Non-Stationary Semi-Markov Decision Processes on a Finite Horizon

We introduce and study a class of non-stationary semi-Markov decision processes on a finite horizon. By constructing an equivalent Markov decision process, we establish the existence of a piecewise open loop relaxed control which is optimal for the finite horizon problem.

FIRST PASSAGE APPROXIMATION FOR NORMAL STATIONARY RANDOM PROCESSES.

A new approximate solution for the first passage probability of a stationary Gaussian random process is presented which is based on the estimation of the mean clump size. A simple expression for the mean clump size is derived in terms of the cumulative normal distribution function, which avoids the lengthy numerical integrations which are required by similar existing techniques. The method is applied to a linear oscillator and an ideal bandpass process and good agreement with published results is obtained. By making a slight modification to an existing analysis it is shown that a widely used empirical result for the asymptotic form of the first passage probability can be deduced theoretically.

Markovian Processes, Two-Sided Autoregressions and Finite-Sample Inference for Stationary and Nonstationary Autoregressive Processes.

In this paper, we develop finite-sample inference procedures for stationary and nonstationary autoregressive (AR) models. The method is based on special properties of Markov processes and a split-sample technique. The results on Markovian processes (intercalary independence and truncation) only require the existence of conditional densities. They are proved for possibly nonstationary and/or non-Gaussian multivariate Markov processes. In the context of a linear regression model with AR(1) errors, we show how these results can be used to simplify the distributional properties of the model by conditioning a subset of the data on the remaining observations. This transformation leads to a new model which has the form of a two-sided autoregression to which standard classical linear regression inference techniques can be applied. We show how to derive tests and confidence sets for the mean and/or autoregressive parameters of the model. We also develop a test on the order of an autoregression. We show that a combination of subsample-based inferences can improve the performance of the procedure. An application to U.S. domestic investment data illustrates the method.

Performance analysis of adaptive lattice filters for FM signals and alpha-stable processes

The performance of an adaptive filter may be studied through the behaviour of the optimal and adaptive coefficients in a given environment. This thesis investigates the performance of finite impulse response adaptive lattice filters for two classes of input signals: (a) frequency modulated signals with polynomial phases of order p in complex Gaussian white noise (as nonstationary signals), and (b) the impulsive autoregressive processes with alpha-stable distributions (as non-Gaussian signals). Initially, an overview is given for linear prediction and adaptive filtering. The convergence and tracking properties of the stochastic gradient algorithms are discussed for stationary and nonstationary input signals. It is explained that the stochastic gradient lattice algorithm has many advantages over the least-mean square algorithm. Some of these advantages are having a modular structure, easy-guaranteed stability, less sensitivity to the eigenvalue spread of the input autocorrelation matrix, and easy quantization of filter coefficients (normally called reflection coefficients). We then characterize the performance of the stochastic gradient lattice algorithm for the frequency modulated signals through the optimal and adaptive lattice reflection coefficients. This is a difficult task due to the nonlinear dependence of the adaptive reflection coefficients on the preceding stages and the input signal. To ease the derivations, we assume that reflection coefficients of each stage are independent of the inputs to that stage. Then the optimal lattice filter is derived for the frequency modulated signals. This is performed by computing the optimal values of residual errors, reflection coefficients, and recovery errors. Next, we show the tracking behaviour of adaptive reflection coefficients for frequency modulated signals. This is carried out by computing the tracking model of these coefficients for the stochastic gradient lattice algorithm in average. The second-order convergence of the adaptive coefficients is investigated by modeling the theoretical asymptotic variance of the gradient noise at each stage. The accuracy of the analytical results is verified by computer simulations. Using the previous analytical results, we show a new property, the polynomial order reducing property of adaptive lattice filters. This property may be used to reduce the order of the polynomial phase of input frequency modulated signals. Considering two examples, we show how this property may be used in processing frequency modulated signals. In the first example, a detection procedure in carried out on a frequency modulated signal with a second-order polynomial phase in complex Gaussian white noise. We showed that using this technique a better probability of detection is obtained for the reduced-order phase signals compared to that of the traditional energy detector. Also, it is empirically shown that the distribution of the gradient noise in the first adaptive reflection coefficients approximates the Gaussian law. In the second example, the instantaneous frequency of the same observed signal is estimated. We show that by using this technique a lower mean square error is achieved for the estimated frequencies at high signal-to-noise ratios in comparison to that of the adaptive line enhancer. The performance of adaptive lattice filters is then investigated for the second type of input signals, i.e., impulsive autoregressive processes with alpha-stable distributions . The concept of alpha-stable distributions is first introduced. We discuss that the stochastic gradient algorithm which performs desirable results for finite variance input signals (like frequency modulated signals in noise) does not perform a fast convergence for infinite variance stable processes (due to using the minimum mean-square error criterion). To deal with such problems, the concept of minimum dispersion criterion, fractional lower order moments, and recently-developed algorithms for stable processes are introduced. We then study the possibility of using the lattice structure for impulsive stable processes. Accordingly, two new algorithms including the least-mean P-norm lattice algorithm and its normalized version are proposed for lattice filters based on the fractional lower order moments. Simulation results show that using the proposed algorithms, faster convergence speeds are achieved for parameters estimation of autoregressive stable processes with low to moderate degrees of impulsiveness in comparison to many other algorithms. Also, we discuss the effect of impulsiveness of stable processes on generating some misalignment between the estimated parameters and the true values. Due to the infinite variance of stable processes, the performance of the proposed algorithms is only investigated using extensive computer simulations.

