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An Adaptive Self-Modeling Network Model for Multilevel Organisational Learning

Authors:
1
An Adaptive Self-Modeling Network Model
for Multilevel Organisational Learning
Gülay Canbaloğlu1,3, Jan Treur2,3, Peter Roelofsma3
1Department of Computer Engineering, Koç University, Istanbul, Turkey
2Social AI Group, Department of Computer Science, Vrije Universiteit Amsterdam
3Delft University of Technology, Center for Safety in Healthcare, Delft, The Netherlands
gcanbaloglu17@ku.edu.tr j.treur@vu.nl
p.h.m.p.roelofsma@tudelft.nl
Abstract. Multilevel organisational learning is often considered to concern mental
models as a vehicle for the interplay of individual, team, and organizational learning.
By learning individual mental models, a basis for formation of shared team mental
models is created, and based on the different shared team mental models, a shared
organisation mental model can be obtained. This pathway is indicated by feed forward
learning. In addition, feedback learning follows the opposite pathway: shared team
mental models can be learned from a shared organisation mental model and individual
mental models can be learned from shared team mental models. These pathways and
their interactions provide complex dynamic and adaptive mechanisms that together
constitute multilevel organizational learning. These mechanisms have been used as a
basis for an adaptive computational network model for multilevel organisational
learning. The model is illustrated by a not too complex but realistic case study.
1. Introduction
Multilevel organizational learning is a complex, dynamic, adaptive, cyclical and non-linear
type of learning involving multiple levels and both dependent on individuals and independent
of individuals. It is multilevel because the learning of an organization involves learning at
the level of individuals and at the level of teams (or groups or projects), and at the level of
the organisation via feed forward and feedback pathways:
Through feed-forward processes, new ideas and actions flow from the individual to the group
to the organization levels. At the same time, what has already been learned feeds back from
the organization to group and individual levels, affecting how people act and think.’ (Crossan,
Lane, White, 1999), p. 532.
‘There is growing consensus in the literature that the theory of organizational learning should
consider individual, team and organizational levels (Wiewiora, Smidt, Chang, 2019), p. 94
There is a huge amount of literature on multilevel organizational learning such as (Argyris,
Schön, 1978; Bogenrieder, 2002; Crossan et al, 1999; Fischhof, Johnson, 1997; Kim, 1993;
McShane, Glinow, 2010; Stelmaszczyk, 2016; Wiewiora et al, 2019; Wiewiora, Chang,
Smidt, 2020). However, systematic approaches to obtain (adaptive) computational models
for it cannot be found. In the current paper, a self-modeling network modeling perspective is
used to model the different adaptive, interacting processes of multilevel organizational
learning.
Computational modeling of multilevel organizational learning provides a more observable
formalization of multilevel organisational learning and provides possibilities to perform ‘in
silico’ (simulation) experiments with it. To this end, the multi-order adaptive network-
2
oriented modeling approach based on self-modeling networks introduced in (Treur, 2020a;
Treur, 2020b) that will be explained in detail in Section 3, is used in this current paper.
First, Section 2 presents how literature provides ideas on mental models at individual,
team and organisation level and their role in multilevel organizational learning. Then, Section
3 explains the characteristics and details of adaptive self-modeling network models and how
they can be used to model the different processes concerning dynamics, adaptation and
control of mental models. In Section 4 the second-order (controlled) adaptive network model
for multilevel organisational learning is introduced. Then in Section 5, an example simulation
scenario is explained in detail. Section 6 is a Discussion section.
2. Background Literature
The quotes in the introduction section illustrate the perspective adopted here. Mental models
are considered a vehicle for the interplay of learning at the individual, team and
organizational level. By learning individual mental models, a basis for formation of shared
team mental models is provided and these shared team mental models provide input for the
shared mental models at the level of the organization. Conversely, these shared organisation
and team mental models are used to improve shared team mental models and individual
mental models, respectively. The picture of the different pathways shown in Fig. 1 is a
slightly rearranged version of Fig. 1 in (Crossan et al, 1999) and also strongly resembles Fig.
4 of (Wiewiora et al, 2019) and Fig. 3 of (Wiewiora et al, 2020).
