First-passage times for non-Markovian processes

First-passage time statistics for non-Markovian processes have heretofore only been developed for processes driven by dichotomous fluctuations that are themselves Markov. Herein we develop a new method applicable to Markov and non-Markovian dichotomous fluctuations and calculate analytic mean first-passage times for particular examples.

Protein turnover, ureagenesis and gluconeogenesis.

The major processes discussed below are protein turnover (degradation and synthesis), degradation into urea, or conversion into glucose (gluconeogenesis, Figure 1). Daily protein turnover is a dynamic process characterized by a double flux of amino acids: the amino acids released by endogenous (body) protein breakdown can be reutilized and reconverted to protein synthesis, with very little loss. Daily rates of protein turnover in humans (300 to 400 g per day) are largely in excess of the level of protein intake (50 to 80 g per day). A fast growing rate, as in premature babies or in children recovering from malnutrition, leads to a high protein turnover rate and a high protein and energy requirement. Protein metabolism (synthesis and breakdown) is an energy-requiring process, dependent upon endogenous ATP supply. The contribution made by whole-body protein turnover to the resting metabolic rate is important: it represents about 20 % in adults and more in growing children. Metabolism of proteins cannot be disconnected from that of energy since energy balance influences net protein utilization, and since protein intake has an important effect on postprandial thermogenesis - more important than that of fats or carbohydrates. The metabolic need for amino acids is essentially to maintain stores of endogenous tissue proteins within an appropriate range, allowing protein homeostasis to be maintained. Thanks to a dynamic, free amino acid pool, this demand for amino acids can be continuously supplied. The size of the free amino acid pool remains limited and is regulated within narrow limits. The supply of amino acids to cover physiological needs can be derived from 3 sources: 1. Exogenous proteins that release amino acids after digestion and absorption 2. Tissue protein breakdown during protein turnover 3. De novo synthesis, including amino acids (as well as ammonia) derived from the process of urea salvage, following hydrolysis and microflora metabolism in the hind gut. When protein intake surpasses the physiological needs of amino acids, the excess amino acids are disposed of by three major processes: 1. Increased oxidation, with terminal end products such as CO₂ and ammonia 2. Enhanced ureagenesis i. e. synthesis of urea linked to protein oxidation eliminates the nitrogen radical 3. Gluconeogenesis, i. e. de novo synthesis of glucose. Most of the amino groups of the excess amino acids are converted into urea through the urea cycle, whereas their carbon skeletons are transformed into other intermediates, mostly glucose. This is one of the mechanisms, essential for life, developed by the body to maintain blood glucose within a narrow range, (i. e. glucose homeostasis). It includes the process of gluconeogenesis, i. e. de novo synthesis of glucose from non-glycogenic precursors; in particular certain specific amino acids (for example, alanine), as well as glycerol (derived from fat breakdown) and lactate (derived from muscles). The gluconeogenetic pathway progressively takes over when the supply of glucose from exogenous or endogenous sources (glycogenolysis) becomes insufficient. This process becomes vital during periods of metabolic stress, such as starvation.

Antigen presentation in the lung: dendritic cells and macrophages.

Antigen presentation is a required prime event before T-cell activation can occur. Cells which constitutively express major histocompatibility antigen class I or II are responsible for presenting antigens. These are essentially alveolar macrophages (AM) residing mostly in the air spaces, and dendritic cells (DC), which create a tight surveillance network just below the epithelial cells of the airways and in the loose connective tissue around the vessels or in the pleura. AM are poor antigen presenting cells compared to DC. AM when encountering foreign particles or organisms may, however, influence the degree of activity or maturation of neighbouring DC, by releasing cytokines. Thus, we will describe how the innate immune processes may influence specific immunity and perhaps Th1 and Th2 differentiation. Following the description of the differences in phenotype and functions of AM and DC, we will provide data showing that in some pathological conditions, such as sarcoidosis, AM can acquire some specificities of DC.

First-passage times for non-Markovian processes: Correlated impacts on a free process

We develop a method to obtain first-passage-time statistics for non-Markovian processes driven by dichotomous fluctuations. The fluctuations themselves need not be Markovian. We calculate analytic first-passage-time distributions and mean first-passage times for exponential, rectangular, and long-tail temporal distributions of the fluctuations.

