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Table 1 Summary of connectivity challenges across different disciplines. Extent to which connectivity challenges are an issue: * do not present a challenge; ** presents a challenge but progress has been made; *** presents a major challenge.

From: Connectivity and complex systems: learning from a multi-disciplinary perspective

  Fundamental Unit (FU) Separating Structural Connectivity (SC) and Functional Connectivity (FC) Understanding Emergent Behaviour Measuring Connectivity
Systems Biology ** • FUs are biologically well defined, based on the biological system rather than measurement process. • A full inventory of functional elements is still missing; also interdependences between different levels of cellular organizations (i.e. among fundamental units from different networks) are often neglected. ** • Generally, a clear time scale separation ensures a distinction between SC and FC. • While FC is a network representation of cellular states (e.g. correlations between metabolite concentrations or gene expression levels), SC is shaped by evolution on a much slower time scale. ** • Concepts such as modularity and hierarchy may provide a starting point for addressing emergent behaviour within the current knowledge of SC and FC, but a true incorporation of the many (spatial and temporal) scales will require novel multiscale methods. • Key challenge: understanding the relation of regulatory mechanisms and emergent collective behaviour. ** • Explosive growth of high-throughput methods providing access to many facets of structural and functional connectivities, but has led to a dramatic diversification of databases, methods and nomenclatures, resulting in a strong need of data and method integration.
Neuroscience * • Defining the fundamental unit of the brain is clear-cut and depends on the level (scale) at which one is working. • The fundamental unit is commonly defined as being the cortical area, although is alternatively defined as the neuron. ** • Different techniques are used to distinguish between SC and FC, but FC is defined (using various techniques) using indirect correlates of brain activity. • Memory affects the relation between SC and FC through its long-lasting anatomical import on the structure of the network. • Understanding the effects of memory remains a key challenge because of the diffuse nature of the anatomical imprint. ** • Great progress has been made in understanding concepts such as attention and emotion as emergent properties of neural activity. • The big challenge today is to push this understanding to its limit and offer a convincing account of how neural activity and its organization in the networks of the brain eventually leads to consciousness. ** • A range of techniques exist to measure connectivity • Due to differences in spatial and temporal resolution between different measurement techniques, hybrid approaches are becoming popular to overcome the challenge of measuring SC and FC at appropriate resolutions. • The main challenge with the [premature] use of hybrid methods is that the final result may be limited to what the least sensitive method can provide. • Measurements of FC are inferred from high-resolution snapshots, rather than being measured directly.
Computational Neuroscience * • The fundamental unit is typically defined as being individual neurons or cortical areas and form the nodes of a network. Identifying these fundamental units is done using anatomical means and neurobiological knowledge. ** • It is increasingly common to directly and quantitatively compare SC and FC (such separations are readily undertaken and pose no major challenges). • A limitation is that SC/FC correlations only tend to look in one direction only – the effect of structure on function. * • Network-based approaches are used, allowing for the interplay of SC and FC allow for the exploration of self-organization and pattern formation – both important characteristics of emergent behaviour. * • Measurements of connectivity are undertaken using a wide range of network-based descriptors of connectivity.
Geomorphology *** • No clear or consistent definition of the fundamental unit (it is dependent on the research question). *** • Separating SC and FC in a meaningful way is challenging because of the myriad of processes operating over a multitude of spatial and temporal scales. • Separating SC and FC is compounded by the imprint of memory and timescales over which it affects connectivity for a meaningful separation of SC and FC. *** • Tools to explore how SC and FC lead to emergent behaviour are lacking. • Multi-method approaches focussing on the interactions of SC and FC over relevant spatio-temporal scales may aide in understanding emergent behaviour. ** • Approaches to measure SC are well developed, and make use of high-resolution techniques where appropriate. • No direct measurement techniques for FC are available and rely on inferring connectivity from snapshots of information. • Modelling is often used as a surrogate for direct measurements of FC.
Ecology ** • Conceptually the fundamental unit is defined as the ecosystem. • In operational terms, defining the FU is more difficult. ** • Linking and separating SC and FC is common, but made challenging where there are time lags in the response of ecological function to changes in ecological structure and vice versa. ** • Many attempts to explain emergent behavior (e.g. using advection-diffusion models) have produced realistic patterns, but at the expense of realistic processes. • A challenge is to study emergent behaviour using model structures that are not inherently designed to produce patterns. ** • A range of techniques exist for measuring SC based on simple indices of patch connectivity, through to network-based approaches. • Measuring FC poses much more of a challenge and requires dealing with complex phenomena that are difficult to quantify and tend to reply upon inferring FC connectivity based on a series of empirical measurements through time. • Advances being made in measuring SC and FC through the use of weighted monopartite and bipartite networks.
Social Network Science * • Traditionally the fundamental unit is defined as the person, although more recently the definition has become less certain with some researchers now using the interaction as the unit of study. *** • The focus tends to be on the connectivity of structural networks. • Approaches to look at dynamics (FC) are limited in terms of analytical power. • In social networks culture is a type of memory effect that affects function (i.e. the response of an individual to social interactions), and the complexity that an evolving mix of cultures brings to social networks is a significant challenge. *** • The emergence of the network property is conditional on entire network interactions, and the challenge of adopting models of social behaviour that recognise the diversity of social interactions across a population complicates matters further. *** • Measuring connectivity is a major challenge due to ethical, practical and philosophical constraints.