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Analysis of complex events in Memory Evolutive
Systems
by Andrée C. Ehresmann (Work in collaboration
with Jean-Paul Vanbremeersch) Université de
Picardie Jules Verne ehres_at_u-picardie.fr http//pa
gesperso-orange.fr/ehres http//pagesperso-orange.
fr/vbm-ehr
ServiceWave 2010, Ghent
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A FRAME FOR COMPLEX EVENTS PROCESSING
We consider an evolutionary adaptive system with
a tangled hierarchy of components, self-organized
thanks to a multiplicity of mutually entailed
functional subsystems, the CoRegulators CR, each
operating at its own rhythm, with the help of a
central Memory. Event processing punctuates the
dynamics, both of the CRs, of their interactions
and of the system itself.. This will be studied
by modelling the system by a Memory Evolutive
System (EV 1987-2009). First we give 2 generic
examples.
FUMEE 3
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THE MEMORY EVOLUTIVE SYSTEM OF AN ENTERPRISE
MEMORY
TOP
The components are the members of the staff, the
multi-level services and departments, and the
various material or immaterial resources the
links model their interactions in the enterprise.
The constantly revised "Memory" stores archives,
past events and the knowledge necessary for
functioning part of it, the Archetypal Core AC,
acts as a flexible internal model.
The dynamics is directed by the
cooperation/competition between the different
departments acting as a net of coregulators CRs,
each operating with its own temporality (daily at
the lower level, up to years at higher levels).
Events can propagate among the services from
bottom to top, and also top-bottom, with higher
CRs able to initiate drastic changes for leading
to a better functioning of the enterprise.
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MENS, MODEL OF A NEURO-COGNITIVE SYSTEM
The neural system of an animal has for components
its neurons, connected by synaptic paths between
them (directed from the first presynaptic neuron
to the last postsynaptic one). It is modeled by
the Evolutive System NEUR. A mental object
corresponds to the activation of a syn-chronous
assembly of neurons, with the possibility that 2
different synchronous assemblies P and P'
activate the same mental object ('degeneracy' of
the neural code, Edelman, 1989). This mental
object is modeled by the 'binding' cP of P (and
also P'), called a category-neuron, in a
'dynamic' model, MENS, including both the neural
and mental systems. MENS is a MES obtained by
successive 'complexifications' of NEUR its
hierarchy of components has neurons at level 0,
and higher category-neurons representing more and
more complex mental objects at higher levels.
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GRAPHS AND CATEGORIES
A category is a graph on which there is given an
internal composition associating to a 2-path (f,
g) a composite fg, This composition is
associative and each object has an identity.
Because of associativity, any path has a unique
composite. Two paths are 'functionally
equiv-alent' if their composites are equal
A (multi-)graph has a set of vertices (or
'objects') A, B, and a set of oriented edges
('arrows' or 'links') between them. A path of
the graph is a sequence of consecutive links (f,
g, k). Example. The graph of neurons with neurons
as vertices and synapses as arrows.
We have to develop a 'dynamic' theory of
categories incorporating time to account for the
dynamics of the system and its various events, in
particular the possible loss or adjunction of
components over time. Thus the system is not
modeled by one category but by an Evolutive
System, namely a family of categories Ht ndexed
by Time, with partial 'transition' functors
between them.
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EVENT FORMATION OF A COMPLEX OBJECT
Ht
level n1
A
levels n
si
si


sj
sj
P
Pi
f
f
Pj
A group of components with a common endeavour is
modeled (in a category Ht) by a pattern P
consisting of objects Pi with distinguished links
between them. A collective link from P to a
component A is a family of links si from Pi to A,
correlated by the distinguished links of P.
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HIERARCHICAL EVOLUTIVE SYSTEM. COMPLEXIFICATION
level n1
level n
level n-1
level 0
Time
t'
t
A Hierarchical Evolutive System H consists of A
timescale Time and for each t in it a
hierarchical category Ht (configuration at t)
for t lt t', a transition functor from a
sub-category of Ht to Ht, these functors satisfy
a transitivity condition so that a component C of
H is a maximal set of objects linked by
transitions.
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BINDING EVENT SIMPLE LINKS
levels n
cluster G
Pj

