What's Wrong with These Observables?

An imprecise measurement of a dynamical variable (such as a spin component) does not, in general, give the value of another dynamical variable (such as a spin component along a slightly different direction). The result of the measurement cannot be interpreted as the value of any observable that has a classical analogue.     

Interactive Statistical Mechanics and Nonlinear Filtering

This paper connects non-equilibrium statistical mechanics and optimal nonlinear filtering. The latter concerns the observation-conditional behaviour of Markov signal processes, and thus provides a tool for investigating statistical mechanics with partial observations. These allow entropy reduction, illustrating Landauer’s Principle in a quantitative way. The joint process comprising a signal and its nonlinear filter is irreversible in its invariant distribution, which therefore corresponds to a non-equilibrium stationary state of the associated joint system. Macroscopic entropy and energy flows are identified for this state. Since these are driven by observations internal to the system, they do not cause entropy increase, and so the joint system makes statistical mechanical sense in reverse time. Time reversal yields a dual system in which the signal and filter exchange roles. Despite the structural similarity of the original and dual systems, there is a substantial asymmetry in their complexities. This reveals the direction of time, despite the systems being in stationary states that do not produce entropy. This work was partially supported by Leverhulme Trust Research Fellowship 2003/0426, by MURI Grant F49620-02-1-0325 (Complex Adaptive Networks for Co-operative Control), by ARO-MURI Grant DAAD19-00-1-0466 (Data Fusion in Large Arrays of Microsensors (sensor web)) and by NSF-ITR Grant CCR-0325774 Collaborative Research: New Approaches to Experimental Design and Statistical Analysis of Genomic and Structural Biological Data from Multiple Sources.     

A remark on control of partially observed Markov chains

A new state variable is introduced for the problem of controlling a Markov chain under partial observations, which, under a suitably altered probability measure, has a simple evolution.     

Parametric inference for discrete observations of diffusion processes with mixed effects

Stochastic differential equations with mixed effects provide means to model intra-individual and inter-individual variability in repeated experiments leading to longitudinal data. We consider N i.i.d. stochastic processes defined by a stochastic differential equation with linear mixed effects which are discretely observed. We study a parametric framework with distributions leading to explicit approximate likelihood functions and investigate the asymptotic behavior of estimators under the asymptotic framework : the number N of individuals (trajectories) and the number n of observations per individual tend to infinity within a fixed time interval. The estimation method is assessed on simulated data for various models.     

Almost sure exponential stabilization by stochastic feedback control based on discrete-time observations

Since Mao initiated the study of stabilization of ordinary differential equations (ODEs) by stochastic feedback controls based on discrete-time state observations in 2016, no more work on this intriguing topic has been reported. This article investigates how to stabilize a given unstable linear non-autonomous ODE by controller σ(t)x(δ_t)dB(t), and how to stabilize an unstable nonlinear hybrid SDE by controller G(r(δ_t))x(δ_t)dB(t), where δ_t represents time points of observation with sufficiently small observation interval, B(t) is a Brownian motion and r(t) is the Markov Chain, in the sense of pth moment (0 < p < 1) and almost sure exponential stability.     

The nisio semigroup for controlled diffusions with partial observations

A one parameter semigroup of nonlinear operators on an appropriate Banach space is constructed in the spirit of Nisio for controlled diffusions with partial observations. The method is based upon considering an equivalent problem of controlling a measure-valued process representing the conditional law of the state given past observations. The latter evolves according to the usual equations of nonlinear filtering. By considering an appropriate augmentation of the class of controls, it is shown that the “minimum cost” operators associated with this control problem indeed form a semigroup of nonlinear contractions on the space of bounded continuous real-valued functions on the state space of the above measure-valued process.     

An identification method to estimate surface shortwave fluxes on temperature and thickness observations of sea ice in CHINARE 2006

In this paper, a parameter identification method to determine surface shortwave fluxes using temperature and thickness measurements of sea ice in CHINARE 2006 is presented. Adopting a new standard for the calculation of the thermodynamic properties of seawater named TEOS‐10, the surface shortwave fluxes are calculated by the temperature and thickness observations that were measured at Nella Fjord around Zhongshan Station, Antarctica. New simulations for temperature profiles in a different measurement period are performed by three parameterization schemes including the present method, Zillman and Shine. All numerical results are compared with in situ measurements. Results show that better simulations of the surface shortwave radiations and temperature distributions are possible with the identification method than Zillman and Shine. Therefore this method is valid, and the obtained shortwave radiation function can be applied in sea ice modeling. Copyright © 2015 John Wiley & Sons, Ltd.     

The nature of low redshift damped Ly-α systems

Damped Ly-α systems are the major repository of the observed neutral HI at high redshift. These systems are most efficiently detected via absorption spectra taken against distant QSOs. In this paper, we review some of the observational constraints on the nature of these objects, and also discuss the implications of recent observations of two low redshift damped absorbers, made with the Giant Metrewave Radio Telescope. We find that, for the lowest redshift (z = 0.0912) damped Ly-α system, if the system is a rotating gas disk, then the total associated HI mass has to be less than 2 × 10⁹ M⊙, if the disk is at low inclination angles, and less than 10¹⁰ M⊙ if the system is edge on. All limits are 3σ.     

Investigation of Homogeneity and Matter Distribution on Large Scales Using Large Quasar Groups

We use 20 large quasar group (LQG) samples in Park et al. (2015) to investigate the homogeneity of the 0.3 z 1.6 Universe (z denotes the redshift). For comparison, we also employ the 12 LQGs samples at 0.5 z 2 in Komberg et al. (1996) to do the analysis. We calculate the bias factor b and the two-point correlation function ξ_LQG for such groups for three different density profiles of the LQG dark matter halos, i.e. the isothermal profile, the Navarro-Frenk-White (NFW) profile, and the (gravitational) lensing profile. We consider the CDM (cold dark matter plus a cosmological constant ) underlying matter power spectrum with Ω_m = 0.28, Ω_Λ= 0.72, the Hubble constant H₀ = 100 h·km·s^-1·Mpc^-1 with h = 0.72. Dividing the samples into three redshift bins, we find that the LQGs with higher redshift are more biased and correlated than those with lower redshift. The homogeneity scale RH of the LQG distribution is also deduced from theory. It is defined as the comoving radius of the sphere inside which the number of LQGs N(< r) is proportional to r³ within 1%, or equivalently above which the correlation dimension of the sample D₂ is within 1% of D₂ = 3. For Park et al.'s samples and the NFW dark matter halo profile, the homogeneity scales of the LQG distribution are R_H ～ 247 h^-1·Mpc for 0.2 < z ≤ 0.6, R_H ～ 360 h^-1·Mpc for 0.6 < z ≤ 1.2, and R_H ～ 480 h^-1·Mpc for 1.2 < z 1.6. The maximum extent of the LQG samples are beyond RH in each bin, showing that the LQG samples are not homogeneously distributed on such a scale, i.e. a length range of ～ 500 h^-1·Mpc and a mass scale of ～ 10¹⁴M_⊙. The possibilities of a top-down structure formation process as was predicted by the hot/warm dark matter (WDM) scenarios and the redshift evolution of bias factor b and correlation amplitude ξ_LQG of the LQGs as a consequence of the cosmic expansion are both discussed. Different results were obtained based on the LQG sample in Komberg et al. (1996) and the possible reasons for such differences were discussed.