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Results for “Stochastic Processes”

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PubMed2001

A stochastic model for CD8(+)T cell dynamics in human immunosenescence: implications for survival and longevity.

We propose here a stochastic model for the CD 8(+)T lymphocyte dynamics on the long time-scale of the human lifespan. Our purpose has been to test the hypothesis, recently proposed on the basis of our experimental data (Fagnoni et al., 2000), that the depletion of virgin CD8(+)T lymphocytes can be considered a reliable biomarker related to the risk of death. This hypothesis is embedded in a more general theory of immunosenescence according to which the accumulation of antigen experienced (AE) T cells and the concomitant exhaustion of antigen non-experienced (ANE) T cells with age, mostly due to the chronic lifelong exposure to antigens, is a major characteristic of the remodeling of the human immune system with age. In our model we considered a deterministic balance of ANE and AE T cell concentrations plus a stochastic forcing, which describes the chronic antigenic stress fluctuations, assuming a mean genetically determined capability of individuals to respond to antigens. The major results of our model is the validation of the above-mentioned hypothesis, since the model is capable of fitting the experimental data concerning the changes of ANE T cell concentration over age, and at the same time to reproduce survival curves similar to the demographic ones. Furthermore, the stochastic process results in being responsible for the peculiar shape of the survival curves.

Aging↗
PubMed2006

Dynamic path analysis-a new approach to analyzing time-dependent covariates.

In this article we introduce a general approach to dynamic path analysis. This is an extension of classical path analysis to the situation where variables may be time-dependent and where the outcome of main interest is a stochastic process. In particular we will focus on the survival and event history analysis setting where the main outcome is a counting process. Our approach will be especially fruitful for analyzing event history data with internal time-dependent covariates, where an ordinary regression analysis may fail. The approach enables us to describe how the effect of a fixed covariate partly is working directly and partly indirectly through internal time-dependent covariates. For the sequence of times of event, we define a sequence of path analysis models. At each time of an event, ordinary linear regression is used to estimate the relation between the covariates, while the additive hazard model is used for the regression of the counting process on the covariates. The methodology is illustrated using data from a randomized trial on survival for patients with liver cirrhosis.

Aged↗
PubMed2006

The distribution of eggs per host in a herbivorous insect--intersection of oviposition, dispersal and population dynamics.

1. The dynamics of parasitic organisms depend critically upon the frequency distribution of parasite individuals per host. However, the processes giving rise to this frequency distribution have rarely been modelled and tested for organisms with complex host selection behaviour. 2. In this study Microrhopala vittata, a chrysomelid beetle, was used to investigate how oviposition behaviour, movement and density of host plants interact in shaping the frequency distribution of egg clusters per host in the field. 3. Enclosures were stocked with two different host species and different beetle densities and various stochastic process models were fitted to egg cluster count data obtained from these enclosures. The different models were derived considering different scenarios, in particular whether or not plant density limits oviposition rate, whether or not ovipositing females actively seek out the most attractive plant within their perception radius and whether a female's oviposition rate is determined by plant intrinsic factors, the plant's egg cluster load or the surrounding beetle density. 4. The model parameters fitted to cage data were used to describe the frequency distribution of egg cluster counts obtained in a release experiment in the field. A total of 220 beetle pairs were released at five locations in a field where this beetle was not observed previously. Each release point was at a border between the two host species. 5. One model predicted for the preferred host species the egg cluster count frequencies in the field from parameters estimated in the cages. This model assumed that egg clusters present on a plant increased subsequent oviposition on this plant. All other models could not describe the distribution of egg cluster counts for either of the two host species. 6. The results suggest that females seek out attractive hosts actively and the attractiveness of a plant increases with its egg cluster load. This behaviour creates a frequency distribution of egg clusters per host that depends only on beetle density but not on plant density. This conclusion has important implications for modelling insect-plant interactions.

Animals↗
PubMed1989

Quantifying uncertainty in medical decisions.

Effective handling of uncertainty is one of the central problems in medical decision making. The sources and effects of uncertainty in medical decision making are examined and some new quantitative approaches for solving the associated problems are outlined. To handle uncertainty in the branching probabilities and node utilities for probability trees representing alternative treatment strategies, a public domain software package that can be used for the construction, analysis and comparison of probability trees with random parameters was developed. To facilitate specification of the random variables that arise in medical decision making problems, public domain software packages for both data-driven and subjective estimation of probability densities from the Johnson translation system of distributions have also been developed. For the analysis of complex problems that cannot be adequately represented by probability trees or by simple stochastic processes such as Markov chains, network simulation approaches that are oriented toward the sequence of activities seen by individual patients in the course of treatment are described.

