2,900 research outputs found
How to Upscale The Kinetics of Complex Microsystems
The rate constants of chemical reactions are typically inferred from slopes
and intersection points of observed concentration curves. In small systems that
operate far below the thermodynamic limit, these concentration profiles become
stochastic and such an inference is less straightforward. By using elements of
queuing theory, we introduce a procedure for inferring (time dependent) kinetic
parameters from microscopic observations that are given by molecular
simulations of many simultaneously reacting species. We demonstrate that with
this procedure it is possible to assimilate the results of molecular
simulations in such a way that the latter become descriptive on the macroscopic
scale. As an example, we upscale the kinetics of a molecular dynamics system
that forms a complex molecular network. Incidentally, we report that the
kinetic parameters of this system feature a peculiar time and temperature
dependences, whereas the probability of a network strand to close a cycle
follows a universal distribution
Topology Discovery of Sparse Random Graphs With Few Participants
We consider the task of topology discovery of sparse random graphs using
end-to-end random measurements (e.g., delay) between a subset of nodes,
referred to as the participants. The rest of the nodes are hidden, and do not
provide any information for topology discovery. We consider topology discovery
under two routing models: (a) the participants exchange messages along the
shortest paths and obtain end-to-end measurements, and (b) additionally, the
participants exchange messages along the second shortest path. For scenario
(a), our proposed algorithm results in a sub-linear edit-distance guarantee
using a sub-linear number of uniformly selected participants. For scenario (b),
we obtain a much stronger result, and show that we can achieve consistent
reconstruction when a sub-linear number of uniformly selected nodes
participate. This implies that accurate discovery of sparse random graphs is
tractable using an extremely small number of participants. We finally obtain a
lower bound on the number of participants required by any algorithm to
reconstruct the original random graph up to a given edit distance. We also
demonstrate that while consistent discovery is tractable for sparse random
graphs using a small number of participants, in general, there are graphs which
cannot be discovered by any algorithm even with a significant number of
participants, and with the availability of end-to-end information along all the
paths between the participants.Comment: A shorter version appears in ACM SIGMETRICS 2011. This version is
scheduled to appear in J. on Random Structures and Algorithm
Detection of Core-Periphery Structure in Networks Using Spectral Methods and Geodesic Paths
We introduce several novel and computationally efficient methods for
detecting "core--periphery structure" in networks. Core--periphery structure is
a type of mesoscale structure that includes densely-connected core vertices and
sparsely-connected peripheral vertices. Core vertices tend to be well-connected
both among themselves and to peripheral vertices, which tend not to be
well-connected to other vertices. Our first method, which is based on
transportation in networks, aggregates information from many geodesic paths in
a network and yields a score for each vertex that reflects the likelihood that
a vertex is a core vertex. Our second method is based on a low-rank
approximation of a network's adjacency matrix, which can often be expressed as
a tensor-product matrix. Our third approach uses the bottom eigenvector of the
random-walk Laplacian to infer a coreness score and a classification into core
and peripheral vertices. We also design an objective function to (1) help
classify vertices into core or peripheral vertices and (2) provide a
goodness-of-fit criterion for classifications into core versus peripheral
vertices. To examine the performance of our methods, we apply our algorithms to
both synthetically-generated networks and a variety of networks constructed
from real-world data sets.Comment: This article is part of EJAM's December 2016 special issue on
"Network Analysis and Modelling" (available at
https://www.cambridge.org/core/journals/european-journal-of-applied-mathematics/issue/journal-ejm-volume-27-issue-6/D245C89CABF55DBF573BB412F7651ADB
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Transforming Graph Representations for Statistical Relational Learning
Relational data representations have become an increasingly important topic
due to the recent proliferation of network datasets (e.g., social, biological,
information networks) and a corresponding increase in the application of
statistical relational learning (SRL) algorithms to these domains. In this
article, we examine a range of representation issues for graph-based relational
data. Since the choice of relational data representation for the nodes, links,
and features can dramatically affect the capabilities of SRL algorithms, we
survey approaches and opportunities for relational representation
transformation designed to improve the performance of these algorithms. This
leads us to introduce an intuitive taxonomy for data representation
transformations in relational domains that incorporates link transformation and
node transformation as symmetric representation tasks. In particular, the
transformation tasks for both nodes and links include (i) predicting their
existence, (ii) predicting their label or type, (iii) estimating their weight
or importance, and (iv) systematically constructing their relevant features. We
motivate our taxonomy through detailed examples and use it to survey and
compare competing approaches for each of these tasks. We also discuss general
conditions for transforming links, nodes, and features. Finally, we highlight
challenges that remain to be addressed
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