Fig. 1. Organisational learning as a dynamic process; adapted from (Crossan et al, 1999), Fig 1. For a
similar picture, see (Wiewiora et al, 2019), Fig. 4 and Fig. 3 of (Wiewiora et al, 2020).
Inspired by this, as a basis for the analysis made here, the considered overall multilevel
organisational learning process consists of the following main processes and interactions; see
also (Crossan et al, 1999; Wiewiora et al, 2019):
3
(a) Individual level
(1) Creating and maintaining individual mental models
(2) Choosing for a specific context a suitable individual mental model as focus
(3) Applying a chosen individual mental model for internal simulation
(4) Improving individual mental models
(b) From individual level to team level (feed forward learning)
(1) Deciding about creation of shared team mental models
(2) Creating shared team mental models based on developed individual mental
models
(c) From team level to organization level (feed forward learning)
(1) Deciding about creation of shared mental models
(2) Creating shared mental models based on developed individual mental models
(d) From organization level to team level (feedback learning)
(1) Deciding about teams to adopt shared organisation mental models
(2) Teams adopting shared mental models
(e) From team level to individual level (feedback learning)
(1) Deciding about individuals to adopt shared team mental models
(2) Individuals adopting shared team mental models by learning them
(f) Individual level
(1) Creating and maintaining individual mental models
(2) Choosing for a specific context a suitable individual mental model as focus
(3) Applying a chosen individual mental model for internal simulation
(4) Improving individual mental models
This overview will provide useful input to the design of the adaptive computational
network model for multilevel organizational learning that will be introduced in Section 4.
3. The Self-Modeling Network Modeling Approach Used
In this section, the network-oriented modeling approach used is briefly introduced. Following
(Treur, 2020b), a network model is characterised by (here X and Y denote nodes of the
network, also called states):
Connectivity characteristics
Connections from a state X to a state Y and their weights X,Y
Aggregation characteristics
For any state Y, some combination function cY(..) defines the aggregation that is
applied to the impacts X,YX(t) on Y from its incoming connections from states X
Timing characteristics
Each state Y has a speed factor Y defining how fast it changes for given causal
impact.
The following difference (or related differential) equations that are used for simulation
purposes and also for analysis of temporal-causal networks, incorporate these network
characteristics ωX,Y, cY(..), ηY in a standard numerical format:
󰇛 󰇜  󰇛󰇜 󰇟󰇛󰇛󰇜 󰇛󰇜󰇜 󰇛󰇜󰇠 (1)
for any state Y and where to are the states from which Y gets its incoming connections.
Within the software environment described in (Treur, 2020b, Ch. 9), a large number of
currently around 50 useful basic combination functions are included in a combination
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function library. The above concepts enable to design network models and their dynamics in
a declarative manner, based on mathematically defined functions and relations. The examples
of basic combination functions that are applied in the model introduced here can be found in
Table 1.
Table 1 The combination functions used in the introduced network model
Notation
Formula
Parameters
Advanced
logistic sum
alogistic,(V1, …,Vk)
󰇟
󰇛
󰇜

󰇜󰇠(1+e-στ)
Steepness > 0
Excitability threshold
Steponce
steponce,(..)
1 if time t is between and ,
else 0
Start time
End time
Hebbian
learning
hebb(V1, V2, V3)

󰇛 󰇜
V1,V2 activation levels of the
connected states; V3 activation
level of the self-model state for
the connection weight.
Persistence factor
Maximum
composed
with
Hebbian
learning
max-hebb(V1, , Vk)
󰇛󰇛
󰇜
󰇜
V1,V2 activation levels of the
connected states; V3 activation
level of the self-model state for
the connection weight.
Persistence factor
Scaled
maximum
smax(V1, , Vk)
max(V1, , Vk)/
Scaling factor
Realistic network models are usually adaptive: often not only their states but also some
of their network characteristics change over time. By using a self-modeling network (also
called a reified network), a similar network-oriented conceptualisation can also be applied to
adaptive networks to obtain a declarative description using mathematically defined functions
and relations for them as well; see (Treur, 2020a; Treur, 2020b). This works through the
addition of new states to the network (called self-model states) which represent (adaptive)
network characteristics. In the graphical 3D-format as shown in Section 4, such additional
states are depicted at a next level (called self-model level or reification level), where the
original network is at the base level.
