Quasistationarity of continuous-time Markov chains with positive drift

We shall study continuous-time Markov chains on the nonnegative integers which are both irreducible and transient, and which exhibit discernible stationarity before drift to infinity sets in. We will show how this 'quasi' stationary behaviour can be modelled using a limiting conditional distribution: specifically, the limiting state probabilities conditional on not having left 0 for the last time. By way of a dual chain, obtained by killing the original process on last exit from 0, we invoke the theory of quasistationarity for absorbing Markov chains. We prove that the conditioned state probabilities of the original chain are equal to the state probabilities of its dual conditioned on non-absorption, thus allowing us to establish the simultaneous existence and then equivalence, of their limiting conditional distributions. Although a limiting conditional distribution for the dual chain is always a quasistationary distribution in the usual sense, a similar statement is not possible for the original chain.

Effect of density on spatial distribution, pit formation and pit diameter of Myrmeleon acer Walker, (Neuroptera : Myrmeleontidae): patterns and processes

The effect of increasing population density on the formation of pits, their size and spatial distribution, and on levels of mortality was examined in the antlion Myrmeleon acer Walker. Antlions were kept at densities ranging from 0.4 to 12.8 individuals per 100 cm(2). The distribution of pits was regular or uniform across all densities, but antlions constructed proportionally fewer and smaller pits as density increased. Mortality through cannibalism was very low and only occurred at densities greater than five individuals per 100 cm(2). Antlions in artificially crowded situations frequently relocated their pits and when more space became available, individuals became more dispersed with time. Redistribution of this species results from active avoidance of other antlions and sand throwing associated with pit construction and maintenance, rather than any attempt to optimise prey capture per se.

Further results on the relationship between mu-invariant measures and quasi-stationary distributions for absorbing continuous-time Markov chains

This note considers continuous-time Markov chains whose state space consists of an irreducible class, C, and an absorbing state which is accessible from C. The purpose is to provide results on mu-invariant and mu-subinvariant measures where absorption occurs with probability less than one. In particular, the well-known premise that the mu-invariant measure, m, for the transition rates be finite is replaced by the more natural premise that m be finite with respect to the absorption probabilities. The relationship between mu-invariant measures and quasi-stationary distributions is discussed. (C) 2000 Elsevier Science Ltd. All rights reserved.

Mathematical models in percutaneous absorption

A number of mathematical models have been used to describe percutaneous absorption kinetics. In general, most of these models have used either diffusion-based or compartmental equations. The object of any mathematical model is to a) be able to represent the processes associated with absorption accurately, b) be able to describe/summarize experimental data with parametric equations or moments, and c) predict kinetics under varying conditions. However, in describing the processes involved, some developed models often suffer from being of too complex a form to be practically useful. In this chapter, we attempt to approach the issue of mathematical modeling in percutaneous absorption from four perspectives. These are to a) describe simple practical models, b) provide an overview of the more complex models, c) summarize some of the more important/useful models used to date, and d) examine sonic practical applications of the models. The range of processes involved in percutaneous absorption and considered in developing the mathematical models in this chapter is shown in Fig. 1. We initially address in vitro skin diffusion models and consider a) constant donor concentration and receptor conditions, b) the corresponding flux, donor, skin, and receptor amount-time profiles for solutions, and c) amount- and flux-time profiles when the donor phase is removed. More complex issues, such as finite-volume donor phase, finite-volume receptor phase, the presence of an efflux. rate constant at the membrane-receptor interphase, and two-layer diffusion, are then considered. We then look at specific models and issues concerned with a) release from topical products, b) use of compartmental models as alternatives to diffusion models, c) concentration-dependent absorption, d) modeling of skin metabolism, e) role of solute-skin-vehicle interactions, f) effects of vehicle loss, a) shunt transport, and h) in vivo diffusion, compartmental, physiological, and deconvolution models. We conclude by examining topics such as a) deep tissue penetration, b) pharmacodynamics, c) iontophoresis, d) sonophoresis, and e) pitfalls in modeling.

Developing qualitative career assessment processes

Assessment has been integral to career counseling since the early 1900s. During that time, the greatest amount of attention was focused on quantitative assessment. Thus, there is still very little to guide the development and conduct of qualitative assessment in career counseling. The authors present an overview of qualitative career assessment and its theoretical underpinnings and propose suggestions that could guide the development of qualitative career assessment instruments.

