47,925 research outputs found
A general representation of dynamical systems for reservoir computing
Dynamical systems are capable of performing computation in a reservoir
computing paradigm. This paper presents a general representation of these
systems as an artificial neural network (ANN). Initially, we implement the
simplest dynamical system, a cellular automaton. The mathematical fundamentals
behind an ANN are maintained, but the weights of the connections and the
activation function are adjusted to work as an update rule in the context of
cellular automata. The advantages of such implementation are its usage on
specialized and optimized deep learning libraries, the capabilities to
generalize it to other types of networks and the possibility to evolve cellular
automata and other dynamical systems in terms of connectivity, update and
learning rules. Our implementation of cellular automata constitutes an initial
step towards a general framework for dynamical systems. It aims to evolve such
systems to optimize their usage in reservoir computing and to model physical
computing substrates.Comment: 5 pages, 3 figures, accepted workshop paper at Workshop on Novel
Substrates and Models for the Emergence of Developmental, Learning and
Cognitive Capabilities at IEEE ICDL-EPIROB 201
"Divide and Conquer" Semiclassical Molecular Dynamics: A practical method for Spectroscopic calculations of High Dimensional Molecular Systems
We extensively describe our recently established "divide-and-conquer"
semiclassical method [M. Ceotto, G. Di Liberto and R. Conte, Phys. Rev. Lett.
119, 010401 (2017)] and propose a new implementation of it to increase the
accuracy of results. The technique permits to perform spectroscopic
calculations of high dimensional systems by dividing the full-dimensional
problem into a set of smaller dimensional ones. The partition procedure,
originally based on a dynamical analysis of the Hessian matrix, is here more
rigorously achieved through a hierarchical subspace-separation criterion based
on Liouville's theorem. Comparisons of calculated vibrational frequencies to
exact quantum ones for a set of molecules including benzene show that the new
implementation performs better than the original one and that, on average, the
loss in accuracy with respect to full-dimensional semiclassical calculations is
reduced to only 10 wavenumbers. Furthermore, by investigating the challenging
Zundel cation, we also demonstrate that the "divide-and-conquer" approach
allows to deal with complex strongly anharmonic molecular systems. Overall the
method very much helps the assignment and physical interpretation of
experimental IR spectra by providing accurate vibrational fundamentals and
overtones decomposed into reduced dimensionality spectra
Observing the origin of superconductivity in quantum critical metals
Despite intense efforts during the last 25 years, the physics of
unconventional superconductors, including the cuprates with a very high
transition temperature, is still a controversial subject. It is believed that
superconductivity in many of these strongly correlated metallic systems
originates in the physics of quantum phase transitions, but quite diverse
perspectives have emerged on the fundamentals of the electron-pairing physics,
ranging from Hertz style critical spin fluctuation glue to the holographic
superconductivity of string theory. Here we demonstrate that the gross energy
scaling differences that are behind these various pairing mechanisms are
directly encoded in the frequency and temperature dependence of the dynamical
pair susceptibility. This quantity can be measured directly via the second
order Josephson effect and it should be possible employing modern experimental
techniques to build a `pairing telescope' that gives a direct view on the
origin of quantum critical superconductivity.Comment: 19 pages, 9 figures; minor changes in the experimental part; added a
new appendix section calculating the pair susceptibility of marginal Fermi
liqui
Resonant Inelastic X-ray Scattering Studies of Elementary Excitations
In the past decade, Resonant Inelastic X-ray Scattering (RIXS) has made
remarkable progress as a spectroscopic technique. This is a direct result of
the availability of high-brilliance synchrotron X-ray radiation sources and of
advanced photon detection instrumentation. The technique's unique capability to
probe elementary excitations in complex materials by measuring their energy-,
momentum-, and polarization-dependence has brought RIXS to the forefront of
experimental photon science. We review both the experimental and theoretical
RIXS investigations of the past decade, focusing on those determining the
low-energy charge, spin, orbital and lattice excitations of solids. We present
the fundamentals of RIXS as an experimental method and then review the
theoretical state of affairs, its recent developments and discuss the different
(approximate) methods to compute the dynamical RIXS response. The last decade's
body of experimental RIXS data and its interpretation is surveyed, with an
emphasis on RIXS studies of correlated electron systems, especially transition
metal compounds. Finally, we discuss the promise that RIXS holds for the near
future, particularly in view of the advent of x-ray laser photon sources.Comment: Review, 67 pages, 44 figure
Power Flow Modelling of Dynamic Systems - Introduction to Modern Teaching Tools
As tools for dynamic system modelling both conventional methods such as
transfer function or state space representation and modern power flow based
methods are available. The latter methods do not depend on energy domain, are
able to preserve physical system structures, visualize power conversion or
coupling or split, identify power losses or storage, run on conventional
software and emphasize the relevance of energy as basic principle of known
physical domains. Nevertheless common control structures as well as analysis
and design tools may still be applied. Furthermore the generalization of power
flow methods as pseudo-power flow provides with a universal tool for any
dynamic modelling. The phenomenon of power flow constitutes an up to date
education methodology. Thus the paper summarizes fundamentals of selected power
flow oriented modelling methods, presents a Bond Graph block library for
teaching power oriented modelling as compact menu-driven freeware, introduces
selected examples and discusses special features.Comment: 12 pages, 9 figures, 4 table
Hybrid Systems and Control With Fractional Dynamics (I): Modeling and Analysis
No mixed research of hybrid and fractional-order systems into a cohesive and
multifaceted whole can be found in the literature. This paper focuses on such a
synergistic approach of the theories of both branches, which is believed to
give additional flexibility and help to the system designer. It is part I of
two companion papers and introduces the fundamentals of fractional-order hybrid
systems, in particular, modeling and stability analysis of two kinds of such
systems, i.e., fractional-order switching and reset control systems. Some
examples are given to illustrate the applicability and effectiveness of the
developed theory. Part II will focus on fractional-order hybrid control.Comment: 2014 International Conference on Fractional Differentiation and its
Application, Ital
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