with numerical reliability. The update set
parameters are studied to propose appropriate values. Different null space
basis generation schemes are analysed to choose methods for sparse and
well-conditioned null space bases resulting in a smaller update set. The Newton
steps are computed in the null space by solving sparse, symmetric positive
definite systems with sparse Cholesky factorizations. By using the constant
structure of the null space system matrices, a single symbolic factorization in
the Cholesky decomposition is used multiple times, reducing the computational
cost of linear solves. The algorithms and analyses are validated using medium
to large-scale water network models.Comment: 15 pages, 9 figures, Preprint extension of Abraham and Stoianov, 2015
(https://dx.doi.org/10.1061/(ASCE)HY.1943-7900.0001089), September 2015.
Includes extended exposition, additional case studies and new simulations and
analysi
Unsupervised discovery of temporal sequences in high-dimensional datasets, with applications to neuroscience.
Identifying low-dimensional features that describe large-scale neural recordings is a major challenge in neuroscience. Repeated temporal patterns (sequences) are thought to be a salient feature of neural dynamics, but are not succinctly captured by traditional dimensionality reduction techniques. Here, we describe a software toolbox-called seqNMF-with new methods for extracting informative, non-redundant, sequences from high-dimensional neural data, testing the significance of these extracted patterns, and assessing the prevalence of sequential structure in data. We test these methods on simulated data under multiple noise conditions, and on several real neural and behavioral datas. In hippocampal data, seqNMF identifies neural sequences that match those calculated manually by reference to behavioral events. In songbird data, seqNMF discovers neural sequences in untutored birds that lack stereotyped songs. Thus, by identifying temporal structure directly from neural data, seqNMF enables dissection of complex neural circuits without relying on temporal references from stimuli or behavioral outputs
- …