Computer Simulation↗
PubMed2003

SNAREs and control of synaptic release probabilities.

Since quantal release was first described, it has been clear that release of neurotransmitters is a stochastic process. Modulation of neurotransmitter release probability by regulatory factors likely affects the transfer of information within the nervous system. Although many rules governing release probabilities at the synapse have been discovered, their molecular basis is still under investigation. Here we analyze stimulus-evoked probabilistic assembly of the SNARE fusion machinery and show that a simple SNARE-based mechanism can account quantitatively for the classical binomial behavior of stochastic neurotransmitter release. Our analysis highlights for the first time how the fusion machinery, which is directly responsible for neurotransmitter release, may also contribute to the rich variety of synaptic responses.

Animals↗
PubMed2000

An improved technique for the extraction of stochastic parameters from stabilograms.

An improved characterization of the dynamics of postural sway can provide a better understanding about the functional organization of the postural control system as well as a more robust tool for postural pattern recognition. To this aim, a novel parameterization was applied to the stabilogram diffusion analysis formerly proposed by Collins and De Luca [Collins JJ, De Luca CJ. Open-loop and closed-loop control of posture: a random-walk analysis of center-of-pressure trajectories. Exp Brain Res 1993;95:308-18] that considered the act of maintaining posture as a stochastic process. The main purpose of the present technique was to overcome some drawbacks of the model presented by Collins and De Luca that may restrain its potential application in clinical practice. The approach uses a unique non-linear model to describe the center of pressure (COP) dynamics that reduces the number of parameters and decreases their intra-subject variability; consequently, fewer trials are required to perform reliable estimates of stochastic parameters and this is of particular importance for subjects that cannot afford many repeated measurements because of age or pathology. Four new statistical mechanics parameters (NSMP) were computed on the log-log stabilogram diffusion plots and their estimates were compared in terms of reliability and sensitivity to the visual conditions with: (1) a minimal set of four summary statistic scores (SSS); and (2) the six statistical mechanics parameters (SMP) proposed by Collins and De Luca. All four NSMP showed at least a fair-to-good reliability (intraclass correlation coefficient, ICC>0.49) while SMP (ICC>0.20) showed some poor reliability. A better overall reliability was also observed with respect to SSS. Moreover, only NSMP had a similar score for eyes open and eyes closed conditions. Three out of four NSMP were also significantly sensitive to eyes open or closed conditions (P<0.001) while only three out of six SMP were sensitive to operating conditions (P<0.01).

Humans↗
PubMed1989

A balance between self-renewal and commitment in the murine erythroleukemia cells with the transferred c-myc gene; an in vitro stochastic model.

When murine erythroleukemia (MEL) cells, having the transferred rat c-myc gene under the control of human metallothionein II gene promoter, are induced to differentiate with dimethyl sulfoxide (DMSO), the level of differentiation is dependent on the c-myc levels which are modulated by the Zn++ ion. The clonal transformant cell line (38-2) can continuously grow in the presence of both DMSO and Zn++ ion. The proportion of differentiated cells in a population of the continuous culture is strongly affected by the concentration of Zn++ ions. These results suggested that a balance between self-renewal and commitment to differentiation of MEL cells is determined by the c-myc level, and that this cell line may be suitable for studying the stochastic process of growth and differentiation of hemopoietic stem cells.

Animals↗
PubMed2001

Stochastic origins of the long-range correlations of ionic current fluctuations in membrane channels.

An explicit stochastic representation of a stationary ionic current signal recorded from a single channel of a biological membrane is presented. In the framework of the proposed approach we show how the dichotomous time structure of the signal leads to the non-Markovian character of the channel current. The rescaled range Hurst and detrended fluctuation analyses confirm the theoretical result. To investigate the ionic current fluctuations we introduce the Orey index as a statistical method providing additional information on the properties of stochastic processes. In order to reveal any differences between the experimental and reconstructed signals, we apply also the statistical tests to the model-based simulations of the channel action.

Cell Membrane↗
PubMed1994

Effects of frailty in survival analysis.

Unobserved individual heterogeneity, also called frailty, is a major concern in the application of survival analysis. Hazard rates do not give direct information on the change over time in the individual risk, but are strongly influenced by selection effects operating in the population. The individuals surviving up to a certain time will on average be less frail than the original population. Models are reviewed that account for this phenomenon, and some medical examples are discussed. It is emphasized that the frailty phenomenon may be modelled in many different ways, and a stochastic process approach is discussed as an alternative to the common proportional frailty model.

Acquired Immunodeficiency Syndrome↗
PubMed2006

Major depressive episodes and random mood.

