Optimized combinatorial clustering for stochastic processes

As a new data processing era like Big Data, Cloud Computing, and Internet of Things approaches, the amount of data being collected in databases far exceeds the ability to reduce and analyze these data without the use of automated analysis techniques, data mining. As the importance of data mining has grown, one of the critical issues to emerge is how to scale data mining techniques to larger and complex databases so that it is particularly imperative for computationally intensive data mining tasks such as identifying natural clusters of instances. In this paper, we suggest an optimized combinatorial clustering algorithm for noisy performance which is essential for large data with random sampling. The algorithm outperforms conventional approaches through various numerical and qualitative thresholds like mean and standard deviation of accuracy and computation speed.     

Partially observed branching processes for stochastic epidemics

At the offset of a (stochastic) epidemic, it is of importance to have a mathematical model that will assist in the making of an informed judgement on whether the epidemic will explode, or will be minor and die out. In this paper, we consider probabilistic inferences related to the event of extinction of a discrete time branching process when this cannot be directly observed. Instead, we are able to observe only a random “trace” of the process, which not only trails the latter, but also directly affects it (in terms of interventions). A simple model is proposed that provides tractability, preserves a marginal branching property, and gives reasonable closed form expressions. Part of this work was done while the author was an academic visitor at the Department of Statistics, University of Oxford.     

Modeling and analysis of stochastic invasion processes

In this paper we derive spatially explicit equations to describe a stochastic invasion process. Parents are assumed to produce a random number of offspring which then disperse according to a spatial redistribution kernel. Equations for population moments, such as expected density and covariance averaged over an ensemble of identical stochastic processes, take the form of deterministic integro-difference equations. These equations describe the spatial spread of population moments as the invasion progresses. We use the second order moments to analyse two basic properties of the invasion. The first property is permanence of form in the correlation structure of the wave. Analysis of the asymptotic form of the invasion wave shows that either (i) the covariance in the leading edge of the wave of invasion asymptotically achieves a permanence of form with a characteristic structure described by an unchanging spatial correlation function, or (ii) the leading edge of the wave has no asymptotic permanence of form with the length scales of spatial correlations continually increasing over time. Which of these two outcomes pertains is governed by a single statistic, φ which depends upon the shape of the dispersal kernel and the net reproductive number. The second property of the invasion is its patchy structure. Patchiness, defined in terms of spatial correlations on separate short (within patch) and long (between patch) spatial scales, is linked to the dispersal kernel. Analysis shows how a leptokurtic dispersal kernel gives rise to patchiness in spread of a population. Received: 11 August 1997 / Revised version: 22 September 1998 / Published online: 4 October 2000     

The propagation of uncertainty in human mortality processes operating in stochastic environments

This paper presents a model describing how the uncertainty due to influential exogenous processes combines with stochasticity intrinsic to physiological aging processes and propagates through time to generate uncertainty about the future physiological state of the population. Variance expressions are derived for (a) the future values of the physiological variables under the assumption that external factors evolve under a linear stochastic diffusion process, and (b) the cohort survival functions and cohort life expectancies which reflect the uncertainty in the future values of the physiological variables. The model implies that a major component of uncertainty in forecasts of the physiological characteristics of a closed cohort is due to differential rates of survival associated with different realizations of the external process. This suggests that the limits to forecasting may be different in physiological systems subject to systematic mortality than in physical systems such as weather where the concepts of closed cohorts and of mortality selection have no simple analog.     

Heat and water rate transfer processes in the human respiratory tract at various altitudes

The process of the respiratory air conditioning as a process of heat and mass exchange at the interface inspired air-airways surface was studied. Using a model of airways (Olson et al., 1970) where the segments of the respiratory tract are like cylinders with a fixed length and diameter, the corresponding heat transfer equations, in the paper are founded basic rate exchange parameters-convective heat transfer coefficient h(c)(W m(-2) degrees C(-1)) and evaporative heat transfer coefficient h(e)(W m(-2)hPa(-1)). The rate transfer parameters assumed as sources with known heat power are connected to airflow rate in different airways segments. Relationships expressing warming rate of inspired air due to convection, warming rate of inspired air due to evaporation, water diffused in the inspired air from the airways wall, i.e. a system of air conditioning parameters, was composed. The altitude dynamics of the relations is studied. Every rate conditioning parameter is an increasing function of altitude. The process of diffusion in the peripheral bronchial generations as a basic transfer process is analysed. The following phenomenon is in effect: the diffusion coefficient increases with altitude and causes a compensation of simultaneous decreasing of O(2)and CO(2)densities in atmospheric air. Due to this compensation, the diffusion in the peripheral generations with altitude is approximately constant. The elements of the human anatomy optimality as well as the established dynamics are discussed and assumed. The square form of the airways after the trachea expressed in terms of transfer supposes (in view of maximum contact surface), that a maximum heat and water exchange is achieved, i.e. high degree of air condition at fixed environmental parameters and respiration regime.     

Simulation and inference for stochastic volatility models driven by Levy processes

We study Ornstein-Uhlenbeck stochastic processes driven by Lévyprocesses, and extend them to more general non-Ornstein-Uhlenbeckmodels. In particular, we investigate the means of making thecorrelation structure in the volatility process more flexible.For one model, we implement a method for introducing quasi long-memoryinto the volatility model. We demonstrate that the models canbe fitted to real share price returns data.     

