Differentiating complex network models: An engineering perspective

AbstractNetwork models that can capture the underlying network’s topologies and functionalities are crucial for the development of complex network algorithms and protocols. In the engineering community, the performances of network algorithms and protocols are usually evaluated by running them on a network model. In most if not all reported work, the criteria used to determine such a network model rely on how close it matches the network data in terms of some basic topological characteristics. However, the intrinsic relations between a network topology and its functionalities are still unclear. A question arises naturally: For a network model which can reproduce some topological characteristics of the underlying network, is it reasonable and valid to use this model to be a test-bed for evaluating the network’s performances? To answer this question, we take a close look at several typical complex network models of the AS-level Internet as examples of study. We find that although a model can represent the Internet in terms of topological metrics, it cannot be used to evaluate the Internet performances. Our findings reveal that the approaches using topological metrics to discriminate network models, which have been widely used in the engineering community, may lead to confusing or even incorrect conclusions

Zhang Neural Networks for Online Solution of Time-Varying Linear Inequalities

In this chapter, a special type of recurrent neural networks termed “Zhang neural network” (ZNN) is presented and studied for online solution of time-varying linear (matrix-vector and matrix) inequalities. Specifically, focusing on solving the time-varying linear matrix-vector inequality (LMVI), we develop and investigate two different ZNN models based on two different Zhang functions (ZFs). Then, being an extension, by defining another two different ZFs, another two ZNN models are developed and investigated to solve the time-varying linear matrix inequality (LMI). For such ZNN models, theoretical results and analyses are presented as well to show their computational performances. Simulation results with two illustrative examples further substantiate the efficacy of the presented ZNN models for time-varying LMVI and LMI solving

Knowledge Mapping Analysis of Rural Landscape Using CiteSpace

This study visualizes and quantifies extant publications of rural landscape research (RLR) inWeb of Science using CiteSpace for a wide range of research topics, from a multi-angle analysis of the overall research profile, while providing a method and approach for quantitative analysis of massive literature data. First, it presents the number of papers published, subject distribution, author network, the fundamental condition of countries, and research organizations involved in RLR through network analysis. Second, it identifies the high-frequency and high betweenness-centrality values of the basic research content of RLR through keyword co-occurrence analysis and keyword time zones. Finally, it identifies research fronts and trending topics of RLR in the decade from 2009 to 2018 by using co-citation clustering, and noun-term burst detection. The results show that basic research content involves protection, management, biodiversity, and land use. Five clearer research frontier pathways and top 20 research trending topics are extracted to show diversified research branch development. All this provides the reader with a general preliminary grasp of RLR, showing that cooperation and analysis involving multiple disciplines, specialties, and angles will become a dominant trend in the field

Optimal Synthesis of Stabilizer Codes via MaxSAT

Quantum Error Correction (QEC) codes are crucial for achieving fault-tolerant quantum computing in the long term. However, efficiently implementing these codes on hardware poses significant challenges, including hardware connectivity matching, efficient circuit scheduling, and fault-tolerance enforcement. In this study, we present an optimal synthesizer that stitches generic stabilizer codes onto diverse hardware structures via MaxSAT. Our evaluation demonstrates (1) the capability of our approach to be applied for various codes and devices and (2) the consistently better efficiency than the best prior heuristic approaches that only target specific QEC codes. By bridging the gap between high-level QEC code design and low-level hardware constraints, this work paves the way toward achieving long-term fault-tolerant quantum computing goals

Kondo Resonance in the Presence of Spin-Polarized Currents

We propose an improved method of the equation of motion approach to study the Kondo problem in spin-dependent non-equilibrium conditions. We find that the previously introduced additional renormalization for non-equilibrium Kondo effects is not required when we use a proper decoupling scheme. Our improved formulation is then applied to address the spin-split Kondo peaks when a spin current injects into a Kondo system.Comment: 4+ pages, 4 eps figure