As an example, the weight ωX,Y of a connection from state X to state Y can be represented
(at a next self-model level) by a self-model state named WX,Y. Similarly, all other network
characteristics from ωX,Y, cY(..), ηY can be made adaptive by including self-model states for
them. For example, an adaptive speed factor ηY can be represented by a self-model state
named HY.
As the outcome of such a process of network reification is also a network model itself, as
has been shown in (Treur, 2020b, Ch 10), this self-modeling network construction can easily
be applied iteratively to obtain multiple orders of self-models at multiple (first-order, second-
order, …) self-model levels. For example, a second-order self-model may include a second-
order self-model state HWX,Y representing the speed factor WX,Y for the (learning) dynamics
of first-order self-model state WX,Y which in turn represents the adaptation of connection
weight X,Y. Similarly, a persistence factor μWX,Y of such a first-order self-model state WX,Y
used for adaptation (e.g., based on Hebbian learning) can be represented by a second-order
self-model state MWX,Y .
In the current paper, this multi-level self-modeling network perspective will be applied to
obtain a second-order adaptive mental network architecture addressing the mental and social
processes underlying organizational learning by proper handling of individual mental models
and shared mental models. In this self-modeling network architecture the base level addresses
the use of a mental model by internal simulation, the first-order self-model the adaptation of
the mental model, and the second-order self-model level the control over this; see Fig. 2. In
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this way the three-level cognitive architecture described in (Van Ments and Treur, 2021) is
formalized computationally in the form of a self-modeling network architecture.
Fig. 2 Computational formalization of the three-level cognitive architecture for mental model
handling from (Van Ments and Treur, 2021) by a self-modeling network architecture
In (Bhalwankar and Treur, 2021a; Bhalwankar and Treur, 2021b) it is shown how specific
forms of learning and their control can be modeled based on this self-modeling network
architecture, in particular learning by observation (Yi and Davis, 2003; Van Gog, Paas,
Marcus, Ayres, Sweller, 2009) and learning by instruction (Hogan, 1997) and combinations
thereof. Some of these forms of learning will also be applied in the model for multilevel
organizational learning introduced here in Section 4.
4. The Adaptive Network Model for Organisational Learning
In the considered case study concerning tasks a, b, c, and d, initially the individual mental
models of 4 people are different and based on some strong and some weak connections; they
don’t use a stronger shared mental model as that does not exist yet. The multilevel
organizational learning addressed to improve the situation covers:
1. Individual (Hebbian) learning by persons of their mental models through internal simulation
which results in stronger but still incomplete and different mental models. Person A and C’s
mental models have no connection from task c to task d and person B and D’s mental
models have no connection from a to b.
2. Formation of two shared team mental models for teams T1 (consisting of persons A and B)
and T2 (consisting of persons C and D) based on the different individual mental models. A
process of unification by aggregation takes place (feed forward learning).
3. Formation of a shared organization mental model based on the two team mental models.
Again, a process of unification by aggregation takes place (feed forward learning).
4. Flow of information and knowledge from organization mental model to team mental
models, e.g., a form of instructional learning (feedback learning).
5. Learning of individual mental models from the shared team mental models, e.g., also a form
of instructional learning (feedback learning).
6. Improvements on these individual mental models by individual learning through internal
simulation which results in stronger and now complete mental models (by Hebbian
learning). Now person A and C’s mental models have a connection from task c to task d,
and person B and D’s mental models have a connection from a to b.
