AN ARTIFICIAL MOLECULAR MODEL TO FOSTER
COMMUNITIES
Christoph Schommer
Department of Computer Science, University Luxembourg, 6 Coudenhove-Kalergi, 1359 Luxembourg, Luxembourg
Keywords:
Bio-inspired modeling, Graph mining, Bibliographic communities.
Abstract:
This paper introduces in extracts a bio-inspired model that understands graphs as artificial chemical constructs.
The main objective is to identify this model as an autonomous and adaptive system that performs internal
tasks, for example a communication with its environment. The model itself focus on artificial atomicity
of nodes, artificial molecular connections in between, and functional proteins, which are self-concentrated
constructs. The model implicates a solid fundament, but fosters an artificial vitality through catalysts: these
merge attacked atomic nodes – in case of common “interests” (inside the molecular model) – to functional
proteins and therefore consequently contribute to a vivid shape of communities. As an application example,
the theoretical model is clarified with bibliographic entries to form bibliographic communities dynamically
while having a bibliographic stream entries as input.
1 A SHAPE OF MOLECULES
Given an actor node, which represents a node within
a network, then we call this node atomic (α
A
i
) in a
sense that it is not divisible. Additionally, each node
α
A
i
shares an activation σ
A
i
and owns a set of items
Γ
A
i
(which will be described later on). An associa-
tion between two actor nodes A
i
and A
j
is then rep-
resented by a molecular bond, which describes a di-
rected relationship on a lower level. Each set of items
Γ
A
i
contains atomic entities, which exist in form of a
hierarchy.
sBond(α
A
i
,α
A
j
) =







ω
A
i
→A
j
: α
A
j
→ α
A
i
∨
α
A
i
→ α
A
j
0 : else
(1)
A single molecular bond has a weight of ω
A
i
→A
j
,
which is expressed by the conditional probability
P(A
j
—A
i
). If the relationship between the two actor
nodes is directed in both directions, then we call this
bi-relationship a double molecular bond:
dBond(α
A
i
,α
A
j
) =





ω
A
i
→A
j
× ω
A
j
→A
i
: α
A
j
→ α
A
i
∧
α
A
i
→ α
A
j
0 : else
(2)
The relationship is then characterized by the com-
mon connection weight ω
A
i
,A
j
, which is the product of
the individual values. Both atomic actor nodes share
an activation as well (σ
A
i
, σ
A
j
). With respect to this,
both structures then own a molecular structure in be-
tween, meaning that any combination of an atomic
structure results in a molecule. Such a molecule might
be of different granularity and size, and being expres-
sive in respect to its arity. As presented in Figure 1, a
single molecular bonds (left) and a double molecular
bonds (right) is shown (each consisting of two atomic
actor nucleus).
Figure 1: Single molecular bonds (top) and double molecu-
lar bonds (bottom) between two atomic actor nucleus.
With Γ
A
i
, we allow each actor to own a number of
items, for example interests that are organized within
a hierarchical system. We then receive levels of dif-
ferent granularity with for example γ
0
= {Root}, γ
1
=
{A,...,Z}, γ
2
= {A
1
,...,Z
n
}, and γ
3
= {A
1
,...,Z
nm
},
etc. The concept is that each time a association is per-
formed, the actor’s interest γ
j
A
i
may be extended by
another interest. The crucial idea is that interests may
be substituted by the superordinate hierarchy γ
j−1
A
i
in
case that a minimum number of interests (= min
k
γ
) on
the specified level exists:
219
Schommer C. (2009).
AN ARTIFICIAL MOLECULAR MODEL TO FOSTER COMMUNITIES.
In Proceedings of the International Conference on Knowledge Discovery and Information Retrieval, pages 219-222
DOI: 10.5220/0002326902190222
Copyright
c
 SciTePress

γ
j
A
i
→ γ
j−1
A
i
(3)
if |(γ
j−1
A
i
| ≥ min
k
γ
for an actor node A
i
. For example, if
an actor A
i
is interested in γ
j
A
i
= {A
11
,A
12
,A
13
,A
14
},
then the interest level may be replaced to γ
j−1
A
i
= {A
1
}
in case that the threshold min
k
γ
is achieved.
a) b)
c) d)
Figure 2: Selected molecular forms with a) a molecular star,
b) a collection of molecular bridges (diamond), c) a molec-
ular bridge with single/double molecular bonds (bottom),
and d) a collection of diamonds.
Some examples of molecule structures are shown
in Figure 2. In Figure 2a), an atomic node α
A
i
is
shown, which is being arranged as a centre of k ad-
jacent nodes. We call this unary structure a molecule
star, because a certain number of actor nodes are
exclusively connected by a single, but centric actor
node:
mStar(α
A
i
) =