Applying the saddlepoint approximation to bivariate stochastic processes

The problem of moment closure is central to the study of multitype stochastic population dynamics since equations for moments up to a given order will generally involve higher-order moments. To obtain a Normal approximation, the standard approach is to replace third- and higher-order moments by zero, which may be severely restrictive on the structure of the p.d.f. The purpose of this paper is therefore to extend the univariate truncated saddlepoint procedure to multivariate scenarios. This has several key advantages: no distributional assumptions are required; it works regardless of the moment order deemed appropriate; and, we obtain an algebraic form for the associated p.d.f. irrespective of whether or not we have complete knowledge of the cumulants. The latter is especially important, since no families of distributions currently exist which embrace all cumulants up to any given order. In general the algorithm converges swiftly to the required p.d.f.; analysis of a severe test case illustrates its current operational limit.     

Frequency-domain identification of the human controller

System identification techniques applied to experimental human-in-the-loop data provide an objective test of three alternative control-theoretical models of the human control system: non-predictive control, predictive control, and intermittent predictive control. A two-stage approach to the identification of a single-input single-output control system is used: first, the closed-loop frequency response is derived using the periodic property of the experimental data, followed by the fitting of a parametric model. While this approach is well-established for non-predictive and predictive control, it is here used for the first time with intermittent predictive control. This technique is applied to data from experiments with human volunteers who use one of two control strategies, focusing either on position or on velocity, to manually control a virtual, unstable load which requires sustained feedback to maintain position or low velocity. The results show firstly that the non-predictive controller does not fit the data as well as the other two models, and secondly that the predictive and intermittent predictive controllers provide equally good models which cannot be distinguished using this approach. Importantly, the second observation implies that sustained visual manual control is compatible with intermittent control, and that previous results suggesting a continuous control model for the human control system do not rule out intermittent control as an alternative hypothesis. Thirdly, the parameters identified reflect the control strategy adopted by the human controller.     

STOCHSIM: modelling of stochastic biomolecular processes

SUMMARY: STOCHSIM is a stochastic simulator for chemical reactions. Molecules are represented as individual software objects that react according to probabilities derived from concentrations and rate constants. Version 1.2 of STOCHSIM provides a novel cross-platform graphical interface written in Perl/Tk. A simple two-dimensional spatial structure has also been implemented, in which nearest-neighbour interactions of molecules in a 2-D lattice can be simulated.     

Heat and mass exchange processes between the surface of the human body and ambient air at various altitudes

 The rates of convection and evaporation at the interface between the human body and the surrounding air are expressed by the parameters convective heat transfer coefficient h _c, in W m^–2°C^–1 and evaporative heat transfer coefficient h _e, W m^–2 hPa^–1. These parameters are determined by heat transfer equations, which also depend on the velocity of the airstream around the body, that is still air (free convection) and moving air (forced convection). The altitude dependence of the parameters is represented as an exponential function of the atmospheric pressure p: h _c∼p ⁿ and h _e∼p ^1–n, where n is the exponent in the heat transfer equation. The numerical values of n are related to airspeed: n=0.5 for free convection, n=0.618 when airspeed is below 2.0 ms^–1 and n=0.805 when airspeed is above 2.0 ms^–1. This study considers the coefficients h _c and h _e with respect to the similarity of the two processes, convection and evaporation. A framework to explain the basis of established relationships is proposed. It is shown that the thickness of the boundary layer over the body surface increases with altitude. As a medium of the transfer processes, the boundary layer is assumed to be a layer of still air with fixed insulation which causes a reduction in the intensity of heat and mass flux propagating from the human body surface to its surroundings. The degree of reduction is more significant at a higher altitude because of the greater thickness of the boundary layer there. The rate of convective and evaporative heat losses from the human body surface at various altitudes in otherwise identical conditions depends on the following factors: (1) during convection – the thickness of the boundary layer, plus the decrease in air density, (2) during evaporation (mass transfer) – the thickness of the boundary layer, plus the increase with altitude in the diffusion coefficient of water vapour in the air. The warming rate of the air volume due to convection and evaporation is also considered. Expressions for the calculation of altitude dependences h _c (p) and h _e (p) are suggested. Received: 23 June 1998 / Accepted: 10 February 1999     

Curve-crossing problem for Gaussian stochastic processes and its application to neural modelling

A first time crossing problem for Gaussian stochastic process and monotonic time curve is considered and results are discussed with application to neural modelling. Using diffusion approximation of the stochastic process, integral equation for probability density function of the first time crossing has been obtained. Exact solution of the equation is given for two kinds of stochastic processes which have correspondingly infinitesimal and infinitely large correlation time; approximation methods are constructed for processes characterized by intermediate values of this parameter.     

Sir-dependent downregulation of various aging processes

Using a new genetic selection approach in yeast termed fitness-based interferential genetics (FIG), genes that are in an antagonistic relationship with the Sir complexes were selected. Many of the functionally well-defined genes belong to various aging processes occurring in this organism. Three genes are somehow involved in glucose utilization (HXT4,YIL107c, EMI2). Another gene, CDC25, encodes the main regulator of the cyclic AMP pathway in response to glucose. STM1 has been implicated in the control of apoptosis, and indeed, this work shows that disruption of this gene results, among other phenotypes, in resistance to aging. LCB4, encoding a sphingoid bases kinase is linked to the cell integrity pathway. Two other genes, FHL1 and PEP5, are involved in the control of ribosome formation and vacuole biogenesis, respectively; and five genes, presently having unknown functions, could be new potentially interesting candidates for further studies in relation to yeast replicative aging. It is proposed that most, if not all, selected genes are downregulated by the Sir complexes. In addition to changing our view of the mechanisms used by the Sir complexes for extending life span in yeast, these findings could contribute to a better understanding of the role of the Sir complexes in the higher eukaryotes.