The connectivity of the designed network model is depicted in Fig. 3; for an overview of
the states at the base level and first-order self-modeling level, see Tables 2 and 3, and for
Control of adaptation
of a mental model
Adaptation
of a mental model
Internal simulation
Second-order self-model
of a mental model
First-order self-model
of a mental model
Base level with a mental model
as subnetwork
Three-level cognitive architecture
Self-modeling network architecture
6
WW
a_T1,b_T1,W
a_B,b_B
WW
a_T1,b_T1,W
a_A,b_A
WW
a_T2,b_T2,Wa_C,b_C
WWb_T2,c_T2,Wb_D,c_D
WW
a_O,b_O,Wa_T2,b_T2
a_D
c_B
a_B
b_B
WWa_T2,b_T2,Wa_D,b_D
c_A
a_A
b_A
more details about the connections and how they relate to (a) to (f) from Section 2.3, see
the Appendix as Linked Data at URL https://www.researchgate.net/publication/354352746.
Fig. 3. The connectivity of the second-order adaptive network model for the second-order self-model
of the mental models: the interactions between the first-order self-model level and the second-order
self-model level: the second-order Hebbian learning for the second-order W-states (the WW-states).
The undermost base level of this model has mental model states for individuals, teams and
organization, and also context states for activation of six different phases (like the (a) to (f)
in Section 2.3) at different times. The mental states of persons are connected to each other
according to the order of the tasks, and the first ones has a connection from first context state
to be able to start to perform internal simulation and learn.
As can be seen in Fig. 3, some connections between task states of persons are dashed,
which means initially there is no connection. Therefore, states where these dashed
connections are, are the ‘hollow’ non-known mental states of persons. These states have
connections from a fifth context state to enable to observe the improvement of individual
with the impact of organization and team mental models in Phase 5. The base level mental
states relate to the basic tasks and can be considered as the basic ingredients of the mental
models representing knowledge on relations between separate tasks.
To make the mental models adaptive, first-order self-model states are added in the
intermediary level. These are W-states representing adaptive weights for each developed
connection of individual, team and organization mental states in the base level. There are also
intralevel W-to-W connections between first-order W-states here to provide feed forward
learning in Phase 2 and Phase 3 and feedback learning in Phase 4 and Phase 5 (Crossan et al,
1999). These W-to-W connections correspond to the arrows for feed forward and feedback
learning shown in Fig. 1. Formations of shared team and organization mental models are
initiated by this feed forward learning mechanism, and the learning from the shared
organisation mental model and the shared team mental model by individuals occurs by the
feedback learning mechanism.
HWO
WWb_O,c_O,Wb_T2,c_T2
Second-order
self-model level
for control of
network adaptation
First-order
self-model level
for network
adaptation
Base level
WWc_T2,d_T2,Wc_D,d_D
WWc_O,d_O,Wc_T2,d_T2c
Wc_O,d_O
Wb_O,c_O
conph4
conph3
c_D
d_D
a_O
b_O
c_O
d_O
conph1
a_C
b_C
c_C
d_C
b_D
d_B
d_A
a_T1
b_T1
c_T1
d_T1
d_T2
c_T2
b_T2
a_T2
Wa_O,b_O
WWa_O,b_O,Wa_T1,b_T1
WWb_O,c_O,Wb_T1,c_T1
WWc_O,d_O,Wc_T1,d_T1c
conph5
conph2
Wc_T1,d_T1
Wc_T2,d_T2
Wb_T1,c_T1
Wb_T2,c_T2
Wa_T1,b_T1
Wa_T2,b_T2
HWC
HWA
HWD
HWB
HWT2
HWT1
Wa_A,b_A
Wb_A,c_A
Wc_A,d_A
Wc_B,d_B
Wb_B,c_B
Wa_B,b_B
Wb_C,c_C
Wc_C,d_C
Wa_C,b_C
Wb_D,c_D
Wc_D,d_D
Wa_D,b_D
WWb_T2,c_T2,Wb_C,c_D
WWc_T2,d_T2,Wc_C,d_D
WWb_T1,c_T1,Wb_A,c_A
WWc_T1,d_T1,Wc_A,d_A
WWb_T1,c_T1,Wb_B,c_B
WWc_T1,d_T1,Wc_B,d_B
7
To control this adaptivity in first-order adaptation level, second-order self-model states
are added in the uppermost level. In first place, there are WW-states (higher-order W-states)
for (intralevel) connections between first-order adaptivity level W-states, in other words
adaptive weight representation of the connections of adaptive weight representation states in
the level below. These control processes are left out of consideration in Fig. 1 based on
(Crossan et al, 1999) and (Wiewiora et al, 2019) but still are crucial for the processes to
function well. Additionally, HW-states for adaptation speeds of connection weights in the
first-order adaptation level, and MW-states for persistence of adaptation are placed here. This
provides the speed and persistence control of the adaptation.
