44,217 research outputs found
Flow-Based Network Analysis of the Caenorhabditis elegans Connectome
We exploit flow propagation on the directed neuronal network of the nematode C. elegans to reveal dynamically relevant features of its connectome. We find flow-based groupings of neurons at different levels of granularity, which we relate to functional and anatomical constituents of its nervous system. A systematic in silico evaluation of the full set of single and double neuron ablations is used to identify deletions that induce the most severe disruptions of the multi-resolution flow structure. Such ablations are linked to functionally relevant neurons, and suggest potential candidates for further in vivo investigation. In addition, we use the directional patterns of incoming and outgoing network flows at all scales to identify flow profiles for the neurons in the connectome, without pre-imposing a priori categories. The four flow roles identified are linked to signal propagation motivated by biological input-response scenarios
Towards a Theory of Scale-Free Graphs: Definition, Properties, and Implications (Extended Version)
Although the ``scale-free'' literature is large and growing, it gives neither
a precise definition of scale-free graphs nor rigorous proofs of many of their
claimed properties. In fact, it is easily shown that the existing theory has
many inherent contradictions and verifiably false claims. In this paper, we
propose a new, mathematically precise, and structural definition of the extent
to which a graph is scale-free, and prove a series of results that recover many
of the claimed properties while suggesting the potential for a rich and
interesting theory. With this definition, scale-free (or its opposite,
scale-rich) is closely related to other structural graph properties such as
various notions of self-similarity (or respectively, self-dissimilarity).
Scale-free graphs are also shown to be the likely outcome of random
construction processes, consistent with the heuristic definitions implicit in
existing random graph approaches. Our approach clarifies much of the confusion
surrounding the sensational qualitative claims in the scale-free literature,
and offers rigorous and quantitative alternatives.Comment: 44 pages, 16 figures. The primary version is to appear in Internet
Mathematics (2005
Language-based Abstractions for Dynamical Systems
Ordinary differential equations (ODEs) are the primary means to modelling
dynamical systems in many natural and engineering sciences. The number of
equations required to describe a system with high heterogeneity limits our
capability of effectively performing analyses. This has motivated a large body
of research, across many disciplines, into abstraction techniques that provide
smaller ODE systems while preserving the original dynamics in some appropriate
sense. In this paper we give an overview of a recently proposed
computer-science perspective to this problem, where ODE reduction is recast to
finding an appropriate equivalence relation over ODE variables, akin to
classical models of computation based on labelled transition systems.Comment: In Proceedings QAPL 2017, arXiv:1707.0366
Mechanisms in Dynamically Complex Systems
In recent debates mechanisms are often discussed in the context of âcomplex systemsâ which are understood as having a complicated compositional structure. I want to draw the attention to another, radically different kind of complex system, in fact one that many scientists regard as the only genuine kind of complex system. Instead of being compositionally complex these systems rather exhibit highly non-trivial dynamical patterns on the basis of structurally simple arrangements of large numbers of non-linearly interacting constituents. The characteristic dynamical patterns in what I call âdynamically complex systemsâ arise from the interaction of the systemâs parts largely irrespective of many properties of these parts. Dynamically complex systems can exhibit surprising statistical characteristics, the robustness of which calls for an explanation in terms of underlying generating mechanisms. However, I want to argue, dynamically complex systems are not sufficiently covered by the available conceptions of mechanisms. I will explore how the notion of a mechanism has to be modified to accommodate this case. Moreover, I will show under which conditions the widespread, if not inflationary talk about mechanisms in (dynamically) complex systems stretches the notion of mechanisms beyond its reasonable limits and is no longer legitimate
Binding Social and Cultural Networks: A Model
Until now, most studies carried onto social or semantic networks have
considered each of these networks independently. Our goal here is to bring a
formal frame for studying both networks empirically as well as to point out
stylized facts that would explain their reciprocal influence and the emergence
of clusters of agents, which may also be regarded as ''cultural cliques''. We
show how to apply the Galois lattice theory to the modeling of the coevolution
of social and conceptual networks, and the characterization of cultural
communities. Basing our approach on Barabasi-Albert's models, we however extend
the usual preferential attachment probability in order to take into account the
reciprocal influence of both networks, therefore introducing the notion of dual
distance. In addition to providing a theoretic frame we draw here a program of
empirical tests which should give root to a more analytical model and the
consequent simulation and validation. In a broader view, adopting and actually
implementing the paradigm of cultural epidemiology, we could proceed further
with the study of knowledge diffusion and explain how the social network
structure affects concept propagation and in return how concept propagation
affects the social network.Comment: 8 pages, 3 figures (v2: typos, minor corrections in section 3.2) (v3:
examples, figures added
Agent-Based Models and Simulations in Economics and Social Sciences: from conceptual exploration to distinct ways of experimenting
Now that complex Agent-Based Models and computer simulations
spread over economics and social sciences - as in most sciences of complex
systems -, epistemological puzzles (re)emerge. We introduce new
epistemological tools so as to show to what precise extent each author is right
when he focuses on some empirical, instrumental or conceptual significance of
his model or simulation. By distinguishing between models and simulations,
between types of models, between types of computer simulations and between
types of empiricity, section 2 gives conceptual tools to explain the rationale of
the diverse epistemological positions presented in section 1. Finally, we claim
that a careful attention to the real multiplicity of denotational powers of
symbols at stake and then to the implicit routes of references operated by
models and computer simulations is necessary to determine, in each case, the
proper epistemic status and credibility of a given model and/or simulation
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