480 research outputs found
Multilayer Networks
In most natural and engineered systems, a set of entities interact with each
other in complicated patterns that can encompass multiple types of
relationships, change in time, and include other types of complications. Such
systems include multiple subsystems and layers of connectivity, and it is
important to take such "multilayer" features into account to try to improve our
understanding of complex systems. Consequently, it is necessary to generalize
"traditional" network theory by developing (and validating) a framework and
associated tools to study multilayer systems in a comprehensive fashion. The
origins of such efforts date back several decades and arose in multiple
disciplines, and now the study of multilayer networks has become one of the
most important directions in network science. In this paper, we discuss the
history of multilayer networks (and related concepts) and review the exploding
body of work on such networks. To unify the disparate terminology in the large
body of recent work, we discuss a general framework for multilayer networks,
construct a dictionary of terminology to relate the numerous existing concepts
to each other, and provide a thorough discussion that compares, contrasts, and
translates between related notions such as multilayer networks, multiplex
networks, interdependent networks, networks of networks, and many others. We
also survey and discuss existing data sets that can be represented as
multilayer networks. We review attempts to generalize single-layer-network
diagnostics to multilayer networks. We also discuss the rapidly expanding
research on multilayer-network models and notions like community structure,
connected components, tensor decompositions, and various types of dynamical
processes on multilayer networks. We conclude with a summary and an outlook.Comment: Working paper; 59 pages, 8 figure
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
When Is network lasso accurate?
The “least absolute shrinkage and selection operator” (Lasso) method has been adapted recently for network-structured datasets. In particular, this network Lasso method allows to learn graph signals from a small number of noisy signal samples by using the total variation of a graph signal for regularization. While efficient and scalable implementations of the network Lasso are available, only little is known about the conditions on the underlying network structure which ensure network Lasso to be accurate. By leveraging concepts of compressed sensing, we address this gap and derive precise conditions on the underlying network topology and sampling set which guarantee the network Lasso for a particular loss function to deliver an accurate estimate of the entire underlying graph signal. We also quantify the error incurred by network Lasso in terms of two constants which reflect the connectivity of the sampled nodes
Computational Studies on the Evolution of Metabolism
Living organisms throughout evolution have developed desired properties, such as the ability
of maintaining functionality despite changes in the environment or their inner structure, the
formation of functional modules, from metabolic pathways to organs, and most essentially
the capacity to adapt and evolve in a process called natural selection. It can be observed in
the metabolic networks of modern organisms that many key pathways such as the citric acid
cycle, glycolysis, or the biosynthesis of most amino acids are common to all of them.
Understanding the evolutionary mechanisms behind this development of complex biological
systems is an intriguing and important task of current research in biology as well as artificial
life. Several competing hypotheses for the formation of metabolic pathways and the mecha-
nisms that shape metabolic networks have been discussed in the literature, each of which finds
support from comparative analysis of extant genomes. However, while being powerful tools
for the investigation of metabolic evolution, these traditional methods do not allow to look
back in evolution far enough to the time when metabolism had to emerge and evolve to the
form we can observe today. To this end, simulation studies have been introduced to discover
the principles of metabolic evolution and the sources for the emergence of metabolism prop-
erties. These approaches differ considerably in the realism and explicitness of the underlying
models. A difficult trade-off between realism and computational feasibility has to be made
and further modeling decisions on many scales have to be taken into account, requiring the
combination of knowledge from different fields such as chemistry, physics, biology and last
but not least also computer science.
In this thesis, a novel computational model for the in silico evolution of early metabolism
is introduced. It comprises all the components on different scales to resemble a situation of
evolving metabolic protocells in an RNA-world. Therefore, the model contains a minimal
RNA-based genetics and an evolving metabolism of catalytic ribozymes that manipulate a
rich underlying chemistry. To allow the metabolic organization to escape from the confines
of the chemical space set by the initial conditions of the simulation and in general an open-
ended evolution, an evolvable sequence-to-function map is used. At the heart of the metabolic
subsystem is a graph-based artificial chemistry equipped with a built-in thermodynamics. The
generation of the metabolic reaction network is realized as a rule-based stochastic simulation.
The necessary reaction rates are calculated from the chemical graphs of the reactants on
the fly. The selection procedure among the population of protocells is based on the optimal metabolic yield of the protocells, which is computed using flux balance analysis.
The introduced computational model allows for profound investigations of the evolution of
early metabolism and the underlying evolutionary mechanisms. One application in this thesis
is the study of the formation of metabolic pathways. Therefore, four established hypothe-
ses, namely the backwards evolution, forward evolution, patchwork evolution and the shell
hypothesis, are discussed within the realms of this in silico evolution study. The metabolic
pathways of the networks, evolved in various simulation runs, are determined and analyzed
in terms of their evolutionary direction. The simulation results suggest that the seemingly
mutually exclusive hypotheses may well be compatible when considering that different pro-
cesses dominate different phases in the evolution of a metabolic system. Further, it is found
that forward evolution shapes the metabolic network in the very early steps of evolution. In
later and more complex stages, enzyme recruitment supersedes forward evolution, keeping a
core set of pathways from the early phase. Backward evolution can only be observed under
conditions of steady environmental change. Additionally, evolutionary history of enzymes
and metabolites were studied on the network level as well as for single instances, showing a
great variety of evolutionary mechanisms at work.
