The derivation of Markov Chain Properties using Generalized Matrix Inverses

In many stochastic models a Markov chain is present either directly or indirectly through some form of embedding. The analysis of many problems of interest associated with these models, eg. stationary distributions, moments of first passage time distributions and moments of occupation time random variables, often requires the solution of a system of linear equations involving I – P, where P is the transition matrix of a finite, irreducible, discrete time Markov chain. Generalized matrix inverses play an important role in the solution of such singular sets of equations. In this presentation we survey the application of generalized inverses to the aforementioned problems focussing primarily on Markov chains

The accurate computation of key properties of Markov and semi-Markov Processes

Based upon the Grassman, Taksar and Heyman algorithm [1] and the equivalent Sheskin State Reduction algorithm [2] for finding the stationary distribution of a finite irreducible Markov chain, Kohlas [3] developed a procedure for fi nding the mean fi rst passage times (MFPTs) (or absorption probabilities) in semi-Markov processes. The method is numerically stable as it doesn't involve subtraction. It works well for focussing on the MFPTs from any state to a fixed state but it is not ideally suited for a global expression for the MFPT matrix. We present a refinement of the Kohlas algorithm which we specialise to the case of Markov chains to find expressions for the MFPT matrix. A consequence of our procedure is that the stationary distribution does not need to be derived in advance but is found from the MFPTs. This also leads to an expression for the group inverse of I - P where P is the transition matrix of the embedded Markov chain. A comparison, using some test problems from the literature, with other techniques using generalised matrix inverses is also presented. References: 1] Grassman W.K., Taksar M.I., and Heyman D.P., Regenerative analysis and steady state distributions for Markov chains, Oper. Res. 33, (1985), 1107-1116. [2] Sheskin T.J., A Markov partitioning algorithm for computing steady state probabilities, Oper. Res. 33 (1985), 228-235. [3] Kohlas J. Numerical computation of mean fi rst passage times and absorption probabilities in Markov and semi-Markov models, Zeit fur Oper Res, 30, (1986), 197-207

A comparison of computational techniques of the key properties of Markov Chains

The presenter has recently been exploring the accurate computation of the stationary distribution for finite Markov chains based upon the Grassman, Taksar and Heyman (GTH) algorithm ([1]) with further extensions of this procedure, based upon the ideas of Kohlas ([2]), for finding the mean first passage time matrix. The methods are numerically stable as they do not involve subtraction. In addition, a number of perturbation techniques, where the rows of the transition matrix are sequentially updated, are also considered for computing these quantities. These techniques, together with some standard techniques using matrix inverses and generalized inverses, are compared for accuracy, using some test problems from the literature. References: [1} Grassman W.K., Taksar M.I., and Heyman D.P., Regenerative analysis and steady state distributions for Markov chains, Oper. Res. 33, (1985), 1107-1116. [2] Kohlas J. Numerical computation of mean first passage times and absorption probabilities in Markov and semi-Markov models, Zeit fur Oper Res, 30, (1986), 197-207

Grapevine physiological response to row orientation-induced spatial radiation and microclimate changes

Terroir factors and vineyard practices largely determine canopy and root system functioning. In this study, changes in soil conditions, multi-level (vertical, horizontal) light interception (quantitative, photographic, schematic, 3D modelled), leaf water potential and photosynthetic activity were measured during the grape ripening period on NS, EW, NE-SW, and NW-SE orientated (Southern Hemisphere) vertically trellised Shiraz grapevine canopies. It was hypothesised that the spatial radiation interception angle and radiation distribution of differently orientated and vertically trained grapevine rows would affect soil conditions and vine physiological activity. Soil water content showed an increase and soil temperature a decreasing gradient with soil depth. In the afternoon, soil layers of EW orientated rows reached their highest temperature. This, along with measured photosynthetic active radiation received by canopies, complimented the diurnally-captured photographic, constructed and 3D modelled images (also schematically) of canopy and soil exposure patterns. The top, bottom and outside of NS canopies mainly received radiation from directly above, from the E and the W; during midday, high radiation was only received from above. The EW rows received the highest radiation component from above and from the N. The NE-SW rows received high levels of radiation from above, from the SE until 10:00, and from the NW from 13:00. A similar profile can be described for NW-SE rows, but with high radiation received from the NE up to 13:00 and from the SW from 16:00. Overall, lowest leaf water potential occurred for NE-SW canopies, followed by those orientated NW-SE, NS and EW. Photosynthetic activity reflected the positive radiation impact of the sun azimuth during the grape ripening period; best overall performance seemed to occur for E and N exposed canopy sides. This was largely driven by the responsiveness of the secondary leaves to radiation. Photosynthetic output decreased from apical to basal canopy zones with low, erratic values in the light-limited canopy centre. The NS and EW orientated canopies generally showed the highest average photosynthesis, while it was lower for the sides facing S, SE and SW. The results provide a better understanding of the physiological functioning of horizontal and vertical leaf layers in differently orientated grapevine canopies, as affected by climatic conditions. The study contributes to the longstanding challenges of capturing the complexity of parallel microclimatic and physiological output of grapevine canopies under open field conditions. The results can be directly applied to the selection of vineyard practices and seasonal management to ensure the attainment of yield, grape composition and wine quality objectives

Expression of a beta-adrenergic receptor kinase 1 inhibitor prevents the development of myocardial failure in gene-targeted mice.

