Stochastic Bounds and Dependence Properties of Survival Times in a Multicomponent Shock Model

AbstractConsider a system that consists of several components. Shocks arrive according to a counting process (which may be non-homogeneous and with correlated interarrival times) and each shock may simultaneously destroy a subset of the components. Shock models of this type arise naturally in reliability modeling in dynamic environments. Due to correlated shock arrivals, individual component lifetimes are statistically dependent, which makes the explicit evaluation of the joint distribution intractable. To facilitate the development of easily computable tight bounds and good approximations, an analytic analysis of the dependence structure of the system is needed. The purpose of this paper is to provide a general framework for studying the correlation structure of shock models in the setup of a multivariate, correlated counting process and to systematically develop upper and lower bounds for its joint component lifetime distribution and survival functions. The thrust of the approach is the interplay between a newly developed notion, majorization with respect to weighted trees, and various stochastic dependence orders, especially orthant dependence orders of random vectors and orthant dependence orders of stochastic processes. It is shown that the dependence nature of the joint lifetime is inherited from spatial dependence and temporal dependence; that is, dependence among various components due to simultaneous arrivals and dependence over different time instants introduced by the shock arrival process. The two types of dependency are investigated separately and their joint impact on the performance of the system is analyzed. The results are used to develop computable bounds for the statistics of the joint component lifetimes, which are tighter than the product-form bounds under certain conditions. The shock model with a non-homogeneous Poisson arrival process is studied as an illustrative example. The result is also applicable to the cumulative damage model with multivariate shock arrival processes

Charybdotoxin binding in the I(Ks) pore demonstrates two MinK subunits in each channel complex.

I(Ks) voltage-gated K(+) channels contain four pore-forming KCNQ1 subunits and MinK accessory subunits in a number that has been controversial. Here, I(Ks) channels assembled naturally by monomer subunits are compared to those with linked subunits that force defined stoichiometries. Two strategies that exploit charybdotoxin (CTX)-sensitive subunit variants are applied. First, CTX on rate, off rate, and equilibrium affinity are found to be the same for channels of monomers and those with a fixed 2:4 MinK:KCNQ1 valence. Second, 3H-CTX and an antibody are used to directly quantify channels and MinK subunits, respectively, showing 1.97 +/- 0.07 MinK per I(Ks) channel. Additional MinK subunits do not enter channels of monomeric subunits or those with fixed 2:4 valence. We conclude that two MinK subunits are necessary, sufficient, and the norm in I(Ks) channels. This stoichiometry is expected for other K(+) channels that contain MinK or MinK-related peptides (MiRPs)

Effect of Thermal Transport on Spatiotemporal Emergence of Lamellar Branching Morphology During Polymer Spherulitic Growth

Spatiotemporal emergence of lamellar branching morphology of polymer spherulite has been investigated theoretically in the framework of a phase field model by coupling a crystal solidification potential pertaining to a nonconserved crystal order parameter with a temperature field generated by latent heat of crystallization. A local free-energy density having an asymmetric double well has been utilized to account for a first-order phase transition such as crystallization. To account for the polymorphous nature of polymer crystallization, the phase field order parameter of crystal at the solidification potential of the double-well local free-energy density is modified to be supercooling dependent. The heat conduction equation, incorporating liberation of latent heat along the nonuniform solid-liquid interface, has led to directional growth of various hierarchical structures including lamella, sheaflike structure, and spherulite. Two-dimensional calculations have been carried out based on experimentally accessible material parameters and experimental conditions for the growth of syndiotactic polypropylene spherulite. The simulations illustrate that, under self-generated thermal field, the initial nucleus is anisotropic having lamellar stacks that transforms to a sheaflike structure and eventually to a lamellar branching morphology with a dual-eye-pocket texture at the core. It appears that the released latent heat is responsible for the lamellar side branching and splaying from the main lamellae. On the same token, the heat build-up seemingly prevents the interface boundaries of neighboring spherulites from over running on each other during impingement, thereby forming the grain boundary. (c) 2005 American Institute of Physics

Phase-Field Modeling on Morphological Landscape of Isotactic Polystyrene Single Crystals

Spatio-temporal growth of isotactic polystyrene single crystals during isothermal crystallization has been investigated theoretically based on the phase field model by solving temporal evolution of a nonconserved phase order parameter coupled with a heat conduction equation. In the description of the total free energy, an asymmetric double-well local free energy density has been adopted to represent the metastable melt and the stable solid crystal. Unlike the small molecule systems, polymer crystallization rarely reaches thermodynamic equilibrium; most polymer crystals are kinetically stabilized in some metastable states. To capture various metastable polymer crystals, the phase field crystal order parameter at the solidification potential has been treated to be supercooling dependent such that it can assume an intermediate value between zero (melt) and unity (perfect crystal), reflecting imperfect polycrystalline nature of polymer crystals. Two-dimensional simulations exhibit various single crystal morphologies of isotactic polystyrene crystals such as faceted hexagonal patterns transforming to nonfaceted snowflakes with increasing supercooling. Of particular interest is that heat liberation from the crystallizing front influences the curvature of the crystal-melt interface, leading to directional growth of lamellar tips and side branches. The landscape of these morphological textures has been established as a function of anisotropy of surface energy and supercooling. With increasing supercooling and decreasing anisotropy, the hexagonal single crystal transforms to the dense lamellar branching morphology in conformity with the experimental findings

Distributed optimization for multi-agent systems with communication delays and external disturbances under a directed network

This article studies the distributed optimization problem for multi-agent systems with communication delays and external disturbances in a directed network. Firstly, a distributed optimization algorithm is proposed based on the internal model principle in which the internal model term can effectively compensate for external environmental disturbances. Secondly, the relationship between the optimal solution and the equilibrium point of the system is discussed through the properties of the Laplacian matrix and graph theory. Some sufficient conditions are derived by using the Lyapunov–Razumikhin theory, which ensures all agents asymptotically reach the optimal value of the distributed optimization problem. Moreover, an aperiodic sampled-data control protocol is proposed, which can be well transformed into the proposed time-varying delay protocol and analyzed by using the Lyapunov–Razumikhin theory. Finally, an example is given to verify the effectiveness of the results