The suitability of DEAE-Cl active groups on customized poly(GMA-co-EDMA) continuous stationary phase for fast enzyme-free isolation of plasmid DNA

The creation of a commercially viable and a large-scale purification process for plasmid DNA (pDNA) production requires a whole-systems continuous or semi-continuous purification strategy employing optimised stationary adsorption phase(s) without the use of expensive and toxic chemicals, avian/bovine-derived enzymes and several built-in unit processes, thus affecting overall plasmid recovery, processing time and economics. Continuous stationary phases are known to offer fast separation due to their large pore diameter making large molecule pDNA easily accessible with limited mass transfer resistance even at high flow rates. A monolithic stationary sorbent was synthesised via free radical liquid porogenic polymerisation of ethylene glycol dimethacrylate (EDMA) and glycidyl methacrylate (GMA) with surface and pore characteristics tailored specifically for plasmid binding, retention and elution. The polymer was functionalised with an amine active group for anion-exchange purification of pDNA from cleared lysate obtained from E. coli DH5α-pUC19 pellets in RNase/protease-free process. Characterization of the resin showed a unique porous material with 70% of the pores sizes above 300 nm. The final product isolated from anion-exchange purification in only 5 min was pure and homogenous supercoiled pDNA with no gDNA, RNA and protein contamination as confirmed with DNA electrophoresis, restriction analysis and SDS page. The resin showed a maximum binding capacity of 15.2 mg/mL and this capacity persisted after several applications of the resin. This technique is cGMP compatible and commercially viable for rapid isolation of pDNA.

Enhancing methacrylate-monolith-based downstream processes to champion plasmid DNA production

Increasing numbers of preclinical and clinical studies are utilizing pDNA (plasmid DNA) as the vector. In addition, there has been a growing trend towards larger and larger doses of pDNA utilized in human trials. The growing demand on pDNA manufacture leads to pressure to make more in less time. A key intervention has been the use of monoliths as stationary phases in liquid chromatography. Monolithic stationary phases offer fast separation to pDNA owing to their large pore size, making pDNA in the size range from 100 nm to over 300 nm easily accessible. However, the convective transport mechanism of monoliths does not guarantee plasmid purity. The recovery of pure pDNA hinges on a proper balance in the properties of the adsorbent phase, the mobile phase and the feedstock. The effects of pH and ionic strength of binding buffer, temperature of feedstock, active group density and the pore size of the stationary phase were considered as avenues to improve the recovery and purity of pDNA using a methacrylate-based monolithic adsorbent and Escherichia coli DH5α-pUC19 clarified lysate as feedstock. pDNA recovery was found to be critically dependent on the pH and ionic strength of the mobile phase. Up to a maximum of approx. 92% recovery was obtained under optimum conditions of pH and ionic strength. Increasing the feedstock temperature to 80°C increased the purity of pDNA owing to the extra thermal stability associated with pDNA over contaminants such as proteins. Results from toxicological studies of the plasmid samples using endotoxin standard (E. coli 0.55:B5 lipopolysaccharide) show that endotoxin level decreases with increasing salt concentration. It was obvious that large quantities of pure pDNA can be obtained with minimal extra effort simply by optimizing process parameters and conditions for pDNA purification.

Characterization of alluvial formation by stochastic modelling of paleo-fluvial processes: The concept and method

Modelling fluvial processes is an effective way to reproduce basin evolution and to recreate riverbed morphology. However, due to the complexity of alluvial environments, deterministic modelling of fluvial processes is often impossible. To address the related uncertainties, we derive a stochastic fluvial process model on the basis of the convective Exner equation that uses the statistics (mean and variance) of river velocity as input parameters. These statistics allow for quantifying the uncertainty in riverbed topography, river discharge and position of the river channel. In order to couple the velocity statistics and the fluvial process model, the perturbation method is employed with a non-stationary spectral approach to develop the Exner equation as two separate equations: the first one is the mean equation, which yields the mean sediment thickness, and the second one is the perturbation equation, which yields the variance of sediment thickness. The resulting solutions offer an effective tool to characterize alluvial aquifers resulting from fluvial processes, which allows incorporating the stochasticity of the paleoflow velocity.