The second major focus of the in silico evolutionary study is the emergence of complex system
properties, such as robustness and modularity. To this end several techniques to analyze the
metabolic systems were used. The measures for complex properties stem from the fields of
graph theory, steady state analysis and neutral network theory. Some are used in general
network analysis and others were developed specifically for the purpose introduced in this
work. To discover potential sources for the emergence of system properties, three different
evolutionary scenarios were tested and compared. The first two scenarios are the same as
for the first part of the investigation, one scenario of evolution under static conditions and
one incorporating a steady change in the set of ”food” molecules. A third scenario was
added that also simulates a static evolution but with an increased mutation rate and regular
events of horizontal gene transfer between protocells of the population. The comparison of all
three scenarios with real world metabolic networks shows a significant similarity in structure
and properties. Among the three scenarios, the two static evolutions yield the most robust
metabolic networks, however, the networks evolved under environmental change exhibit their
own strategy to a robustness more suited to their conditions. As expected from theory,
horizontal gene transfer and changes in the environment seem to produce higher degrees
of modularity in metabolism. Both scenarios develop rather different kinds of modularity,
while horizontal gene transfer provides for more isolated modules, the modules of the second
scenario are far more interconnected
Computational Studies on the Evolution of Metabolism
Living organisms throughout evolution have developed desired properties, such as the ability
of maintaining functionality despite changes in the environment or their inner structure, the
formation of functional modules, from metabolic pathways to organs, and most essentially
the capacity to adapt and evolve in a process called natural selection. It can be observed in
the metabolic networks of modern organisms that many key pathways such as the citric acid
cycle, glycolysis, or the biosynthesis of most amino acids are common to all of them.
Understanding the evolutionary mechanisms behind this development of complex biological
systems is an intriguing and important task of current research in biology as well as artificial
life. Several competing hypotheses for the formation of metabolic pathways and the mecha-
nisms that shape metabolic networks have been discussed in the literature, each of which finds
support from comparative analysis of extant genomes. However, while being powerful tools
for the investigation of metabolic evolution, these traditional methods do not allow to look
back in evolution far enough to the time when metabolism had to emerge and evolve to the
form we can observe today. To this end, simulation studies have been introduced to discover
the principles of metabolic evolution and the sources for the emergence of metabolism prop-
erties. These approaches differ considerably in the realism and explicitness of the underlying
models. A difficult trade-off between realism and computational feasibility has to be made
and further modeling decisions on many scales have to be taken into account, requiring the
combination of knowledge from different fields such as chemistry, physics, biology and last
but not least also computer science.
In this thesis, a novel computational model for the in silico evolution of early metabolism
is introduced. It comprises all the components on different scales to resemble a situation of
evolving metabolic protocells in an RNA-world. Therefore, the model contains a minimal
RNA-based genetics and an evolving metabolism of catalytic ribozymes that manipulate a
rich underlying chemistry. To allow the metabolic organization to escape from the confines
of the chemical space set by the initial conditions of the simulation and in general an open-
ended evolution, an evolvable sequence-to-function map is used. At the heart of the metabolic
subsystem is a graph-based artificial chemistry equipped with a built-in thermodynamics. The
generation of the metabolic reaction network is realized as a rule-based stochastic simulation.
The necessary reaction rates are calculated from the chemical graphs of the reactants on
the fly. The selection procedure among the population of protocells is based on the optimal metabolic yield of the protocells, which is computed using flux balance analysis.
The introduced computational model allows for profound investigations of the evolution of
early metabolism and the underlying evolutionary mechanisms. One application in this thesis
is the study of the formation of metabolic pathways. Therefore, four established hypothe-
ses, namely the backwards evolution, forward evolution, patchwork evolution and the shell
hypothesis, are discussed within the realms of this in silico evolution study. The metabolic
pathways of the networks, evolved in various simulation runs, are determined and analyzed
in terms of their evolutionary direction. The simulation results suggest that the seemingly
mutually exclusive hypotheses may well be compatible when considering that different pro-
cesses dominate different phases in the evolution of a metabolic system. Further, it is found
that forward evolution shapes the metabolic network in the very early steps of evolution. In
later and more complex stages, enzyme recruitment supersedes forward evolution, keeping a
core set of pathways from the early phase. Backward evolution can only be observed under
conditions of steady environmental change. Additionally, evolutionary history of enzymes
and metabolites were studied on the network level as well as for single instances, showing a
great variety of evolutionary mechanisms at work.
The second major focus of the in silico evolutionary study is the emergence of complex system
properties, such as robustness and modularity. To this end several techniques to analyze the
metabolic systems were used. The measures for complex properties stem from the fields of
graph theory, steady state analysis and neutral network theory. Some are used in general
network analysis and others were developed specifically for the purpose introduced in this
work. To discover potential sources for the emergence of system properties, three different
evolutionary scenarios were tested and compared. The first two scenarios are the same as
for the first part of the investigation, one scenario of evolution under static conditions and
one incorporating a steady change in the set of ”food” molecules. A third scenario was
added that also simulates a static evolution but with an increased mutation rate and regular
events of horizontal gene transfer between protocells of the population. The comparison of all
three scenarios with real world metabolic networks shows a significant similarity in structure
and properties. Among the three scenarios, the two static evolutions yield the most robust
metabolic networks, however, the networks evolved under environmental change exhibit their
own strategy to a robustness more suited to their conditions. As expected from theory,
horizontal gene transfer and changes in the environment seem to produce higher degrees
of modularity in metabolism. Both scenarios develop rather different kinds of modularity,
while horizontal gene transfer provides for more isolated modules, the modules of the second
scenario are far more interconnected
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