Refining the perfusion-diffusion mismatch hypothesis

Background and Purpose-The Echoplanar Imaging Thrombolysis Evaluation Trial ( EPITHET) tests the hypothesis that perfusion-weighted imaging (PWI)-diffusion-weighted imaging (DWI) mismatch predicts the response to thrombolysis. There is no accepted standardized definition of PWI-DWI mismatch. We compared common mismatch definitions in the initial 40 EPITHET patients. Methods-Raw perfusion images were used to generate maps of time to peak (TTP), mean transit time (MTT), time to peak of the impulse response (Tmax) and first moment transit time (FMT). DWI, apparent diffusion coefficient ( ADC), and PWI volumes were measured with planimetric and thresholding techniques. Correlations between mismatch volume (PWIvol-DWIvol) and DWI expansion (T2(Day) (90-vol)-DWIAcute-vol) were also assessed. Results-Mean age was 68 +/- 11, time to MRI 4.5 +/- 0.7 hours, and median National Institutes of Health Stroke Scale (NIHSS) score 11 (range 4 to 23). Tmax and MTT hypoperfusion volumes were significantly lower than those calculated with TTP and FMT maps (P < 0.001). Mismatch >= 20% was observed in 89% (Tmax) to 92% (TTP/FMT/MTT) of patients. Application of a +4s ( relative to the contralateral hemisphere) PWI threshold reduced the frequency of positive mismatch volumes (TTP 73%/FMT 68%/Tmax 54%/MTT 43%). Mismatch was not significantly different when assessed with ADC maps. Mismatch volume, calculated with all parameters and thresholds, was not significantly correlated with DWI expansion. In contrast, reperfusion was correlated inversely with infarct growth (R= -0.51; P = 0.009). Conclusions-Deconvolution and application of PWI thresholds provide more conservative estimates of tissue at risk and decrease the frequency of mismatch accordingly. The precise definition may not be critical; however, because reperfusion alters tissue fate irrespective of mismatch.

The selection of intended actions and the observation of others' actions: A time-resolved fMRI study

Whenever we plan, imagine, or observe an action, the motor systems that would be involved in preparing and executing that action are similarly engaged. The way in which such common motor activation is formed, however, is likely to differ depending on whether it arises from our own intentional selection of action or from the observation of another's action. In this study, we use time-resolved event-related functional MRI to tease apart neural processes specifically related to the processing of observed actions, the selection of our own intended actions, the preparation for movement, and motor response execution. Participants observed a finger gesture movement or a cue indicating they should select their own finger gesture to perform, followed by a 5-s delay period; participants then performed the observed or self-selected action. During the preparation and readiness for action, prior to initiation, we found activation in a common network of higher motor areas, including dorsal and ventral premotor areas and the pre-supplementary motor area (pre-SMA); the more caudal SMA showed greater activation during movement execution. Importantly, the route to this common motor activation differed depending on whether participants freely selected the actions to perform or whether they observed the actions performed by another person. Observation of action specifically involved activation of inferior and superior parietal regions, reflecting involvement of the dorsal visual pathway in visuomotor processing required for planning the action. In contrast, the selection of action specifically involved the dorsal lateral prefrontal and anterior cingulate cortex, reflecting the role of these prefrontal areas in attentional selection and guiding the selection of responses. (c) 2005 Elsevier Inc. All rights reserved.

Nmr imaging of the diffusion of water into poly(tetrahydrofurfuryl methacrylate-co-hydroxyethyl methacrylate)

0Nuclear magnetic resonance (n.m.r.) imaging was used to study the ingress of water into poly(tetrahydrofurfuryl methacrylate-co-hydroxyethyl methacrylate). The study offers strong evidence that the diffusion is Fickian in nature. The diffusion coefficient, D, obtained by fitting the underlying diffusion profile, attainable from the images, according to the equation for Fickian diffusion, is 1.5 x 10(-11) m(2) s(-1), which is in good correlation with the value of 2.1 x 10(-11) m(2) s(-1), obtained from mass uptake measurements. Additionally, from the T-2-weighted images, Superimposed features observed in addition to the underlying Fickian diffusion profiles were shown to have a longer spin-spin relaxation time, T-2. This Suggests the presence of two types of water within the polymer matrix; a less mobile phase of absorbed water that is interacting strongly with the polymer matrix and a more mobile phase of absorbed water residing within the cracks observed in the environmental scanning electron micrograph. (C) 1997 Elsevier Science Ltd.