Pi

P

P'
P'i'
If P and P' are 2 patterns, a cluster G from P to
P' consists of links from each Pi to at least
one P'k, these links being well correlated by the
distinguished links of P and P' .
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MULTIPLICITY PRINCIPLE AT THE ROOT OF EMERGENCE
level n1
level n1
C
Pi
Q
Pj
levels n
levels n
The flexibility (and impredicability) of complex
systems comes from the following "degeneracy
property" (in the sense of Edelman 1989) there
are patterns which are functionally equivalent,
but not interconnected, e.g. a mental object can
activate different neuronal assemblies.
Formally Multiplicity Principle (MP) There are
objects C, called n-multiform, which bind 2
patterns Q and P of levels n which are not
connected by a cluster. The passage from P to Q
is a complex switch.
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COMPLEXITY ORDER
level n1
C
level n
P
Pi
Pi
P
level 0
In a HES, a component C of level n1 binds at
least one pattern P of strictly lower levels (in
a category Ht). Now each Pi also binds a pattern
of lower levels, and so on. We thus construct a
ramification of C down to the level 0 of the
hierarchy. Its length can be lt level of C.
The ramifications of C have not always the same
length. We define the complexity order of C as
the smallest length of such a ramification. It
measures the smallest number of events necessary
for constructing C from level 0 up by successive
binding processes.
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EMERGENCE OF COMPLEX EVENTS
Ht'
level n1
Ht
level n
level 0
Time
EMERGENCE THEOREM. In a Hierarchical Evolutive
System, the Multiplicity Principle is the
condition characterising the existence of
components of complexity order gt 1, and the
possibility of emergence over time of components
of strictly increasing complexity order.
If the MP is not satisfied, any component is the
simple binding of a pattern contained in the
level 0. This would characterize a 'pure'
reductionism. In the SEM we consider, the MP is
always satisfied, and it allows the emergence of
higher complexity at the root of the processing
of complex events. We can speak of an emergentist
reductionism (in the sense of Mario Bunge).
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MEMORY EVOLUTIVE SYSTEM (MES)
AC
An evolutionary hierarchical adaptive system will
be modeled by a Memory Evolutive System MES. It
is a HES whose self-organization is directed by
the cooperative and/or competitive interactions
between a net of specialized functional evolutive
subsystems, the coregulators. with the help of an
evolutive sub-system Mem modeling a central
flexible memory (which may develop a robust
though flexible internal model AC of the system).
We suppose that the MP is satisfied and that each
link has a propagation delay and a strenth (both
in R). Each CR has its own complexity level,
its own discrete timescale extracted from the
continuous timescale of the system, and a
differential access to Mem it participates in
the formation of the transitions (via
complexification processes) by selecting
procedures depending on its function.
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ONE STEP OF A CR WITH ITS VARIOUS EVENTS
Temps
t'
Formation of Lt
t
A CR acts stepwise at its own rhythm as a hybrid
system using both its own discrete timescale and
the continuous time between 2 successive times t
and t' of this scale.
(i) The first event of the step is the formation
of its landscape at t (modeled by a category Lt)
with the partial information it can access.
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interplay between CRs
Fracture
CR'
CR
CR procedures
Coregulators
The procedures of the various CRs at a given time
may not fit together. since their rhythms and
perspectives are different.
In particular each CR has structural temporal
constraints to be respected so that its step
beginning at t be achieved in time. They are
expressed by the inequalities ("laws of
synch) p(t) ltlt d(t) ltlt z(t) where p(t) is the
time lag ( mean propagation delay of the links
in the landscape), d(t) is the period of the CR
( mean length of its preceding steps) and z(t)
is the smallest stability span of the necessary
components C ( period during which C has a
stable lower order decomposition).
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DIFFERENT KINDS OF EVENTS FOR A CR
The non-respect of the temporal conditions of a
CR may cause various events, and in particular
fractures in the following cases (i) an increase
of the time lags, so that information and
commands are not sent in time the landscape is
not well constructed or the procedure is not
realized in time (ii) no admissible procedure S
is found, or the commands of S cannot be
effected (iii) a decrease of the stability
spans the information is no more valid or the
strategy cannot be realized. A fracture not
repaired at the next step causes a more severe
event, namely a dyschrony if it persists, it
might necessitate a change of period of the CR,
which we call a re-synchronization of the CR.
This may backfire to CRs of increasing levels,
leading to systemic complex events such as a
cascade of re-synchronizations, or even a
systemic "dynamic disease".
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DIALECTICS BETWEEN HETEROGENEOUS CRs
CR is a lower coregulator, with small steps, and
CR' is a much higher one with much longer steps.
A sequence of events at CR during successive
steps, and the corresponding changes at the lower
level are not transmitted in real time to CR'
(propagation delays,). However their
accumulation may cause a noticeable event for CR'
up to causing a fracture. The response of CR' and
its change of procedure may backfire to CR by
causing a fracture at its level, and the process
can repeat.
FUMEE 3
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COMPLEX EVENTS PROCESSING AMONG CRs
How different kinds of events for a CR backfire
to CRs of other levels, with possibly severe
consequences, such as a cascade of fractures,
itself leading to a cascade of re-synchronizations
at various levels to avoid a systemic disease.
This CEP is at the root of our physiologically
inspired Theory of Aging for an organism by a
cascade of re-synchronizations (EV 1993), which
would also apply to a social system
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THE ARCHETYPAL CORE AT THE BASIS OF U-CEP
Memory
CR1
CR2
AC
A
Cognitive systems develop over time a sub-system
of the memory, the Archetypal Core AC, which
integrates and intertwines recurring memories and
notable events. and acts as a flexible internal
model of the system, memorizing its identity. AC
consists of higher order components linked by
strong and swift links forming self-maintained
loops.
This sequence of events is transmitted back to
higher CRs which can unite their landscapes into
a longer term global landscape on which
ubiquitous complex events can be processed.
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U-CEP. CONSCIOUS PROCESSES
Attention ?
AC is activated
S
Activated domain ?
Activated intentional CRs cooperate
In cognitive systems, a non-expected event S
increases the attention, that leads to an
activation of a large part of AC, hence to the
formation of a global landscape GL, in which
conscious processes, characterized by an
integration of the time dimension, can develop
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FOR MORE INFORMATION Memory Evolutive Systems
Hierarchy, Emergence, Cognition, Elsevier,
2007. MENS, a mathematical model for cognitive
systems, JMT 0-2, 2009. The following internet
sites contain a number of papers, in particular
more recent ones http//pagesperso-orange.fr/ehre
s http//pagesperso-orange.fr/vbm-ehr THANKS