Coordinate-Descent Diffusion Learning by Networked Agents

This work examines the mean-square error performance of diffusion stochastic algorithms under a generalized coordinate-descent scheme. In this setting, the adaptation step by each agent is limited to a random subset of the coordinates of its stochastic gradient vector. The selection of coordinates varies randomly from iteration to iteration and from agent to agent across the network. Such schemes are useful in reducing computational complexity at each iteration in power-intensive large data applications. They are also useful in modeling situations where some partial gradient information may be missing at random. Interestingly, the results show that the steady-state performance of the learning strategy is not always degraded, while the convergence rate suffers some degradation. The results provide yet another indication of the resilience and robustness of adaptive distributed strategies.Comment: Accepted for publicatio

Method of constructing braid group representation and entanglement in a Yang-Baxter sysytem

In this paper we present reducible representation of the $n^{2}$ braid group representation which is constructed on the tensor product of n-dimensional spaces. By some combining methods we can construct more arbitrary $n^{2}$ dimensional braiding matrix S which satisfy the braid relations, and we get some useful braiding matrix S. By Yang-Baxteraition approach, we derive a $9\times9$ unitary $\breve{R}$ according to a $9\times9$ braiding S-matrix we have constructed. The entanglement properties of $\breve{R}$-matrix is investigated, and the arbitrary degree of entanglement for two-qutrit entangled states can be generated via $\breve{R}(\theta, \phi_{1},\phi_{2})$-matrix acting on the standard basis.Comment: 9 page

Attributable Risk Function in the Proportional Hazards Model

As an epidemiological parameter, the population attributable fraction is an important measure to quantify the public health attributable risk of an exposure to morbidity and mortality. In this article, we extend this parameter to the attributable fraction function in survival analysis of time-to-event outcomes, and further establish its estimation and inference procedures based on the widely used proportional hazards models. Numerical examples and simulations studies are presented to validate and demonstrate the proposed methods