PecanPy: a fast, efficient, and parallelized Python implementation of node2vec

Summary Learning low-dimensional representations (embeddings) of nodes in large graphs is key to applying machine learning on massive biological networks. Node2vec is the most widely used method for node embedding. However, its original Python and C ++ implementations scale poorly with network density, failing for dense biological networks with hundreds of millions of edges. We have developed PecanPy, a new Python implementation of node2vec that uses cache-optimized compact graph data structures and precomputing/parallelization to result in fast, high-quality node embeddings for biological networks of all sizes and densities. Availability PecanPy software is freely available at https://github.com/krishnanlab/PecanPy Supplementary information Supplementary data are available at Bioinformatics online.

PecanPy: a fast, efficient, and parallelized Python implementation of node2vec

Learning low-dimensional representations (embeddings) of nodes in large graphs is key to applying machine learning on massive biological networks. Node2vec is the most widely used method for node embedding. However, its original Python and C++ implementations scale poorly with network density, failing for dense biological networks with hundreds of millions of edges. We have developed PecanPy, a new Python implementation of node2vec that uses cache-optimized compact graph data structures and precomputing/parallelization to result in fast, high-quality node embeddings for biological networks of all sizes and densities. PecanPy software and documentation are available at https://github.com/krishnanlab/pecanpy.

Graph Based Translation Memory for Neural Machine Translation

A translation memory (TM) is proved to be helpful to improve neural machine translation (NMT). Existing approaches either pursue the decoding efficiency by merely accessing local information in a TM or encode the global information in a TM yet sacrificing efficiency due to redundancy. We propose an efficient approach to making use of the global information in a TM. The key idea is to pack a redundant TM into a compact graph and perform additional attention mechanisms over the packed graph for integrating the TM representation into the decoding network. We implement the model by extending the state-of-the-art NMT, Transformer. Extensive experiments on three language pairs show that the proposed approach is efficient in terms of running time and space occupation, and particularly it outperforms multiple strong baselines in terms of BLEU scores.

Scale Invariant Effective Hamiltonians for a Graph with a Small Compact Core

We consider a compact metric graph of size ε and attach to it several edges (leads) of length of order one (or of infinite length). As ε goes to zero, the graph G ε obtained in this way looks like the star-graph formed by the leads joined in a central vertex. On G ε we define an Hamiltonian H ε , properly scaled with the parameter ε . We prove that there exists a scale invariant effective Hamiltonian on the star-graph that approximates H ε (in a suitable norm resolvent sense) as ε → 0 . The effective Hamiltonian depends on the spectral properties of an auxiliary ε -independent Hamiltonian defined on the compact graph obtained by setting ε = 1 . If zero is not an eigenvalue of the auxiliary Hamiltonian, in the limit ε → 0 , the leads are decoupled.

Stackings and the W-cycles Conjecture

We prove Wise’s W-cycles conjecture. Consider a compact graph Γ' immersing into another graph Γ. For any immersed cycle Λ: S1 ⟶ Γ, we consider the map Λ' from the circular components 𝕊 of the pullback to Γ'. Unless Λ' is reducible, the degree of the covering map 𝕊 ⟶ S1 is bounded above by minus the Euler characteristic of Γ'. As a corollary, any finitely generated subgroup of a one-relator group has a finitely generated Schur multiplier.

Perfect non-commuting graphs of matrices over chains

In this paper, we study the non-commuting graph [Formula: see text] of strictly upper triangular [Formula: see text] matrices over an [Formula: see text]-element chain [Formula: see text]. We prove that [Formula: see text] is a compact graph. From [Formula: see text], we construct a poset [Formula: see text]. We further prove that [Formula: see text] is a dismantlable lattice and its zero-divisor graph is isomorphic to [Formula: see text]. Lastly, we prove that [Formula: see text] is a perfect graph.