871 research outputs found
Topological orderings of weighted directed acyclic graphs
We call a topological ordering of a weighted directed acyclic graph
non-negative if the sum of weights on the vertices in any prefix of the
ordering is non-negative. We investigate two processes for constructing
non-negative topological orderings of weighted directed acyclic graphs. The
first process is called a mark sequence and the second is a generalization
called a mark-unmark sequence. We answer a question of Erickson by showing that
every non-negative topological ordering that can be realized by a mark-unmark
sequence can also be realized by a mark sequence. We also investigate the
question of whether a given weighted directed acyclic graph has a non-negative
topological ordering. We show that even in the simple case when every vertex is
a source or a sink the question is NP-complete.Comment: Included an addendum remarking on an independent proof of one of our
main theorems; added references; corrected typo
Inferring Regulatory Networks by Combining Perturbation Screens and Steady State Gene Expression Profiles
Reconstructing transcriptional regulatory networks is an important task in
functional genomics. Data obtained from experiments that perturb genes by
knockouts or RNA interference contain useful information for addressing this
reconstruction problem. However, such data can be limited in size and/or are
expensive to acquire. On the other hand, observational data of the organism in
steady state (e.g. wild-type) are more readily available, but their
informational content is inadequate for the task at hand. We develop a
computational approach to appropriately utilize both data sources for
estimating a regulatory network. The proposed approach is based on a three-step
algorithm to estimate the underlying directed but cyclic network, that uses as
input both perturbation screens and steady state gene expression data. In the
first step, the algorithm determines causal orderings of the genes that are
consistent with the perturbation data, by combining an exhaustive search method
with a fast heuristic that in turn couples a Monte Carlo technique with a fast
search algorithm. In the second step, for each obtained causal ordering, a
regulatory network is estimated using a penalized likelihood based method,
while in the third step a consensus network is constructed from the highest
scored ones. Extensive computational experiments show that the algorithm
performs well in reconstructing the underlying network and clearly outperforms
competing approaches that rely only on a single data source. Further, it is
established that the algorithm produces a consistent estimate of the regulatory
network.Comment: 24 pages, 4 figures, 6 table
Dependency Mapping Software for Jira, Project Management Tool
Efficiently managing a software development project is extremely important in industry and is often overlooked by the software developers on a project. Pieces of development work are identified by developers and are then handed off to project managers, who are left to organize this information. Project managers must organize this to set expectations for the client, and ensure the project stays on track and on budget. The main block in this process are dependency chains between tasks. Dependency chains can cause a project to take much longer than anticipated or result in the under utilization of developers on a project. While project managers do have access to project management tools, few have capabilities to effectively visualize dependencies. The goal of this research was to interact with a project management tool\u27s API, pull down dependency information for a project, and build out possible timelines for a set of tasks. We visualize this problem with a directed graph, where each node is a task and edges in the graph indicate dependencies. The relationships between this problem and more well-known problems in graph theory are used to inform the development of the algorithms. Two algorithms are explored to handle the problem and are then run under different conditions. Analysis of the results provide insight to what structures of dependency chains can be handled by the algorithms. The resulting software could be used to save companies both time and money when planning software development projects
Advances in Learning Bayesian Networks of Bounded Treewidth
This work presents novel algorithms for learning Bayesian network structures
with bounded treewidth. Both exact and approximate methods are developed. The
exact method combines mixed-integer linear programming formulations for
structure learning and treewidth computation. The approximate method consists
in uniformly sampling -trees (maximal graphs of treewidth ), and
subsequently selecting, exactly or approximately, the best structure whose
moral graph is a subgraph of that -tree. Some properties of these methods
are discussed and proven. The approaches are empirically compared to each other
and to a state-of-the-art method for learning bounded treewidth structures on a
collection of public data sets with up to 100 variables. The experiments show
that our exact algorithm outperforms the state of the art, and that the
approximate approach is fairly accurate.Comment: 23 pages, 2 figures, 3 table
Differentiable Bayesian Structure Learning with Acyclicity Assurance
Score-based approaches in the structure learning task are thriving because of
their scalability. Continuous relaxation has been the key reason for this
advancement. Despite achieving promising outcomes, most of these methods are
still struggling to ensure that the graphs generated from the latent space are
acyclic by minimizing a defined score. There has also been another trend of
permutation-based approaches, which concern the search for the topological
ordering of the variables in the directed acyclic graph in order to limit the
search space of the graph. In this study, we propose an alternative approach
for strictly constraining the acyclicty of the graphs with an integration of
the knowledge from the topological orderings. Our approach can reduce inference
complexity while ensuring the structures of the generated graphs to be acyclic.
Our empirical experiments with simulated and real-world data show that our
approach can outperform related Bayesian score-based approaches.Comment: Accepted as a regular paper (9.37%) at the 23rd IEEE International
Conference on Data Mining (ICDM 2023
On the Stability of Community Detection Algorithms on Longitudinal Citation Data
There are fundamental differences between citation networks and other classes
of graphs. In particular, given that citation networks are directed and
acyclic, methods developed primarily for use with undirected social network
data may face obstacles. This is particularly true for the dynamic development
of community structure in citation networks. Namely, it is neither clear when
it is appropriate to employ existing community detection approaches nor is it
clear how to choose among existing approaches. Using simulated data, we attempt
to clarify the conditions under which one should use existing methods and which
of these algorithms is appropriate in a given context. We hope this paper will
serve as both a useful guidepost and an encouragement to those interested in
the development of more targeted approaches for use with longitudinal citation
data.Comment: 17 pages, 7 figures, presenting at Applications of Social Network
Analysis 2009, ETH Zurich Edit, August 17, 2009: updated abstract, figures,
text clarification
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