Motivated by applications in domains such as social networks and
computational biology, we study the problem of community recovery in graphs
with locality. In this problem, pairwise noisy measurements of whether two
nodes are in the same community or different communities come mainly or
exclusively from nearby nodes rather than uniformly sampled between all nodes
pairs, as in most existing models. We present an algorithm that runs nearly
linearly in the number of measurements and which achieves the information
theoretic limit for exact recovery.

本文研究在带有局部性质的图中恢复社区的问题，提出了一种算法，它在测量数量上近线性，并且能够实现恢复的信息理论限制。

具有局部性的图中的社区恢复

Community Recovery in Graphs with Locality

A fundamental problem in the study of complex networks is to provide
quantitative measures of correlation and information flow between different
parts of a system. To this end, several notions of communicability have been
introduced and applied to a wide variety of real-world networks in recent
years. Several such communicability functions are reviewed in this paper. It is
emphasized that communication and correlation in networks can take place
through many more routes than the shortest paths, a fact that may not have been
sufficiently appreciated in previously proposed correlation measures. In
contrast to these, the communicability measures reviewed in this paper are
defined by taking into account all possible routes between two nodes, assigning
smaller weights to longer ones. This point of view naturally leads to the
definition of communicability in terms of matrix functions, such as the
exponential, resolvent, and hyperbolic functions, in which the matrix argument
is either the adjacency matrix or the graph Laplacian associated with the
network. Considerable insight on communicability can be gained by modeling a
network as a system of oscillators and deriving physical interpretations, both
classical and quantum-mechanical, of various communicability functions.
Applications of communicability measures to the analysis of complex systems are
illustrated on a variety of biological, physical and social networks. The last
part of the paper is devoted to a review of the notion of locality in complex
networks and to computational aspects that by exploiting sparsity can greatly
reduce the computational efforts for the calculation of communicability
functions for large networks.

本文综述了多种通信性能度量方法，定义了通过考虑所有可能的路径来定义通信性能度量，使用矩阵函数并介绍了该方法在复杂网络中的应用，同时还包括局部性和计算效率的问题。

复杂网络中可通信性的物理学

The Physics of Communicability in Complex Networks

Consider a linear [n,k,d]_q code C. We say that that i-th coordinate of C has
locality r, if the value at this coordinate can be recovered from accessing
some other r coordinates of C. Data storage applications require codes with
small redundancy, low locality for information coordinates, large distance, and
low locality for parity coordinates. In this paper we carry out an in-depth
study of the relations between these parameters.
We establish a tight bound for the redundancy n-k in terms of the message
length, the distance, and the locality of information coordinates. We refer to
codes attaining the bound as optimal. We prove some structure theorems about
optimal codes, which are particularly strong for small distances. This gives a
fairly complete picture of the tradeoffs between codewords length, worst-case
distance and locality of information symbols.
We then consider the locality of parity check symbols and erasure correction
beyond worst case distance for optimal codes. Using our structure theorem, we
obtain a tight bound for the locality of parity symbols possible in such codes
for a broad class of parameter settings. We prove that there is a tradeoff
between having good locality for parity checks and the ability to correct
erasures beyond the minimum distance.

本文深入研究了线性码本地性、冗余度、距离、信息符号本地性之间的关系，提出最优码这一概念，并探究了极限码的结构定理以及可纠删码中奇偶校验符号本地性与纠删误差能力之间的权衡。

编码词符号的本地性

On the Locality of Codeword Symbols

I discuss the general principles underlying quantum field theory, and attempt
to identify its most profound consequences. The deepest of these consequences
result from the infinite number of degrees of freedom invoked to implement
locality. I mention a few of its most striking successes, both achieved and
prospective. Possible limitations of quantum field theory are viewed in the
light of its history.

本文讨论量子场论的基本原则，并尝试确定其最深远的影响，最深远的影响来自于实现局域性所涉及的无限自由度。作者列出了它的一些最引人注目的成功，包括已经实现的和有前景的成功，并在历史的光辉下，讨论了量子场论的可能局限性。