Time lag in a diffusion model of information

AbstractA new approach is suggested to investigate the effects of time lag in stochastic models for diffusion of information in a social group. The stochastic approach is based on a generalized master equation incorporating the idea of memory function. The results for the statistical moments of the variable of interest are obtained for two choices of memory functions and they are found to depict damped oscillatory behaviour under certain conditions

Trend Detection in Annual Temperature & Precipitation using the Mann Kendall Test – A Case Study to Assess Climate Change on Select States in the Northeastern United States

The impact of climate change on annual air temperature and precipitation has received a great deal of attention by scholars worldwide. Many studies have been conducted to illustrate that changes in annual temperature and precipitation are becoming evident on a global scale. This study focuses on detecting trends in annual temperature and precipitation for the nine states in the Northeastern United States. For this study, the widely used modified Mann-Kendall test was run at 5% significance level on time series data for each of the nine states for the time period, 1900 to 2011. The resultant Mann- Kendall test statistic (S) indicates how strong the trend in temperature and precipitation is and whether it is increasing or decreasing. For temperature, all the states indicate statistically significant increasing trends, except for Pennsylvania and Maine that do not indicate statistically significant trends. In the case of precipitation, the states of New Hampshire and Maine do not show statistically significant results, while the other states show statistically significant increasing trends. On the contrary, linear trend line plotting indicates increasing trend in temperature for all nine northeastern states in the range of 0.00006 to 0.02 °F/yr, while a US EPA study demonstrates that the US average temperature rise is 1.3°F/century. [1] For precipitation, the linear trend line indicates a decreasing trend for Maine, while the other eight states have an increasing trend that ranges from 0.03 to 0.13 mm/yr

Role of Rating Value of Words and Displaced Rehearsal in Semantic Rating Tasks

Two experiments were carried out to investigate the role of rating task, displaced rehearsal, and the value of words on the retention of items processed at the semantic level. In Experiment I, the subjects rated medium value words for either pleasantness or frequency under free rehearsal conditions. The results revealed no retention differences between words judged for pleasantness and those judged for frequency. In Experiment II, high and low pleasantness and high and low frequency values were factorially combined within a single list of words. In the free rehearsal condition, words were judged on either the pleasantness or frequency rating dimensions. In the forced rehearsal condition I, subjects compared the target words with a pair of intralist comparison words. In the forced rehearsal condition II, subjects compared the target words with a pair of extralist words. Recall was found to be significantly higher for words judged on the pleasantness that the frequency dimension in all three rehearsal conditions. This indicated the superiority of the pleasantness rating task over the frequency rating task when high and low value words were used. Existence of retention differences between the pleasantness and frequency tasks in the forced rehearsal conditions I and II also indicate that factors other than displaced rehearsal may be operating. Better recall of high pleasantness words than low pleasantness words for low frequency value but not for high frequency value suggested that item properties (values) interact

Statistical Characterisation of Speckle in Clinical Echocardiographic Images with Pearson Family of Distributions

The statistical characterisation of gray level distribution of echocardiographic images is commonly done in terms of unimodal probability densities such as Rayleigh, Gamma, Weibull, Nakagami, and Lognormal. Amongst these distributions, the Gamma density is found to provide better empirical model that fits to real data sets. We propose to extend the class of probability distributions by exploring Pearson family to characterise blood and tissue in echocardiographic images. It is found that Pearson Type I characterises the tissue regions whereas Type I, Type IV and Type VI classify blood regions. The statistical measures viz. Jensen-Shannon (JS) divergence and Kolmogorov-Smirnov (KS) statistics reveal that Pearson family of curves outperforms the Gamma distribution.Defence Science Journal, 2011, 61(5), pp.473-478, DOI:http://dx.doi.org/10.14429/dsj.62.116

Stochastic stability of structures under active control with distributed time delays

The pathwise behaviour of a single degree of freedom (SDOF) system with symmetric nonlinearity and distributed delays is investigated under the presence of seismic excitation and multiplicative noise. Besides distributed time delays and finite build-up time of control force are taken into consideration. The system is modelled as stochastic integro-differential equation with exponential type kernels. Interpreting stochastic equations in Stratonovich sense, stochastic stability is analyzed in terms of Lyapunov exponents. Estimates of frequencies with which sample paths of displacement of SDOF system cross certain critical values are also obtained. Studies of stochastic linear and nonlinear systems are carried out by resorting to numerical techniques for the solution of (ordinary) stochastic differential equations

Effects of distributed delays on the stability of structures under seismic excitation and multiplicative noise

The effects of seismic excitation and multiplicative noise (arising from environmental fluctuations) on the stability of a single degree of freedom system with distributed delays are investigated. The system is modelled in the form of a stochastic integro-differential equation interpreted in Stratonovich sense. Both deterministic stability and stochastic moment stability are examined for the system in the absence of seismic excitation. The model is also extended to incorporate effects of symmetric nonlinearity. The simulation of stochastic linear and nonlinear systems are carried out by resorting to numerical techniques for the solution of stochastic differential equations

Moment evolution of the outflow-rate from nonlinear conceptual reservoirs

The temporal evolution of moments of outflow-rate is investigated in a stochastically perturbed nonlinear reservoir due to precipitation. The detailed stochastic behaviour of outflow is obtained from the numerical solution of a nonlinear stochastic differential equation with multiplicative noise. The timedevelopment of first two moments is studied for various choices of parameters. Using Stratonovich interpretation, it turns out that the mean outflow-rate is above that given by the deterministic solution. Based on the set of 9000 simulation runs, 90 % confidence intervals for the mean evolution of outflow-rate are computed. The effect of stochastic perturbations with finite correlation time is also investigated

Inhomogeneous point-process entropy: an instantaneous measure of complexity in discrete systems

Measures of entropy have been widely used to characterize complexity, particularly in physiological dynamical systems modeled in discrete time. Current approaches associate these measures to finite single values within an observation window, thus not being able to characterize the system evolution at each moment in time. Here, we propose a new definition of approximate and sample entropy based on the inhomogeneous point-process theory. The discrete time series is modeled through probability density functions, which characterize and predict the time until the next event occurs as a function of the past history. Laguerre expansions of the Wiener-Volterra autoregressive terms account for the long-term nonlinear information. As the proposed measures of entropy are instantaneously defined through probability functions, the novel indices are able to provide instantaneous tracking of the system complexity. The new measures are tested on synthetic data, as well as on real data gathered from heartbeat dynamics of healthy subjects and patients with cardiac heart failure and gait recordings from short walks of young and elderly subjects. Results show that instantaneous complexity is able to effectively track the system dynamics and is not affected by statistical noise properties