Discrete-Time Risk-Sensitive Filters with Non-Gaussian Initial Conditions and Their Ergodic Properties

In this paper, we study asymptotic stability properties of risk-sensitive filters with respect to their initial conditions. In particular, we consider a linear time-invariant systems with initial conditions that are not necessarily Gaussian. We show that in the case of Gaussian initial conditions, the optimal risk-sensitive filter asymptotically converges to a suboptimal filter initialized with an incorrect covariance matrix for the initial state vector in the mean square sense provided the incorrect initializing value for the covariance matrix results in a risk-sensitive filter that is asymptotically stable, that is, results in a solution for a Riccati equation that is asymptotically stabilizing. For non-Gaussian initial conditions, we derive the expression for the risk-sensitive filter in terms of a finite number of parameters. Under a boundedness assumption satisfied by the fourth order absolute moment of the initial state variable and a slow growth condition satisfied by a certain Radon-Nikodym derivative, we show that a suboptimal risk-sensitive filter initialized with Gaussian initial conditions asymptotically approaches the optimal risk-sensitive filter for non-Gaussian initial conditions in the mean square sense. Some examples are also given to substantiate our claims.     

Symmetry properties for a generalised thin film equation

Symmetry properties are presented for a fourth-order parabolic equation written in conservation form. It was introduced in the literature as a generalisation of the fourth-order thin film equation. We derive equivalence transformations, Lie symmetries, potential symmetries, non-classical symmetries and potential non-classical symmetries. A chain of such equations is introduced. We conclude by presenting similar results for the third-order equation of this chain.     

Stochastic Uncertain Systems Subject to Relative Entropy Constraints: Induced Norms and Monotonicity Properties of Minimax Games

Entropy and relative entropy are fundamental concepts on which information theory is founded on, and in general, telecommunication systems design. On the other hand, dissipation inequalities, minimax strategies, and induced norms are the basic concepts on which robustness of uncertain control and estimation of systems are founded on. In this paper, the precise relation between these notions is investigated. In particular, it will be shown that the higher the dissipation the higher the entropy of the system, which has implications in computing the induced norm associated with robustness. These connections are obtained by considering stochastic optimal uncertain control systems, in which uncertainty is described by a relative entropy constraint between the nominal and uncertain measures, while the pay-off is a linear functional of the uncertain measure. This is a minimax game, in which the controller measure seeks to minimize the pay-off, while the disturbance measure aims at maximizing the pay-off. Salient properties of the minimax solution are derived, including a characterization of the optimal sensitivity reduction, computation of the induced norm, monotonicity properties of minimax solution, and relations between dissipation and relative entropy of the system. The theory is developed in an abstract setting and then applied to nonlinear partially observable continuous-time uncertain controlled systems, in which the nominal and uncertain systems are described by conditional distributions. In addition, existence of the optimal control policy among the class of policies known as wide-sense control laws is shown, and an explicit formulae for the worst case conditional measure is derived. The results are applied to linear-quadratic-Gaussian problems     

Partially observable nonlinear risk-sensitive control problems:dynamic programming and verification theorems

In this paper, we consider continuous-time partially observable optimal control problems with exponential-of-integral cost criteria. We derive a rigorous verification theorem when the state and control enter nonlinear in the dynamics. In addition, we show that the quadratic sensor problem is estimation-solvable with respect to a certain cost criterion. The framework relies on dynamic programming and the Hamilton-Jacobi theory     

New finite-dimensional risk-sensitive filters: small noise limits

The paper is concerned with continuous-time nonlinear risk-sensitive filters. It is shown that for large classes of nonlinearities entering both the dynamics and measurements, these filters are finite-dimensional generalizations of the Benes filters. Specific examples are discussed. The small noise limiting analog is discussed using change of probability measures     

Investigation of temperature approximation methods during flash sintering of ZnO

The lattice expansion in ZnO, using in-situ X ray diffraction, has been investigated during flash sintering with varying current densities. While current flow through the specimen enhances the kinetics of sintering for ZnO, the temperature is not high enough to claim thermal runaway or localized melting. Unlike the case of yttria stabilized zirconia [1,2], experimental temperature approximations predict comparable specimen temperature to conventional sintering temperature of ZnO. Microstructural analysis supports the findings of the in-situ temperature approximations. In comparison with black body radiation, a gap between theoretical value and measured value was found due to flaws in the theoretical model. In addition, a new type of flash sintering was introduced, with current ramp, to avoid the power spike which has been the source of much debate about the transition from voltage to current control. The advantage of this method is in the controlled sintering kinetics thus avoiding the channeling found in dielectric materials [3].     

