4,298 research outputs found
Dynamical Systems on Networks: A Tutorial
We give a tutorial for the study of dynamical systems on networks. We focus
especially on "simple" situations that are tractable analytically, because they
can be very insightful and provide useful springboards for the study of more
complicated scenarios. We briefly motivate why examining dynamical systems on
networks is interesting and important, and we then give several fascinating
examples and discuss some theoretical results. We also briefly discuss
dynamical systems on dynamical (i.e., time-dependent) networks, overview
software implementations, and give an outlook on the field.Comment: 39 pages, 1 figure, submitted, more examples and discussion than
original version, some reorganization and also more pointers to interesting
direction
Time-delayed model of immune response in plants
In the studies of plant infections, the plant immune response is known to play an essential role. In this paper we derive and analyse a new mathematical model of plant immune response with particular account for post-transcriptional gene silencing (PTGS). Besides biologically accurate representation of the PTGS dynamics, the model explicitly includes two time delays to represent the maturation time of the growing plant tissue and the non-instantaneous nature of the PTGS. Through analytical and numerical analysis of stability of the steady states of the model we identify parameter regions associated with recovery
and resistant phenotypes, as well as possible chronic infections. Dynamics of the system in these regimes is illustrated by numerical simulations of the model
Towards dynamical network biomarkers in neuromodulation of episodic migraine
Computational methods have complemented experimental and clinical
neursciences and led to improvements in our understanding of the nervous
systems in health and disease. In parallel, neuromodulation in form of electric
and magnetic stimulation is gaining increasing acceptance in chronic and
intractable diseases. In this paper, we firstly explore the relevant state of
the art in fusion of both developments towards translational computational
neuroscience. Then, we propose a strategy to employ the new theoretical concept
of dynamical network biomarkers (DNB) in episodic manifestations of chronic
disorders. In particular, as a first example, we introduce the use of
computational models in migraine and illustrate on the basis of this example
the potential of DNB as early-warning signals for neuromodulation in episodic
migraine.Comment: 13 pages, 5 figure
Network Inoculation: Heteroclinics and phase transitions in an epidemic model
In epidemiological modelling, dynamics on networks, and in particular
adaptive and heterogeneous networks have recently received much interest. Here
we present a detailed analysis of a previously proposed model that combines
heterogeneity in the individuals with adaptive rewiring of the network
structure in response to a disease. We show that in this model qualitative
changes in the dynamics occur in two phase transitions. In a macroscopic
description one of these corresponds to a local bifurcation whereas the other
one corresponds to a non-local heteroclinic bifurcation. This model thus
provides a rare example of a system where a phase transition is caused by a
non-local bifurcation, while both micro- and macro-level dynamics are
accessible to mathematical analysis. The bifurcation points mark the onset of a
behaviour that we call network inoculation. In the respective parameter region
exposure of the system to a pathogen will lead to an outbreak that collapses,
but leaves the network in a configuration where the disease cannot reinvade,
despite every agent returning to the susceptible class. We argue that this
behaviour and the associated phase transitions can be expected to occur in a
wide class of models of sufficient complexity.Comment: 26 pages, 11 figure
Epidemic processes in complex networks
In recent years the research community has accumulated overwhelming evidence
for the emergence of complex and heterogeneous connectivity patterns in a wide
range of biological and sociotechnical systems. The complex properties of
real-world networks have a profound impact on the behavior of equilibrium and
nonequilibrium phenomena occurring in various systems, and the study of
epidemic spreading is central to our understanding of the unfolding of
dynamical processes in complex networks. The theoretical analysis of epidemic
spreading in heterogeneous networks requires the development of novel
analytical frameworks, and it has produced results of conceptual and practical
relevance. A coherent and comprehensive review of the vast research activity
concerning epidemic processes is presented, detailing the successful
theoretical approaches as well as making their limits and assumptions clear.
Physicists, mathematicians, epidemiologists, computer, and social scientists
share a common interest in studying epidemic spreading and rely on similar
models for the description of the diffusion of pathogens, knowledge, and
innovation. For this reason, while focusing on the main results and the
paradigmatic models in infectious disease modeling, the major results
concerning generalized social contagion processes are also presented. Finally,
the research activity at the forefront in the study of epidemic spreading in
coevolving, coupled, and time-varying networks is reported.Comment: 62 pages, 15 figures, final versio
Causality, Information and Biological Computation: An algorithmic software approach to life, disease and the immune system
Biology has taken strong steps towards becoming a computer science aiming at
reprogramming nature after the realisation that nature herself has reprogrammed
organisms by harnessing the power of natural selection and the digital
prescriptive nature of replicating DNA. Here we further unpack ideas related to
computability, algorithmic information theory and software engineering, in the
context of the extent to which biology can be (re)programmed, and with how we
may go about doing so in a more systematic way with all the tools and concepts
offered by theoretical computer science in a translation exercise from
computing to molecular biology and back. These concepts provide a means to a
hierarchical organization thereby blurring previously clear-cut lines between
concepts like matter and life, or between tumour types that are otherwise taken
as different and may not have however a different cause. This does not diminish
the properties of life or make its components and functions less interesting.
On the contrary, this approach makes for a more encompassing and integrated
view of nature, one that subsumes observer and observed within the same system,
and can generate new perspectives and tools with which to view complex diseases
like cancer, approaching them afresh from a software-engineering viewpoint that
casts evolution in the role of programmer, cells as computing machines, DNA and
genes as instructions and computer programs, viruses as hacking devices, the
immune system as a software debugging tool, and diseases as an
information-theoretic battlefield where all these forces deploy. We show how
information theory and algorithmic programming may explain fundamental
mechanisms of life and death.Comment: 30 pages, 8 figures. Invited chapter contribution to Information and
Causality: From Matter to Life. Sara I. Walker, Paul C.W. Davies and George
Ellis (eds.), Cambridge University Pres
Challenges in Complex Systems Science
FuturICT foundations are social science, complex systems science, and ICT.
The main concerns and challenges in the science of complex systems in the
context of FuturICT are laid out in this paper with special emphasis on the
Complex Systems route to Social Sciences. This include complex systems having:
many heterogeneous interacting parts; multiple scales; complicated transition
laws; unexpected or unpredicted emergence; sensitive dependence on initial
conditions; path-dependent dynamics; networked hierarchical connectivities;
interaction of autonomous agents; self-organisation; non-equilibrium dynamics;
combinatorial explosion; adaptivity to changing environments; co-evolving
subsystems; ill-defined boundaries; and multilevel dynamics. In this context,
science is seen as the process of abstracting the dynamics of systems from
data. This presents many challenges including: data gathering by large-scale
experiment, participatory sensing and social computation, managing huge
distributed dynamic and heterogeneous databases; moving from data to dynamical
models, going beyond correlations to cause-effect relationships, understanding
the relationship between simple and comprehensive models with appropriate
choices of variables, ensemble modeling and data assimilation, modeling systems
of systems of systems with many levels between micro and macro; and formulating
new approaches to prediction, forecasting, and risk, especially in systems that
can reflect on and change their behaviour in response to predictions, and
systems whose apparently predictable behaviour is disrupted by apparently
unpredictable rare or extreme events. These challenges are part of the FuturICT
agenda
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