5,140 research outputs found
Interactions between Causal Structures in Graph Rewriting Systems
Graph rewrite formalisms are a powerful approach to modeling complex
molecular systems. They capture the intrinsic concurrency of molecular
interactions, thereby enabling a formal notion of mechanism (a partially
ordered set of events) that explains how a system achieves a particular outcome
given a set of rewrite rules. It is then useful to verify whether the
mechanisms that emerge from a given model comply with empirical observations
about their mutual interference. In this work, our objective is to determine
whether a specific event in the mechanism for achieving X prevents or promotes
the occurrence of a specific event in the mechanism for achieving Y. Such
checks might also be used to hypothesize rules that would bring model
mechanisms in compliance with observations. We define a rigorous framework for
defining the concept of interference (positive or negative) between mechanisms
induced by a system of graph-rewrite rules and for establishing whether an
asserted influence can be realized given two mechanisms as an input.Comment: In Proceedings CREST 2018, arXiv:1901.0007
Causal graph dynamics
We extend the theory of Cellular Automata to arbitrary, time-varying graphs.
In other words we formalize, and prove theorems about, the intuitive idea of a
labelled graph which evolves in time - but under the natural constraint that
information can only ever be transmitted at a bounded speed, with respect to
the distance given by the graph. The notion of translation-invariance is also
generalized. The definition we provide for these "causal graph dynamics" is
simple and axiomatic. The theorems we provide also show that it is robust. For
instance, causal graph dynamics are stable under composition and under
restriction to radius one. In the finite case some fundamental facts of
Cellular Automata theory carry through: causal graph dynamics admit a
characterization as continuous functions, and they are stable under inversion.
The provided examples suggest a wide range of applications of this mathematical
object, from complex systems science to theoretical physics. KEYWORDS:
Dynamical networks, Boolean networks, Generative networks automata, Cayley
cellular automata, Graph Automata, Graph rewriting automata, Parallel graph
transformations, Amalgamated graph transformations, Time-varying graphs, Regge
calculus, Local, No-signalling.Comment: 25 pages, 9 figures, LaTeX, v2: Minor presentation improvements, v3:
Typos corrected, figure adde
A knowledge representation meta-model for rule-based modelling of signalling networks
The study of cellular signalling pathways and their deregulation in disease
states, such as cancer, is a large and extremely complex task. Indeed, these
systems involve many parts and processes but are studied piecewise and their
literatures and data are consequently fragmented, distributed and sometimes--at
least apparently--inconsistent. This makes it extremely difficult to build
significant explanatory models with the result that effects in these systems
that are brought about by many interacting factors are poorly understood.
The rule-based approach to modelling has shown some promise for the
representation of the highly combinatorial systems typically found in
signalling where many of the proteins are composed of multiple binding domains,
capable of simultaneous interactions, and/or peptide motifs controlled by
post-translational modifications. However, the rule-based approach requires
highly detailed information about the precise conditions for each and every
interaction which is rarely available from any one single source. Rather, these
conditions must be painstakingly inferred and curated, by hand, from
information contained in many papers--each of which contains only part of the
story.
In this paper, we introduce a graph-based meta-model, attuned to the
representation of cellular signalling networks, which aims to ease this massive
cognitive burden on the rule-based curation process. This meta-model is a
generalization of that used by Kappa and BNGL which allows for the flexible
representation of knowledge at various levels of granularity. In particular, it
allows us to deal with information which has either too little, or too much,
detail with respect to the strict rule-based meta-model. Our approach provides
a basis for the gradual aggregation of fragmented biological knowledge
extracted from the literature into an instance of the meta-model from which we
can define an automated translation into executable Kappa programs.Comment: In Proceedings DCM 2015, arXiv:1603.0053
Distributed execution of bigraphical reactive systems
The bigraph embedding problem is crucial for many results and tools about
bigraphs and bigraphical reactive systems (BRS). Current algorithms for
computing bigraphical embeddings are centralized, i.e. designed to run locally
with a complete view of the guest and host bigraphs. In order to deal with
large bigraphs, and to parallelize reactions, we present a decentralized
algorithm, which distributes both state and computation over several concurrent
processes. This allows for distributed, parallel simulations where
non-interfering reactions can be carried out concurrently; nevertheless, even
in the worst case the complexity of this distributed algorithm is no worse than
that of a centralized algorithm
Normalisation Control in Deep Inference via Atomic Flows
We introduce `atomic flows': they are graphs obtained from derivations by
tracing atom occurrences and forgetting the logical structure. We study simple
manipulations of atomic flows that correspond to complex reductions on
derivations. This allows us to prove, for propositional logic, a new and very
general normalisation theorem, which contains cut elimination as a special
case. We operate in deep inference, which is more general than other syntactic
paradigms, and where normalisation is more difficult to control. We argue that
atomic flows are a significant technical advance for normalisation theory,
because 1) the technique they support is largely independent of syntax; 2)
indeed, it is largely independent of logical inference rules; 3) they
constitute a powerful geometric formalism, which is more intuitive than syntax
Complex event types for agent-based simulation
This thesis presents a novel formal modelling language, complex event types (CETs), to describe behaviours
in agent-based simulations. CETs are able to describe behaviours at any computationally
represented level of abstraction. Behaviours can be specified both in terms of the state transition rules of
the agent-based model that generate them and in terms of the state transition structures themselves.
Based on CETs, novel computational statistical methods are introduced which allow statistical dependencies
between behaviours at different levels to be established. Different dependencies formalise
different probabilistic causal relations and Complex Systems constructs such as ‘emergence’ and ‘autopoiesis’.
Explicit links are also made between the different types of CET inter-dependency and the
theoretical assumptions they represent.
With the novel computational statistical methods, three categories of model can be validated and
discovered: (i) inter-level models, which define probabilistic dependencies between behaviours at different
levels; (ii) multi-level models, which define the set of simulations for which an inter-level model
holds; (iii) inferred predictive models, which define latent relationships between behaviours at different
levels.
The CET modelling language and computational statistical methods are then applied to a novel
agent-based model of Colonic Cancer to demonstrate their applicability to Complex Systems sciences
such as Systems Biology. This proof of principle model provides a framework for further development
of a detailed integrative model of the system, which can progressively incorporate biological data from
different levels and scales as these become available
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