319 research outputs found
Symbolic transfer entropy rate is equal to transfer entropy rate for bivariate finite-alphabet stationary ergodic Markov processes
Transfer entropy is a measure of the magnitude and the direction of
information flow between jointly distributed stochastic processes. In recent
years, its permutation analogues are considered in the literature to estimate
the transfer entropy by counting the number of occurrences of orderings of
values, not the values themselves. It has been suggested that the method of
permutation is easy to implement, computationally low cost and robust to noise
when applying to real world time series data. In this paper, we initiate a
theoretical treatment of the corresponding rates. In particular, we consider
the transfer entropy rate and its permutation analogue, the symbolic transfer
entropy rate, and show that they are equal for any bivariate finite-alphabet
stationary ergodic Markov process. This result is an illustration of the
duality method introduced in [T. Haruna and K. Nakajima, Physica D 240, 1370
(2011)]. We also discuss the relationship among the transfer entropy rate, the
time-delayed mutual information rate and their permutation analogues.Comment: 18 page
Symbolic local information transfer
Recently, the permutation-information theoretic approach has been used in a
broad range of research fields. In particular, in the study of highdimensional
dynamical systems, it has been shown that this approach can be effective in
characterizing global properties, including the complexity of their
spatiotemporal dynamics. Here, we show that this approach can also be applied
to reveal local spatiotemporal profiles of distributed computations existing at
each spatiotemporal point in the system. J. T. Lizier et al. have recently
introduced the concept of local information dynamics, which consists of
information storage, transfer, and modification. This concept has been
intensively studied with regard to cellular automata, and has provided
quantitative evidence of several characteristic behaviors observed in the
system. In this paper, by focusing on the local information transfer, we
demonstrate that the application of the permutation-information theoretic
approach, which introduces natural symbolization methods, makes the concept
easily extendible to systems that have continuous states. We propose measures
called symbolic local transfer entropies, and apply these measures to two test
models, the coupled map lattice (CML) system and the Bak-Sneppen model
(BS-model), to show their relevance to spatiotemporal systems that have
continuous states.Comment: 20 pages, 7 figure
Exploiting short-term memory in soft body dynamics as a computational resource
Soft materials are not only highly deformable but they also possess rich and
diverse body dynamics. Soft body dynamics exhibit a variety of properties,
including nonlinearity, elasticity, and potentially infinitely many degrees of
freedom. Here we demonstrate that such soft body dynamics can be employed to
conduct certain types of computation. Using body dynamics generated from a soft
silicone arm, we show that they can be exploited to emulate functions that
require memory and to embed robust closed-loop control into the arm. Our
results suggest that soft body dynamics have a short-term memory and can serve
as a computational resource. This finding paves the way toward exploiting
passive body dynamics for control of a large class of underactuated systems.Comment: 22 pages, 11 figures; email address correcte
Boosting computational power through spatial multiplexing in quantum reservoir computing
Quantum reservoir computing provides a framework for exploiting the natural
dynamics of quantum systems as a computational resource. It can implement
real-time signal processing and solve temporal machine learning problems in
general, which requires memory and nonlinear mapping of the recent input stream
using the quantum dynamics in computational supremacy region, where the
classical simulation of the system is intractable. A nuclear magnetic resonance
spin-ensemble system is one of the realistic candidates for such physical
implementations, which is currently available in laboratories. In this paper,
considering these realistic experimental constraints for implementing the
framework, we introduce a scheme, which we call a spatial multiplexing
technique, to effectively boost the computational power of the platform. This
technique exploits disjoint dynamics, which originate from multiple different
quantum systems driven by common input streams in parallel. Accordingly, unlike
designing a single large quantum system to increase the number of qubits for
computational nodes, it is possible to prepare a huge number of qubits from
multiple but small quantum systems, which are operationally easy to handle in
laboratory experiments. We numerically demonstrate the effectiveness of the
technique using several benchmark tasks and quantitatively investigate its
specifications, range of validity, and limitations in detail.Comment: 15 page
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