On the Influence of Informed Agents on Learning and Adaptation over Networks

Adaptive networks consist of a collection of agents with adaptation and learning abilities. The agents interact with each other on a local level and diffuse information across the network through their collaborations. In this work, we consider two types of agents: informed agents and uninformed agents. The former receive new data regularly and perform consultation and in-network tasks, while the latter do not collect data and only participate in the consultation tasks. We examine the performance of adaptive networks as a function of the proportion of informed agents and their distribution in space. The results reveal some interesting and surprising trade-offs between convergence rate and mean-square performance. In particular, among other results, it is shown that the performance of adaptive networks does not necessarily improve with a larger proportion of informed agents. Instead, it is established that the larger the proportion of informed agents is, the faster the convergence rate of the network becomes albeit at the expense of some deterioration in mean-square performance. The results further establish that uninformed agents play an important role in determining the steady-state performance of the network, and that it is preferable to keep some of the highly connected agents uninformed. The arguments reveal an important interplay among three factors: the number and distribution of informed agents in the network, the convergence rate of the learning process, and the estimation accuracy in steady-state. Expressions that quantify these relations are derived, and simulations are included to support the theoretical findings. We further apply the results to two models that are widely used to represent behavior over complex networks, namely, the Erdos-Renyi and scale-free models.Comment: 35 pages, 8 figure

Diffusion Strategies Outperform Consensus Strategies for Distributed Estimation over Adaptive Networks

Adaptive networks consist of a collection of nodes with adaptation and learning abilities. The nodes interact with each other on a local level and diffuse information across the network to solve estimation and inference tasks in a distributed manner. In this work, we compare the mean-square performance of two main strategies for distributed estimation over networks: consensus strategies and diffusion strategies. The analysis in the paper confirms that under constant step-sizes, diffusion strategies allow information to diffuse more thoroughly through the network and this property has a favorable effect on the evolution of the network: diffusion networks are shown to converge faster and reach lower mean-square deviation than consensus networks, and their mean-square stability is insensitive to the choice of the combination weights. In contrast, and surprisingly, it is shown that consensus networks can become unstable even if all the individual nodes are stable and able to solve the estimation task on their own. When this occurs, cooperation over the network leads to a catastrophic failure of the estimation task. This phenomenon does not occur for diffusion networks: we show that stability of the individual nodes always ensures stability of the diffusion network irrespective of the combination topology. Simulation results support the theoretical findings.Comment: 37 pages, 7 figures, To appear in IEEE Transactions on Signal Processing, 201

Switchable valley functionalities of an n−n−−nn-n^{-}-n junction in 2D semiconductors

We show that an $n-n^{-}-n$ junction in 2D semiconductors can flexibly realize two basic valleytronic functions, i.e. valley filter and valley source, with gate controlled switchability between the two. Upon carrier flux passing through the junction, the valley filter and valley source functions are enabled respectively by intra- and inter-valley scatterings, and the two functions dominate respectively at small and large band-offset between the $n$ and $n^{-}$ regions. It can be generally shown that, the valley filter effect has an angular dependent polarity and vanishes under angular integration, by the same constraint from time-reversal symmetry that leads to its absence in one-dimension. These findings are demonstrated for monolayer transition metal dichalcogenides and graphene using tight-binding calculations. We further show that junction along chiral directions can concentrate the valley pump in an angular interval largely separated from the bias direction, allowing efficient havest of valley polarization in a cross-bar device

On the Erdos-Sos Conjecture for Graphs on n=k+4 Vertices

The Erd\H{o}s-S\'{o}s Conjecture states that if $G$ is a simple graph of order $n$ with average degree more than $k-2,$ then $G$ contains every tree of order $k$. In this paper, we prove that Erd\H{o}s-S\'{o}s Conjecture is true for $n=k+4$.Comment: 18 page

3次元アトムプローブ法を用いたシリコンデバイス中の不純物分布のナノスケール分析

Tohoku University永井康介課