Ferroelectric liquid crystal mixtures containing chiral ether and ester compounds with the 2-arylidene-p-menthan-3-one skeleton

Some 1R,4R-2-(4-phenylbenzylidene)-p-menthane-3-one derivatives containing the ether or ester linking group between benzene rings of the arylidene fragment have been studied as chiral dopants in ferroelectric liquid crystal systems based on the eutectic mixture (1:1) of two phenylbenzoate derivatives CmH2m+1OC6H4COOC6 H4OCnH2n+1 (n = 6; m = 8, 10). The ferroelectric properties of these compositions (spontaneous polarization, rotation viscosity, smectic tilt angle as well as quantitative characteristics of their concentration dependences) were compared with those for systems including chiral dopants containing no linking group. Ferroelectric parameters of the induced ferroelectric compositions studied have been shown to depend essentially on the presence of the linking group between benzene rings and its nature as well as on the number of the benzene rings in the rigid molecular core of the chiral dopants used. For all ferroelectric liquid crystal systems studied, the influence of the chiral dopants on the thermal stability of N*, SmA and SmC* mesophases has been quantified. The influence of the linking group nature in the dopant molecules on the characteristics of the systems studied is discussed taking into account results of the conformational analysis carried out by the semi-empirical AM1 and PM3 methods.

An overview of Sequential Monte Carlo methods for parameter estimation in general state-space models

Nonlinear non-Gaussian state-space models arise in numerous applications in control and signal processing. Sequential Monte Carlo (SMC) methods, also known as Particle Filters, provide very good numerical approximations to the associated optimal state estimation problems. However, in many scenarios, the state-space model of interest also depends on unknown static parameters that need to be estimated from the data. In this context, standard SMC methods fail and it is necessary to rely on more sophisticated algorithms. The aim of this paper is to present a comprehensive overview of SMC methods that have been proposed to perform static parameter estimation in general state-space models. We discuss the advantages and limitations of these methods. © 2009 IFAC.

An Online Expectation-Maximization Algorithm for Changepoint Models

Changepoint models are widely used to model the heterogeneity of sequential data. We present a novel sequential Monte Carlo (SMC) online Expectation-Maximization (EM) algorithm for estimating the static parameters of such models. The SMC online EM algorithm has a cost per time which is linear in the number of particles and could be particularly important when the data is representable as a long sequence of observations, since it drastically reduces the computational requirements for implementation. We present an asymptotic analysis for the stability of the SMC estimates used in the online EM algorithm and demonstrate the performance of this scheme using both simulated and real data originating from DNA analysis.

An Online Expectation-Maximization Algorithm for Changepoint Models

Changepoint models are widely used to model the heterogeneity of sequential data. We present a novel sequential Monte Carlo (SMC) online Expectation-Maximization (EM) algorithm for estimating the static parameters of such models. The SMC online EM algorithm has a cost per time which is linear in the number of particles and could be particularly important when the data is representable as a long sequence of observations, since it drastically reduces the computational requirements for implementation. We present an asymptotic analysis for the stability of the SMC estimates used in the online EM algorithm and demonstrate the performance of this scheme using both simulated and real data originating from DNA analysis.

Low molar mass organosiloxane liquid crystals for telecommunication applications

Mixtures of two proprietary low molar mass organosiloxane liquid crystals were studied in order to improve their alignment and optimize their electro-optic properties for telecommunication applications. Over a certain concentration range, mixtures exhibited an isotropic-chiral smectic A-chiral smectic C (Iso-SmA*-SmC*) phase sequence leading to exceptionally good alignment. At room temperature, the spontaneous polarization of these samples was reduced from 225 nC cm -2 in the pure SmC* liquid crystal to as low as 75 nC cm -2 in the mixture. Within this concentration range, the ferroelectric tilt angle could be varied between 35° and 15°, while the rise time decreased by 69.4%. The rise times were < 45 μs for moderate electric fields of ± 10 V μm -1 in the SmC* phase and ∼ 4 μs, independent of electric field, in the SmA* phase. At λ = 1550 nm, these mixtures exhibited very large extinction ratios of {\sim} 60 dB for binary switching in the SmC* phase and ∼ 55 dB continuous variable attenuation in the SmA* phase. © 2012 IEEE.

Approximate Bayesian Computation for Smoothing

We consider a method for approximate inference in hidden Markov models (HMMs). The method circumvents the need to evaluate conditional densities of observations given the hidden states. It may be considered an instance of Approximate Bayesian Computation (ABC) and it involves the introduction of auxiliary variables valued in the same space as the observations. The quality of the approximation may be controlled to arbitrary precision through a parameter ε > 0. We provide theoretical results which quantify, in terms of ε, the ABC error in approximation of expectations of additive functionals with respect to the smoothing distributions. Under regularity assumptions, this error is, where n is the number of time steps over which smoothing is performed. For numerical implementation, we adopt the forward-only sequential Monte Carlo (SMC) scheme of [14] and quantify the combined error from the ABC and SMC approximations. This forms some of the first quantitative results for ABC methods which jointly treat the ABC and simulation errors, with a finite number of data and simulated samples. © Taylor & Francis Group, LLC.