Orderings of component level versus system level at active redundancies for coherent systems with dependent components

This paper investigates the issue of stochastic comparison of multi-active redundancies at the component level versus the system level. Based on the assumption that all components are statistically dependent, in the case of complete matching and nonmatching spares, we present some interesting comparison results in the sense of the hazard rate, reversed hazard rate and likelihood ratio orders, respectively. And we also obtain two comparison results between relative agings of resulting systems at the component level and the system level. Several numerical examples are provided to illustrate the theoretical results.

Stochastic comparison of synchronization in activator- and repressor-based coupled gene oscillators

Inside living cells, proteins or mRNA can show oscillations even without a periodic driving force. Such genetic oscillations are precise timekeepers for cell-cycle regulations, pattern formation during embryonic development in higher animals, and daily cycle maintenance in most organisms. The synchronization between oscillations in adjacent cells happens via intercellular coupling, which is essential for periodic segmentation formation in vertebrates and other biological processes. While molecular mechanisms of generating sustained oscillations are quite well understood, how do simple intercellular coupling produces robust synchronizations are still poorly understood? To address this question, we investigate two models of coupled gene oscillators - activator-based coupled oscillators (ACO) and repressor-based coupled oscillators (RCO) models. In our study, a single autonomous oscillator (that operates in a single cell) is based on a negative feedback, which is delayed by intracellular dynamics of an intermediate species. For the ACO model (RCO), the repressor protein of one cell activates (represses) the production of another protein in the neighbouring cell after a intercellular time delay. We investigate the coupled models in the presence of intrinsic noise due to the inherent stochasticity of the biochemical reactions. We analyze the collective oscillations from stochastic trajectories in the presence and absence of explicit coupling delay and make careful comparison between two models. Our results show no clear synchronizations in the ACO model when the coupling time delay is zero. However, a non-zero coupling delay can lead to anti-phase synchronizations in ACO. Interestingly, the RCO model shows robust in-phase synchronizations in the presence and absence of the coupling time delay. Our results suggest that the naturally occurring intercellular couplings might be based on repression rather than activation where in-phase synchronization is crucial.

Sydney Metro and Melbourne Metro Rail Stochastic Comparison and Review

This paper aims to review an innovative artificial intelligence (AI) apparatus to enhance the rail transportation performance. In this light, the Sydney Metro and Melbourne Metro rail will be compared, since both of these Australian rail networks employ complex AI as part of their overall performance enhancement schemes. These two case studies further highlight the novel critical aspects of AI in rail transportation sector such as recalibration through smart system design and automation, nonlinear controls and precise design, modeling and control apparatus, and so on. As a part of such a view, different aspects of AI systems such as increased reliability and safety were also investigated. This research found that with such enhancements of system performance, the overall transportation functioning would ultimately be significantly improved. Subsequently, AI in the Australian context can be further refined based on comprehensive integration of the key factors.

Data set from shake table tests of free-standing rocking bodies

In earthquake engineering, structural models are validated by performing a time history analysis and comparing its maximum to the maximum response obtained by a shake table test. It has been shown that this is a sufficient (but not a necessary) precondition to accept a numerical model. Numerical models can fail to predict the planar rocking response of a rigid block, but may succeed in predicting the statistics of the response to an ensemble of ground motions. As seismic response is inherently stochastic, comparison of the statistics of the numerically simulated response to the statistics of the experimentally obtained benchmark response for the same ensemble of earthquake excitation is a sufficient (and easier to pass) model validation test. This article describes the publicly available data of a set of 12 free rocking vibration and 115 shake table tests of six three-dimensional rocking and sliding columns, designed at ETH Zurich and performed at EQUALS Laboratory, University of Bristol. The data can be used to statistically validate different approaches that aim to model three-dimensional rocking structures.

Stochastic comparison of parallel systems with Pareto components

Pareto distribution is an important distribution in extreme value theory. In this paper, we consider parallel systems with Pareto components and study the effect of heterogeneity on skewness of such systems. It is shown that, when the lifetimes of components have different shape parameters, the parallel system with heterogeneous Pareto component lifetimes is more skewed than the system with independent and identically distributed Pareto components. However, for the case when the lifetimes of components have different scale parameters, the result gets reversed in the sense of star ordering. We also establish the relation between star ordering and dispersive ordering by extending the result of Deshpande and Kochar [(1983). Dispersive ordering is the same as tail ordering. Advances in Applied Probability 15(3): 686–687] from support $(0, \infty )$ to general supports $(a, \infty )$ , $a > 0$ . As a consequence, we obtain some new results on dispersion of order statistics from heterogeneous Pareto samples with respect to dispersive ordering.

On inactivity times of failed components of coherent system under double monitoring

This article discusses the stochastic behavior and reliability properties for the inactivity times of failed components in coherent systems under double monitoring. A mixture representation of reliability function is obtained for the inactivity times of failed components, and some stochastic comparison results are also established. Furthermore, some sufficient conditions are developed in terms of the aging properties of the inactivity times of failed components. Finally, some numerical examples are presented to illustrate the theoretical results.

Results on Varextropy Measure of Random Variables

In 2015, Lad, Sanfilippo and Agrò proposed an alternative measure of uncertainty dual to the entropy known as extropy. This paper provides some results on a dispersion measure of extropy of random variables which is called varextropy and studies several properties of this concept. Especially, the varextropy measure of residual and past lifetimes, order statistics, record values and proportional hazard rate models are discussed. Moreover, the conditional varextropy is considered and some properties of this measure are studied. Finally, a new stochastic comparison method, named varextropy ordering, is introduced and some of its properties are presented.

Complex Dynamics of a Stochastic Two-Patch Predator-Prey Population Model with Ratio-Dependent Functional Responses

This paper investigates a stochastic two-patch predator-prey model with ratio-dependent functional responses. First, the existence of a unique global positive solution is proved via the stochastic comparison theorem. Then, two different methods are used to discuss the long-time properties of the solutions pathwise. Next, sufficient conditions for extinction and persistence in mean are obtained. Moreover, stochastic persistence of the model is discussed. Furthermore, sufficient conditions for the existence of an ergodic stationary distribution are derived by a suitable Lyapunov function. Next, we apply the main results in some special models. Finally, some numerical simulations are introduced to support the main results obtained. The results in this paper generalize and improve the previous related results.