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Collective action and group formation are fundamental behaviors among both organisms cooperating to maximize their fitness, and people forming socioeconomic organizations. Researchers have extensively explored social interaction structures via game theory and homophilic linkages, such as kin selection and scalar stress, to understand emergent cooperation in complex systems. However, we still lack a general theory capable of predicting how agents benefit from heterogeneous preferences, joint information, or skill complementarities in statistical environments. Here, we derive general statistical dynamics for the origin of cooperation based on the management of resources and pooled information. Specifically, we show how groups that optimally combine complementary agent knowledge about resources in statistical environments maximize their growth rate. We show that these advantages are quantified by the information synergy embedded in the conditional probability of environmental states given agents' signals, such that groups with a greater diversity of signals maximize their collective information. It follows that, when constraints are placed on group formation, agents must intelligently select with whom they cooperate to maximize the synergy available to their own signal. Our results show how the general properties of information underlie the optimal collective formation and dynamics of groups of heterogeneous agents across social and biological phenomena., Comment: 14 pages, 4 figures

Renormalization group (RG) methods are emerging as tools in biology and computer science to support the search for simplifying structure in distributions over high-dimensional spaces. We show that mixture models can be thought of as having multiple coexisting, exactly independent RG flows, each with its own notion of scale. We define this property as ``multi-relevance''. As an example, we construct a model that has two distinct notions of scale, each corresponding to the state of an unobserved categorical variable. In the regime where this latent variable can be inferred using a linear classifier, the vertex expansion approach in non-perturbative RG can be applied successfully but will give different answers depending the choice of expansion point in state space. In the regime where linear estimation of the latent state fails, we show that the vertex expansion predicts a decrease in the total number of relevant couplings from four to three and does not admit a good polynomial truncation scheme. This indicates oversimplification. One consequence of this is that principal component analysis (PCA) may be a poor choice of coarse-graining scheme in multi-relevant systems, since it imposes a notion of scale which is incorrect from the RG perspective. Taken together, our results indicate that RG and PCA can lead to oversimplification when multi-relevance is present and not accounted for., Comment: 15 pages, 2 figures

The renormalization group (RG) is a class of theoretical techniques used to explain the collective physics of interacting, many-body systems. It has been suggested that the RG formalism may be useful in finding and interpreting emergent low-dimensional structure in complex systems outside of the traditional physics context, such as in biology or computer science. In such contexts, one common dimensionality-reduction framework already in use is information bottleneck (IB), in which the goal is to compress an ``input'' signal $X$ while maximizing its mutual information with some stochastic ``relevance'' variable $Y$. IB has been applied in the vertebrate and invertebrate processing systems to characterize optimal encoding of the future motion of the external world. Other recent work has shown that the RG scheme for the dimer model could be ``discovered'' by a neural network attempting to solve an IB-like problem. This manuscript explores whether IB and any existing formulation of RG are formally equivalent. A class of soft-cutoff non-perturbative RG techniques are defined by families of non-deterministic coarsening maps, and hence can be formally mapped onto IB, and vice versa. For concreteness, this discussion is limited entirely to Gaussian statistics (GIB), for which IB has exact, closed-form solutions. Under this constraint, GIB has a semigroup structure, in which successive transformations remain IB-optimal. Further, the RG cutoff scheme associated with GIB can be identified. Our results suggest that IB can be used to impose a notion of ``large scale'' structure, such as biological function, on an RG procedure., Comment: 21 pages, 2 figures

Contact electrification of dielectric grains forms the basis for a myriad of physical phenomena. However, even the basic aspects of collisional charging between grains are still unclear. Here we develop a new experimental method, based on acoustic levitation, which allows us to controllably and repeatedly collide two sub-millimeter grains and measure the evolution of their electric charges. This is therefore the first tribocharging experiment to provide complete electric isolation for the grain-grain system from its surroundings. We use this method to measure collisional charging rates between pairs of grains for three different material combinations: polyethylene-polyethylene, polystyrene-polystyrene, and polystyrene-sulfonated polystyrene. The ability to directly and noninvasively collide particles of different constituent materials, chemical functionality, size, and shape opens the door to detailed studies of collisional charging in granular materials.