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

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

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

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

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

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

Fast Community Identification by Hierarchical Growth

A new method for community identification is proposed which is founded on the analysis of successive neighborhoods, reached through hierarchical growth from a starting vertex, and on the definition of communities as a subgraph whose number of inner connections is larger than outer connections. In order to determine the precision and speed of the method, it is compared with one of the most popular community identification approaches, namely Girvan and Newman's algorithm. Although the hierarchical growth method is not as precise as Girvan and Newman's method, it is potentially faster than most community finding algorithms.Comment: 6 pages, 5 figure

Outlier Edge Detection Using Random Graph Generation Models and Applications

Outliers are samples that are generated by different mechanisms from other normal data samples. Graphs, in particular social network graphs, may contain nodes and edges that are made by scammers, malicious programs or mistakenly by normal users. Detecting outlier nodes and edges is important for data mining and graph analytics. However, previous research in the field has merely focused on detecting outlier nodes. In this article, we study the properties of edges and propose outlier edge detection algorithms using two random graph generation models. We found that the edge-ego-network, which can be defined as the induced graph that contains two end nodes of an edge, their neighboring nodes and the edges that link these nodes, contains critical information to detect outlier edges. We evaluated the proposed algorithms by injecting outlier edges into some real-world graph data. Experiment results show that the proposed algorithms can effectively detect outlier edges. In particular, the algorithm based on the Preferential Attachment Random Graph Generation model consistently gives good performance regardless of the test graph data. Further more, the proposed algorithms are not limited in the area of outlier edge detection. We demonstrate three different applications that benefit from the proposed algorithms: 1) a preprocessing tool that improves the performance of graph clustering algorithms; 2) an outlier node detection algorithm; and 3) a novel noisy data clustering algorithm. These applications show the great potential of the proposed outlier edge detection techniques.Comment: 14 pages, 5 figures, journal pape

Suppression of Zeeman gradients by nuclear polarization in double quantum dots

We use electric dipole spin resonance to measure dynamic nuclear polarization in InAs nanowire quantum dots. The resonance shifts in frequency when the system transitions between metastable high and low current states, indicating the presence of nuclear polarization. We propose that the low and the high current states correspond to different total Zeeman energy gradients between the two quantum dots. In the low current state, dynamic nuclear polarization efficiently compensates the Zeeman gradient due to the $g$-factor mismatch, resulting in a suppressed total Zeeman gradient. We present a theoretical model of electron-nuclear feedback that demonstrates a fixed point in nuclear polarization for nearly equal Zeeman splittings in the two dots and predicts a narrowed hyperfine gradient distribution