Exact face-landing probabilities for bouncing objects: Edge probability in the coin toss and the three-sided die problem.

Have you ever taken a disputed decision by tossing a coin and checking its landing side? This ancestral "heads or tails" practice is still widely used when facing undecided alternatives since it relies on the intuitive fairness of equiprobability. However, it critically disregards an interesting third outcome: the possibility of the coin coming at rest on its edge. Provided this evident yet elusive possibility, previous works have already focused on capturing all three landing probabilities of thick coins, but have only succeeded computationally. Hence, an exact analytical solution for the toss of bouncing objects still remains an open problem due to the strongly nonlinear processes induced at each bounce. In this Letter we combine the classical equations of collisions with a statistical-mechanics approach to derive an exact analytical solution for the outcome probabilities of the toss of a bouncing object, i.e., the coin toss with arbitrarily inelastic bouncing. We validate the theoretical prediction by comparing it to previously reported simulations and experimental data; we discuss the moderate discrepancies arising at the highly inelastic regime; we describe the differences with previous, approximate models; we propose the optimal geometry for the fair cylindrical three-sided die; and we finally discuss the impact of current results within and beyond the coin toss problem.

Synthetic Lateral Inhibition in Periodic Pattern Forming Microbial Colonies.

Multicellular entities are characterized by intricate spatial patterns, intimately related to the functions they perform. These patterns are often created from isotropic embryonic structures, without external information cues guiding the symmetry breaking process. Mature biological structures also display characteristic scales with repeating distributions of signals or chemical species across space. Many candidate patterning modules have been used to explain processes during development and typically include a set of interacting and diffusing chemicals or agents known as morphogens. Great effort has been put forward to better understand the conditions in which pattern-forming processes can occur in the biological domain. However, evidence and practical knowledge allowing us to engineer symmetry-breaking is still lacking. Here we follow a different approach by designing a synthetic gene circuit in E. coli that implements a local activation long-range inhibition mechanism. The synthetic gene network implements an artificial differentiation process that changes the physicochemical properties of the agents. Using both experimental results and modeling, we show that the proposed system is capable of symmetry-breaking leading to regular spatial patterns during colony growth. Studying how these patterns emerge is fundamental to further our understanding of the evolution of biocomplexity and the role played by self-organization. The artificial system studied here and the engineering perspective on embryogenic processes can help validate developmental theories and identify universal properties underpinning biological pattern formation, with special interest for the area of synthetic developmental biology.

Statistical physics of liquid brains.

Liquid neural networks (or 'liquid brains') are a widespread class of cognitive living networks characterized by a common feature: the agents (ants or immune cells, for example) move in space. Thus, no fixed, long-term agent-agent connections are maintained, in contrast with standard neural systems. How is this class of systems capable of displaying cognitive abilities, from learning to decision-making? In this paper, the collective dynamics, memory and learning properties of liquid brains is explored under the perspective of statistical physics. Using a comparative approach, we review the generic properties of three large classes of systems, namely: standard neural networks (solid brains), ant colonies and the immune system. It is shown that, despite their intrinsic physical differences, these systems share key properties with standard neural systems in terms of formal descriptions, but strongly depart in other ways. On one hand, the attractors found in liquid brains are not always based on connection weights but instead on population abundances. However, some liquid systems use fluctuations in ways similar to those found in cortical networks, suggesting a relevant role for criticality as a way of rapidly reacting to external signals. This article is part of the theme issue 'Liquid brains, solid brains: How distributed cognitive architectures process information'.

Nonequilibrium Entropic Bounds for Darwinian Replicators.

Life evolved on our planet by means of a combination of Darwinian selection and innovations leading to higher levels of complexity. The emergence and selection of replicating entities is a central problem in prebiotic evolution. Theoretical models have shown how populations of different types of replicating entities exclude or coexist with other classes of replicators. Models are typically kinetic, based on standard replicator equations. On the other hand, the presence of thermodynamical constraints for these systems remain an open question. This is largely due to the lack of a general theory of statistical methods for systems far from equilibrium. Nonetheless, a first approach to this problem has been put forward in a series of novel developements falling under the rubric of the extended second law of thermodynamics. The work presented here is twofold: firstly, we review this theoretical framework and provide a brief description of the three fundamental replicator types in prebiotic evolution: parabolic, malthusian and hyperbolic. Secondly, we employ these previously mentioned techinques to explore how replicators are constrained by thermodynamics. Finally, we comment and discuss where further research should be focused on.

The architecture of mutualistic networks as an evolutionary spandrel.

Mutualistic networks have been shown to involve complex patterns of interactions among animal and plant species, including a widespread presence of nestedness. The nested structure of these webs seems to be positively correlated with higher diversity and resilience. Moreover, these webs exhibit marked measurable structural patterns, including broad distributions of connectivity, strongly asymmetrical interactions and hierarchical organization. Hierarchical organization is an especially interesting property, since it is positively correlated with biodiversity and network resilience, thus suggesting potential selection processes favouring the observed web organization. However, here we show that all these structural quantitative patterns-and nestedness in particular-can be properly explained by means of a very simple dynamical model of speciation and divergence with no selection-driven coevolution of traits. The agreement between observed and modelled networks suggests that the patterns displayed by real mutualistic webs might actually represent evolutionary spandrels.