21,652 research outputs found
A pathway-based mean-field model for E. coli chemotaxis: Mathematical derivation and Keller-Segel limit
A pathway-based mean-field theory (PBMFT) was recently proposed for E. coli
chemotaxis in [G. Si, T. Wu, Q. Quyang and Y. Tu, Phys. Rev. Lett., 109 (2012),
048101]. In this paper, we derived a new moment system of PBMFT by using the
moment closure technique in kinetic theory under the assumption that the
methylation level is locally concentrated. The new system is hyperbolic with
linear convection terms. Under certain assumptions, the new system can recover
the original model. Especially the assumption on the methylation difference
made there can be understood explicitly in this new moment system. We obtain
the Keller-Segel limit by taking into account the different physical time
scales of tumbling, adaptation and the experimental observations. We also
present numerical evidence to show the quantitative agreement of the moment
system with the individual based E. coli chemotaxis simulator.Comment: 21 pages, 3 figure
Cluster-GCN: An Efficient Algorithm for Training Deep and Large Graph Convolutional Networks
Graph convolutional network (GCN) has been successfully applied to many
graph-based applications; however, training a large-scale GCN remains
challenging. Current SGD-based algorithms suffer from either a high
computational cost that exponentially grows with number of GCN layers, or a
large space requirement for keeping the entire graph and the embedding of each
node in memory. In this paper, we propose Cluster-GCN, a novel GCN algorithm
that is suitable for SGD-based training by exploiting the graph clustering
structure. Cluster-GCN works as the following: at each step, it samples a block
of nodes that associate with a dense subgraph identified by a graph clustering
algorithm, and restricts the neighborhood search within this subgraph. This
simple but effective strategy leads to significantly improved memory and
computational efficiency while being able to achieve comparable test accuracy
with previous algorithms. To test the scalability of our algorithm, we create a
new Amazon2M data with 2 million nodes and 61 million edges which is more than
5 times larger than the previous largest publicly available dataset (Reddit).
For training a 3-layer GCN on this data, Cluster-GCN is faster than the
previous state-of-the-art VR-GCN (1523 seconds vs 1961 seconds) and using much
less memory (2.2GB vs 11.2GB). Furthermore, for training 4 layer GCN on this
data, our algorithm can finish in around 36 minutes while all the existing GCN
training algorithms fail to train due to the out-of-memory issue. Furthermore,
Cluster-GCN allows us to train much deeper GCN without much time and memory
overhead, which leads to improved prediction accuracy---using a 5-layer
Cluster-GCN, we achieve state-of-the-art test F1 score 99.36 on the PPI
dataset, while the previous best result was 98.71 by [16]. Our codes are
publicly available at
https://github.com/google-research/google-research/tree/master/cluster_gcn.Comment: In Proceedings of the 25th ACM SIGKDD International Conference on
Knowledge Discovery & Data Mining (KDD'19
- …