CONTEXT: Mathematical models describing changes in mood in affective disorders may assist in the identification of underlying pathologic and neurobiologic mechanisms and in differentiating between alternative interpretations of psychiatric data. OBJECTIVE: Using time-to-event data from a large epidemiologic survey on recovery from major depression, to model the survival probability, in terms of an underlying process, with parameters which might be recognized and influenced in clinical practice. DESIGN: We present a sequential-phase model for survival analysis, which describes depression as a state with or without an additional incubation phase. Recovery is seen as the transition to a nondepressive state. We show that this sequential-phase model finds a microscopic realization in a dynamic description, the random-mood model, which depicts mood as governed by an Ornstein-Uhlenbeck type of stochastic process, driven by intermittent gaussian noise. RESULTS: For reversible depression (80%), the fractional probability of recovery is remarkably independent of the history of the depression. Analysis with the sequential-phase model suggests single exponential decay in this group, possibly with a short incubation phase. Within the random-mood model, the data for this reversibly depressed cohort are compatible with an intermittent noise pattern of stimuli with average spacing of 4 months and incompatible with nonintermittent noise. CONCLUSIONS: Time-to-event data from psychiatric epidemiologic studies can be conceptualized through modeling as intrasubject processes. The proposed random-mood model reproduces the time-to-event data and explains the incubation phase as an artifact due to the inclusion criterion of 14 days in most current psychiatric diagnostic systems. Depression is found to result more often from pileup of negative stimuli than from single life events. Time sequences, generated using the random-mood model, produce power plots, phase-space trajectories, and pair-correlation sums, similar to recent results for individual patients. This suggests possible clinical relevance along with the model's use as a tool in survival analysis.

Affect↗
PubMed1984

[Nature of the phenotypic variability of somatic cells in culture: unstable phenotypic changes].

It was stated elsewhere ( Glebov , Abramyan , 1983) that the appearance of a number of phenotypic variants detected in somatic cell populations with high frequency should be provided by genetical unstable alterations. The properties of somatic cell variants that reproduce unstably a changable phenotype in the course of cell generations are analysed. These variants: (1) appear accidentally and independently on selectivity agent; (2) as a rule, the frequency of the variant arising does not increase under the action of mutagens; (3) the phenotypic reversion of unstable variants is a stochastic process; (4) such variants are characterized by intraclonal heterogeneity and by the segregation of stable alternative variants. The number of properties of phenotypically unstable variants isolated by one-step selection is similar to those for somatic cell variants isolated in the course of multistep selection. The latter are characterized by phenotypic reversion too. The appearance of unstable phenotypic variants is concluded to be associated with the genetical unstable alterations. It is argued that at least part of above alterations should be induced by the insertion of mobile genetic elements. The features of karyotypical variation in somatic cell population allow to conclude that the karyotype of cultured somatic cells is a genetically unstable attribute. The features mentioned above are: a high frequency of karyotypical alterations which is inherited by the cells with difference in the frequency of arising of karyotypical alteratons . The unstability of karyotype is restricted to the genetic unstability that is seen from non-random karyotypic variation, and interclonal difference in the chromosome stability. The site-specificity of karyotype alterations that proceed with high frequency allow to put forward a hypothesis that the process of mobile genetic element transposition is induced on the early stages of the history of constant cultured cell lines.

Animals↗
PubMed1993

Langevin equation, Fokker-Planck equation and cell migration.

Cell migration can be characterized by two independent variables: the speed, v, and the migration angle, phi. Each variable can be described by a stochastic differential equation--a Langevin equation. The migration behaviour of an ensemble of cells can be predicted due to the stochastic processes involved in the signal transduction/response system of each cell. Distribution functions, correlation functions, etc. are determined by using the corresponding Fokker-Planck equation. The model assumptions are verified by experimental results. The theoretical predictions are mainly compared with the galvanotactic response of human granulocytes. The coefficient characterizing the mean effect of the signal transduction/response system of the cell is experimentally determined to 0.08 mm/V sec (galvanotaxis) or 0.7 mm/sec (chemotaxis) and the characteristic time characterizing stochastic effects in the signal transduction/response system is experimentally determined as 30 sec. The temporal directed response induced by electric field pulses is investigated: the experimental cells react slower but are more sensitive than predicted by theory.

Cell Movement↗
PubMed1993

Patchiness and correlations in DNA sequences.

The highly nonrandom character of genomic DNA can confound attempts at modeling DNA sequence variation by standard stochastic processes (including random walk or fractal models). In particular, the mosaic character of DNA consisting of patches of different composition can fully account for apparent long-range correlations in DNA.

Analysis of Variance↗
PubMed2026

Reconstructing the early spatial spread of pandemic respiratory viruses in the United States.

