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Register a new userThe entropic basis of collective behaviour
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In this paper, we identify a radically new viewpoint on the collective behaviour of groups of intelligent agents. We first develop a highly general abstract model for the possible future lives that these agents may encounter as a result of their decisions. In the context of these possible futures, we show that the causal entropic principle, whereby agents follow behavioural rules that maximise their entropy over all paths through the future, predicts many of the observed features of social interactions between individuals in both human and animal groups. Our results indicate that agents are often able to maximise their future path entropy by remaining cohesive as a group, and that this cohesion leads to collectively intelligent outcomes that depend strongly on the distribution of the number of future paths that are possible. We derive social interaction rules that are consistent with maximum-entropy group behaviour for both discrete and continuous decision spaces. Our analysis further predicts that social interactions are likely to be fundamentally based on Webers law of response to proportional stimuli, supporting many studies that find a neurological basis for this stimulus-response mechanism, and providing a novel basis for the common assumption of linearly additive social forces in simulation studies of collective behaviour.
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The simulation of complex stochastic network dynamics arising, for instance, from models of coupled biomolecular processes remains computationally challenging. Often, the necessity to scan a models dynamics over a large parameter space renders full-fledged stochastic simulations impractical, motivating approximation schemes. Here we propose an approximation scheme which improves upon the standard linear noise approximation while retaining similar computational complexity. The underlying idea is to minimize, at each time step, the Kullback-Leibler divergence between the true time evolved probability distribution and a Gaussian approximation (entropic matching). This condition leads to ordinary differential equations for the mean and the covariance matrix of the Gaussian. For cases of weak nonlinearity, the method is more accurate than the linear method when both are compared to stochastic simulations.
We show that univariate and symmetric multivariate Hawkes processes are only weakly causal: the true log-likelihoods of real and reversed event time vectors are almost equal, thus parameter estimation via maximum likelihood only weakly depends on the direction of the arrow of time. In ideal (synthetic) conditions, tests of goodness of parametric fit unambiguously reject backward event times, which implies that inferring kernels from time-symmetric quantities, such as the autocovariance of the event rate, only rarely produce statistically significant fits. Finally, we find that fitting financial data with many-parameter kernels may yield significant fits for both arrows of time for the same event time vector, sometimes favouring the backward time direction. This goes to show that a significant fit of Hawkes processes to real data with flexible kernels does not imply a definite arrow of time unless one tests it.
In this paper, by using a stochastic reaction-diffusion-taxis model, we analyze the picophytoplankton dynamics in the basin of the Mediterranean Sea, characterized by poorly mixed waters. The model includes intraspecific competition of picophytoplankton for light and nutrients. The multiplicative noise sources present in the model account for random fluctuations of environmental variables. Phytoplankton distributions obtained from the model show a good agreement with experimental data sampled in two different sites of the Sicily Channel. The results could be extended to analyze data collected in different sites of the Mediterranean Sea and to devise predictive models for phytoplankton dynamics in oligotrophic waters.
A notion of biologic system or just a system implies a functional wholeness of comprising system components. Positive and negative feedback are the examples of how the idea to unite anatomical elements in the whole functional structure was successfully used in practice to explain regulatory mechanisms in biology and medicine. There are numerous examples of functional and metabolic pathways which are not regulated by feedback loops and have a structure of reciprocal relationships. Expressed in the matrix form positive feedback, negative feedback, and reciprocal links represent three basis elements of a Lie algebra sl(2,R)of a special linear group SL(2,R). It is proposed that the mathematical group structure can be realized through the three regulatory elements playing a role of a functional basis of biologic systems. The structure of the basis elements endows the space of biological variables with indefinite metric. Metric structure resembles Minkowskis space-time (+, -, -) making the carrier spaces of biologic variables and the space of transformations inhomogeneous. It endows biologic systems with a rich functional structure, giving the regulatory elements special differentiating features to form steady autonomous subsystems reducible to one-dimensional components.
The widespread adoption of online courses opens opportunities for the analysis of learner behaviour and for the optimisation of web-based material adapted to observed usage. Here we introduce a mathematical framework for the analysis of time series collected from online engagement of learners, which allows the identification of clusters of learners with similar online behaviour directly from the data, i.e., the groups of learners are not pre-determined subjectively but emerge algorithmically from the analysis and the data.The method uses a dynamic time warping kernel to create a pairwise similarity between time series of learner actions, and combines it with an unsupervised multiscale graph clustering algorithm to cluster groups of learners with similar patterns of behaviour. We showcase our approach on online engagement data of adult learners taking six web-based courses as part of a post-graduate degree at Imperial Business School. Our analysis identifies clusters of learners with statistically distinct patterns of engagement, ranging from distributed to massed learning, with different levels of adherence to pre-planned course structure and/or task completion, and also revealing outlier learners with highly sporadic behaviour. A posteriori comparison with performance showed that, although the majority of low-performing learners are part of in the massed learning cluster, the high performing learners are distributed across clusters with different traits of online engagement. We also show that our methodology is able to identify low performing learners more accurately than common classification methods based on raw statistics extracted from the data.
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