Dynamic processes in the contingent valuation of an endangered mammal species

Reports experimental results involving 204 members of the public who were asked their willingness to pay for the conservation of the mahogany glider Petaurus gracilis on three occasions: prior to information being provided to them about the glider and other wildlife species; after such information was provided, and after participants had an opportunity to see live specimens of this endangered species. Variations in the mean willingness to pay are analysed. Concerns arise about whether information provision and experience reveal ‘true’ contingent valuations of public goods and about the choice of the relevant contingent valuation measure.

Evaluation of the buccal vestibule-palatal diffusion of 4% articaine hydrochloride in impacted maxillary third molar extractions

Aims: The aim of this study was to evaluate the vestibular-palatal diffusion of 4% articaine with epinephrine 1: 100,000 and 1: 200,000, in impacted maxillary third molar extractions, without palatal injection. Materials and Method: Two hundred teeth were selected from patients age 15 to 46. Patients were divided into 4 groups: 1A, were anesthetized with 4% articaine 1: 100,000 and the surgery was initiated 5 minutes following anesthesia. 1B, used 4% articaine 1: 100,000 but the surgery was started 10 minutes after anesthesia. 2A, used 4% articaine 1: 200,000 the surgery was started 5 minutes after. 2B, used 4% articaine 1: 200,000 but 10 minutes was allowed for anesthetic diffusion before the initiation of in groups (50 extractions each) only buccal vestibule anesthesia was initially administered (i.e. no palatal injections were used). Results: The rate of sufficient vestibule-palatal diffusion, as determined by the lack of necessity of supplemental palatal anesthesia, was: 1A(84%), 1B(98%), 2A(78%), 2B(82%). Chi-square (X2) and residual analyses showed that a higher vestibule-palatal diffusion was obtained using 4% articaine 1: 100,000 with a period of 10 minutes (p<0.05). Conclusions: Most of the extractions could be performed only with vestibule anesthesia. However, vasoconstrictor concentration and the time interval between administration of the anesthetic and initiation of surgery did influence buccal vestibule-palatal diffusion of 4% articaine in the extraction models used.

Diffusion modeling of percutaneous absorption kinetics: 2. Finite vehicle volume and solvent deposited solids

The diffusion model for percutaneous absorption is developed for the specific case of delivery to the skin being limited by the application of a finite amount of solute. Two cases are considered; in the first, there is an application of a finite donor (vehicle) volume, and in the second, there are solvent-deposited solids and a thin vehicle with a high partition coefficient. In both cases, the potential effect of an interfacial resistance at the stratum corneum surface is also considered. As in the previous paper, which was concerned with the application of a constant donor concentration, clearance limitations due to the viable eqidermis, the in vitro sampling rate, or perfusion rate in vivo are included. Numerical inversion of the Laplace domain solutions was used for simulations of solute flux and cumulative amount absorbed and to model specific examples of percutaneous absorption of solvent-deposited solids. It was concluded that numerical inversions of the Laplace domain solutions for a diffusion model of the percutaneous absorption, using standard scientific software (such as SCIENTIST, MicroMath Scientific software) on modern personal computers, is a practical alternative to computation of infinite series solutions. Limits of the Laplace domain solutions were used to define the moments of the flux-time profiles for finite donor volumes and the slope of the terminal log flux-time profile. The mean transit time could be related to the diffusion time through stratum corneum, viable epidermal, and donor diffusion layer resistances and clearance from the receptor phase. Approximate expressions for the time to reach maximum flux (peak time) and maximum flux were also derived. The model was then validated using reported amount-time and flux-time profiles for finite doses applied to the skin. It was concluded that for very small donor phase volume or for very large stratum corneum-vehicle partitioning coefficients (e.g., for solvent deposited solids), the flux and amount of solute absorbed are affected by receptor conditions to a lesser extent than is obvious for a constant donor constant donor concentrations. (C) 2001 Wiley-Liss, Inc. and the American Pharmaceutical Association J Pharm Sci 90:504-520, 2001.

A dynamic model with on-line identification for rotary sugar drying processes

A dynamic modelling methodology, which combines on-line variable estimation and parameter identification with physical laws to form an adaptive model for rotary sugar drying processes, is developed in this paper. In contrast to the conventional rate-based models using empirical transfer coefficients, the heat and mass transfer rates are estimated by using on-line measurements in the new model. Furthermore, a set of improved sectional solid transport equations with localized parameters is developed in this work to reidentified on-line using measurement data, the model is able to closely track the dynamic behaviour of rotary drying processes within a broad range of operational conditions. This adaptive model is validated against experimental data obtained from a pilot-scale rotary sugar dryer. The proposed modelling methodology can be easily incorporated into nonlinear model based control schemes to form a unified modelling and control framework.place the global correlation for the computation of solid retention time. Since a number of key model variables and parameters are identified on-line using measurement data, the model is able to closely track the dynamic behaviour of rotary drying processes within a broad range of operational conditions. This adaptive model is validated against experimental data obtained from a pilot-scale rotary sugar dryer. The proposed modelling methodology can be easily incorporated into nonlinear model based control schemes to form a unified modelling and control framework.

