12,322 research outputs found
A Library for Pattern-based Sparse Matrix Vector Multiply
Pattern-based Representation (PBR) is a novel approach to improving the performance of Sparse Matrix-Vector Multiply (SMVM) numerical kernels. Motivated by our observation that many matrices can be divided into blocks that share a small number of distinct patterns, we generate custom multiplication kernels for frequently recurring block patterns.
The resulting reduction in index overhead significantly reduces memory bandwidth requirements and improves performance. Unlike existing methods, PBR requires neither detection of dense blocks nor zero filling, making it particularly advantageous for matrices that lack dense nonzero concentrations. SMVM kernels for PBR can benefit from explicit prefetching and vectorization, and are amenable to parallelization. The analysis and format conversion to PBR is implemented as a library, making it suitable for applications that generate matrices dynamically at runtime. We present sequential and parallel performance results for PBR on two current multicore architectures, which show that PBR outperforms available alternatives for the matrices to which it is applicable,
and that the analysis and conversion overhead is amortized in realistic application scenarios
Pattern phase diagram for 2D arrays of coupled limit-cycle oscillators
Arrays of coupled limit-cycle oscillators represent a paradigmatic example
for studying synchronization and pattern formation. They are also of direct
relevance in the context of currently emerging experiments on nano- and
optomechanical oscillator arrays. We find that the full dynamical equations for
the phase dynamics of such an array go beyond previously studied Kuramoto-type
equations. We analyze the evolution of the phase field in a two-dimensional
array and obtain a "phase diagram" for the resulting stationary and
non-stationary patterns. The possible observation in optomechanical arrays is
discussed briefly
Correlator expansion approach to stationary states of weakly coupled cavity arrays
We introduce a method for calculating the stationary state of a translation
invariant array of weakly coupled cavities in the presence of dissipation and
coherent as well as incoherent drives. Instead of computing the full density
matrix our method directly calculates the correlation functions which are
relevant for obtaining all local quantities of interest. It considers an
expansion of the correlation functions and their equations of motion in powers
of the photon tunneling rate between adjacent cavities, leading to an exact
second order solution for any number of cavities. Our method provides a
controllable approximation for weak tunneling rates applicable to the strongly
correlated regime that is dominated by nonlinearities in the cavities and thus
of high interest.Comment: contribution to J. Phys. B special issue celebrating Jaynes-Cummings
physic
Memristors for the Curious Outsiders
We present both an overview and a perspective of recent experimental advances
and proposed new approaches to performing computation using memristors. A
memristor is a 2-terminal passive component with a dynamic resistance depending
on an internal parameter. We provide an brief historical introduction, as well
as an overview over the physical mechanism that lead to memristive behavior.
This review is meant to guide nonpractitioners in the field of memristive
circuits and their connection to machine learning and neural computation.Comment: Perpective paper for MDPI Technologies; 43 page
Phase--coherence Effects in Antidot Lattices: A Semiclassical Approach to Bulk Conductivity
We derive semiclassical expressions for the Kubo conductivity tensor. Within
our approach the oscillatory parts of the diagonal and Hall conductivity are
given as sums over contributions from classical periodic orbits in close
relation to Gutzwiller's trace formula for the density of states. Taking into
account the effects of weak disorder and temperature we reproduce recently
observed anomalous phase coherence oscillations in the conductivity of large
antidot arrays.Comment: 11 pages, 2 figures available under request, RevTe
Shaped extensions of singular spectrum analysis
Extensions of singular spectrum analysis (SSA) for processing of
non-rectangular images and time series with gaps are considered. A circular
version is suggested, which allows application of the method to the data given
on a circle or on a cylinder, e.g. cylindrical projection of a 3D ellipsoid.
The constructed Shaped SSA method with planar or circular topology is able to
produce low-rank approximations for images of complex shapes. Together with
Shaped SSA, a shaped version of the subspace-based ESPRIT method for frequency
estimation is developed. Examples of 2D circular SSA and 2D Shaped ESPRIT are
presented
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