36,593 research outputs found
An efficient algorithm for the parallel solution of high-dimensional differential equations
The study of high-dimensional differential equations is challenging and
difficult due to the analytical and computational intractability. Here, we
improve the speed of waveform relaxation (WR), a method to simulate
high-dimensional differential-algebraic equations. This new method termed
adaptive waveform relaxation (AWR) is tested on a communication network
example. Further we propose different heuristics for computing graph partitions
tailored to adaptive waveform relaxation. We find that AWR coupled with
appropriate graph partitioning methods provides a speedup by a factor between 3
and 16
An intrinsic Hamiltonian formulation of the dynamics of LC-circuits
First, the dynamics of LC-circuits are formulated as a Hamiltonian system defined with respect to a Poisson bracket which may be degenerate, i.e., nonsymplectic. This Poisson bracket is deduced from the network graph of the circuit and captures the dynamic invariants due to Kirchhoff's laws. Second, the antisymmetric relations defining the Poisson bracket are realized as a physical network using the gyrator element and partially dualizing the network graph constraints. From the network realization of the Poisson bracket, the reduced standard Hamiltonian system as well as the realization of the embedding standard Hamiltonian system are deduce
Exotic aromatic B-series for the study of long time integrators for a class of ergodic SDEs
We introduce a new algebraic framework based on a modification (called
exotic) of aromatic Butcher-series for the systematic study of the accuracy of
numerical integrators for the invariant measure of a class of ergodic
stochastic differential equations (SDEs) with additive noise. The proposed
analysis covers Runge-Kutta type schemes including the cases of partitioned
methods and postprocessed methods. We also show that the introduced exotic
aromatic B-series satisfy an isometric equivariance property.Comment: 33 page
Cortical spatio-temporal dimensionality reduction for visual grouping
The visual systems of many mammals, including humans, is able to integrate
the geometric information of visual stimuli and to perform cognitive tasks
already at the first stages of the cortical processing. This is thought to be
the result of a combination of mechanisms, which include feature extraction at
single cell level and geometric processing by means of cells connectivity. We
present a geometric model of such connectivities in the space of detected
features associated to spatio-temporal visual stimuli, and show how they can be
used to obtain low-level object segmentation. The main idea is that of defining
a spectral clustering procedure with anisotropic affinities over datasets
consisting of embeddings of the visual stimuli into higher dimensional spaces.
Neural plausibility of the proposed arguments will be discussed
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