26,799 research outputs found
Hierarchical Composition of Memristive Networks for Real-Time Computing
Advances in materials science have led to physical instantiations of
self-assembled networks of memristive devices and demonstrations of their
computational capability through reservoir computing. Reservoir computing is an
approach that takes advantage of collective system dynamics for real-time
computing. A dynamical system, called a reservoir, is excited with a
time-varying signal and observations of its states are used to reconstruct a
desired output signal. However, such a monolithic assembly limits the
computational power due to signal interdependency and the resulting correlated
readouts. Here, we introduce an approach that hierarchically composes a set of
interconnected memristive networks into a larger reservoir. We use signal
amplification and restoration to reduce reservoir state correlation, which
improves the feature extraction from the input signals. Using the same number
of output signals, such a hierarchical composition of heterogeneous small
networks outperforms monolithic memristive networks by at least 20% on waveform
generation tasks. On the NARMA-10 task, we reduce the error by up to a factor
of 2 compared to homogeneous reservoirs with sigmoidal neurons, whereas single
memristive networks are unable to produce the correct result. Hierarchical
composition is key for solving more complex tasks with such novel nano-scale
hardware
Efficient Synthesis of Room Acoustics via Scattering Delay Networks
An acoustic reverberator consisting of a network of delay lines connected via
scattering junctions is proposed. All parameters of the reverberator are
derived from physical properties of the enclosure it simulates. It allows for
simulation of unequal and frequency-dependent wall absorption, as well as
directional sources and microphones. The reverberator renders the first-order
reflections exactly, while making progressively coarser approximations of
higher-order reflections. The rate of energy decay is close to that obtained
with the image method (IM) and consistent with the predictions of Sabine and
Eyring equations. The time evolution of the normalized echo density, which was
previously shown to be correlated with the perceived texture of reverberation,
is also close to that of IM. However, its computational complexity is one to
two orders of magnitude lower, comparable to the computational complexity of a
feedback delay network (FDN), and its memory requirements are negligible
Fast and compact self-stabilizing verification, computation, and fault detection of an MST
This paper demonstrates the usefulness of distributed local verification of
proofs, as a tool for the design of self-stabilizing algorithms.In particular,
it introduces a somewhat generalized notion of distributed local proofs, and
utilizes it for improving the time complexity significantly, while maintaining
space optimality. As a result, we show that optimizing the memory size carries
at most a small cost in terms of time, in the context of Minimum Spanning Tree
(MST). That is, we present algorithms that are both time and space efficient
for both constructing an MST and for verifying it.This involves several parts
that may be considered contributions in themselves.First, we generalize the
notion of local proofs, trading off the time complexity for memory efficiency.
This adds a dimension to the study of distributed local proofs, which has been
gaining attention recently. Specifically, we design a (self-stabilizing) proof
labeling scheme which is memory optimal (i.e., bits per node), and
whose time complexity is in synchronous networks, or time in asynchronous ones, where is the maximum degree of
nodes. This answers an open problem posed by Awerbuch and Varghese (FOCS 1991).
We also show that time is necessary, even in synchronous
networks. Another property is that if faults occurred, then, within the
requireddetection time above, they are detected by some node in the locality of each of the faults.Second, we show how to enhance a known
transformer that makes input/output algorithms self-stabilizing. It now takes
as input an efficient construction algorithm and an efficient self-stabilizing
proof labeling scheme, and produces an efficient self-stabilizing algorithm.
When used for MST, the transformer produces a memory optimal self-stabilizing
algorithm, whose time complexity, namely, , is significantly better even
than that of previous algorithms. (The time complexity of previous MST
algorithms that used memory bits per node was , and
the time for optimal space algorithms was .) Inherited from our proof
labelling scheme, our self-stabilising MST construction algorithm also has the
following two properties: (1) if faults occur after the construction ended,
then they are detected by some nodes within time in synchronous
networks, or within time in asynchronous ones, and (2) if
faults occurred, then, within the required detection time above, they are
detected within the locality of each of the faults. We also show
how to improve the above two properties, at the expense of some increase in the
memory
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