4. Future lines of Research and Applications

Future lines of research will attempt to:

  • ·Consider meta-structural research also in sequences of configurations of correlated, but even non-interacting elements such as points of sequences of images, notes in music or words in a written text. The focus is not placed upon relations, nor upon interactions between variables, but rather upon the properties of sequences;
  • Explore possible theoretical relationships between models of local (Shannon-Turing) and global information such as Tsallis or Fisher information [Frieden and Gatenby, 2006; 2009] and Meta-Structures. We expect, given our purely mesoscopic approach, the meta-structural properties are “invisible” to local information, but may show interesting characteristics of information which takes into consideration the system as a whole.

There are two levels of application proposed: 

  • ·computational, applied, for instance, to modelling collective entities established by coherent, i.e., acquiring emergent properties, information as for human-machine interface data, customer profiling, image recognition and image understanding where meta-structural properties may relate to categories; 
  • ·methodological, applied, for instance, to model collective entities established by coherent behaviours, i.e., collective behaviours such as industrial districts, markets, cities, processes  such as climate change, military and safety scenarios where meta-structural properties may model, in order to facilitate their management, induction, retention, modification of properties, and their merging.

4.1 Prescription of Meta-Structural properties

We may distinguish between problems in prescribing Meta-Structural properties for a) elements interacting without setting collective behaviours and b) collective behaviours in order to vary the properties acquired.

 4.1.1 Induction of emergence of collective behaviour in populations of interacting elements.

Processes of interacting elements consist of sequences of configurations of elements interacting, i.e., one’s behaviour influences that of another, for instance by multiple independent behavioural rules randomly followed per instant, in different ways for individual elements and, because of that, computed to subsequent, new and emerging environmental conditions. The term random is applied to ways of changing which have different levels of conceptual unpredictability given, for instance, by probability distributions. The eventual existence of only local or global stable rules consist of degrees of freedom to avoid clashes.

In this case there are no processes of emergence of acquired properties, i.e., there is no coherence. For example, as occurs with multitudes of birds flying above an open dump and unstructured craw, i.e., without boundaries within free, undifferentiated space. A similar systemically corresponding situation may be intended to occur with populations of organic agents, e.g., micro-organisms, within environments having, even temporary, undifferentiated bio-chemical properties, such as distilled water. Such processes of interaction without emergence occur within undifferentiated contexts where initial possible evolutionary steps are equivalent and may both maintain or dissolve over time. While simple interaction rules for elements of spatial collective behaviours, e.g., swarms, flocks and fish schools, may be:

a)        max distance between elements a < M;

b)        min distance between elements > m;

c)        distances between elements always changing with time;

d)        different directions among elements, but with angles  < α,

simple interaction rules for processes of interacting elements may be a subset, such as:

1.        max distance between elements a < M;

2.        min distance between elements > m;

where M may increase over time to allow dilution.

At this moment the only way to realise eventual establishment of coherence is through the detection of emergent properties by the observer at a suitable scalarity.

In the literature, processes of collective coherent behaviours have been considered as being modelled and given by processes of interacting elements when following suitable, stable, local and global rules stated by appropriated models and simulations, see, for instance among many, approaches related to flocks [Bajec et al., 2005; 2007; Ballerini et al., 2008; Heppner and Grenader, 1990; Hildenbrandt, 2010],  swarms [Bonabeau et al., 2000; 1999;  Theraulaz and Deneubourg, 1984], fish schools [Huth and Wissel, 1992; Inada,and Kawachi, 2002; Kunz and Hemelrijk, 2003; Vabo and Nottestad, 1997], ants [Gordon, 2000; 2007; Millonas, 1992; 1994;], Industrial Districts [Karlsson  et al., 2005] and general [Marshall, 2008; Minati and Collen, 2009; Weinstock,  2010].

The thesis of our approach is that processes of interacting elements turn into processes of collective interaction when following meta-structural properties, the former being a particular case of the latter.

On one hand this allows the researcher to identify processes of collective behaviours when the related acquired emergent properties have not yet been identified.

On the other, it leaves the problem of prescribing meta-structural properties for interacting elements in order to induce emergence of collective behaviours open as a future line of research.

Section ahead introduces some possible hypothetical approaches to induce the emergence of collective behaviour in populations of interacting elements.

4.1.2 Variation of collective emergent phenomena to change, regulate and maintain acquired properties

In the homogeneous approach, when interacting elements are considered as being  indistinguishable, the possibility of influencing emergent collective phenomena and their acquired properties actually focuses upon rules of interaction, energy available for the process of interaction, communications and environmental conditions. Eventual actions upon properties possessed by elements relate to their ability to react to, or elaborate interactions while their relations with emergent acquired properties is no longer reductionistically considered as being linearly consequential of their properties. However, properties of single, specific elements may influence the emergent behaviour established by the network of interactions. This applies in the non-homogeneous approach, i.e., when elements are not considered as being indistinguishable as in biological systems [Pessa, 2006]. The non-linear network of relations provides that this influence be non-linear and suitable models and approaches should be introduced. In this case we may conceptually deal with order parameters as in Synergetics [Haken, 1987; 2004].