First-passage times for non-Markovian processes: Correlated impacts on bound processes

Our previously developed stochastic trajectory analysis technique has been applied to the calculation of first-passage time statistics of bound processes. Explicit results are obtained for linearly bound processes driven by dichotomous fluctuations having exponential and rectangular temporal distributions.

First-passage times for non-Markovian processes: Shot noise

The stochastic-trajectory-analysis technique is applied to the calculation of the mean¿first-passage-time statistics for processes driven by external shot noise. Explicit analytical expressions are obtained for free and bound processes.

First-passage times for non-Markovian processes: Multivalued noise

A new method for the calculation of first-passage times for non-Markovian processes is presented. In addition to the general formalism, some familiar examples are worked out in detail.

Long-range-interactions induced ordered structures in deposition processes

We present a new model of sequential adsorption in which the adsorbing particles experience dipolar interactions. We show that in the presence of these long-range interactions, highly ordered structures in the adsorbed layer may be induced at low temperatures. The new phenomenology is manifest through significant variations of the pair correlation function and the jamming limit, with respect to the case of noninteracting particles. Our study could be relevant in understanding the adsorption of magnetic colloidal particles in the presence of a magnetic field.

MORM--a Petri net based model for assessing OH&S risks in industrial processes: modeling qualitative aspects.

Because of the increase in workplace automation and the diversification of industrial processes, workplaces have become more and more complex. The classical approaches used to address workplace hazard concerns, such as checklists or sequence models, are, therefore, of limited use in such complex systems. Moreover, because of the multifaceted nature of workplaces, the use of single-oriented methods, such as AEA (man oriented), FMEA (system oriented), or HAZOP (process oriented), is not satisfactory. The use of a dynamic modeling approach in order to allow multiple-oriented analyses may constitute an alternative to overcome this limitation. The qualitative modeling aspects of the MORM (man-machine occupational risk modeling) model are discussed in this article. The model, realized on an object-oriented Petri net tool (CO-OPN), has been developed to simulate and analyze industrial processes in an OH&S perspective. The industrial process is modeled as a set of interconnected subnets (state spaces), which describe its constitutive machines. Process-related factors are introduced, in an explicit way, through machine interconnections and flow properties. While man-machine interactions are modeled as triggering events for the state spaces of the machines, the CREAM cognitive behavior model is used in order to establish the relevant triggering events. In the CO-OPN formalism, the model is expressed as a set of interconnected CO-OPN objects defined over data types expressing the measure attached to the flow of entities transiting through the machines. Constraints on the measures assigned to these entities are used to determine the state changes in each machine. Interconnecting machines implies the composition of such flow and consequently the interconnection of the measure constraints. This is reflected by the construction of constraint enrichment hierarchies, which can be used for simulation and analysis optimization in a clear mathematical framework. The use of Petri nets to perform multiple-oriented analysis opens perspectives in the field of industrial risk management. It may significantly reduce the duration of the assessment process. But, most of all, it opens perspectives in the field of risk comparisons and integrated risk management. Moreover, because of the generic nature of the model and tool used, the same concepts and patterns may be used to model a wide range of systems and application fields.

Exact solution to the mean exit time problem for free inertial processes driven by Gaussian white noise

We obtain the exact analytical expression, up to a quadrature, for the mean exit time, T(x,v), of a free inertial process driven by Gaussian white noise from a region (0,L) in space. We obtain a completely explicit expression for T(x,0) and discuss the dependence of T(x,v) as a function of the size L of the region. We develop a new method that may be used to solve other exit time problems.

First-passage-time noninteger moments for some diffusion and dichotomous processes

We calculate noninteger moments ¿tq¿ of first passage time to trapping, at both ends of an interval (0,L), for some diffusion and dichotomous processes. We find the critical behavior of ¿tq¿, as a function of q, for free processes. We also show that the addition of a potential can destroy criticality.

Fractal dimension for Gaussian colored processes

The exact analytical expression for the Hausdorff dimension of free processes driven by Gaussian noise in n-dimensional space is obtained. The fractal dimension solely depends on the time behavior of the arbitrary correlation function of the noise, ranging from DX=1 for Orstein-Uhlenbeck input noise to any real number greater than 1 for fractional Brownian motions.

Second-order processes driven by dichotomous noise

We study free second-order processes driven by dichotomous noise. We obtain an exact differential equation for the marginal density p(x,t) of the position. It is also found that both the velocity ¿(t) and the position X(t) are Gaussian random variables for large t.