Heart failure is accompanied by severely impaired beta-adrenergic receptor (betaAR) function, which includes loss of betaAR density and functional uncoupling of remaining receptors. An important mechanism for the rapid desensitization of betaAR function is agonist-stimulated receptor phosphorylation by the betaAR kinase (betaARK1), an enzyme known to be elevated in failing human heart tissue. To investigate whether alterations in betaAR function contribute to the development of myocardial failure, transgenic mice with cardiac-restricted overexpression of either a peptide inhibitor of betaARK1 or the beta2AR were mated into a genetic model of murine heart failure (MLP-/-). In vivo cardiac function was assessed by echocardiography and cardiac catheterization. Both MLP-/- and MLP-/-/beta2AR mice had enlarged left ventricular (LV) chambers with significantly reduced fractional shortening and mean velocity of circumferential fiber shortening. In contrast, MLP-/-/betaARKct mice had normal LV chamber size and function. Basal LV contractility in the MLP-/-/betaARKct mice, as measured by LV dP/dtmax, was increased significantly compared with the MLP-/- mice but less than controls. Importantly, heightened betaAR desensitization in the MLP-/- mice, measured in vivo (responsiveness to isoproterenol) and in vitro (isoproterenol-stimulated membrane adenylyl cyclase activity), was completely reversed with overexpression of the betaARK1 inhibitor. We report here the striking finding that overexpression of this inhibitor prevents the development of cardiomyopathy in this murine model of heart failure. These findings implicate abnormal betaAR-G protein coupling in the pathogenesis of the failing heart and point the way toward development of agents to inhibit betaARK1 as a novel mode of therapy

Local Ugandan Production of Stable 0.2% Chlorhexidine Eye Drops

Purpose: The purpose of this study was to develop a protocol to prepare buffered chlorhexidine (CHX) eye drops (0.2% w/v) in the United Kingdom that can be reproduced at a production facility in Uganda. Buffered CHX eye drops can prevent CHX degradation and improve ocular tolerability during the treatment of fungal keratitis. Methods: Buffered CHX eye drops in amber glass containers were prepared using sodium acetate buffer at pH 5.90 to 6.75. Two commercial CHX solutions and CHX in water were used as controls. Eye drops were stored at 40°C (70% humidity, 21 months) in the United Kingdom and at ambient temperature in Uganda (30 months). High-performance liquid chromatography was used to determine CHX stability over time, and pH was monitored. Sterility was achieved using an autoclave (121°C, 15 minutes) and water bath (100°C, 30 minutes). Results: The pH of acetate-buffered CHX eye drops did not change over 21 months a40°C or at ambient temperature (30 months), whereas the pH of the unbuffered aqueouCHX displayed significant fluctuations, with an increase in acidity. The CHX concentration remained the same in both buffered and unbuffered eye-drop solutions. Eye dropsterilization was successful using an autoclave and a water bath. Conclusions: Stable, sterile, buffered CHX eye drops (pH 6.75) were successfully prepared first in the United Kingdom and then reproducibly in Uganda. This eye drops can be prepared in a hospital or pharmacy setting with limited resources, thus providing a cost-effective treatment for fungal keratitis. Translational Relevance: A protocol has been developed to prepare buffered CHX eydrops in low-and middle-income countries to treat fungal keratitis

Site-specific incorporation of phosphotyrosine using an expanded genetic code.

Access to phosphoproteins with stoichiometric and site-specific phosphorylation status is key to understanding the role of protein phosphorylation. Here we report an efficient method to generate pure, active phosphotyrosine-containing proteins by genetically encoding a stable phosphotyrosine analog that is convertible to native phosphotyrosine. We demonstrate its general compatibility with proteins of various sizes, phosphotyrosine sites and functions, and reveal a possible role of tyrosine phosphorylation in negative regulation of ubiquitination

Approximation for Cooperative Interactions of a Spatially-Detailed Cardiac Sarcomere Model

We developed a novel ordinary differential equation (ODE) model, which produced results that correlated well with the Monte Carlo (MC) simulation when applied to a spatially-detailed model of the cardiac sarcomere. Configuration of the novel ODE model was based on the Ising model of myofilaments, with the “co-operative activation” effect introduced to incorporate nearest-neighbor interactions. First, a set of parameters was estimated using arbitrary Ca transient data to reproduce the combinational probability for the states of three consecutive regulatory units, using single unit probabilities for central and neighboring units in the MC simulation. The parameter set thus obtained enabled the calculation of the state transition of each unit using the ODE model with reference to the neighboring states. The present ODE model not only provided good agreement with the MC simulation results but was also capable of reproducing a wide range of experimental results under both steady-state and dynamic conditions including shortening twitch. The simulation results suggested that the nearest-neighbor interaction is a reasonable approximation of the cooperativity based on end-to-end interactions. Utilizing the modified ODE model resulted in a reduction in computational costs but maintained spatial integrity and co-operative effects, making it a powerful tool in cardiac modeling

Star forming dwarf galaxies

Star forming dwarf galaxies (SFDGs) have a high gas content and low metallicities, reminiscent of the basic entities in hierarchical galaxy formation scenarios. In the young universe they probably also played a major role in the cosmic reionization. Their abundant presence in the local volume and their youthful character make them ideal objects for detailed studies of the initial stellar mass function (IMF), fundamental star formation processes and its feedback to the interstellar medium. Occasionally we witness SFDGs involved in extreme starbursts, giving rise to strongly elevated production of super star clusters and global superwinds, mechanisms yet to be explored in more detail. SFDGs is the initial state of all dwarf galaxies and the relation to the environment provides us with a key to how different types of dwarf galaxies are emerging. In this review we will put the emphasis on the exotic starburst phase, as it seems less important for present day galaxy evolution but perhaps fundamental in the initial phase of galaxy formation.Comment: To appear in JENAM Symposium "Dwarf Galaxies: Keys to Galaxy Formation and Evolution", P. Papaderos, G. Hensler, S. Recchi (eds.). Lisbon, September 2010, Springer Verlag, in pres