For a full specification of the network model by role matrices, see the Appendix as Linked
Data at URL https://www.researchgate.net/publication/354352746.
Table 3 Base level states of the introduced adaptive network model
Nr
State
Explanation
X1
a_A
Individual mental model state for person A for task a
X2
b_A
Individual mental model state for person A for task b
X3
c_A
Individual mental model state for person A for task c
X4
d_A
Individual mental model state for person A for task d
X5
a_B
Individual mental model state for person B for task a
X6
b_B
Individual mental model state for person B for task b
X7
c_B
Individual mental model state for person B for task c
X8
d_B
Individual mental model state for person B for task d
X9
a_C
Individual mental model state for person C for task a
X10
b_C
Individual mental model state for person C for task b
X11
c_C
Individual mental model state for person C for task c
X12
d_C
Individual mental model state for person C for task d
X13
a_D
Individual mental model state for person D for task a
X14
b_D
Individual mental model state for person D for task b
X15
c_D
Individual mental model state for person D for task c
X16
d_D
Individual mental model state for person D for task d
X17
a_T1
Shared mental model state for team T1 for task a
X18
b_T1
Shared mental model state for team T1 for task b
X19
c_T1
Shared mental model state for team T1 for task c
X20
d_T1
Shared mental model state for team T1 for task d
X21
a_T2
Shared mental model state for team T2 for task a
X22
b_T2
Shared mental model state for team T2 for task b
X23
c_T2
Shared mental model state for team T2 for task c
X24
d_T2
Shared mental model state for team T2 for task d
X25
a_O
Shared mental model state for organization O for task a
X26
b_O
Shared mental model state for organization O for task b
X27
c_O
Shared mental model state for organization O for task c
X28
d_O
Shared mental model state for organization O for task d
X29
conph1
Context state for Phase 1: individual mental model simulation and learning
X30
conph2
Context state for Phase 2: creation of shared mental models for teams T1 and T2
X31
conph3
Context state for Phase 3: creation of a shared mental model for organization O
X32
conph4
Context state for Phase 4: learning shared team mental models from the shared
mental model for organization O
X33
conph5
Context state for Phase 5: learning individual mental models from the shared mental
models for teams T1 and T2
X34
conph6
Context state for Phase 6: individual mental model simulation and learning
5. Example Simulation Scenario
In this scenario, for reasaons of presentation a multi-phase approach is applied to get a clear
picture of the progress of multilevel organizational learning via teams. In general, the model
can also process all phases simultaneously. It is possible to see the feed forward flow of the
development of shared team mental models from individual mental models first, formation
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of the shared organization mental model originating from teams mental models then, and
finally by the feedback flow the impact of these shared mental models on teams and
individuals. In practice and also in the model, these phases also can overlap or take place
entirely simultaneously. The considered six phases are as follows:
Table 4 First-order self-model states of the introduced adaptive network model
Nr
State
Explanation
X35
Wa_A,b_A
First-order self-model state for the weight of the connection from a to b within
the individual mental model of person A
X36
Wb_A,c_A
First-order self-model state for the weight of the connection from b to c within
the individual mental model of person A
X37
Wc_A,d_A
First-order self-model state for the weight of the connection from c to d within
the individual mental model of person A
X38
Wa_B,b_B
First-order self-model state for the weight of the connection from a to b within
the individual mental model of person B
X39
Wb_B,c_B
First-order self-model state for the weight of the connection from b to c within
the individual mental model of person B
X40
Wc_B,d_B
First-order self-model state for the weight of the connection from c to d within
the individual mental model of person B
X41
Wa_C,b_C
First-order self-model state for the weight of the connection from a to b within
the individual mental model of person C
X42
Wb_C,c_C
First-order self-model state for the weight of the connection from b to c within
the individual mental model of person C
X43
Wc_C,d_C
First-order self-model state for the weight of the connection from c to d within
the individual mental model of person C
X44
Wa_D,b_D
First-order self-model state for the weight of the connection from a to b within
the individual mental model of person D
