Pointwise convergence of multiple ergodic averages and strictly ergodic models

By building some suitable strictly ergodic models, we prove that for an ergodic system $(X,\mathcal{X},\mu, T)$, $d\in{\mathbb N}$, $f_1, \ldots, f_d \in L^{\infty}(\mu)$, the averages $$\frac{1}{N^2} \sum_{(n,m)\in [0,N-1]^2} f_1(T^nx)f_2(T^{n+m}x)\ldots f_d(T^{n+(d-1)m}x)$$ converge $\mu$ a.e. Deriving some results from the construction, for distal systems we answer positively the question if the multiple ergodic averages converge a.e. That is, we show that if $(X,\mathcal{X},\mu, T)$ is an ergodic distal system, and $f_1, \ldots, f_d \in L^{\infty}(\mu)$, then multiple ergodic averages $$\frac 1 N\sum_{n=0}^{N-1}f_1(T^nx)\ldots f_d(T^{dn}x)$$ converge $\mu$ a.e.Comment: 35 pages, revised version following referees' report

RIOT OS Paves the Way for Implementation of High-Performance MAC Protocols

Implementing new, high-performance MAC protocols requires real-time features, to be able to synchronize correctly between different unrelated devices. Such features are highly desirable for operating wireless sensor networks (WSN) that are designed to be part of the Internet of Things (IoT). Unfortunately, the operating systems commonly used in this domain cannot provide such features. On the other hand, "bare-metal" development sacrifices portability, as well as the mul-titasking abilities needed to develop the rich applications that are useful in the domain of the Internet of Things. We describe in this paper how we helped solving these issues by contributing to the development of a port of RIOT OS on the MSP430 microcontroller, an architecture widely used in IoT-enabled motes. RIOT OS offers rich and advanced real-time features, especially the simultaneous use of as many hardware timers as the underlying platform (microcontroller) can offer. We then demonstrate the effectiveness of these features by presenting a new implementation, on RIOT OS, of S-CoSenS, an efficient MAC protocol that uses very low processing power and energy.Comment: SCITEPRESS. SENSORNETS 2015, Feb 2015, Angers, France. http://www.scitepress.or