1 : 6 ∃sbond(α
A
j
,α
A
x
)∧
(
V
sBond(α
A
i
,α
A
j
)∨
V
dBond(α
A
i
,α
A
j
))
0 : else
(4)
∀1 ≤ j ≤ k with i /∈ {1,...,k} and x ∈ N. With
that, the situation inside a molecular star is that each
non-centric actor is only associated with the centric
actor node. The connection is generally a single bond,
either from the centric actor node α
A
i
to each neigh-
bors α
A
j
or vice versa. In case that two actor nodes
α
A
i
and α
A
j
share a double molecular bond, we call
this a molecular bridge. The molecule structure is of
a binary type since exactly two atomic nodes are in-
volved (Figure 2b) and Figure 2c)).
mBridge(α
A
i
,α
A
j
) = dBond(α
A
i
,α
A
j
) (5)
Besides, atomic actor nodes may play a role in-
side each molecule, being either a node that actively
stimulates another or a node that is passively stimu-
lated by another node, for example atomic triggers
and atomic reactors (Figure 1a)). A decomposition
of a molecule concerning a semantic assignment may
then be as follows: let α
A
i
, α
A
j
and α
A
k
disjunctive
atomic actor nodes, 1 ≤ i 6= j 6= k ≤ n natural num-
bers, and n the total number of nodes, then an atomic
actor node α
A
i
is a atomic reactor:
mReactor(α
A
i
) = ∃α
A
j
: sBond(α
A
j
,α
A
i
) (6)
On the other hand, an atomic actor node α
A
i
is an
atomic trigger:
mTrigger(α
A
i
) = ∃α
A
j
: sBond(α
A
i
,α
A
j
) (7)
An actor node α
A
i
is a atomic trigger if it influ-
ences another actor α
A
j
(α
A
i
⇒ α
A
j
) with ω
A
i
→A
j
ex-
ceeding min
ω
. An actor node α
A
i
is a atomic reactor
if α
A
i
is influenced by another actor α
A
j
(α
A
j
⇒ α
A
i
)
with with ω
A
j
→A
i
exceeding min
ω
. Third, we may de-
scribe an actor node α
A
i
as a atomic center if it is the
central point inside a molecular star.
There exist operational functions that are applica-
ble to relationships inside the molecules from a prac-
tical point of view. A first measure is the distance be-
tween two actor nodes d(α
A
i
, α
A
j
), which leads to us
the shortest path problem from α
A
i
to α
A
j
. But while
passing inner actor nodes, the distance, however, must
be influenced by the corresponding activation states
σ
A
i
as well. We therefore propose a distance measure
that sums up all actor node activities being on the the
shortest path from α
A
i
to α
A
j
. Since we can not guar-
antee that an actor node A
j
can be reached from actor
node A
i
and as we do not know if all participating ac-
tor nodes share at least a single molecular bond with
its successor, we suggest
d(α
A
i
,α
A
j
) =

∑
j
k=i
σ
A
k
: A
i
→ A
j
unde f ined : else
(8)
Depending on the relationship, the strength
s(α
A
i
,...α
A
j
of a relationship must be calculated in
a different way. For example, a molecular star is cer-
tainly depending on the number of associated actor
nodes α
A
j
, their activation states σ
A
j
, and the connec-
tion weights ω
A
i
→A
j
and ω
A
j
→A
i
, respectively, among
them:
s
mStar
(α
A
1
,...α
A
n
) =
n
∏
k,l=1
ω
A
k
→A
l
(9)
with k < l. For molecular bridges, however, the
“harmony” between the double bonds justifies a
stronger bridge (than a bridge with more varying sin-
gle bonds). The more harmonic a double bonds is the
stronger the bridge is.
s
mBridge
(α
A
i
,α
A
j
) = ω
A
i
→A
j
× ω
A
j
→A
i
(10)
with k < l.
KDIR 2009 - International Conference on Knowledge Discovery and Information Retrieval
220

