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: $\, x_{t} = x_{t-1} - \gamma_{t-1} y_t$,\, $t=1,\ 2,\ldots$, where $y_t = \varphi(x_{t-1}) + \xi_t$ is the value of \vphi measured at $x_{t-1}$ and $\xi_t$ 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 $y_{t-1} y_t > 0$, and $\gamma_t = d\, \gamma_{t-1}$, otherwise, where $0 < d < 1 0$. That is, at each iteration \gam_t is multiplied either by $u$ or by $d$, provided that the resulting value does not exceed the predetermined value \mstep. The function \vphi may have one or several zeros; the random values $\xi_t$ are independent and identically distributed, with zero mean and finite variance. Under some additional assumptions on \vphi, $\xi_t$, and \mstep, the conditions on $u$ and $d$ guaranteeing a.s. convergence of the sequence $\{ x_t \}$, as well as a.s. divergence, are determined. In particular, if $\P (\xi_1 > 0) = \P (\xi_1 < 0) = 1/2$ and $\P (\xi_1 = x) = 0$ for any $x \in \R$, one has convergence for $ud 1$. Due to the multiplicative updating rule for \gam_t, the sequence $\{ x_t \}$ 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 $u$ and $d$, 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

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