In this paper, we review and compare the stochastic quantum mechanics of Nelson and the scale relativity theory of Nottale. We consider both nonrelativistic and relativistic frameworks and include the electromagnetic field. These theories propose a derivation of the Schrödinger and Klein–Gordon equations from microscopic processes. We show their formal equivalence. Specifically, we show that the real and imaginary parts of the complex Lorentz equation in Nottale’s theory are equivalent to the Nelson equations, which are themselves equivalent to the Madelung and de Broglie hydrodynamical representations of the Schrödinger and Klein–Gordon equations, respectively. We discuss the different physical interpretations of the Nelson and Nottale theories and stress their strengths and weaknesses. We mention potential applications of these theories to dark matter.

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Biohybrid systems in which robotic lures interact with animals have become compelling tools for probing and identifying the mechanisms underlying collective animal behavior. One key challenge lies in the transfer of social interaction models from simulations to reality, using robotics to validate the modeling hypotheses. This challenge arises in bridging what we term the 'biomimicry gap', which is caused by imperfect robotic replicas, communication cues and physics constraints not incorporated in the simulations, that may elicit unrealistic behavioral responses in animals. In this work, we used a biomimetic lure of a rummy-nose tetra fish (Hemigrammus rhodostomus) and a neural network (NN) model for generating biomimetic social interactions. Through experiments with a biohybrid pair comprising a fish and the robotic lure, a pair of real fish, and simulations of pairs of fish, we demonstrate that our biohybrid system generates social interactions mirroring those of genuine fish pairs. Our analyses highlight that: 1) the lure and NN maintain minimal deviation in real-world interactions compared to simulations and fish-only experiments, 2) our NN controls the robot efficiently in real-time, and 3) a comprehensive validation is crucial to bridge the biomimicry gap, ensuring realistic biohybrid systems.

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Despite 15 years of extensive investigation, the fabrication and study of nanofluidic devices that incorporate a single carbon nanotube (CNT) still represents a remarkable experimental challenge. In this study, we present the fabrication of nanofluidic devices that integrate an individual single-walled CNT (SWCNT), showcasing a notable reduction in noise by 1 -3 orders of magnitude compared to conventional devices. This achievement was made possible by employing high dielectric constant materials for both the substrate and the CNT-covering layer. Furthermore, we provide a detailed account of the crucial factors contributing to the successful fabrication of SWCNT-based nanofluidic devices that are reliably leak-free, plug-free, and long-lived. Key considerations include the quality of the substrate-layer interface, the nanotube opening, and the effective removal of photoresist residues and trapped microbubbles. We demonstrate that these devices, characterized by a high signal-tonoise ratio, enable spectral noise analysis of ionic transport through an individual SWCNT, thus showing that SWCNTs obey Hooge's law in 1/ f at low frequencies. Beyond advancing our fundamental understanding of ion transport in SWCNTs, these ultralow-noise measurements open avenues for leveraging SWCNTs in nanopore sensing applications for single-molecule detection, offering high sensitivity and identification capabilities.

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Stigmergy is a generic coordination mechanism widely used by animal societies, in which traces left by individuals in the environment guide and stimulate the subsequent actions of the same or different individuals. In the human context, with the digitization of society, new forms of stigmergic processes have emerged through the development of online services that extensively exploit the digital traces left by their users, in particular, using rating-based recommendation systems. Therefore, understanding the impact of these digital traces on both individual and collective decision-making is essential. This study pursues two main objectives. First, I investigate and modelize the interactions of groups of individuals with their digital traces, and determine how they can exploit these traces to cooperate in an information search task. Subsequently, the research explores the impact of intragroup and intergroup competition on the dynamics of cooperation in the framework of this information search task. To answer these questions, we have developed the online multiplayer Stigmer game, on which we base 16 series of experiments under varying conditions. In this game, groups of individuals leave and exploit digital traces in an information search task that implements a 5-star rating system. This system is similar to recommendation systems used by many online marketplaces and platforms, where users can evaluate products, services, or sellers. In the game, all individuals interact with a grid of hidden values, searching for cells with the highest values, and using only indirect information provided in the form of colored traces resulting from their collective ratings. This controlled environment allows for a thorough and quantitative analysis of individual and collective behaviors, and offers the possibility of manipulating and studying the combined impact of intragroup and intergroup competition on cooperation. The experimental and modeling results indicate that the type and intensity of competition determine how individuals interpret and use digital traces, and impact the reliability of the information delivered via these traces. This study reveals that individuals can be classified into three behavioral profiles that differ in their degree of cooperation: collaborators, neutrals, and defectors. When there is no competition, digital traces spontaneously induce cooperation among individuals, highlighting the potential for stigmergic processes to foster collaboration in human groups. Likewise, competition between two groups also promotes cooperative behavior among group members who aim to outperform the members of the other group. However, intragroup competition can prompt deceptive behaviors, as individuals may manipulate their ratings to gain a competitive advantage over the other group members. In this situation, the presence of misinformation reinforces the use of private information over social information in the decision-making process. Finally, situations that combine both intragroup and intergroup competition display varying levels of cooperation between individuals, that we explain. This research establishes the foundations for understanding stigmergic interactions in digital environments, shedding light on the relationships between competition, cooperation, deception, and decision-making. The insights gained may contribute to the development of sustainable and cooperative personalized decision-making algorithms and artificial collective intelligence systems grounded in stigmergy.

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