13th International Conference on Membrane Computing - MTA Sztaki

R. Pagliarini, O. Agrigoroaiei, G. Ciobanu, V. Manca
From a statistical point of view, causality is the relationship between an
event, the cause, and a second event, the effect, where the second event is understood
as a consequence of the first. Causality can also be seen as the relationship
between a set of factors and a phenomenon. The statistical notion can be estimated
directly by observational studies and experimental data, for which causal
direction can be inferred if information about time is available. This is due to
the fact that causes must precede their effects in the time line. Then the use of
temporal data can permit to discover causal direction.
Differently, from a quantitative point of view, causality is studied in terms
of multisets of objects and of multisets of rules in presence of non-determinism
and parallelism. To this goal, several approaches have been proposed to translate
them into different formalisms to study cause-effect relationships, as for example
[3,5,11]. The main drawback of these approaches is that they neglect quantitative
aspects involved in the definition of evolution for membrane systems. For
this reason, a quantitative approach to causality was started in [1] and has been
extended in [2]. This approach requires a reaction model representing the membrane
system under consideration. Along this research line, if a set of rules is not
known, a question arises: “is it possible to study quantitative causality starting
from a set of experimental data”?
The aim of this work is twofold. Firstly, it introduces the two approaches
that we developed to study cause-effect relationships. Secondly, it proposes a
framework which integrates the two approaches in order to study quantitative
causality by means of membrane systems, from temporal series of data collected
on the concentration of different reactants. It integrates two different methods.
In a first step, interrelations between elements are interpreted by means of correlation
analysis and measures of similarity based on time-lagged time series. In
this way, a set of rules modelling statistical causalities is inferred. This set can
give us indication about the network topology of the reactions and the regulative
mechanisms in the phenomena under study. In a second step, this set of rules is
used to building up a reaction model useful to study quantitative causality by
means of membrane systems.
The paper is organized as follows. Section 2 recalls the concepts of membrane
systems and multisets, and introduces causality over multisets of objects.
In Section 3, a theoretical network analysis which can be used to distinguish statistical
causal interactions in biological pathways starting from pure observations
of species dynamics is described. Section 4 proposes a procedure to integrate the
two approaches, while Section 5 considers two case studies. Finally, Section 6
ends the paper by some discussions on the proposed approach and some possible
future theoretical studies useful to analyze the relationships between quantitative
and correlative causality.
2 Quantitative Causality in Membrane Systems
Membrane computing is a branch of natural computing, the area of research
concerned with computation taking place in nature and with human-designed
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