In the approach introduced here meta-structural properties conceptually apply in both homogeneous and non-homogeneous cases since we are considering mesoscopic variables and their properties. However, the non-homogeneous case may more properly be considered as being related to the occurrence of mutations in elements, perturbations and noise such as the appearance of predators, obstacles or changes of spatial properties.

The related future line of research consists of identifying suitable approaches to influence the emergence of acquired properties in a non-invasive way, i.e., without directly acting both on interactions and elements.

Section 4.4 introduces some possible hypothetical approaches to indirectly prescribe meta-structures for collective behaviours, i.e., by maintaining as much as possible the current process of emergence.

A possible future line of research relates to the study of collective behaviours as being modelled not only by meta-structural properties assumed valid for coherent sequences of entire configurations, i.e., established by all the component elements, but by coherent dynamic sequences of partial configurations. The research relates to coherent sequences and global dynamic coherence among them by hypothesising as a sort of super meta-structural properties of dynamic sequences of meta-structural properties.

4.2 Merging of different collective behaviours

Two different collective behaviours may be intended to merge when both acquire a new different property with cognitive Gestalt continuity with the previous ones.

The new acquired property is not necessarily an average composition of the previous individual ones, but may even be given by possible total or partial superimposition of one over the other.

In our approach we consider the future line of research as having the purpose of meta-structurally prescribing for two or more different collective behaviours, processes of  merging in a formal way, i.e., by meta-structural properties,  and not only in an observer-dependent way such as considering cognitive Gestalt continuity.

Section 4.4 introduces some hypothetical approaches mentioning the concept of meta-structural computing.

4.3 Dissolution of collective behaviours

When can a collective behaviour be considered to dissolve, or degenerate into processes of interaction as introduced in Section 4.1.1?

The general answer is ‘when no longer maintaining the acquired emergent properties and without acquiring a new one’. However this criterion is completely observer-dependent and depends, for instance, on scalarity. In our approach we can consider that a collective behaviour dissolves when no longer having the previous meta-structural properties. On the other hand, a meta-structural property may be lost in the process of acquiring a new substituting one as, for instance, in transient processes.

An important line of research relates to the possibility of formally being able to state that no meta-structural properties are present or even possible in established processes of interaction, whatever the mesoscopic level of description acquired by the experimenter.

4.4 Hypothetical research approaches

In this conclusive section we briefly mention hypothetical approaches to induce collective behaviour in processes of interacting elements, to vary collective behaviours with their acquired emergent properties and merge collective behaviours by: 

Acting, for instance, on environmental conditions, reduction of degrees of freedom and homogeneity in such a way as to induce the desired changes assumed here as possessing corresponding meta-structural properties;

Prescribing suitable corresponding meta-structural properties. Prescription presumes non-invasive, non-linear and implicit actions while other invasive, linear and explicit, i.e., reductionistic approaches, are unsuitable at mesoscopic and macroscopic levels where different configurations of microscopic values are equivalent. 

We list now some possible hypothetical approaches to be eventually considered as lines of research.

4.4.1 Actions able to induce the acquisition of meta-structural properties Environmental conditions

One approach may consist of acting upon environmental conditions, e.g., available energy, perturbations and boundary conditions such as structures, reduction of degrees of freedom -see Section 6.1, point d) equations 4 and 10. The possibility of inducing processes of acquisition of specific emergent properties both in collective behaviours and in processes of interacting elements through suitable structures is studied by Architecture when considering the effects on social habitats. This approach involves different interdisciplinary aspects studied, for instance, by environmental psychology, cognitive science with various functional dimensions such as energetic, safety, pollution, water distribution, traffic, transport, waste management and town planning, see, for instance [[Marshal, 2008; Minati and Collen, 2004; Weinstock, 2010]. 

The line of research relates to relationships between environmental conditions and meta-structural properties induced within social habitats. Microscopic changes

Another  more general possible approach may relate to simulations and controlled collective behaviours, i.e., when elements can introduce continuous, decided and organised microscopic changes in their behaviour to regulate the emergence of acquired properties with the purpose of establishing the desired property through summative, balancing microscopic changes. Examples are given by cars self-regulating their speed in traffic and buyers self-regulating their action of buying when knowing in advance the target property to be acquired. 

A second possible application may relate to prescribing microscopic suitable changes for steering elements followed by gregarious elements to vary, for example, direction and altitude in flocks and swarms. Non-homogeneous elements

When considering non-homogeneous phenomena, it is possible to act on properties of non-homogeneous elements by breaking equivalence between different configurations of microscopic values. Their non-homogeneity relates to different processes of changing, no longer ruled by degrees of freedom nor by models. It is possible to consider that unexpected processes of emergence occur at the level of elements not considered previously as systems or as being emergent. 

Examples are mutations and phase transitions. Similar situations may be considered when interacting agents randomly acquire properties from a set of available ones or are able to learn. 