Figure 3: Reaction of two independent molecules to a functional protein. The merge is initiated by a catalyst τ that forms a
catalytic bridge between α
A
2
and α
A
8
. The merge evolves because of a common interest B
1
: in this case, it is an identical
classification chapter within the ACM classification system.
2 CATALYTIC BRIDGES
So far, the described molecular model stands for a
static description of the theory of graph. Therefore,
to overcome such a static molecular existence, we ex-
tend our model by taking advantage of the set of items
Γ
A
i
for each α
A
i
. It is interesting that each atomic ac-
tor node is allowed to react with another α
A
j
through
a catalyst τ: in case that an actor node α
A
i
with a set
of items ξ
i
owns the same or a subset of interests than
another actor node α
A
j
, then both may react, merge
and establish a catalytic bridge τ
A
i
,A
j
(Figure 3).
A functional protein Π
k
is therefore unlike a static
collection of nodes but moreover a vivid (artificial)
and autonomous system. Besides, we understand
these functional proteins as an operating structure that
is commissioned to complete tasks: it is conceivable
to send information and to describe the structure it
obsesses. Functional proteins may be forced to con-
tinuously improve its own structure: such an improve-
ment may be the update of existing single or double
bonds or atomic nodes (decrease/increase).
3 AN APPLICATION EXAMPLE
In case of bibliographic networks, the existence of
molecular stars and bridges leads to a more detailed
characterization of an author (node); for example, a
protein may (autonomously) inform about experts –
who form a central part (node) within a molecular
star – inside a community and/or about noticeable
actor/co-authorships through molecular bridges. A
functional protein may therefore autonomously (and
independently) send information to its environment,
for example to natural users while providing them
with information about the existence of “interests”
and/or the structure of the associated community (re-
trieve). With the mentioned semantic roles of an ac-
tor, the activity of the protein – and with it the com-
munity as well – can be measured. The more active
atomic trigger exist, the more active the community
generally will be. On the other side, a more reactive
community exists if the number of reactor nodes are
lower.
If actor atomic author nodes are interconnected by
a catalytic bridge, then they substantiate a common
interest. For example, this may occur with respect
to common research topics, possibly identified by the
ACM classification system. In any case, a merge be-
tween author nodes foster a dynamic-adaptive net-
work behavior, because novel connections between
actor nodes may be established depending on their
“interest” and the bibliographic stream of incoming
publications.
As a consequence, a bibliographic community is
therefore not only a set of relationships among au-
thor nodes but consequently previously independent
molecules by a catalytic bridge. So, we understand
bibliographic communities as mental systems that are
physically expressed by even such functional proteins
with relationships (author A
i
is associated to A
j
) and
semantic roles (A
i
is a trigger, A
j
the central point of a
star). These communities change over time while fig-
uring out the protein generation process in response
to a bibliographic stream, but will definitely operate
AN ARTIFICIAL MOLECULAR MODEL TO FOSTER COMMUNITIES
221

in a non-stream environment as well.
4 CONCLUSIONS
This position paper contains in extracts a bio-inspired
model, which follows the natural example of a molec-
ular world and which understands graph-related struc-
tures as molecular entities. The main objective is to
define a model that autonomously and adaptively be-
haves while performing internal tasks like the com-
munication with its environment, for example inside
communities. In this respect, fundamental compo-
nents like single/double bonds have been presented as
well as simple molecular shapes.
Currently, we are working on the stability of
atomic node, molecules, and proteins: a first approach
towards the stability of proteins is surely to count the
number of actor nodes at time points t and t − 1, re-
spectively, where we then get
∆(Π
i
,t) =
α
t
A
i
− α
t−1
A
i
α
t−1
A
i
(11)
The stability of a protein decreases, if ∆(Π
i
,t) ≤
0; it increases, if ∆(Π
i
,t) > 0. Even better, the corre-
sponding activity weights ω
A
i
→A
j
of the bonds and the
activation state of the atomic actor node σ
A
i
shall be
taken into account. However, the question concerning
the stability of molecular bonds and atomic actors is
herewith not answered and we for example check up
if a “valency” can be simulated as well and if other
criteria may be taken to fulfill a merge between ac-
tor nodes: when a catalyst starts its activity, does it
make a difference to start with some actor node or is
it of interesting to distinguish between “begin” and
“end” actor nodes? Furthermore, the semantic roles
inside a protein surely plays a promising aspect to-
wards the stability, since if all actor nodes are satisfied
and “convivial” in some way then the stability surely
is stronger than in another situation. Another inter-
esting point is the communication of a protein with
its environment, respective with other proteins: how
can information smoothly addressed to all proteins?
Here, we are currently thinking on taking into account
achievements from other bio-inspired systems like ar-
tificial immune systems.
ACKNOWLEDGEMENTS
The work is currently been done at the MINE re-
search group of the ILIAS Laboratory, Department of
Computer Science and Communication, University of
Luxembourg.
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