STOCHASTIC LINEAR QUADRATIC OPTIMAL CONTROL PROBLEMS WITH RANDOM COEFFICIENTS

61. IntroductionLet (fi, F, P, {R}tZo) be a complete filtered probability space on which a standard onedimensional Brownian motion w(') is defined such that {R}tZo is the natural filtrationgenerated by w(.), augmented by all the p-null sets in i. We consider the following stateequationwhere T E T[0, TI, the set of all {R}tZo-stopping times taking values in [0, T], (E sigLlt (fi;IR"); A, B, C, D are matrix-valued {R}tZo-adapted bounded processes. In the above, u(.) EU[T, T]gLI(T, T…     

Study on the lifetime and attenuation properties of microbubbles coated with carboxylic acid salts

Four kinds of surfactants, sodium laurate, sodium myristate, sodium palmitate and sodium oleate were used to study the effects of surfactant coatings on the lifetime and attenuation of microbubbles. The changes in the size distribution of microbubbles prepared with these surfactants in saline were measured with a Coulter Multisizer (Coulter Electronics Ltd., Luton, UK). Frequency characteristics of ultrasonic attenuation of the microbubble suspensions were measured between 400 kHz and 6 MHz. From the changes in attenuation in the microbubble suspensions over time, it was found that the lifetime of microbubbles in a suspension also depends on the frequency of the irradiating ultrasound. The effect of surfactants on the frequency characteristics of attenuation was also studied, and characteristics of the surfactant coating, including shell elasticity and shell friction parameters were calculated from the measurement results. Microbubbles produced with sodium palmitate had the longest lifetime and the smallest average size. The shell had very little effect on the ultrasonic properties of microbubbles produced with sodium palmitate, suggesting that the sodium palmitate microbubbles behaved ultrasonically as free microbubbles.     

基于AVR单片机的万能材料试验机控制系统

采用AVR单片机AT90S8515作为控制核心,通过步进电机带动丝杠运动,利用光栅编码器、高精度力传感器、2个引伸计分别测量了位移、力及试件横、纵变形,在老式电子万能材料实验机上建立了新型计算机控制系统,可方便测定弹性模量和泊松比.     

A modified NaSch model with density-dependent randomization for traffic flow

Based on the Nagel-Schreckenberg (NaSch) model of traffic flow, a modified cellular automaton (CA) traffic model with the density-dependent randomization (abbreviated as the DDR model) is proposed to simulate traffic flow. The fundamental diagram obtained by simulation shows the ability of this modified NaSch model to capture the essential features of traffic flow, e.g., synchronized flow, metastable state, hysteresis and phase separation at higher densities. Comparisons are made between this DDR model and the NaSch model, also between this DDR model and the VDR model. And the underlying mechanism is analyzed. All these results indicate that the presented model is reasonable and more realistic.     

On stochastic parameter estimation using data assimilation

Data assimilation-based parameter estimation can be used to deterministically tune forecast models. This work demonstrates that it can also be used to provide parameter distributions for use by stochastic parameterization schemes. While parameter estimation is (theoretically) straightforward to perform, it is not clear how one should physically interpret the parameter values obtained. Structural model inadequacy implies that one should not search for a deterministic “best” set of parameter values, but rather allow the parameter values to change as a function of state; different parameter values will be needed to compensate for the state-dependent variations of realistic model inadequacy. Over time, a distribution of parameter values will be generated and this distribution can be sampled during forecasts. The current work addresses the ability of ensemble-based parameter estimation techniques utilizing a deterministic model to estimate the moments of stochastic parameters. It is shown that when the system of interest is stochastic the expected variability of a stochastic parameter is biased when a deterministic model is employed for parameter estimation. However, this bias is ameliorated through application of the Central Limit Theorem, and good estimates of both the first and second moments of the stochastic parameter can be obtained. It is also shown that the biased variability information can be utilized to construct a hybrid stochastic/deterministic integration scheme that is able to accurately approximate the evolution of the true stochastic system.     

Adaptive modeling, adaptive data assimilation and adaptive sampling

For efficient progress, model properties and measurement needs can adapt to oceanic events and interactions as they occur. The combination of models and data via data assimilation can also be adaptive. These adaptive concepts are discussed and exemplified within the context of comprehensive real-time ocean observing and prediction systems. Novel adaptive modeling approaches based on simplified maximum likelihood principles are developed and applied to physical and physical–biogeochemical dynamics. In the regional examples shown, they allow the joint calibration of parameter values and model structures. Adaptable components of the Error Subspace Statistical Estimation (ESSE) system are reviewed and illustrated. Results indicate that error estimates, ensemble sizes, error subspace ranks, covariance tapering parameters and stochastic error models can be calibrated by such quantitative adaptation. New adaptive sampling approaches and schemes are outlined. Illustrations suggest that these adaptive schemes can be used in real time with the potential for most efficient sampling.     

Statistical equilibrium in simple exchange games I

This erratum corrects a mistake in reference [E. Scalas, U. Garibaldi, S. Donadio, Eur. Phys. J. B 53, 267 (2006)]. In that paper, we needed an aperiodic version of the BDY game, but, in formula (1), we incorrectly presented a periodic transition matrix of period 2 in the special case of g = 2 agents. Here, we present the right aperiodic version.     

Sustainment and Controlment of Noise-Induced Circadian Oscillations in <Emphasis Type="Italic">Neurospora</Emphasis>: Noise and External Signal Effects

The effect of light noise on a Neurospora circadian clock system in the steady states is investigated. It is found that the circadian oscillations could be induced by light noise, leading to various resonance phenomena including internal signal stochastic resonance (ISSR) and ISSR without tuning in the system. The strength of ISSR could be significantly reinforced with the decrease of the distance of the control parameter to the Hopf bifurcation point of the system. The fundamental frequency of noise-induced circadian oscillations almost does not change with the increment of light noise intensity, which implies that the Neurospora system could sustain intrinsic circadian rhythms. In addition, the ISSR and ISSR without tuning could be both amplified, suppressed or destroyed by tuning the frequency or amplitude of external signal.     

Emergence of bimodality in noisy systems with single-well potential

We study the stationary probability density of a Brownian particle in a potential with a single-well subject to the purely additive thermal and dichotomous noise sources. We find situations where bimodality of stationary densities emerges due to presence of dichotomous noise. The solutions are constructed using stochastic dynamics (Langevin equation) or by discretization of the corresponding Fokker-Planck equations. We find that in models with both noises being additive the potential has to grow faster than |x| in order to obtain bimodality. For potentials ∝|x| stationary solutions are always of the double exponential form.     

On causal stochastic equations for log-stable multiplicative cascades

We reformulate various versions of infinitely divisible cascades proposed in the literature using stochastic equations. This approach sheds a new light on the differences and common points of several formulations that have been recently provided by several teams. In particular, we focus on the simplification occurring when the infinitely divisible noise at the heart of such model is stable: an independently scattered random measure becomes a stable stochastic integral. In the last section we discuss the D-dimensional generalization.