X45
Wb_D,c_D
First-order self-model state for the weight of the connection from b to c within
the individual mental model of person D
X46
Wc_D,d_D
First-order self-model state for the weight of the connection from c to d within
the individual mental model of person D
X47
Wa_T1,b_T1
First-order self-model state for the weight of the connection from a to b within
the shared mental model of team T1
X48
Wb_T1,c_T1
First-order self-model state for the weight of the connection from b to c within
the shared mental model of team T1
X49
Wc_T1,d_T1
First-order self-model state for the weight of the connection from c to d within
the shared mental model of team T1
X50
Wa_T2,b_T2
First-order self-model state for the weight of the connection from a to b within
the shared mental model of team T2
X51
Wb_T2,c_T2
First-order self-model state for the weight of the connection from b to c within
the shared mental model of team T2
X52
Wc_T2,d_T2
First-order self-model state for the weight of the connection from c to d within
the shared mental model of team T2
X53
Wa_O,b_O
First-order self-model state for the weight of the connection from a to b within
the shared mental model of the organisation O
X54
Wb_O,c_O
First-order self-model state for the weight of the connection from b to c within
the shared mental model of the organisation O
X55
Wc_O,d_O
First-order self-model state for the weight of the connection from c to d within
the shared mental model of the organisation O
Phase 1: Individual mental model usage and learning
This relates to (a) in Section 2. Different individual mental models by four
different persons are constructed and strengthened here. The knowledge levels of
people for the tasks, initially, are not same. Thus, the learning levels are different
as can be seen in the first phase between time 25 and 200 in the simulation graph
in Fig. 4 below. For example, activation levels of first three base states for tasks a
to c of person A from Team 1 and person C from Team 2 (a_A to c_A and a_C to
c_C) increase while the activation levels of states for task d (d_A and d_C) remain
at zero indicating that they do not have knowledge on this task. A similar lack of
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knowledge is observed for the other persons B from Team 1 and D from Team 2,
for task a this time. Therefore, the activation levels of their states a_B and a_D
remain at zero in this phase, while others get increased (b_B to d_B and b_D to
d_D). After this first individual learning phase, forgetting takes place for all
persons because they do not have perfect persistence factors self-model M-state
values (values < 1, meaning imperfection). Increased W-states during phase 1,
start to slightly decrease after phase 1 at different rates representing the differences
between persons concerning forgetting speed.
Phase 2: Shared team mental model formation (feed forward learning)
This relates to (b) in Section 2. Formation of two shared team mental models
happens in this phase. The collaboration of the individuals creates the aggregation
of their mental models as part of feed forward organizational learning (in this case
team learning). The W-states of the teams (Wa_T1,b_T1 to Wc_T1,d_T1 and Wa_T2,b_T2 to
Wc_T2,d_T2) increase at different rates in Phase 2 between time 250 and 300 in Fig.
4. Team 1 becomes better at the connection cd, and Team 2 becomes better at
connection ab because the teams have different persons. Then, these shared
mental models are maintained by the two teams.
Phase 3: Shared organization mental model formation (feed forward
learning)
This relates to (c) in Section 2. A shared organization mental model is formed in
this phase from the unification and aggregation of the two shared team mental
models. The values of shared organization mental model W-states (Wa_O,b_O to
Wc_O,d_O) increase here between time 350 and 400.
Phase 4: Feedback learning of the shared team mental model from the shared
organization mental model This relates to (d) in Section 2. Knowledge from the
shared organization mental model is received by the team mental models as a form
of (instructional) feedback learning here in this phase. The (higher-order adaptive)
connections from organization W-states to teams W-states (X68 to X73) become
activated, and the teams start to get stronger connections about tasks.
Phase 5: Feedback learning of the individual mental models from the shared
team mental models This relates to (e) in Section 2. Improved knowledge from
shared team mental models is received by individuals as a form of (instructional)
feedback learning in this phase. Higher-order adaptive weight states for
connections from teams W-states to individual W-states (X56 to X67) are activated.
