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A model of magnetic universe based on nonlinear electrodynamics has been introduced by Kruglov. This model describes an early inflation era followed by a radiation era. We show that this model is related to our model of universe based on a quadratic equation of state. We discuss two quantitatively different models of early universe. In Model I, the primordial density of the universe is identified with the Planck density. At $t=0$, the universe had the characteristics of a Planck black hole. During the inflation, which takes place on a Planck timescale, the size of the universe evolves from the Planck length to a size comparable to the Compton wavelength of the neutrino. If we interpret the radius of the universe at the end of the inflation (neutrino's Compton wavelength) as a minimum length related to quantum gravity and use Zeldovich's first formula of the vacuum energy, we obtain the correct value of the cosmological constant. In Model II, the primordial density of the universe is identified with the electron density as a consequence of nonlinear electrodynamics. At $t=0$, the universe had the characteristics of an electron. During the inflation, which takes place on a gravitoelectronic timescale, the size of the universe evolves from the electron's classical radius to a size comparable to the size of a dark energy star of the stellar mass. If we interpret the radius of the universe at the begining of the inflation (electron's classical radius) as a minimum length related to quantum gravity and use Zeldovich's second formula of the vacuum energy, we obtain the correct value of the cosmological constant. This provides an accurate form of Eddington relation between the cosmological constant and the mass of the electron. We also introduce a nonlinear electromagnetic Lagrangian that describes simultaneously the early inflation, the radiation era, and the dark energy era.

A harmonically trapped active Brownian particle exhibits two types of positional distributions—one has a single peak and the other has a single well—that signify steady-state dynamics with low and high activity, respectively. Adding inertia to the translational motion preserves this strict classification of either single-peak or single-well densities but shifts the dividing boundary between the states in the parameter space. We characterize this shift for the dynamics in one spatial dimension using the static Fokker-Planck equation for the full joint distribution of the state space. We derive local results analytically with a perturbation method for a small rotational velocity and then extend them globally with a numerical approach.

T-cell cytotoxic function relies on the cooperation between the highly specific but poorly adhesive T-cell receptor (TCR) and the integrin LFA-1. How LFA-1-mediated adhesion may scale with TCR stimulation strength is ill-defined. Here, we show that LFA-1 conformation activation scales with TCR stimulation to calibrate human T-cell cytotoxicity. Super-resolution microscopy analysis reveals that >1000 LFA-1 nanoclusters provide a discretized platform at the immunological synapse to translate TCR engagement and density of the LFA-1 ligand ICAM-1 into graded adhesion. Indeed, the number of high-affinity conformation LFA-1 nanoclusters increases as a function of TCR triggering strength. Blockade of LFA-1 conformational activation impairs adhesion to target cells and killing. However, it occurs at a lower TCR stimulation threshold than lytic granule exocytosis implying that it licenses, rather than directly controls, the killing decision. We conclude that the organization of LFA-1 into nanoclusters provides a calibrated system to adjust T-cell killing to the antigen stimulation strength.

Modern computing has enhanced our understanding of how social interactions shape collective behaviour in animal societies. Although analytical models dominate in studying collective behaviour, this study introduces a deep learning model to assess social interactions in the fish species Hemigrammus rhodostomus . We compare the results of our deep learning approach with experiments and with the results of a state-of-the-art analytical model. To that end, we propose a systematic methodology to assess the faithfulness of a collective motion model, exploiting a set of stringent individual and collective spatio-temporal observables. We demonstrate that machine learning (ML) models of social interactions can directly compete with their analytical counterparts in reproducing subtle experimental observables. Moreover, this work emphasizes the need for consistent validation across different timescales, and identifies key design aspects that enable our deep learning approach to capture both short- and long-term dynamics. We also show that our approach can be extended to larger groups without any retraining, and to other fish species, while retaining the same architecture of the deep learning network. Finally, we discuss the added value of ML in the context of the study of collective motion in animal groups and its potential as a complementary approach to analytical models.

We complete the kinetic theory of inhomogeneous systems with long-range interactions initiated in previous works. We use a simpler and more physical formalism. We consider a system of particles submitted to a small external stochastic perturbation and determine the response of the system to the perturbation. We derive the diffusion tensor and the friction by polarization of a test particle. We introduce a general Fokker–Planck equation involving a diffusion term and a friction term. When the friction by polarization can be neglected, we obtain a secular dressed diffusion equation sourced by the external noise. When the external perturbation is created by a discrete collection of N field particles, we obtain the inhomogeneous Lenard–Balescu kinetic equation reducing to the inhomogeneous Landau kinetic equation when collective effects are neglected. We consider a multi-species system of particles. When the field particles are at statistical equilibrium (thermal bath), we establish the proper expression of the fluctuation–dissipation theorem for systems with long-range interactions relating the power spectrum of the fluctuations to the response function of the system. In that case, the friction and diffusion coefficients satisfy the Einstein relation and the Fokker–Planck equation reduces to the inhomogeneous Kramers equation. We also consider a gas of Brownian particles with long-range interactions described by N coupled stochastic Langevin equations and determine its mean and mesoscopic evolution. We discuss the notion of stochastic kinetic equations and the role of fluctuations possibly triggering random transitions from one equilibrium state to the other. Our presentation parallels the one given for the kinetic theory of two-dimensional point vortices in a previous paper (Chavanis in Eur Phys J Plus 138:136, 2023).

## Subjets

Computational modelling
Diffusion
Quantum chromodynamics axion
Entropy
Distributed Control
Collective motion
Gravitation collapse
Einstein
TASEP
Dark matter halo
Wave function
Cosmological model
Dark matter density
Field theory scalar
Chemotaxis
Random walker
Asymptotic behavior
Equation of state
Numerical calculations
Dark matter fuzzy
Fermion
Fermion dark matter
Catastrophe theory
Mouvement brownien
General relativity
Kinetic theory
Electromagnetic
Gravitational collapse
Halo
Marcheur aléatoire
Transition vitreuse
Black hole
Smoluchowski equation
Turbulence
Gravitation self-force
Stability
Axion
Collective behaviour
DNA
Energy high
Pressure
Denaturation
Keller-Segel
9862Gq
Bose–Einstein condensates
Dark matter theory
Gas Chaplygin
Energy internal
Chemotaxie
Condensation Bose-Einstein
Nonrelativistic
Collisionless stellar-systems
Fokker-Planck
Quantum mechanics
Cosmological constant
Galaxy
Effondrement gravitationnel
Physique statistique
Formation
Dark matter condensation
Critical phenomena
Bose-Einstein
Hydrodynamics
9880-k
Euler-Maclaurin
9535+d
9530Sf
Current fluctuations
Axion star
Dissipation
Collapse
Gravitation
Density
Expansion acceleration
Computational modeling
Brownian motion
Dark matter
Statistical mechanics
Mass density
Evaporation
Smoluchowski-Poisson
Scalar field
Energy density
Scattering length
Feedback
Dark energy
Effect relativistic
Fermions
Phase separation
Nanofiltration
Thermodynamics
9536+x
Fermi gas
Collective behavior
Structure
Cosmology
Rotation
Bethe ansatz
Atmosphere
Competition