Related papers: A transformational approach to collective behavior

A continuum model for self-organized dynamics is numerically investigated. The model describes systems of particles subject to alignment interaction and short-range repulsion. It consists of a non-conservative hyperbolic system for the…

In this sequel (to [Phys. Rev. Res. 3, 023044(2021)], arXiv:2006.10072), we study randomly driven $(1+1)$ dimensional conformal field theories (CFTs), a family of quantum many-body systems with soluble non-equilibrium quantum dynamics. The…

Quantum-Induced Stochastic Dynamics arises from the coupling between a classical system and a quantum environment. Unlike standard thermal reservoirs, this environment acts as a dynamic bath, capable of simultaneously exchanging heat and…

Collective motion - or flocking - is an emergent phenomena that underlies many biological processes of relevance, from cellular migrations to animal groups movement. In this work, we derive scaling relations for the fluctuations of the mean…

The stochastic scenario of relaxation in the complex systems is presented. It is based on a general probabilistic formalism of limit theorems. The nonexponential relaxation is shown to result from the asymptotic self-similar properties in…

We study a random model of deep multi-head self-attention in which the weights are resampled independently across layers and heads, as at initialization of training. Viewing depth as a time variable, the residual stream defines a…

According to the stochastic-quantum correspondence, a quantum system can be understood as a stochastic process unfolding in an old-fashioned configuration space based on ordinary notions of probability and `indivisible' stochastic laws,…

A one-dimensional rule-based model for flocking, that combines velocity alignment and long-range centering interactions, is presented and studied. The induced cohesion in the collective motion of the self-propelled agents leads to a unique…

A distributional route to Gaussianity, associated with the concept of Conservative Mixing Transformations in ensembles of random vector-valued variables, is proposed. This route is completely different from the additive mechanism…

To study discrete dynamical systems of different types --- deterministic, statistical and quantum --- we develop various approaches. We introduce the concept of a system of discrete relations on an abstract simplicial complex and develop…

We introduce a stochastic agent-based model for the flocking dynamics of self-propelled particles that exhibit velocity-alignment interactions with neighbours within their field of view. The stochasticity in the dynamics of the model arises…

We define a stochastic reaction-diffusion process that describes a consensus formation in a non-sedentary population. The process is a diffusive version of the Majority Vote model, where the state update follows two stages: in the first…

The hidden Markov model (HMM) is a generative model that treats sequential data under the assumption that each observation is conditioned on the state of a discrete hidden variable that evolves in time as a Markov chain. In this paper, we…

In this paper we consider first order differential models of collective behaviors of groups of agents based on the mass conservation equation. Models are formulated taking the spatial distribution of the agents as the main unknown,…

This work presents the basic elements of the formalism involved in the treatment of Hamiltonian dynamical systems with symmetry and the geometrical description of collective motion.

It is shown that for quantum ensembles consisting of equal particles, the collective micro-causality does not contradict the quantum theory. The amplitudes of the states of such an ensemble can be divided into small portions, for each of…

We propose a model of collective behavior in self-propelled active agents that incorporates a perceptual decision-making process. In this framework, the decision-making dynamics is modeled using quantum formalism. The perceptual decision…

We study the Hamilton-Jacobi formulation of effective mechanical actions associated with holographic renormalization group flows when the field theory is put on the sphere and mass terms are turned on. Although the system is supersymmetric…

A theoretical scheme, based on a probabilistic generalization of the Hamilton's principle, is elaborated to obtain an unified description of more general dynamical behaviors determined both from a lagrangian function and by mechanisms not…

We derive a multiconfigurational time-dependent Hartree theory for systems with particle conversion. In such systems particles of one kind can convert to another kind and the total number of particles varies in time. The theory thus extends…