In-situ observation of oxygen mobility and abnormal lattice expansion in ceria during flash sintering

Flash sintering has been shown to be an effective method of sintering for many types of ceramics. However, the characteristics of flash sintering for each type of ceramic varies. When ionically conducting ceramics are sintered under a DC electric field, a strong dependence of densification with respect to position is observed. Microstructural analysis of the effect of electric field on oxygen ion conductors shows non-stoichiometry (oxygen deficiency) at the cathode which continues to build up over time under flash. In oxygen ion conductors, dominant charge carriers during flash are oxygen ions and the final density of the specimen is related to the availability of oxygen. This effect is no longer evident when using an AC power supply. Thus, use of AC instead of DC electric field is preferable for flash sintering of ionically conducting ceramics.     

Tracing correlations of corrosion products and microclimate data on outdoor bronze monuments by Principal Component Analysis

Although the corrosion of outdoor bronzes has been extensively studied for the last decades, there is no quantitative correlation of corrosion products to microclimatic factors. The present work aims to demonstrate how Principal Component Analysis (PCA) can serve this purpose. Thirty corrosion product samples were collected from the bronze monument of Theodoros Kolokotronis (Nafplio, Greece) and analysed using X-Ray Diffractometry (XRD). The quantitative XRD data together with data on surface orientation and exposure to rain or wind were treated by PCA and three distinct groups were found. Each group includes samples of similar composition and microclimate characteristics showing that PCA may give useful information on corrosion mechanisms.     

Cannabinoid-Induced Conditioned Place Preference,Intravenous Self-Administration,and Behavioral Stimulation Influenced by Ghrelin Receptor Antagonism in Rats

Cannabis/cannabinoids are widely used for recreational and therapy purposes, but their risks are largely disregarded. However, cannabinoid-associated use disorders and dependence are alarmingly increasing and an effective treatment is lacking. Recently, the growth hormone secretagogue receptor (GHSR1A) antagonism was proposed as a promising mechanism for drug addiction therapy. However, the role of GHS-R1A and its endogenous ligand ghrelin in cannabinoid abuse remains unclear. Therefore, the aim of our study was to investigate whether the GHS-R1A antagonist JMV2959 could reduce the tetrahydrocannabinol (THC)-induced conditioned place preference (CPP) and behavioral stimulation, the WIN55,212-2 intravenous self-administration (IVSA), and the tendency to relapse. Following an ongoing WIN55,212-2 self-administration, JMV2959 3 mg/kg was administered intraperitoneally 20 min before three consequent daily 120-min IVSA sessions under a fixed ratio FR1, which significantly reduced the number of the active lever-pressing, the number of infusions, and the cannabinoid intake. Pretreatment with JMV2959 suggested reduction of the WIN55,212-2-seeking/relapse-like behavior tested in rats on the twelfth day of the forced abstinence period. On the contrary, pretreatment with ghrelin significantly increased the cannabinoid IVSA as well as enhanced the relapse-like behavior. Co-administration of ghrelin with JMV2959 abolished/reduced the significant efficacy of the GHS-R1A antagonist in the cannabinoid IVSA. Pretreatment with JMV2959 significantly and dose-dependently reduced the manifestation of THC-induced CPP. The THC-CPP development was reduced after the simultaneous administration of JMV2959 with THC during conditioning. JMV2959 also significantly reduced the THC-induced behavioral stimulation in the LABORAS cage. Our findings suggest that GHS-R1A importantly participates in the rewarding/reinforcing effects of cannabinoids.     

Influence of soil structures on corrosion performance of floating-DC transit systems

The production of stray currents by DC-transit systems leads to the corrosion of nearby buried metallic structures, such as pipelines and cable sheaths. The paper details the corrosion performance of a DC transit system with a floating return rail, for a number of different soil-resistivity structures: uniform, horizontal and vertical-layer models. This builds on previous work carried out in homogenous soils. It is shown that a variation in soil type along the route of a transit system can lead to high local leakage-current densities on buried metallic structures, increasing their vulnerability to corrosion damage.