Continuous-time norm-constrained Kalman filtering

This paper considers continuous-time state estimation when part of the state estimate or the entire state estimate is norm-constrained. In the former case continuous-time state estimation is considered by posing a constrained optimization problem. The optimization problem can be broken up into two separate optimization problems, one which solves for the optimal observer gain associated with the unconstrained state estimates, while the other solves for the optimal observer gain associated with the constrained state estimates. The optimal constrained state estimate is found by projecting the time derivative of an unconstrained estimate onto the tangent space associated with the norm constraint. The special case where the entire state estimate is norm-constrained is briefly discussed. The utility of the filtering results developed are highlighted through a spacecraft attitude estimation example. Numerical simulation results are included.     

Implicit Bayesian Inference Using Option Prices

Abstract. A Bayesian approach to option pricing is presented in which posterior inference about the underlying returns process is conducted implicitly via observed option prices. A range of models allowing for conditional leptokurtosis, skewness and time‐varying volatility in returns are considered, with posterior parameter distributions and model probabilities backed out from the option prices. Models are ranked according to several criteria, including out‐of‐sample predictive and hedging performance. The methodology accommodates heteroscedasticity and autocorrelation in the option pricing errors, as well as regime shifts across contract groups. The method is applied to intraday option price data on the S&P500 stock index for 1995. While the results provide support for models that accommodate leptokurtosis and skewness, no one model dominates when all criteria are considered.     

Dual approaches to strictly positive real controller synthesis with a performance using linear matrix inequalities

The synthesis of controllers that minimize a performance index subject to a strictly positive real (SPR) constraint is considered. Two controller synthesis methods are presented that are then combined into an iterative algorithm. Each method synthesizes optimal SPR controllers by posing a convex optimization problem where constraints are enforced via linear matrix inequalities. Additionally, each method fixes the controller state‐feedback gain matrix and finds an observer gain matrix such that an upper bound on the closed‐loop ‐norm is minimized and the controller is SPR. The first method retools the standard ‐optimal control problem by using a common Lyapunov matrix variable to satisfy both the criteria and the SPR constraint. The second method overcomes bilinear matrix inequality issues associated with the performance and the SPR constraint by employing a completing the square method and an overbounding technique. Both synthesis methods are used within an iterative scheme to find optimal SPR controllers in a sequential manner. Comparison of our synthesis methods to existing methods in the literature is presented. Copyright © 2012 John Wiley & Sons, Ltd.     

Effect of polyaluminium chloride on phosphorus removal in constructed wetlands treated with swine wastewater

Total phosphorus (TP) removal in aged constructed wetlands poses a challenge, especially when treated with swine wastewater with high concentrations of phosphorus (P). Our earlier studies with anaerobic lagoon swine wastewater treatment in constructed wetlands showed a decline in P removal (45-22%) with increased years of operation. These particular wetlands have been treated with swine wastewater every year since the first application in 1997. Preliminary lab-scale studies were conducted to evaluate the efficiency of polyaluminium chloride (PAC) in the removal of phosphate-P (PO4-P) from swine wastewater. The experimental objective was to increase the phosphorus treatment efficiency in constructed wetland by adding PAC as a precipitating agent. PAC was added by continuous injection to each wetland system at a rate of 3 L day(-1) (1:5 dilution of concentrated PAC). Swine wastewater was added from an anaerobic lagoon to four constructed wetland cells (11m wide x 40m long) at TP loads of 5.4-6.1 kg ha(-1) day(-1) in two experimental periods, September to November of 2008 and 2009. Treatment efficiency of two wetland systems: marsh-pond-marsh (M-P-M) and continuous marsh (CM) was compared. The wetlands were planted with cattails (Typha latifolia L.) and bulrushes (Scirpus americanus). In 2008, PAC treatment showed an increase of 27.5 and 40.8% of TP removal over control in M-P-M and CM respectively. Similar trend was also observed in the following year. PAC as a flocculant and precipitating agent showed potential to enhance TP removal in constructed wetlands treated with swine wastewater.     

Conjugate mixture models for clustering multimodal data

The problem of multimodal clustering arises whenever the data are gathered with several physically different sensors. Observations from different modalities are not necessarily aligned in the sense there there is no obvious way to associate or compare them in some common space. A solution may consist in considering multiple clustering tasks independently for each modality. The main difficulty with such an approach is to guarantee that the unimodal clusterings are mutually consistent. In this letter, we show that multimodal clustering can be addressed within a novel framework: conjugate mixture models. These models exploit the explicit transformations that are often available between an unobserved parameter space (objects) and each of the observation spaces (sensors). We formulate the problem as a likelihood maximization task and derive the associated conjugate expectation-maximization algorithm. The convergence properties of the proposed algorithm are thoroughly investigated. Several local and global optimization techniques are proposed in order to increase its convergence speed. Two initialization strategies are proposed and compared. A consistent model selection criterion is proposed. The algorithm and its variants are tested and evaluated within the task of 3D localization of several speakers using both auditory and visual data.     

Monomers of human beta 1 beta 1 alcohol dehydrogenase exhibit activity that differs from the dimer

A previously unreported enzymatic activity is described for monomers of the beta 1 beta 1 isoenzyme of human alcohol dehydrogenase that were prepared from dimeric enzyme by freeze-thaw in liquid nitrogen. Whereas the dimeric enzyme has optimal activity at low substrate concentrations (2.5 mM ethanol, 50 microM NAD+; "low Km" activity), the monomer has its highest activity at high substrate concentrations (1.5 M ethanol, 2.5 mM NAD+; "high Km" activity). While the activity of the monomer does not appear to be saturated at 1.5 M ethanol, its maximal activity at this high ethanol concentration exceeds the Vmax of the dimer by about 3-fold. The apparent Km of NAD+ with monomers is 270 microM, and no activity could be detected with nicotinamide mononucleotide as cofactor. During gel filtration the high Km activity elutes at a lower apparent molecular weight position than the dimer. The kinetics of monomer-to-dimer reassociation are consistent with a second-order process with a rate constant of 240 M-1 s-1. The reassociation rate is markedly enhanced by the presence of NAD+. During refolding of beta 1 beta 1 following denaturation in 6 M guanidine hydrochloride, an enzyme species with high Km activity and spectral properties similar to the freeze-thaw monomer is observed, indicating that a catalytically active monomer is an intermediate in the refolding pathway. The enzymatic activity of the monomer implies that the intersubunit contacts of beta 1 beta 1 are not crucial in establishing a catalytically competent enzyme. However, the differences in specific activity and Km between monomer and dimer suggest that dimerization may serve to modulate the catalytic properties.     

Habituation of the orienting response: a gating mechanism subserving selective attention

Possibilities of involution of changes in lesser circulation after closure of experimental aortopulmonary anastomosis were studied. 37 observations at various intervals after closure of anastomosis (several minutes to 13.5 months) in 25 dogs were analyzed. Before closure the anastomosis had functioned for 1-7 months. The results of histological examinations of lungs, pressure measurements in lesser circulation, heart weight, electrocardiographic and spirographic examinations were analyzed. It was found that complete involution of changes in lesser circulation was possible only in first month of existence of anastomosis, in this case with changes of both "early" and "late" types. "Late"-type changes after four months function of anastomosis had both reversible and irreversible character, whereas "early"-type changes became irreversible already after three-month duration of anastomosis. With the "late"-type changes, the operation itself (closure of anastomosis) was accompanied by symptoms of pulmonary vasomotor paresis and heart failure, whereas in the presence of "early"-type changes the operation elicited no morphological or functional changes.