2,603 research outputs found
Computing Scalable Multivariate Glocal Invariants of Large (Brain-) Graphs
Graphs are quickly emerging as a leading abstraction for the representation
of data. One important application domain originates from an emerging
discipline called "connectomics". Connectomics studies the brain as a graph;
vertices correspond to neurons (or collections thereof) and edges correspond to
structural or functional connections between them. To explore the variability
of connectomes---to address both basic science questions regarding the
structure of the brain, and medical health questions about psychiatry and
neurology---one can study the topological properties of these brain-graphs. We
define multivariate glocal graph invariants: these are features of the graph
that capture various local and global topological properties of the graphs. We
show that the collection of features can collectively be computed via a
combination of daisy-chaining, sparse matrix representation and computations,
and efficient approximations. Our custom open-source Python package serves as a
back-end to a Web-service that we have created to enable researchers to upload
graphs, and download the corresponding invariants in a number of different
formats. Moreover, we built this package to support distributed processing on
multicore machines. This is therefore an enabling technology for network
science, lowering the barrier of entry by providing tools to biologists and
analysts who otherwise lack these capabilities. As a demonstration, we run our
code on 120 brain-graphs, each with approximately 16M vertices and up to 90M
edges.Comment: Published as part of 2013 IEEE GlobalSIP conferenc
The Minimum Wiener Connector
The Wiener index of a graph is the sum of all pairwise shortest-path
distances between its vertices. In this paper we study the novel problem of
finding a minimum Wiener connector: given a connected graph and a set
of query vertices, find a subgraph of that connects all
query vertices and has minimum Wiener index.
We show that The Minimum Wiener Connector admits a polynomial-time (albeit
impractical) exact algorithm for the special case where the number of query
vertices is bounded. We show that in general the problem is NP-hard, and has no
PTAS unless . Our main contribution is a
constant-factor approximation algorithm running in time
.
A thorough experimentation on a large variety of real-world graphs confirms
that our method returns smaller and denser solutions than other methods, and
does so by adding to the query set a small number of important vertices
(i.e., vertices with high centrality).Comment: Published in Proceedings of the 2015 ACM SIGMOD International
Conference on Management of Dat
An Automated Images-to-Graphs Framework for High Resolution Connectomics
Reconstructing a map of neuronal connectivity is a critical challenge in
contemporary neuroscience. Recent advances in high-throughput serial section
electron microscopy (EM) have produced massive 3D image volumes of nanoscale
brain tissue for the first time. The resolution of EM allows for individual
neurons and their synaptic connections to be directly observed. Recovering
neuronal networks by manually tracing each neuronal process at this scale is
unmanageable, and therefore researchers are developing automated image
processing modules. Thus far, state-of-the-art algorithms focus only on the
solution to a particular task (e.g., neuron segmentation or synapse
identification).
In this manuscript we present the first fully automated images-to-graphs
pipeline (i.e., a pipeline that begins with an imaged volume of neural tissue
and produces a brain graph without any human interaction). To evaluate overall
performance and select the best parameters and methods, we also develop a
metric to assess the quality of the output graphs. We evaluate a set of
algorithms and parameters, searching possible operating points to identify the
best available brain graph for our assessment metric. Finally, we deploy a
reference end-to-end version of the pipeline on a large, publicly available
data set. This provides a baseline result and framework for community analysis
and future algorithm development and testing. All code and data derivatives
have been made publicly available toward eventually unlocking new biofidelic
computational primitives and understanding of neuropathologies.Comment: 13 pages, first two authors contributed equally V2: Added additional
experiments and clarifications; added information on infrastructure and
pipeline environmen
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