3,030 research outputs found
Quantum Fluctuations of Coulomb Potential as a Source of Flicker Noise. The Influence of External Electric Field
Fluctuations of the electromagnetic field produced by quantized matter in
external electric field are investigated. A general expression for the power
spectrum of fluctuations is derived within the long-range expansion. It is
found that in the whole measured frequency band, the power spectrum of
fluctuations exhibits an inverse frequency dependence. A general argument is
given showing that for all practically relevant values of the electric field,
the power spectrum of induced fluctuations is proportional to the field
strength squared. As an illustration, the power spectrum is calculated
explicitly using the kinetic model with the relaxation-type collision term.
Finally, it is shown that the magnitude of fluctuations produced by a sample
generally has a Gaussian distribution around its mean value, and its dependence
on the sample geometry is determined. In particular, it is demonstrated that
for geometrically similar samples, the power spectrum is inversely proportional
to the sample volume. Application of the obtained results to the problem of
flicker noise is discussed.Comment: 14 pages, 3 figure
Quantum Theory of Flicker Noise in Metal Films
Flicker (1/f^gamma) voltage noise spectrum is derived from finite-temperature
quantum electromagnetic fluctuations produced by elementary charge carriers in
external electric field. It is suggested that deviations of the frequency
exponent \gamma from unity, observed in thin metal films, can be attributed to
quantum backreaction of the conducting medium on the fluctuating field of the
charge carrier. This backreaction is described phenomenologically in terms of
the effective momentum space dimensionality, D. Using the dimensional
continuation technique, it is shown that the combined action of the photon heat
bath and external field results in a 1/f^gamma-contribution to the spectral
density of the two-point correlation function of electromagnetic field. The
frequency exponent is found to be equal to 1 + delta, where delta = 3 - D is a
reduction of the momentum space dimensionality. This result is applied to the
case of a biased conducting sample, and a general expression for the voltage
power spectrum is obtained which possesses all characteristic properties of
observed flicker noise spectra. The range of validity of this expression covers
well the whole measured frequency band. Gauge independence of the power
spectrum is proved. It is shown that the obtained results naturally resolve the
problem of divergence of the total noise power. A detailed comparison with the
experimental data on flicker noise measurements in metal films is given.Comment: 20 pages, 2 tables, 2 figure
The Epidemiology of Multiple Sclerosis in Scotland: Inferences from Hospital Admissions
PMCID: PMC3029296This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited
On the exchange of intersection and supremum of sigma-fields in filtering theory
We construct a stationary Markov process with trivial tail sigma-field and a
nondegenerate observation process such that the corresponding nonlinear
filtering process is not uniquely ergodic. This settles in the negative a
conjecture of the author in the ergodic theory of nonlinear filters arising
from an erroneous proof in the classic paper of H. Kunita (1971), wherein an
exchange of intersection and supremum of sigma-fields is taken for granted.Comment: 20 page
Ergodicity, Decisions, and Partial Information
In the simplest sequential decision problem for an ergodic stochastic process
X, at each time n a decision u_n is made as a function of past observations
X_0,...,X_{n-1}, and a loss l(u_n,X_n) is incurred. In this setting, it is
known that one may choose (under a mild integrability assumption) a decision
strategy whose pathwise time-average loss is asymptotically smaller than that
of any other strategy. The corresponding problem in the case of partial
information proves to be much more delicate, however: if the process X is not
observable, but decisions must be based on the observation of a different
process Y, the existence of pathwise optimal strategies is not guaranteed.
The aim of this paper is to exhibit connections between pathwise optimal
strategies and notions from ergodic theory. The sequential decision problem is
developed in the general setting of an ergodic dynamical system (\Omega,B,P,T)
with partial information Y\subseteq B. The existence of pathwise optimal
strategies grounded in two basic properties: the conditional ergodic theory of
the dynamical system, and the complexity of the loss function. When the loss
function is not too complex, a general sufficient condition for the existence
of pathwise optimal strategies is that the dynamical system is a conditional
K-automorphism relative to the past observations \bigvee_n T^n Y. If the
conditional ergodicity assumption is strengthened, the complexity assumption
can be weakened. Several examples demonstrate the interplay between complexity
and ergodicity, which does not arise in the case of full information. Our
results also yield a decision-theoretic characterization of weak mixing in
ergodic theory, and establish pathwise optimality of ergodic nonlinear filters.Comment: 45 page
Spatiotemporal complexity of the universe at subhorizon scales
This is a short note on the spatiotemporal complexity of the dynamical
state(s) of the universe at subhorizon scales (up to 300 Mpc). There are
reasons, based mainly on infrared radiative divergences, to believe that one
can encounter a flicker noise in the time domain, while in the space domain,
the scaling laws are reflected in the (multi)fractal distribution of galaxies
and their clusters. There exist recent suggestions on a unifying treatment of
these two aspects within the concept of spatiotemporal complexity of dynamical
systems driven out of equilibrium. Spatiotemporal complexity of the subhorizon
dynamical state(s) of the universe is a conceptually nice idea and may lead to
progress in our understanding of the material structures at large scalesComment: references update
IMU-based smartphone-to-vehicle positioning
This is the author accepted manuscript. The final version is available from the publisher via the DOI in this recordIn this paper, we address the problem of using inertial measurements to position a smartphone with respect to a vehicle-fixed accelerometer. Using rigid body kinematics, this is cast as a nonlinear filtering problem. Unlike previous publications, we consider the complete three-dimensional kinematics, and do not approximate the angular acceleration to be zero. The accuracy of an estimator based on the unscented Kalman filter is compared with the Cramer-Rao bound. As is illustrated, the estimates can be expected to be better in the horizontal plane than in the vertical direction of the vehicle frame. Moreover, implementation issues are discussed and the system model is motivated by observability arguments. The efficiency of the method is demonstrated in a field study which shows that the horizontal RMSE is in the order of 0.5 [m]. Last, the proposed estimator is benchmarked against the state-of-the-art in left/right classification. The framework can be expected to find use in both insurance telematics and distracted driving solutions
A discrete invitation to quantum filtering and feedback control
The engineering and control of devices at the quantum-mechanical level--such
as those consisting of small numbers of atoms and photons--is a delicate
business. The fundamental uncertainty that is inherently present at this scale
manifests itself in the unavoidable presence of noise, making this a novel
field of application for stochastic estimation and control theory. In this
expository paper we demonstrate estimation and feedback control of quantum
mechanical systems in what is essentially a noncommutative version of the
binomial model that is popular in mathematical finance. The model is extremely
rich and allows a full development of the theory, while remaining completely
within the setting of finite-dimensional Hilbert spaces (thus avoiding the
technical complications of the continuous theory). We introduce discretized
models of an atom in interaction with the electromagnetic field, obtain
filtering equations for photon counting and homodyne detection, and solve a
stochastic control problem using dynamic programming and Lyapunov function
methods.Comment: 76 pages, 12 figures. A PDF file with high resolution figures can be
found at http://minty.caltech.edu/papers.ph
Optimal Design of Robust Combinatorial Mechanisms for Substitutable Goods
In this paper we consider multidimensional mechanism design problem for
selling discrete substitutable items to a group of buyers. Previous work on
this problem mostly focus on stochastic description of valuations used by the
seller. However, in certain applications, no prior information regarding
buyers' preferences is known. To address this issue, we consider uncertain
valuations and formulate the problem in a robust optimization framework: the
objective is to minimize the maximum regret. For a special case of
revenue-maximizing pricing problem we present a solution method based on
mixed-integer linear programming formulation
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