A Bayesian Filtering Algorithm for Gaussian Mixture Models

A Bayesian filtering algorithm is developed for a class of state-space systems that can be modelled via Gaussian mixtures. In general, the exact solution to this filtering problem involves an exponential growth in the number of mixture terms and this is handled here by utilising a Gaussian mixture reduction step after both the time and measurement updates. In addition, a square-root implementation of the unified algorithm is presented and this algorithm is profiled on several simulated systems. This includes the state estimation for two non-linear systems that are strictly outside the class considered in this paper

The Point Spectrum of Smooth Noncompact Hyperbolic Surfaces with Finite Area

We construct a sequence of boundary value problems on compact subsets of smooth noncompact hyperbolic surfaces of finite area. We prove that the sesquilinear forms associated to these boundary value problems are stable as well as consistent at continuous functions which vanish at cusps. We also give an explicit form for the symbol expansion of the Dirichlet-to-Neumann operator of a certain Schrodinger operator. The symbols appearing in the expansion of this Dirichlet-to-Neumann operator can be calculated quickly by a computer using the formulas we provide in this paper

A Molecular Investigation of Absorption onto Mineral Pigments

Pigment suspensions are important in several processes such as ceramics, paints, inks, and coatings. In the wet state, pigments are combined with a variety of chemical species such as polymers, surfactants, and polyelectrolytes which produce a complex colloidal system. The adsorption, desorption, and redistribution of these species at the pigment - aqueous solution interface can have an impact on the behavior in both the wet state or its final dried state. The goal of this work is to establish a molecular picture of the adsorption properties of these pigmented systems. A novel in situ infrared technique has been developed which allows the detection of adsorbed surface species on pigment particles in an aqueous environment. The technique involves the use of a polymeric binder to anchor the colloidal pigment particles to the surface of an internal reflection element (IRE). The binder only weakly perturbs about 25% of the reactive surface sites (hydroxyl groups) on silica. The reaction of succinic anhydride with an aminosilanized silica surface has been quantified using this technique. The adsorption dynamics of the cationic surfactant cetyltrimethylamrnonium bromide (C16TAB) at the Ti02 - aqueous solution interface has been investigated using Fourier transform infrared - attenuated total reflection spectroscopy (FTIR-ATR) and electrokinetic analysis. At low bulk concentrations, C16TAB is shown to adsorb as isolated islands with a defective bilayer structure. Anionic probe molecules are shown to effectively tune the adsorbed surfactant microstructure. The results indicate that the structure of the adsorbed surfactant layer, and not the amount of adsorbed surfactant, dictates the subsequent adsorption behavior of the system. Atomic Layer Deposition is used to deposit a TiO2 layer onto the surfaces of silica and kaolin pigments. The process involves the cyclic reaction sequence of the vapors of TiC14 and H2O. Three complete deposition cycles are needed before the surfaces of the modified pigments are dominated by the presence of TiO2. The modified kaolin pigments display increased dispersion stability as compared to the parent kaolin. The electrokinetic behavior of the modified kaolin is shown to be identical to that of pure TiO2 pigments

Variational System Identification for Nonlinear State-Space Models

This paper considers parameter estimation for nonlinear state-space models, which is an important but challenging problem. We address this challenge by employing a variational inference (VI) approach, which is a principled method that has deep connections to maximum likelihood estimation. This VI approach ultimately provides estimates of the model as solutions to an optimisation problem, which is deterministic, tractable and can be solved using standard optimisation tools. A specialisation of this approach for systems with additive Gaussian noise is also detailed. The proposed method is examined numerically on a range of simulated and real examples focusing on the robustness to parameter initialisation; additionally, favourable comparisons are performed against state-of-the-art alternatives

NE-EPISTEMIČKA MODALNOST ŠIROKOG DOMETA I NJEZIN GRAMATIČKI KONTEKST U RUSKOME I ARMENSKOME JEZIKU

In diesem Artikel werden die Beziehungen zwischen der grammatischen Kategorie des Aspekts und der Modalität mit weitem Skopus analysiert. Die richtige Klassifizierung dieser Modalitätsart, ob sie nun zur epistemischen oder zur nicht-epistemischen gehört, ist hilfreich bei der Beobachtung der grammatischen Umgebung, die mit dieser Modalitätsart verbunden ist, und hilft ebenfalls bei der Klärung der aspektuellen Relationen. Die Untersuchung des Möglichkeitsausdruckes im Armenischen und im Russischen ergibt, daß die Modalität mit weitem Skopus meistens mit dem perfektiven Aspekt verbunden ist, was sie deutlich als eine nicht-epistemische Modalität kennzeichnet.U prilogu se analiziraju odnosi između gramatičke kategorije vida i modalnosti širokog dometa. Točna klasifikacija te vrste modalnosti, bilo epistemičkog bilo ne-epistemičkog tipa, od pomoći je u utvrđivanju gramatičkog konteksta povezanog s ovom vrstom modal-nosti, isto kao i pri objašnjavanju aspektualnih odnosa. Ispitivanje izraza za mogućnost u ruskom i armenskom pokazuje da se modalnost širokog dometa najčešće pojavljuje uz svršeni vid, što navodi na zaključak da je riječ o ne-epistemičkoj modalnosti