Understanding the geographic spread of emerging respiratory viruses is critical for pandemic preparedness, yet the early spatiotemporal dynamics of the 2009 H1N1 pandemic influenza and severe acute respiratory syndrome coronavirus 2 in the United States remain unclear. While mobility and genomic data have revealed important aspects of pandemic spatial spread, several key questions remain: Did the two pandemics follow similar spatial transmission routes? How rapidly did they spread across the United States? What role did stochastic processes play in early spatial transmission? To address these questions, we integrated high-resolution disease data with a robust, data-efficient inference framework combining air travel, commuting flows, and pathogen superspreading potentials to reconstruct their spatial spread across US metropolitan areas. The two pandemics exhibited distinct transmission pathways across locations; however, both pandemics established local circulation in most metropolitan areas within weeks, driven by several shared transmission hubs. Early spatial spread was more strongly associated with air travel than with commuting, though stochastic dynamics introduced substantial uncertainty in transmission routes, creating challenges for timely detection and control. Simulations indicate that broad wastewater surveillance coverage beyond top transmission hubs coupled with effective infection control may slow initial spatial expansion. Our findings highlight the rapid, stochastic spread of pandemic respiratory pathogens and the difficulties of early outbreak containment.

Humans↗
PubMed1993

Sequential monitoring of clinical trials: the role of information and Brownian motion.

Sequential monitoring has been a topic of major interest in clinical trials methodology over the past two decades. This paper presents a unified conceptual framework for sequential monitoring that covers a wide variety of monitoring procedures in a wide variety of clinical trial settings. The central elements of this framework consist of a suitable concept of statistical information and a scheme for using this concept as a basis for summarizing the accumulating results of a trial in a standardized form, through a stochastic process that can be shown to approximate classical Brownian motion. The ideas are developed in a simple step-by-step fashion and illustrated by several practical examples.

Biophysical Phenomena↗
PubMed1997

How reliably does a neuron in the visual motion pathway of the fly encode behaviourally relevant information?

How reliably neurons convey information depends on the extent to which their activity is affected by stochastic processes which are omnipresent in the nervous system. The functional consequences of neuronal noise can only be assessed if the latter is related to the response components that are induced in a normal behavioural situation. In the present study the reliability of neural coding was investigated for an identified neuron in the pathway processing visual motion information of the fly (Lucilia cuprina). The stimuli used to investigate the neuronal performance were not exclusively defined by the experimenter. Instead, they were generated by the fly itself, i.e. by its own actions and reactions in a behavioural closed-loop experiment, and subsequently replayed to the animal while the activity of an identified motion-sensitive neuron was recorded. Although the time course of the neuronal responses is time-locked to the stimulus, individual response traces differ slightly from each other due to stochastic fluctuations in the timing and number of action potentials. Individual responses thus consist of a stimulus-induced and a stochastic response component. The stimulus-induced response component can be recovered most reliably from noisy neuronal signals if these are smoothed by intermediate-sized time windows (40-100 ms). At this time scale the best compromise is achieved between smoothing out the noise and maintaining the temporal resolution of the stimulus-induced response component. Consequently, in the visual motion pathway of the fly, behaviourally relevant motion stimuli can be resolved best at a time scale where the timing of individual spikes does not matter.

Animals↗
PubMed2000

A stochastic-covariate failure model with an application to case-control analysis.

A stochastic process X(t) is periodically stationary (and ergodic) if, for every k> or =1 and every (t(1),ellipsis,t(k)) in R(k), the sequence of random vectors (X(t(1)+n),ellipsis,X(t(k)+n))n=0,+1, ellipsis, is stationary (and ergodic). For such an ergodic process, let T be a positive random variable defined on the sample space of the process, representing a time of failure. The local failure-rate function is assumed to be of the form up(x),-infinity 0 is a small number, tending to 0; and, for each u,T=T(u) is the corresponding failure-time. It is shown that X(T(u)) and uT(u) have, for u-->0, a limiting joint distribution and are, in fact, asymptotically independent. The marginal distributions are explicitly given. Let Y be a random variable whose distribution is the limit of that of X(T(u)). Under the hypothesis that p(x) is unknown or of known functional form but with unknown parameters, it is shown how p(x) can be estimated on the basis of independent copies of the random variable Y. The results are applied to the analysis of a case-control study featuring a 'marker' process X(t) and an 'event-time' T. The event in the study is considered to be particularly rare, and this is reflected in the assumption u-->0. The control-distribution is identified with the average marginal distribution of the (periodically stationary) marker process X(t), and the case-distribution is identified with that of Y. The particular application is a biomedical trial to determine the risk of stroke in terms of the level of an anticoagulant in the blood of the patient.

Anticoagulants↗