1,560 research outputs found
Optimal waveform estimation for classical and quantum systems via time-symmetric smoothing
Classical and quantum theories of time-symmetric smoothing, which can be used
to optimally estimate waveforms in classical and quantum systems, are derived
using a discrete-time approach, and the similarities between the two theories
are emphasized. Application of the quantum theory to homodyne phase-locked loop
design for phase estimation with narrowband squeezed optical beams is studied.
The relation between the proposed theory and Aharonov et al.'s weak value
theory is also explored.Comment: 13 pages, 5 figures, v2: changed the title to a more descriptive one,
corrected a minor mistake in Sec. IV, accepted by Physical Review
A stochastic approximation algorithm with multiplicative step size modification
An algorithm of searching a zero of an unknown function \vphi : \,
\R \to \R is considered: ,\,
, where is the
value of \vphi measured at and is the
measurement error. The step sizes \gam_t > 0 are modified in the
course of the algorithm according to the rule: \, \gamma_t =
\min\{u\, \gamma_{t-1},\, \mstep\} if , and , otherwise, where . That is, at each iteration \gam_t is
multiplied either by or by , provided that the resulting
value does not exceed the predetermined value \mstep. The function
\vphi may have one or several zeros; the random values are
independent and identically distributed, with zero mean and finite
variance. Under some additional assumptions on \vphi, , and
\mstep, the conditions on and guaranteeing a.s.
convergence of the sequence , as well as a.s. divergence,
are determined. In particular, if and for any , one has
convergence for . Due to the
multiplicative updating rule for \gam_t, the sequence
converges rapidly: like a geometric progression (if convergence
takes place), but the limit value may not coincide with, but
instead, approximates one of the zeros of \vphi. By adjusting the
parameters and , one can reach arbitrarily high precision of
the approximation; higher precision is obtained at the expense of
lower convergence rate
A Quantum Langevin Formulation of Risk-Sensitive Optimal Control
In this paper we formulate a risk-sensitive optimal control problem for
continuously monitored open quantum systems modelled by quantum Langevin
equations. The optimal controller is expressed in terms of a modified
conditional state, which we call a risk-sensitive state, that represents
measurement knowledge tempered by the control purpose. One of the two
components of the optimal controller is dynamic, a filter that computes the
risk-sensitive state.
The second component is an optimal control feedback function that is found by
solving the dynamic programming equation. The optimal controller can be
implemented using classical electronics.
The ideas are illustrated using an example of feedback control of a two-level
atom
Multi-agent Coordination in Directed Moving Neighborhood Random Networks
In this paper, we consider the consensus problem of dynamical multiple agents
that communicate via a directed moving neighborhood random network. Each agent
performs random walk on a weighted directed network. Agents interact with each
other through random unidirectional information flow when they coincide in the
underlying network at a given instant. For such a framework, we present
sufficient conditions for almost sure asymptotic consensus. Some existed
consensus schemes are shown to be reduced versions of the current model.Comment: 9 page
Alcohol use disorders and the course of depressive and anxiety disorders
BACKGROUND: Inconsistent findings have been reported on the role of comorbid alcohol use disorders as risk factors for a persistent course of depressive and anxiety disorders. AIMS: To determine whether the course of depressive and/or anxiety disorders is conditional on the type (abuse or dependence) or severity of comorbid alcohol use disorders. METHOD: In a large sample of participants with current depression and/or anxiety (n = 1369) we examined whether the presence and severity of DSM-IV alcohol abuse or alcohol dependence predicted the 2-year course of depressive and/or anxiety disorders. RESULTS: The persistence of depressive and/or anxiety disorders at the 2-year follow-up was significantly higher in those with remitted or current alcohol dependence (persistence 62% and 67% respectively), but not in those with remitted or current alcohol abuse (persistence 51% and 46% respectively), compared with no lifetime alcohol use disorder (persistence 53%). Severe (meeting six or seven diagnostic criteria) but not moderate (meeting three to five criteria) current dependence was a significant predictor as 95% of those in the former group still had a depressive and/or anxiety disorder at follow-up. This association remained significant after adjustment for severity of depression and anxiety, psychosocial factors and treatment factors. CONCLUSIONS: Alcohol dependence, especially severe current dependence, is a risk factor for an unfavourable course of depressive and/or anxiety disorders, whereas alcohol abuse is not
Rate of convergence of truncated stochastic approximation procedures with moving bounds
The paper is concerned with stochastic approximation procedures having three
main characteristics: truncations with random moving bounds, a matrix valued
random step-size sequence, and a dynamically changing random regression
function. We study convergence and rate of convergence. Main results are
supplemented with corollaries to establish various sets of sufficient
conditions, with the main emphases on the parametric statistical estimation.
The theory is illustrated by examples and special cases.Comment: 30 page
Geometry of GL_n(C) on infinity: complete collineations, projective compactifications, and universal boundary
Consider a finite dimensional (generally reducible) polynomial representation
\rho of GL_n. A projective compactification of GL_n is the closure of
\rho(GL_n) in the space of all operators defined up to a factor (this class of
spaces can be characterized as equivariant projective normal compactifications
of GL_n). We give an expicit description for all projective compactifications.
We also construct explicitly (in elementary geometrical terms) a universal
object for all projective compactifications of GL_n.Comment: 24 pages, corrected varian
Heisenberg Picture Approach to the Stability of Quantum Markov Systems
Quantum Markovian systems, modeled as unitary dilations in the quantum
stochastic calculus of Hudson and Parthasarathy, have become standard in
current quantum technological applications. This paper investigates the
stability theory of such systems. Lyapunov-type conditions in the Heisenberg
picture are derived in order to stabilize the evolution of system operators as
well as the underlying dynamics of the quantum states. In particular, using the
quantum Markov semigroup associated with this quantum stochastic differential
equation, we derive sufficient conditions for the existence and stability of a
unique and faithful invariant quantum state. Furthermore, this paper proves the
quantum invariance principle, which extends the LaSalle invariance principle to
quantum systems in the Heisenberg picture. These results are formulated in
terms of algebraic constraints suitable for engineering quantum systems that
are used in coherent feedback networks
Surface electrons at plasma walls
In this chapter we introduce a microscopic modelling of the surplus electrons
on the plasma wall which complements the classical description of the plasma
sheath. First we introduce a model for the electron surface layer to study the
quasistationary electron distribution and the potential at an unbiased plasma
wall. Then we calculate sticking coefficients and desorption times for electron
trapping in the image states. Finally we study how surplus electrons affect
light scattering and how charge signatures offer the possibility of a novel
charge measurement for dust grains.Comment: To appear in Complex Plasmas: Scientific Challenges and Technological
Opportunities, Editors: M. Bonitz, K. Becker, J. Lopez and H. Thomse
- …