Embedding of global attractors and their dynamics

Using shape theory and the concept of cellularity, we show that if $A$ is the global attractor associated with a dissipative partial differential equation in a real Hilbert space $H$ and the set $A-A$ has finite Assouad dimension $d$, then there is an ordinary differential equation in ${\mathbb R}^{m+1}$, with $m >d$, that has unique solutions and reproduces the dynamics on $A$. Moreover, the dynamical system generated by this new ordinary differential equation has a global attractor $X$ arbitrarily close to $LA$, where $L$ is a homeomorphism from $A$ into ${\mathbb R}^{m+1}$

A Multi-perspective Analysis of Carrier-Grade NAT Deployment

As ISPs face IPv4 address scarcity they increasingly turn to network address translation (NAT) to accommodate the address needs of their customers. Recently, ISPs have moved beyond employing NATs only directly at individual customers and instead begun deploying Carrier-Grade NATs (CGNs) to apply address translation to many independent and disparate endpoints spanning physical locations, a phenomenon that so far has received little in the way of empirical assessment. In this work we present a broad and systematic study of the deployment and behavior of these middleboxes. We develop a methodology to detect the existence of hosts behind CGNs by extracting non-routable IP addresses from peer lists we obtain by crawling the BitTorrent DHT. We complement this approach with improvements to our Netalyzr troubleshooting service, enabling us to determine a range of indicators of CGN presence as well as detailed insights into key properties of CGNs. Combining the two data sources we illustrate the scope of CGN deployment on today's Internet, and report on characteristics of commonly deployed CGNs and their effect on end users

Delay-Optimal User Scheduling and Inter-Cell Interference Management in Cellular Network via Distributive Stochastic Learning

In this paper, we propose a distributive queueaware intra-cell user scheduling and inter-cell interference (ICI) management control design for a delay-optimal celluar downlink system with M base stations (BSs), and K users in each cell. Each BS has K downlink queues for K users respectively with heterogeneous arrivals and delay requirements. The ICI management control is adaptive to joint queue state information (QSI) over a slow time scale, while the user scheduling control is adaptive to both the joint QSI and the joint channel state information (CSI) over a faster time scale. We show that the problem can be modeled as an infinite horizon average cost Partially Observed Markov Decision Problem (POMDP), which is NP-hard in general. By exploiting the special structure of the problem, we shall derive an equivalent Bellman equation to solve the POMDP problem. To address the distributive requirement and the issue of dimensionality and computation complexity, we derive a distributive online stochastic learning algorithm, which only requires local QSI and local CSI at each of the M BSs. We show that the proposed learning algorithm converges almost surely (with probability 1) and has significant gain compared with various baselines. The proposed solution only has linear complexity order O(MK)