Bounds for the regularity of local cohomology of bigraded modules

Let $M$ be a finitely generated bigraded module over the standard bigraded polynomial ring $S=K[x_1,...,x_m, y_1,...,y_n]$, and let $Q=(y_1,...,y_n)$. The local cohomology modules $H^k_Q(M)$ are naturally bigraded, and the components H^k_Q(M)_j=\Dirsum_iH^k_Q(M)_{(i,j)} are finitely generated graded $K[x_1,...,x_m]$-modules. In this paper we study the regularity of $H^k_Q(M)_j$, and show in several cases that \reg H^k_Q(M)_j is linearly bounded as a function of $j$

Fake news and rumors: a trigger for proliferation or fading away

The dynamics of fake news and rumor spreading is investigated using a model with three kinds of agents who are respectively the Seeds, the Agnostics and the Others. While Seeds are the ones who start spreading the rumor being adamantly convinced of its truth, Agnostics reject any kind of rumor and do not believe in conspiracy theories. In between, the Others constitute the main part of the community. While Seeds are always Believers and Agnostics are always Indifferents, Others can switch between being Believer and Indifferent depending on who they are discussing with. The underlying driving dynamics is implemented via local updates of randomly formed groups of agents. In each group, an Other turns into a Believer as soon as $m$ or more Believers are present in the group. However, since some Believers may lose interest in the rumor as time passes by, we add a flipping fixed rate $0<d<1$ from Believers into Indifferents. Rigorous analysis of the associated dynamics reveals that switching from $m=1$ to $m\ge2$ triggers a drastic qualitative change in the spreading process. When $m=1$ even a small group of Believers may manage to convince a large part of the community very quickly. In contrast, for $m\ge 2$, even a substantial fraction of Believers does not prevent the rumor dying out after a few update rounds. Our results provide an explanation on why a given rumor spreads within a social group and not in another, and also why some rumors will not spread in neither groups

Building Programmable Wireless Networks: An Architectural Survey

In recent times, there have been a lot of efforts for improving the ossified Internet architecture in a bid to sustain unstinted growth and innovation. A major reason for the perceived architectural ossification is the lack of ability to program the network as a system. This situation has resulted partly from historical decisions in the original Internet design which emphasized decentralized network operations through co-located data and control planes on each network device. The situation for wireless networks is no different resulting in a lot of complexity and a plethora of largely incompatible wireless technologies. The emergence of "programmable wireless networks", that allow greater flexibility, ease of management and configurability, is a step in the right direction to overcome the aforementioned shortcomings of the wireless networks. In this paper, we provide a broad overview of the architectures proposed in literature for building programmable wireless networks focusing primarily on three popular techniques, i.e., software defined networks, cognitive radio networks, and virtualized networks. This survey is a self-contained tutorial on these techniques and its applications. We also discuss the opportunities and challenges in building next-generation programmable wireless networks and identify open research issues and future research directions.Comment: 19 page