Constructing graphs from genetic encodings

Our understanding of real-world connected systems has benefited from studying their evolution, from random wirings and rewirings to growth-dependent topologies. Long overlooked in this search has been the role of the innate: networks that connect based on identity-dependent compatibility rules. Inspired by the genetic principles that guide brain connectivity, we derive a network encoding process that can utilize wiring rules to reproducibly generate specific topologies. To illustrate the representational power of this approach, we propose stochastic and deterministic processes for generating a wide range of network topologies. Specifically, we detail network heuristics that generate structured graphs, such as feed-forward and hierarchical networks. In addition, we characterize a Random Genetic (RG) family of networks, which, like Erdős–Rényi graphs, display critical phase transitions, however their modular underpinnings lead to markedly different behaviors under targeted attacks. The proposed framework provides a relevant null-model for social and biological systems, where diverse metrics of identity underpin a node’s preferred connectivity.

OpenKG Chain: A Blockchain Infrastructure for Open Knowledge Graphs

The early concept of knowledge graph originates from the idea of the Semantic Web, which aims at using structured graphs to model the knowledge of the world and record the relationships that exist between things. Currently publishing knowledge bases as open data on the Web has gained significant attention. In China, CIPS(Chinese Information Processing Society) launched the OpenKG in 2015 to foster the development of Chinese Open Knowledge Graphs. Unlike existing open knowledge-based programs, OpenKG chain is envisioned as a blockchain-based open knowledge infrastructure. This article introduces the first attempt at the implementation of sharing knowledge graphs on OpenKG chain, a blockchain-based trust network. We have completed the test of the underlying blockchain platform, as well as the on-chain test of OpenKG's dataset and toolset sharing as well as fine-grained knowledge crowdsourcing at the triple level. We have also proposed novel definitions: K-Point and OpenKG Token, which can be considered as a measurement of knowledge value and user value. 1033 knowledge contributors have been involved in two months of testing on the blockchain, and the cumulative number of on-chain recordings triggered by real knowledge consumers has reached 550,000 with an average daily peak value of more than 10,000. For the first time, We have tested and realized on-chain sharing of knowledge at entity/triple granularity level. At present, all operations on the datasets and toolset in OpenKG.CN, as well as the triplets in OpenBase, are recorded on the chain, and corresponding value will also be generated and assigned in a trusted mode. Via this effort, OpenKG chain looks to provide a more credible and traceable knowledge-sharing platform for the knowledge graph community.

Constructing Graphs from Genetic Encodings

Our understanding of real-world connected systems has benefited from studying their evolution, from random wirings and rewirings to growth-dependent topologies. Long overlooked in this search has been the role of the innate: networks that connect based on identity-dependent compatibility rules. Inspired by the genetic principles that guide brain connectivity, we derive a network encoding process that can utilize wiring rules to reproducibly generate specific topologies. To illustrate the representational power of this approach, we propose stochastic and deterministic processes for generating a wide range of network topologies. Specifically, we detail network heuristics that generate structured graphs, such as feed-forward and hierarchical networks. In addition, we characterize a Random Genetic (RG) family of networks, which, like Erdős-Rényi graphs, display critical phase transitions, however their modular underpinnings lead to markedly different behaviors under targeted attacks. The proposed framework provides a relevant null-model for social and biological systems, where diverse metrics of identity underpin a node’s preferred connectivity.

Fast Spectral Approximation of Structured Graphs with Applications to Graph Filtering

To analyze and synthesize signals on networks or graphs, Fourier theory has been extended to irregular domains, leading to a so-called graph Fourier transform. Unfortunately, different from the traditional Fourier transform, each graph exhibits a different graph Fourier transform. Therefore to analyze the graph-frequency domain properties of a graph signal, the graph Fourier modes and graph frequencies must be computed for the graph under study. Although to find these graph frequencies and modes, a computationally expensive, or even prohibitive, eigendecomposition of the graph is required, there exist families of graphs that have properties that could be exploited for an approximate fast graph spectrum computation. In this work, we aim to identify these families and to provide a divide-and-conquer approach for computing an approximate spectral decomposition of the graph. Using the same decomposition, results on reducing the complexity of graph filtering are derived. These results provide an attempt to leverage the underlying topological properties of graphs in order to devise general computational models for graph signal processing.

Learning cognitive maps as structured graphs for vicarious evaluation

Cognitive maps are mental representations of spatial and conceptual relationships in an environment. These maps are critical for flexible behavior as they permit us to navigate vicariously, but their underlying representation learning mechanisms are still unknown. To form these abstract maps, hippocampus has to learn to separate or merge aliased observations appropriately in different contexts in a manner that enables generalization, efficient planning, and handling of uncertainty. Here we introduce a specific higher-order graph structure – clone-structured cognitive graph (CSCG) – which forms different clones of an observation for different contexts as a representation that addresses these problems. CSCGs can be learned efficiently using a novel probabilistic sequence model that is inherently robust to uncertainty. We show that CSCGs can explain a variety cognitive map phenomena such as discovering spatial relations from an aliased sensory stream, transitive inference between disjoint episodes of experiences, formation of transferable structural knowledge, and shortcut-finding in novel environments. By learning different clones for different contexts, CSCGs explain the emergence of splitter cells and route-specific encoding of place cells observed in maze navigation, and event-specific graded representations observed in lap-running experiments. Moreover, learning and inference dynamics of CSCGs offer a coherent explanation for a variety of place cell remapping phenomena. By lifting the aliased observations into a hidden space, CSCGs reveal latent modularity that is then used for hierarchical abstraction and planning. Altogether, learning and inference using a CSCG provides a simple unifying framework for understanding hippocampal function, and could be a pathway for forming relational abstractions in artificial intelligence.

Vertex Labeling and Routing for Farey-Type Symmetrically-Structured Graphs

The generalization of Farey graphs and extended Farey graphs all originate from Farey graphs. They are simultaneously scale-free and small-world. A labeling of the vertices for them are proposed here. All of the shortest paths between any two vertices in these two graphs can be determined only on their labels. The number of shortest paths between any two vertices is the product of two Fibonacci numbers; it is increasing almost linearly with the order or size of the graphs. However, the label-based routing algorithm runs in logarithmic time O(logn). Our efficient routing protocol for Farey-type models should help contribute toward the understanding of several physical dynamic processes.

Vertex Labeling and Routing for Farey-Type Symmetrically-Structured Graphs

The generalization of Farey graphs and extended Farey graphs are all originated from Farey graph and scale-free and small-world simultaneously. We propose a labeling of the vertices for it that allows determining all the shortest paths routing between any two vertices only based on their labels. The maximum number of shortest paths between any two vertices is huge as the product of two Fibonacci numbers, however, the label-based routing algorithm runs in linear time O(n). The existence of an efficient routing protocol for Farey-type models should help the understanding of several physical dynamic processes on it.