Nuclear spin pumping and electron spin susceptibilities

In this work we present a new formalism to evaluate the nuclear spin dynamics driven by hyperfine interaction with non-equilibrium electron spins. To describe the dynamics up to second order in the hyperfine coupling, it suffices to evaluate the susceptibility and fluctuations of the electron spin. Our approach does not rely on a separation of electronic energy scales or the specific choice of electronic basis states, thereby overcoming practical problems which may arise in certain limits when using a more traditional formalism based on rate equations.Comment: 9 pages, 2 figure

Quantum Tunneling Detection of Two-photon and Two-electron Processes

We analyze the operation of a quantum tunneling detector coupled to a coherent conductor. We demonstrate that in a certain energy range the output of the detector is determined by two-photon processes, two-electron processes and the interference of the two. We show how the individual contributions of these processes can be resolved in experiments.Comment: 4 pages, 4 figure

Benchmark graphs for testing community detection algorithms

Community structure is one of the most important features of real networks and reveals the internal organization of the nodes. Many algorithms have been proposed but the crucial issue of testing, i.e. the question of how good an algorithm is, with respect to others, is still open. Standard tests include the analysis of simple artificial graphs with a built-in community structure, that the algorithm has to recover. However, the special graphs adopted in actual tests have a structure that does not reflect the real properties of nodes and communities found in real networks. Here we introduce a new class of benchmark graphs, that account for the heterogeneity in the distributions of node degrees and of community sizes. We use this new benchmark to test two popular methods of community detection, modularity optimization and Potts model clustering. The results show that the new benchmark poses a much more severe test to algorithms than standard benchmarks, revealing limits that may not be apparent at a first analysis.Comment: 6 pages, 8 figures. Extended version published on Physical Review E. The code to build the new benchmark graphs can be downloaded from http://santo.fortunato.googlepages.com/inthepress

Identifying network communities with a high resolution

Community structure is an important property of complex networks. An automatic discovery of such structure is a fundamental task in many disciplines, including sociology, biology, engineering, and computer science. Recently, several community discovery algorithms have been proposed based on the optimization of a quantity called modularity (Q). However, the problem of modularity optimization is NP-hard, and the existing approaches often suffer from prohibitively long running time or poor quality. Furthermore, it has been recently pointed out that algorithms based on optimizing Q will have a resolution limit, i.e., communities below a certain scale may not be detected. In this research, we first propose an efficient heuristic algorithm, Qcut, which combines spectral graph partitioning and local search to optimize Q. Using both synthetic and real networks, we show that Qcut can find higher modularities and is more scalable than the existing algorithms. Furthermore, using Qcut as an essential component, we propose a recursive algorithm, HQcut, to solve the resolution limit problem. We show that HQcut can successfully detect communities at a much finer scale and with a higher accuracy than the existing algorithms. Finally, we apply Qcut and HQcut to study a protein-protein interaction network, and show that the combination of the two algorithms can reveal interesting biological results that may be otherwise undetectable.Comment: 14 pages, 5 figures. 1 supplemental file at http://cic.cs.wustl.edu/qcut/supplemental.pd

Benchmarks for testing community detection algorithms on directed and weighted graphs with overlapping communities

Many complex networks display a mesoscopic structure with groups of nodes sharing many links with the other nodes in their group and comparatively few with nodes of different groups. This feature is known as community structure and encodes precious information about the organization and the function of the nodes. Many algorithms have been proposed but it is not yet clear how they should be tested. Recently we have proposed a general class of undirected and unweighted benchmark graphs, with heterogenous distributions of node degree and community size. An increasing attention has been recently devoted to develop algorithms able to consider the direction and the weight of the links, which require suitable benchmark graphs for testing. In this paper we extend the basic ideas behind our previous benchmark to generate directed and weighted networks with built-in community structure. We also consider the possibility that nodes belong to more communities, a feature occurring in real systems, like, e. g., social networks. As a practical application, we show how modularity optimization performs on our new benchmark.Comment: 9 pages, 13 figures. Final version published in Physical Review E. The code to create the benchmark graphs can be freely downloaded from http://santo.fortunato.googlepages.com/inthepress

Community Detection as an Inference Problem

We express community detection as an inference problem of determining the most likely arrangement of communities. We then apply belief propagation and mean-field theory to this problem, and show that this leads to fast, accurate algorithms for community detection.Comment: 4 pages, 2 figure

Optimal map of the modular structure of complex networks

Modular structure is pervasive in many complex networks of interactions observed in natural, social and technological sciences. Its study sheds light on the relation between the structure and function of complex systems. Generally speaking, modules are islands of highly connected nodes separated by a relatively small number of links. Every module can have contributions of links from any node in the network. The challenge is to disentangle these contributions to understand how the modular structure is built. The main problem is that the analysis of a certain partition into modules involves, in principle, as many data as number of modules times number of nodes. To confront this challenge, here we first define the contribution matrix, the mathematical object containing all the information about the partition of interest, and after, we use a Truncated Singular Value Decomposition to extract the best representation of this matrix in a plane. The analysis of this projection allow us to scrutinize the skeleton of the modular structure, revealing the structure of individual modules and their interrelations.Comment: 21 pages, 10 figure

The Implementation of the Global Minimum Tax (GloBE): The Need for an Effective Dispute Prevention and Resolution Mechanism

The successful implementation of the Global Anti-Base Erosion (GloBE) rules on aglobal scale cannot be achieved without an international effective dispute prevention and reso-lution mechanism. However, the development of a dispute prevention and resolution frameworkfor the GloBE rules faces significant challenges. This article offers two possible options for aneffective dispute prevention and resolution mechanism: a model based on reciprocal domesticlegislations and the multilateral convention model

Impact of boundaries on fully connected random geometric networks

Many complex networks exhibit a percolation transition involving a macroscopic connected component, with universal features largely independent of the microscopic model and the macroscopic domain geometry. In contrast, we show that the transition to full connectivity is strongly influenced by details of the boundary, but observe an alternative form of universality. Our approach correctly distinguishes connectivity properties of networks in domains with equal bulk contributions. It also facilitates system design to promote or avoid full connectivity for diverse geometries in arbitrary dimension.Comment: 6 pages, 3 figure