Effect of probe stimulus intensity on the dissociation between autonomic orienting and secondary probe reaction time

Information processing accounts propose that autonomic orienting reflects the amount of resources allocated to process a stimulus. However, secondary task reaction time (RT), a supposed measure of processing resources, has shown a dissociation from autonomic orienting. The present study tested the hypothesis that secondary task RT reflects a serial processing mechanism. Participants (N = 24) were presented with circle and ellipse shapes and asked to count the number of longer-than-usual presentations of one shape (task-relevant) and to ignore presentations of a second shape (task-irrelevant). Concurrent with the counting task, participants performed a secondary RT task to an auditory probe presented at either a high or low intensity and at two different probe positions following shape onset (50 and 300 ms). Electrodermal orienting was larger during task-relevant shapes than during task-irrelevant shapes, but secondary task RT to the high-intensity probe was slower during the latter. In addition, an underadditive interaction between probe stimulus intensity and probe position was found in secondary RT. The findings are consistent with a serial processing model of secondary RT and suggest that the notion of processing stages should be incorporated into current information-processing models of autonomic orienting.

Analytical validation for a series of marker compounds used to assess renal drug elimination processes

Renal drug elimination is determined by glomerular filtration, tubular secretion, and tubular reabsorption. Changes in the integrity of these processes influence renal drug clearance, and these changes may not be detected by conventional measures of renal function such as creatinine clearance. The aim of the current study was to examine the analytic issues needed to develop a cocktail of marker drugs (fluconazole, rac-pindolol, para-aminohippuric acid, sinistrin) to measure simultaneously the mechanisms contributing to renal clearance. High-performance liquid chromatographic methods of analysis for fluconazole, pindolol, para-aminohippuric acid, and creatinine and an enzymatic assay for sinistrin were developed or modified and then validated to allow determination of each of the compounds in both plasma and urine in the presence of all other marker drugs. A pilot clinical study in one volunteer was conducted to ensure that the assays were suitable for quantitating all the marker drugs to the sensitivity and specificity needed to allow accurate determination of individual renal clearances. The performance of all assays (plasma and urine) complied with published validation criteria. All standard curves displayed linearity over the concentration ranges required, with coefficients of correlation greater than 0.99. The precision of the interday and intraday variabilities of quality controls for each marker in plasma and urine were all less than 11.9% for each marker. Recoveries of markers (and internal standards) in plasma and urine were all at least 90%. All markers investigated were shown to be stable when plasma or urine was frozen and thawed. For all the assays developed, there were no interferences from other markers or endogenous substances. In a pilot clinical study, concentrations of all markers could be accurately and reproducibly determined for a sufficient duration of time after administration to calculate accurate renal clearance for each marker. This article presents details of the analytic techniques developed for measuring concentrations of marker drugs for different renal elimination processes administered as a single dose to define the processes contributing to renal drug elimination.

MRI based diffusion and perfusion predictive model to estimate stroke evolution

In this study we present a novel automated strategy for predicting infarct evolution, based on MR diffusion and perfusion images acquired in the acute stage of stroke. The validity of this methodology was tested on novel patient data including data acquired from an independent stroke clinic. Regions-of-interest (ROIs) defining the initial diffusion lesion and tissue with abnormal hemodynamic function as defined by the mean transit time (MTT) abnormality were automatically extracted from DWI/PI maps. Quantitative measures of cerebral blood flow (CBF) and volume (CBV) along with ratio measures defined relative to the contralateral hemisphere (r(a)CBF and r(a)CBV) were calculated for the MTT ROIs. A parametric normal classifier algorithm incorporating these measures was used to predict infarct growth. The mean r(a)CBF and r(a)CBV values for eventually infarcted MTT tissue were 0.70 +/-0.19 and 1.20 +/-0.36. For recovered tissue the mean values were 0.99 +/-0.25 and 1.87 +/-0.71, respectively. There was a significant difference between these two regions for both measures (P