On Games on Non-Wellfounded Sets and Stationary Sets

In this thesis we study a few games related to non-wellfounded and stationary sets. Games have turned out to be an important tool in mathematical logic ranging from semantic games defining the truth of a sentence in a given logic to for example games on real numbers whose determinacies have important effects on the consistency of certain large cardinal assumptions. The equality of non-wellfounded sets can be determined by a so called bisimulation game already used to identify processes in theoretical computer science and possible world models for modal logic. Here we present a game to classify non-wellfounded sets according to their branching structure. We also study games on stationary sets moving back to classical wellfounded set theory. We also describe a way to approximate non-wellfounded sets with hereditarily finite wellfounded sets. The framework used to do this is domain theory. In the Banach-Mazur game, also called the ideal game, the players play a descending sequence of stationary sets and the second player tries to keep their intersection stationary. The game is connected to precipitousness of the corresponding ideal. In the pressing down game first player plays regressive functions defined on stationary sets and the second player responds with a stationary set where the function is constant trying to keep the intersection stationary. This game has applications in model theory to the determinacy of the Ehrenfeucht-Fraisse game. We show that it is consistent that these games are not equivalent.

Nonthermal-Plasma-Promoted Catalysis for the Removal of NOx From a Stationary Diesel-Engine Exhaust

A detailed study on the removal of oxides of nitrogen (NOx) from the exhaust of a stationary diesel engine was carried out using nonthermal-plasma (pulsed electrical-discharge plasma)-promoted catalytic process. In this paper, the filtered exhaust from the diesel engine is made to pass through a combination of nonthermal plasma reactor and a catalytic reactor connected in series. This combination is referred to as cascade. Two types of cascaded systems were studied. In one type, the plasma treating filtered exhaust was cascaded with a reduction catalyst V2O5/TiO2 using ammonia as reducing agent, and in the other type, the plasma treating filtered exhaust was cascaded with activated-alumina catalyst without any additive. Improved NOx-removal performance of both the cascaded processes and the role of nonthermal plasma in promoting catalysis are explained. Along with the NOx, total hydrocarbon and aldehydes were also removed. Furthermore, experiments were conducted at different temperatures and engine-loading conditions.

Pulsed plasma treatment for NOx reduction from filtered/unfiltered stationary diesel engine exhaust

A detailed study on the removal of oxides of nitrogen (NOx) from the filtered/unfiltered exhaust of a stationary diesel engine was carried out using non-thermal plasma (pulsed electrical discharge plasma) process and cascaded processes namely plasma- adsorbent and plasma-catalyst processes. The superior performance of discharge plasma with regard to NOx removal, energy consumption and formation of by-products in unfiltered exhaust environment is identified. In the cascaded plasma-adsorbent process, the plasma was cascaded with adsorbents (MS13X/Activated alumina/Activated charcoal). The cascaded process treating unfiltered exhaust exhibits a very high NOx removal compared to the individual processes and further, the cascaded process gives almost the same NOx removal efficiency irrespective of type of adsorbent used. In the cascaded plasma- catalyst process, the plasma was cascaded with activated alumina catalyst at high temperature. The synergy effect and improved performance of the cascaded process are explained. Further, experiments were conducted at room temperature as well as at higher temperatures.

Chiral separation of enantiomers of amino acid derivatives by high-performance liquid chromatography on a norvancomycin-bonded chiral stationary phase

A novel norvancomycin-bonded chiral stationary phase (NVC-CSP) was synthesized by using the chiral selector of norvancomycin. The chiral separation of enantiomers of several dansyl-amino acids by high-performance liquid chromatography (HPLC) in the reversed-phase mode is described. The effects of some parameters, such as organic modifier concentration, column temperature, pH and flow rate of the mobile phase, on the retention and enantioselectivity were investigated. The study showed that ionic, as well as hydrophobic interactions were engaged between the analyte and macrocycle in this chromatographic system. Increasing pH of buffers usually improved the chiral resolution for dansyl-alpha-amino-n-butyric acid (Dns-But), dansyl-methionine (Dns-Met) and dansyl-threonine (Dns-Thr), but not for dansyl-glutamic acid (Dns-Glu) which contains two carboxylic groups in its molecular structure. The natural logarithms of selectivity factors (In alpha) of all the investigated compounds depended linearly on the reciprocal of temperature (1/T), most processes of enantioseparation were controlled enthalpically. Interestingly, the process of enantioseparation for dansyl-threonine was enthalpy-controlled at pH of 3.5, while at pH of 7.0, it was entropy-controlled according to thermodynamic parameters Delta(R,S)DeltaHdegrees and Delta(R,S)DeltaSdegrees afforded by Van't Hoff plots. In order to get baseline separation for all the solutes researched, norvancomycin was also used as a chiral mobile phase additive. In combination with the NVC-CSP remarkable increases in enanselectivity were observed for all the compounds, as the result of a "synergistic" effect. (C) 2003 Elsevier B.V. All rights reserved.