This provides the learning of individual mental models and gives persons the
chance of improving their unknown connections in the next phase. For instance,
the person A starts to learn about the task d that it does not know in the beginning
by the help of its team. In Fig. 4, the W-states of persons make jumps in this Phase
5 between time 650 and 800.
Phase 6: Individual mental model usage and learning
This relates to (f) in Section 2. Persons start to further improve their knowledge
and skills (their mental models) already strengthened in Phase 5 by Hebbian
learning. Person A’s knowledge on task d (state d_A) becomes nonzero now
(obtained via shared team mental model) and similar improvements are observed
for other persons and their ‘hollow’ unknown states.
10
Fig. 4. Simulation graph showing all states
6. Discussion
Within mainstream organisational learning literature such as (Crossan et al, 1999; Wiewiora
et al., 2019), mental models at individual, team and organisation levels and the interplay of
them are considered to be a vehicle for organizational learning. This is called multilevel
organisational learning. Based on developed individual mental models, by socalled feed
forward learning the formation of shared team mental models can take place and based on
them, a shared mental model for the level of the organization as a whole (see also Fig. 1
adopted from the mentioned literature). Once these shared mental models have been formed,
they can be adopted by individuals within the organization, indicated as feedback learning.
This involves a number of mechanisms of different types that by their cyclical interaction
together can be considered to form the basis of multilevel organizational learning. These
mechanisms have been formalized in a computational manner here and brought together in
an adaptive self-modeling network architecture. The model was illustrated by a relatively
simple but realistic case study. For the sake of presentation, in the case study scenario the
different types of mechanisms have been controlled in such a manner that they are
sequentially over time. This is not inherent in the designed computational network model:
these processes can equally well work simultaneously. The two lowest levels of the three-
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
1.1
050 100 150 200 250 300 350 400 450 500 550 600 650 700 750 800 850 900 950 1000
Overall Simulation
X1 - a_A X2 - b_A X3 - c_A X4 - d_A
X5 - a_B X6 - b_B X7 - c_B X8 - d_B
X9 - a_C X10 - b_C X11 - c_C X12 - d_C
X13 - a_D X14 - b_D X15 - c_D X16 - d_D
X17 - a_T1 X18 - b_T1 X19 - c_T1 X20 - d_T1
X21 - a_T2 X22 - b_T2 X23 - c_T2 X24 - d_T2
X25 - a_O X26 - b_O X27 - c_O X28 - d_O
X29 - con_ph1 X30 - con_ph2 X31 - con_ph3 X32 - con_ph4
X33 - con_ph5 X34 - con_ph6 X35 - Wa_A,b_A X36 - Wb_A,c_A
X37 - Wc_A,d_A X38 - Wa_B,b_B X39 - Wb_B,c_B X40 - Wc_B,d_B
X41 - Wa_C,b_C X42 - Wb_C,c_C X43 - Wc_C,d_C X44 - Wa_D,b_D
X45 - Wb_D,c_D X46 - Wc_D,d_D X47 - Wa_T1,b_T1 X48 - Wb_T1,c_T1
X49 - Wc_T1,d_T1 X50 - Wa_T2,b_T2 X51 - Wb_T2,c_T2 X52 - Wc_T2,d_T2
X53 - Wa_O,b_O X54 - Wb_O,c_O X55 - Wc_O,d_O X56 - W-Wa_T1,b_T1,Wa_A,b_A
X57 - W-Wb_T1,c_T1,Wb_A,c_A X58 - W-Wc_T1,d_T1,Wc_A,d_A X59 - W-Wa_T1,b_T1,Wa_B,b_B X60 - W-Wb_T1,c_T1,Wb_B,c_B
X61 - W-Wc_T1,d_T1,Wc_B,d_B X62 - W-Wa_T2,b_T2,Wa_C,b_C X63 - W-Wb_T2,c_T2,Wb_C,c_C X64 - W-Wc_T2,d_T2,Wc_C,d_C
X65 - W-Wa_T2,b_T2,Wa_D,b_D X66 - W-Wb_T2,c_T2,Wb_D,c_D X67 - W-Wc_T2,d_T2,Wc_D,d_D X68 - W-Wa_O,b_O,Wa_T1,b_T1
X69 - W-Wb_O,c_O,Wb_T1,c_T1 X70 - W-Wc_O,d_O,Wc_T1,d_T1 X71 - W-Wa_O,b_O,Wa_T2,b_T2 X72 - W-Wb_O,c_O,Wb_T2,c_T2
X73 - W-Wc_O,d_O,Wc_T2,d_T2 X74 - H-W-A X75 - H-W-B X76 - H-W-C
X77 - H-W-D X78 - H-W-T1 X79 - H-W-T2 X80 - H-W-O
X81 - M-Wa_A,b_A X82 - M-Wb_A,c_A X83 - M-Wc_A,d_A X84 - M-Wa_B,b_B
X85 - M-Wb_B,c_B X86 - M-Wc_B,d_B X87 - M-Wa_C,b_C X88 - M-Wb_C,c_C
X89 - M-Wc_C,d_C X 90 - M-Wa_D,b_D X91 - M-Wb_D,c_D X92 - M-Wc_D,d_D
