1,138,182 research outputs found
Multiscale Analysis of Information Dynamics for Linear Multivariate Processes
In the study of complex physical and physiological systems represented by
multivariate time series, an issue of great interest is the description of the
system dynamics over a range of different temporal scales. While
information-theoretic approaches to the multiscale analysis of complex dynamics
are being increasingly used, the theoretical properties of the applied measures
are poorly understood. This study introduces for the first time a framework for
the analytical computation of information dynamics for linear multivariate
stochastic processes explored at different time scales. After showing that the
multiscale processing of a vector autoregressive (VAR) process introduces a
moving average (MA) component, we describe how to represent the resulting VARMA
process using state-space (SS) models and how to exploit the SS model
parameters to compute analytical measures of information storage and
information transfer for the original and rescaled processes. The framework is
then used to quantify multiscale information dynamics for simulated
unidirectionally and bidirectionally coupled VAR processes, showing that
rescaling may lead to insightful patterns of information storage and transfer
but also to potentially misleading behaviors
Quantum Darwinism and non-Markovian dissipative dynamics from quantum phases of the spin-1/2 XX model
Quantum Darwinism explains the emergence of a classical description of
objects in terms of the creation of many redundant registers in an environment
containing their classical information. This amplification phenomenon, where
only classical information reaches the macroscopic observer and through which
different observers can agree on the objective existence of such object, has
been revived lately for several types of situations, successfully explaining
classicality. We explore quantum Darwinism in the setting of an environment
made of two level systems which are initially prepared in the ground state of
the XX model, which exhibits different phases; we find that the different
phases have different ability to redundantly acquire classical information
about the system, being the "ferromagnetic phase" the only one able to complete
quantum Darwinism. At the same time we relate this ability to how non-Markovian
the system dynamics is, based on the interpretation that non-Markovian dynamics
is associated to back flow of information from environment to system, thus
spoiling the information transfer needed for Darwinism. Finally, we explore
mixing of bath registers by allowing a small interaction among them, finding
that this spoils the stored information as previously found in the literature
The coherent interaction between matter and radiation - A tutorial on the Jaynes-Cummings model
The Jaynes-Cummings (JC) model is a milestone in the theory of coherent
interaction between a two-level system and a single bosonic field mode. This
tutorial aims to give a complete description of the model, analyzing the
Hamiltonian of the system, its eigenvalues and eigestates, in order to
characterize the dynamics of system and subsystems. The Rabi oscillations,
together with the collapse and revival effects, are distinguishing features of
the JC model and are important for applications in Quantum Information theory.
The framework of cavity quantum electrodynamics (cQED) is chosen and two
fundamental experiments on the coherent interaction between Rydberg atoms and a
single cavity field mode are described.Comment: 22 pages, 7 figures. Tutorial. Submitted to a special issue of EPJ -
ST devoted to the memory of Federico Casagrand
An Optimal Medium Access Control with Partial Observations for Sensor Networks
We consider medium access control (MAC) in multihop sensor networks, where only partial information about the shared medium is available to the transmitter. We model our setting as a queuing problem in which the service rate of a queue is a function of a partially observed Markov chain representing the available bandwidth, and in which the arrivals are controlled based on the partial observations so as to keep the system in a desirable mildly unstable regime. The optimal controller for this problem satisfies a separation property: we first compute a probability measure on the state space of the chain, namely the information state, then use this measure as the new state on which the control decisions are based. We give a formal description of the system considered and of its dynamics, we formalize and solve an optimal control problem, and we show numerical simulations to illustrate with concrete examples properties of the optimal control law. We show how the ergodic behavior of our queuing model is characterized by an invariant measure over all possible information states, and we construct that measure. Our results can be specifically applied for designing efficient and stable algorithms for medium access control in multiple-accessed systems, in particular for sensor networks
Intermittency in an interacting generalization of the geometric Brownian motion model
We propose a minimal interacting generalization of the geometric Brownian motion model, which turns out to be formally equivalent to a model describing the dynamics of networks of analogue neurons. For sufficiently strong interactions, such systems may have many meta-stable states. Transitions between meta-stable states are associated with macroscopic reorganizations of the system, which can be triggered by random external forcing. Such a system will exhibit intermittent dynamics within a large part of its parameter space. We propose market dynamics as a possible application of this model, in which case random external forcing would correspond to the arrival of important information. The emergence of a model of interacting prices of the type considered here can be argued to follow naturally from a general argument based on integrating out all non-price degrees of freedom from the dynamics of a hypothetical complete description of economic dependences. PACS numbers: 02.50.−r, 05.40.−a, 89.65.Gh, 89.75.Da 1
On the use of simple dynamical systems for climate predictions: A Bayesian prediction of the next glacial inception
Over the last few decades, climate scientists have devoted much effort to the
development of large numerical models of the atmosphere and the ocean. While
there is no question that such models provide important and useful information
on complicated aspects of atmosphere and ocean dynamics, skillful prediction
also requires a phenomenological approach, particularly for very slow
processes, such as glacial-interglacial cycles. Phenomenological models are
often represented as low-order dynamical systems. These are tractable, and a
rich source of insights about climate dynamics, but they also ignore large
bodies of information on the climate system, and their parameters are generally
not operationally defined. Consequently, if they are to be used to predict
actual climate system behaviour, then we must take very careful account of the
uncertainty introduced by their limitations. In this paper we consider the
problem of the timing of the next glacial inception, about which there is
on-going debate. Our model is the three-dimensional stochastic system of
Saltzman and Maasch (1991), and our inference takes place within a Bayesian
framework that allows both for the limitations of the model as a description of
the propagation of the climate state vector, and for parametric uncertainty.
Our inference takes the form of a data assimilation with unknown static
parameters, which we perform with a variant on a Sequential Monte Carlo
technique (`particle filter'). Provisional results indicate peak glacial
conditions in 60,000 years.Comment: superseeds the arXiv:0809.0632 (which was published in European
Reviews). The Bayesian section has been significantly expanded. The present
version has gone scientific peer review and has been published in European
Physics Special Topics. (typo in DOI and in Table 1 (psi -> theta) corrected
on 25th August 2009
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