Synthesis and characterisation of novel superficially porous silica based stationary phases for use in liquid chromatography

The concept of pellicular particles was suggested by Horváth and Lipsky over fifty years ago. The reasoning behind the idea of these particles was to improve column efficiency by shortening the pathways analyte molecules can travel, therefore reducing the effect of the A and C terms. Several types of shell particles were successfully marketed around this time, however with the introduction of high quality fully porous silica under 10 μm, shell particles faded into the background. In recent years a new generation of core shell particles have become popular within the separation science community. These particles allow fast and efficient separations that can be carried out on conventional HPLC systems. Chapter 1 of this thesis introduces the chemistry of chromatographic stationary phases, with an emphasis on silica bonded phases, particularly focusing on the current state of technology in this area. The main focus is on superficially porous silica particles as a support material for liquid chromatography. A summary of the history and development of these particles over the past few decades is explored, along with current methods of synthesis of shell particles. While commercial shell particles have a rough outer surface, Chapter 2 focuses on the novel approach to growth of smooth surface superficially porous particles in a step-by-step manner. From the Stöber methodology to the seeded growth technique, and finally to the layer-bylayer growth of the porous shell. The superficially porous particles generated in this work have an overall diameter of 2.6 μm with a 350 nm porous shell; these silica particles were characterised using SEM, TEM and BET analysis. The uniform spherical nature of the particles along with their surface area, pore size and particle size distribution are examined in this chapter. I discovered that these smooth surface shell particles can be synthesised to give comparable surface area and pore size in comparison to commercial brands. Chapter 3 deals with the bonding of the particles prepared in Chapter 2 with C18 functionality; one with a narrow and one with a wide particle size distribution. This chapter examines the chromatographic and kinetic performance of these silica stationary phases, and compares them to a commercial superficially porous silica phase with a rough outer surface. I found that the particle size distribution does not seem to be the major contributor to the improvement in efficiency. The surface morphology of the particles appears to play an important role in the packing process of these particles and influences the Van Deemter effects. Chapter 4 focuses on the functionalisation of 2.6 μm smooth surface superficially porous particles with a variety of fluorinated and phenyl silanes. The same processes were carried out on 3.0 μm fully porous silica particles to provide a comparison. All phases were accessed using elemental analysis, thermogravimetric analysis, nitrogen sorption analysis and chromatographically evaluated using the Neue test. I observed comparable results for the 2.6 μm shell pentaflurophenyl propyl silica when compared to 3.0 μm fully porous silica. Chapter 5 moves towards nano-particles, with the synthesis of sub-1 μm superficially porous particles, their characterisation and use in chromatography. The particles prepared are 750 nm in total with a 100 nm shell. All reactions and testing carried out on these 750 nm core shell particles are also carried out on 1.5 μm fully porous particles in order to give a comparative result. The 750 nm core shell particles can be synthesised quickly and are very uniform. The main drawback in their use for HPLC is the system itself due to the backpressure experienced using sub – 1 μm particles. The synthesis of modified Stöber particles is also examined in this chapter with a range of non-porous silica and shell silica from 70 nm – 750 nm being tested for use on a Langmuir – Blodgett system. These smooth surface shell particles have only been in existence since 2009. The results displayed in this thesis demonstrate how much potential smooth surface shell particles have provided more in-depth optimisation is carried out. The results on packing studies reported in this thesis aims to be a starting point for a more sophisticated methodology, which in turn can lead to greater chromatographic improvements.

Tidal flow over a sill in Muchalat Inlet, Nootka Sound, and the resultant mixing processes

Senior thesis written for Oceanography 445

Parameter Estimation in Minification Processes

In this article it is proved that the stationary Markov sequences generated by minification models are ergodic and uniformly mixing. These results are used to establish the optimal properties of estimators for the parameters in the model. The problem of estimating the parameters in the exponential minification model is discussed in detail.