A possible line of research relates to investigate combinations of approaches by acting on meta-structural properties and the role of processes introduced by non-homogeneous elements.

4.4.2 Prescription by propagation

A more general approach, i.e., suitable for processes established by interacting elements not necessarily provided with complex cognitive systems such as flocks, swarms, herds, fish schools and systems such as industrial districts, markets and traffic, may be based on, first, to generate and catalogue both computational and phenomenological processes of emergence and related acquired properties. Secondly, the approach may consist of inserting within established collective behaviours or processes of interacting elements suitable sub-clusters provided with the desired meta-structural properties from the catalogue above. 

The term ‘within’ means the act of putting in the interacting area one or more of such sub-clusters on the assumption, to be investigated, that such properties, under suitable conditions, could propagate. The line of research relates to finding effective approaches for identifying suitable topological positions, numbers of clusters and their eventual dynamics.

4.4.3 Meta-structural computing

We mention another possible future line of research dealing with collective behaviours modelled by suitable meta-structural properties as introduced above and diluted in such a way to leave empty zones within.

The adjective diluted relates to various possible approaches. One consists in acting on the scalarity of the collective phenomena under study. It is possible to consider, for instance, zones within collective phenomena at different scalarities. In this way one can study the elements at a higher resolution within zones within collective phenomena, such as interacting particles within areas of macroscopic collective behaviour observed at lower resolution , e.g., particles within swarms or molecules within Bénard rolls.

Another may consist in keeping the same scale, but changing the relationship between the geometrical dimensions of the collectively interacting elements and other dimensions such as distances between them and time with consequences, for instance, on speed.

Within this conceptual framework we may identify a scale and relationships suitable for considering empty zones, i.e., spatial zones without interacting elements within them. Such zones may be dynamic within real collective phenomena.

Using such a general view, collective phenomena may be intended as generators of empty zones, i.e. empty environments within them.

The proposed line of research consists of exploring their eventual properties. In particular, whether they maintain the meta-structural properties of the hosting collective phenomena. In other words, are elements interacting within these zones, on a different scale or possessing different dimensions of variables, influenced by the same meta-structural properties of the hosting collective phenomena? An extreme case occurs when they adopt the same properties.

How can one detect eventual meta-structural environmental properties? Which scale can be chosen to make them collapse, i.e., to become effective on the matter inside?

Can they be assumed to represent properties of the physical vacuum, i.e., fluctuations considered by quantum physics?


In the approaches mentioned above the idea is to explore properties of the empty zones intended as sub-zones of the entire area over which the collective phenomena occur, whereas a different, but related approach may be considered using reverse scaling. The idea is to use a phenomenon of collective behaviour or, in general, a small system of elements interacting by following meta-structural properties appropriate for  the scale of larger phenomena. For instance, we may consider only a few boids interacting by using meta-structural properties appropriate for a larger flock. The idea is that because the meta-structural properties are appropriate for the dimension of a flock, insertion of the small group will lead to propagation of the meta-structural rules adopted by the small group to the larger one. The idea is to prescribe meta-structural properties suitable for the collective phenomena to be influenced on a smaller scale. The crucial point is whether the meta-structural properties used by the small system are appropriate for the larger one.


These conceptual frameworks and approaches should be studied within the framework of results available in the literature for scale invariance and dilatation or conformal symmetry considered when adopting the microscopic or macroscopic levels of description. In the same way, one should consider the renormalization group [Gallavotti, 1985; Shirkov and  Kovalev, 2001] used in research in order to identify the ‘correct’ and physically ‘stable’ phenomenological scales.


 Can meta-structural properties be considered in some way as being scale-free? In the positive case, what are the conditions of validity? How can they eventually transform through a process of scale change?


How does the research issue mentioned above relate to meta-structures and not to structures?

As introduced in Section 2.1, structures are intended as fixed analytical representations of rules of interaction between microscopic or macroscopic state variables used to model a dynamic system. The microscopic or macroscopic nature of variables considered makes structures significant only if variables are effectively present and with a suitable scalarity.

As introduced above, Meta-structural properties are expected to be suitable for systems of high mesoscopic degrees of freedom in situations of unpredictable emergence. This is why, to consider a paradoxical example, it is not possible to prescribe, by adopting a hypothetical reverse reasoning, statistical properties for the behaviour of microscopic elements nor to hypothesise their influence on phenomena occurring in zones considered at different scalarities. The degrees of freedom they possess cannot bet regulated.

It is possible to prescribe macroscopic values, e.g., temperature, when renouncing the prescription of microscopic properties.


A real, although questionable, case to be explored by considering the approaches outlined above, is homeopathy. The topic, once accepted conceptually, is explored by considering approaches of quantum physics to explain eventual effectiveness of high dilutions of matter [Del Giudice, et al., 2002; Del Giudice and  Vitiello, 2006;  Montagnier, 2009].

 Another real case relates to the possibility of modifying emerging informal organisations by introducing small subsystems composed of elements which interact by following suitable meta-structural properties, such as corporations, hospitals and schools.