11
level network model describe Fig. 1 very well, especially the intralevel connections within
the middle level directly correspond to the arrows in Fig. 1. However, the necessary control
of these processes is left out of consideration in Fig. 1, but is fully addressed here by the
highest (third) level.
One of the extension possibilities concerns the type of aggregation used for the process
of shared mental model formation. In the current model this has been based on the maximal
knowledge about a specific mental model connection. But other forms of aggregation can
equally well be applied, for example weighted averages. Another possible extension is to
make states used for the control adaptive in a more context-sensitive manner, such as the
second-order self-model H- and M-states for the individuals, which for the sake of simplicity
were kept constant in the current example scenario.
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This book addresses the challenging topic of modeling adaptive networks, which often have inherently complex behaviour. Networks by themselves usually can be modeled using a neat, declarative and conceptually transparent Network-Oriented Modeling approach. For adaptive networks changing the network’s structure, it is different; often separate procedural specifications are added for the adaptation process. This leaves you with a less transparent, hybrid specification, part of which often is more at a programming level than at a modeling level. This book presents an overall Network-Oriented Modeling approach by which designing adaptive network models becomes much easier, as also the adaptation process is modeled in a neat, declarative and conceptually transparent network-oriented manner, like the network itself. Due to this dedicated overall Network-Oriented Modeling approach, no procedural, algorithmic or programming skills are needed to design complex adaptive network models. A dedicated software environment is available to run these adaptive network models from their high-level specifications. Moreover, as adaptive networks are described in a network format as well, the approach can simply be applied iteratively, so that higher-order adaptive networks in which network adaptation itself is adaptive too, can be modeled just as easily; for example, this can be applied to model metaplasticity from Cognitive Neuroscience. The usefulness of this approach is illustrated in the book by many examples of complex (higher-order) adaptive network models for a wide variety of biological, mental and social processes. The book has been written with multidisciplinary Master and Ph.D. students in mind without assuming much prior knowledge, although also some elementary mathematical analysis is not completely avoided. The detailed presentation makes that it can be used as an introduction in Network-Oriented Modelling for adaptive networks. Sometimes overlap between chapters can be found in order to make it easier to read each chapter separately. In each of the chapters, in the Discussion section, specific publications and authors are indicated that relate to the material presented in the chapter. The specific mathematical details concerning difference and differential equations have been concentrated in Chapters 10 to 15 in Part IV and Part V, which easily can be skipped if desired. For a modeler who just wants to use this modeling approach, Chapters 1 to 9 provide a good introduction. The material in this book is being used in teaching undergraduate and graduate students with a multidisciplinary background or interest. Lecturers can contact me for additional material such as slides, assignments, and software. Videos of lectures for many of the chapters can be found at https://www.youtube.com/watch?v=8Nqp_dEIipU&list=PLF-Ldc28P1zUjk49iRnXYk4R-Jm4lkv2b.
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