16 research outputs found
Cooper Pair Boxes Weakly Coupled to External Environments
We study the behaviour of charge oscillations in Superconducting Cooper Pair
Boxes weakly interacting with an environment. We found that, due to the noise
and dissipation induced by the environment, the stability properties of these
nanodevices differ according to whether the charge oscillations are interpreted
as an effect of macroscopic quantum coherence, or semiclassically in terms of
the Gross-Pitaevskii equation. More specifically, occupation number states,
used in the quantum interpretation of the oscillations, are found to be much
more unstable than coherent ones, typical of the semiclassical explanation.Comment: 12 pages, LaTe
Statistical mechanics of budget-constrained auctions
Finding the optimal assignment in budget-constrained auctions is a
combinatorial optimization problem with many important applications, a notable
example being the sale of advertisement space by search engines (in this
context the problem is often referred to as the off-line AdWords problem).
Based on the cavity method of statistical mechanics, we introduce a message
passing algorithm that is capable of solving efficiently random instances of
the problem extracted from a natural distribution, and we derive from its
properties the phase diagram of the problem. As the control parameter (average
value of the budgets) is varied, we find two phase transitions delimiting a
region in which long-range correlations arise.Comment: Minor revisio
A Quantum-Assisted Algorithm for Sampling Applications in Machine Learning
An increase in the efficiency of sampling from Boltzmann distributions would have a significant impact in deep learning and other machine learning applications. Recently, quantum annealers have been proposed as a potential candidate to speed up this task, but several limitations still bar these state-of-the-art technologies from being used effectively. One of the main limitations is that, while the device may indeed sample from a Boltzmann-like distribution, quantum dynamical arguments suggests it will do so with an instance-dependent effective temperature, different from the physical temperature of the device. Unless this unknown temperature can be unveiled, it might not be possible to effectively use a quantum annealer for Boltzmann sampling. In this talk, we present a strategy to overcome this challenge with a simple effective-temperature estimation algorithm. We provide a systematic study assessing the impact of the effective temperatures in the learning of a kind of restricted Boltzmann machine embedded on quantum hardware, which can serve as a building block for deep learning architectures. We also provide a comparison to k-step contrastive divergence (CD-k) with k up to 100. Although assuming a suitable fixed effective temperature also allows to outperform one step contrastive divergence (CD-1), only when using an instance-dependent effective temperature we find a performance close to that of CD-100 for the case studied here. We discuss generalizations of the algorithm to other more expressive generative models, beyond restricted Boltzmann machines
Effects of noise on convergent game learning dynamics
We study stochastic effects on the lagging anchor dynamics, a reinforcement
learning algorithm used to learn successful strategies in iterated games, which
is known to converge to Nash points in the absence of noise. The dynamics is
stochastic when players only have limited information about their opponents'
strategic propensities. The effects of this noise are studied analytically in
the case where it is small but finite, and we show that the statistics and
correlation properties of fluctuations can be computed to a high accuracy. We
find that the system can exhibit quasicycles, driven by intrinsic noise. If
players are asymmetric and use different parameters for their learning, a net
payoff advantage can be achieved due to these stochastic oscillations around
the deterministic equilibrium.Comment: 17 pages, 8 figure
Demographic noise and piecewise deterministic Markov processes
We explore a class of hybrid (piecewise deterministic) systems characterized
by a large number of individuals inhabiting an environment whose state is
described by a set of continuous variables. We use analytical and numerical
methods from nonequilibrium statistical mechanics to study the influence that
intrinsic noise has on the qualitative behavior of the system. We discuss the
application of these concepts to the case of semiarid ecosystems. Using a
system-size expansion we calculate the power spectrum of the fluctuations in
the system. This predicts the existence of noise-induced oscillations.Comment: 11 pages, 5 figures, minor change
Demographic noise and resilience in a semi-arid ecosystem model
The scarcity of water characterising drylands forces vegetation to adopt appropriate survival strategies.
Some of these generate water–vegetation feedback mechanisms that can lead to spatial self-organisation
of vegetation, as it has been shown with models representing plants by a density of biomass, varying
continuously in time and space. However, although plants are usually quite plastic they also display
discrete qualities and stochastic behaviour. These features may give rise to demographic noise, which in
certain cases can influence the qualitative dynamics of ecosystem models. In the present work we
explore the effects of demographic noise on the resilience of a model semi-arid ecosystem. We introduce
a spatial stochastic eco-hydrological hybrid model in which plants are modelled as discrete entities
subject to stochastic dynamical rules, while the dynamics of surface and soil water are described by
continuous variables. The model has a deterministic approximation very similar to previous continuous
models of arid and semi-arid ecosystems. By means of numerical simulations we show that demographic
noise can have important effects on the extinction and recovery dynamics of the system. In particular we
find that the stochastic model escapes extinction under a wide range of conditions for which the
corresponding deterministic approximation predicts absorption into desert states
Statistical physics of piecewise deterministic dynamics: theory and application to the resilience of semi-arid ecosystems
Demographic noise and resilience in a semi-arid ecosystem model
The scarcity of water characterising drylands forces vegetation to adopt appropriate survival strategies. Some of these generate water–vegetation feedback mechanisms that can lead to spatial self-organisation of vegetation, as it has been shown with models representing plants by a density of biomass, varying continuously in time and space. However, although plants are usually quite plastic they also display discrete qualities and stochastic behaviour. These features may give rise to demographic noise, which in certain cases can influence the qualitative dynamics of ecosystem models. In the present work we explore the effects of demographic noise on the resilience of a model semi-arid ecosystem. We introduce a spatial stochastic eco-hydrological hybrid model in which plants are modelled as discrete entities subject to stochastic dynamical rules, while the dynamics of surface and soil water are described by continuous variables. The model has a deterministic approximation very similar to previous continuous models of arid and semi-arid ecosystems. By means of numerical simulations we show that demographic noise can have important effects on the extinction and recovery dynamics of the system. In particular we find that the stochastic model escapes extinction under a wide range of conditions for which the corresponding deterministic approximation predicts absorption into desert states