Multiscale Modelling Tool: Mathematical modelling of collective behaviour without the maths

Mobile cognition: imaging the human brain in the 'real world'

Cognitive neuroscience studies in humans have enabled decades of impactful discoveries but have primarily been limited to recording the brain activity of immobile participants in a laboratory setting. In recent years, advances in neuroimaging technologies have enabled recordings of human brain activity to be obtained during freely moving behaviours in the real world. Here, we propose that these mobile neuroimaging methods can provide unique insights into the neural mechanisms of human cognition and contribute to the development of novel treatments for neurological and psychiatric disorders. We further discuss the challenges associated with studying naturalistic human behaviours in complex real-world settings as well as strategies for overcoming them. We conclude that mobile neuroimaging methods have the potential to bring about a new era of cognitive neuroscience in which neural mechanisms can be studied with increased ecological validity and with the ability to address questions about natural behaviour and cognitive processes in humans engaged in dynamic real-world experiences.

Mathematical Modeling Research Output Impacting New Technological Development: An Axiomatization to Build Novelty

The mathematical modeling of research-based output impacting new technology development is crucial for a developing country. However, the complexity of modern mathematical modeling research output makes it unclear over how it can impact the development of new technology. Therefore, this study aims to explore, categorize and formulize the axioms of mathematical modeling research output that impacts the development of new technology. Seven participants were involved in this research. Interviews were conducted to explore their remarkable mathematical modeling output and how the output can impact the development of new technology. The categorization axioms are: i. mathematical modeling for theorizing, ii. mathematical modeling for simulations, iii. mathematical modeling for useable innovation and iv. patent and product commercialization. Finally, the categorization can be formulized as an axiom of mathematical modeling novelty, which is the desired research output. Moreover, patents and commercialization are the elements that mathematical modeling should possess for new technological development. The limited number of participants involved in this study makes this study formulation limited to only some types of mathematical modeling output. However, this substantive formulation could give some ideas in proposing the path and processes on how to enhance the effort for society to develop the culture of mathematical modeling in developing new technology.

Negative feedback may suppress variation to improve collective foraging performance

Social insect colonies use negative as well as positive feedback signals to regulate foraging behaviour. In ants and bees individual foragers have been observed to use negative pheromones or mechano-auditory signals to indicate that forage sources are not ideal, for example being unrewarded, crowded, or dangerous. Here we propose an additional function for negative feedback signals during foraging, variance reduction. We show that while on average populations will converge to desired distributions over forage patches both with and without negative feedback signals, in small populations negative feedback reduces variation around the target distribution compared to the use of positive feedback alone. Our results are independent of the nature of the target distribution, providing it can be achieved by foragers collecting only local information. Since robustness is a key aim for biological systems, and deviation from target foraging distributions may be costly, we argue that this could be a further important and hitherto overlooked reason that negative feedback signals are used by foraging social insects.

Social insect colonies regulate the number of insects foraging at different food sources through a combination of positive and negative feedback signals. Through positive feedback signals—such as ants’ pheromone trails and bees’ waggle dances—insects recruit each other to increase the number of foragers committed to a food source that has been evaluated as profitable. Negative feedbacks are instead inhibitory signals that are delivered to reduce commitment to a food source where an unfavourable change has been detected, for example the arrival of a predator or a decrease in nutritional reward. Our mathematical analysis explains an additional function for negative feedback; inhibitory signals can also be useful in static conditions to reduce the variance in the number of insects allocated to each food source, thus better distributing insects among the available sources. Our results can help explain field observations that are not fully understood yet, such as the periodic delivery of a small number of inhibitory signals among honeybees visiting the same forage patch even in static conditions.

Noise-induced effects in collective dynamics and inferring local interactions from data

In animal groups, individual decisions are best characterized by probabilistic rules. Furthermore, animals of many species live in small groups. Probabilistic interactions among small numbers of individuals lead to a so-called intrinsic noise at the group level. Theory predicts that the strength of intrinsic noise is not a constant but often depends on the collective state of the group; hence, it is also called a state-dependent noise or a multiplicative noise. Surprisingly, such noise may produce collective order. However, only a few empirical studies on collective behaviour have paid attention to such effects owing to the lack of methods that enable us to connect data with theory. Here, we demonstrate a method to characterize the role of stochasticity directly from high-resolution time-series data of collective dynamics. We do this by employing two well-studied individual-based toy models of collective behaviour. We argue that the group-level noise may encode important information about the underlying processes at the individual scale. In summary, we describe a method that enables us to establish connections between empirical data of animal (or cellular) collectives and the phenomenon of noise-induced states, a field that is otherwise largely limited to the theoretical literature. This article is part of the theme issue 'Multi-scale analysis and modelling of collective migration in biological systems'.