The problem of obtaining physical parameters that cannot be directly measured from observed data arises in several scientific fields. In the classic approach, the well-known maximum likelihood estimation associated with a Gaussian distribution is employed to obtain the model parameters of a complex system. Although this approach is quite popular in statistical physics, only a handful of spurious observations (outliers) make this approach ineffective, violating the Gauss-Markov theorem. In this work, starting from the generalized logarithmic function associated to the Sharma-Taneja-Mittal (STM) information measure, we propose an outlier-resistant approach based on the generalized log-likelihood estimation. In particular, our proposal deforms the Gaussian distribution based on a two-parameter generalization of the ordinary logarithmic function. We have tested the effectiveness of our proposal considering a classic geophysical inverse problem with a very noisy data set. The results show that the task of obtaining physical parameters based on the STM measure from noisy data with several outliers outperforms the classic approach, and therefore, our proposal is a useful tool for statistical physics, information theory, and statistical inference problems.

Reconstructing the Kolmogorov-Arnold-Moser (KAM) dynamics diagram of Hamiltonian system from the time series of a limited number of parameters is an outstanding question in nonlinear science, especially when the Hamiltonian governing the system dynamics is unknown. Here we demonstrate that this question can be addressed by the machine learning approach knowing as reservoir computing (RC). Specifically, we show that without prior knowledge about the Hamilton equations of motion, the trained RC is able to not only predict the short-term evolution of the system state, but also replicate the long-term ergodic properties of the system dynamics. Furthermore, using the architecture of parameter-aware RC, we show that the RC trained by the time series acquired at a handful parameters is able to reconstruct the entire KAM dynamics diagram with a high precision by tuning a control parameter externally. The feasibility and efficiency of the learning techniques are demonstrated in two classical nonlinear Hamiltonian systems, namely, the double-pendulum oscillator and the standard map. Our study indicates that, as a complex dynamical system, RC is able to learn from data the Hamiltonian.

We study the quantum dissipative Duffing oscillator across a range of system sizes and environmental couplings under varying semiclassical approximations. Using spatial complexity metrics based on Kullback-Leibler distances between phase-space attractors and temporal complexity metrics based on the Lyapunov exponent, we isolate the effect of the environment on quantum-classical differences. Moreover, we quantify the system sizes where quantum dynamics cannot be simulated using semiclassical or noise-added classical approximations. We find that a remarkable parametrically invariant meta-attractor emerges at a specific length scale and noise-added classical models deviate strongly from quantum dynamics below this scale. We also generalize the previous surprising result that classically regular orbits can have the greatest quantum-classical differences in the semiclassical regime and show that the dynamical growth of quantum-classical differences is not determined by the degree of classical chaos.

Biological systems need to react to stimuli over a broad spectrum of timescales. If and how this ability can emerge without external fine-tuning is a puzzle. We consider here this problem in discrete Markovian systems, where we can leverage results from random matrix theory. Indeed, generic large transition matrices are governed by universal results, which predict the absence of long timescales unless fine-tuned. We consider an ensemble of transition matrices and motivate a temperature-like variable that controls the dynamic range of matrix elements, which we show plays a crucial role in the applicability of the large matrix limit: as the dynamic range increases, a phase transition occurs whereby the random matrix theory result is avoided, and long relaxation times ensue, in the entire “ordered” phase. We furthermore show that this phase transition is accompanied by a drop in the entropy rate and a peak in complexity, as measured by predictive information [Bialek, Nemenman, and Tishby Neural Comput. 13, 2409 (2001)]. Extending the Markov model to a Hidden Markov model (HMM), we show that observable sequences inherit properties of the hidden sequences, allowing HMMs to be understood in terms of more accessible Markov models. We then apply our findings to fMRI data from 820 human subjects scanned at wakeful rest. We show that the data can be quantitatively understood in terms of the random model, and that brain activity lies close to the phase transition when engaged in unconstrained, task-free cognition—supporting the brain criticality hypothesis in this context.

Boltzmann machines (BMs) are widely used as generative models. For example, pairwise Potts models (PMs), which are instances of the BM class, provide accurate statistical models of families of evolutionarily related protein sequences. Their parameters are the local fields, which describe site-specific patterns of amino acid conservation, and the two-site couplings, which mirror the coevolution between pairs of sites. This coevolution reflects structural and functional constraints acting on protein sequences during evolution. The most conservative choice to describe the coevolution signal is to include all possible two-site couplings into the PM. This choice, typical of what is known as Direct Coupling Analysis, has been successful for predicting residue contacts in the three-dimensional structure, mutational effects, and generating new functional sequences. However, the resulting PM suffers from important overfitting effects: many couplings are small, noisy, and hardly interpretable; the PM is close to a critical point, meaning that it is highly sensitive to small parameter perturbations. In this work, we introduce a general parameter-reduction procedure for BMs, via a controlled iterative decimation of the less statistically significant couplings, identified by an information-based criterion that selects either weak or statistically unsupported couplings. For several protein families, our procedure allows one to remove more than $90\%$ of the PM couplings, while preserving the predictive and generative properties of the original dense PM, and the resulting model is far away from criticality, hence more robust to noise.

Turbulent compressible flows are traditionally simulated using explicit time integrators applied to discretized versions of the Navier-Stokes equations. However, the associated Courant-Friedrichs-Lewy condition severely restricts the maximum time-step size. Exploiting the Lagrangian nature of the Boltzmann equation's material derivative, we now introduce a feasible three-dimensional semi-Lagrangian lattice Boltzmann method (SLLBM), which circumvents this restriction. While many lattice Boltzmann methods for compressible flows were restricted to two dimensions due to the enormous number of discrete velocities in three dimensions, the SLLBM uses only 45 discrete velocities. Based on compressible Taylor-Green vortex simulations we show that the new method accurately captures shocks or shocklets as well as turbulence in 3D without utilizing additional filtering or stabilizing techniques other than the filtering introduced by the interpolation, even when the time-step sizes are up to two orders of magnitude larger compared to simulations in the literature. Our new method therefore enables researchers to study compressible turbulent flows by a fully explicit scheme, whose range of admissible time-step sizes is dictated by physics rather than spatial discretization.

Caveolae are cell membrane invaginations of defined lipid and protein composition that flatten with increasing membrane tension. Super-resolution light microscopy and electron microscopy have revealed that caveolae can take a variety of cuplike shapes. We show here that, for the range in membrane tension relevant for cell membranes, the competition between membrane tension and membrane bending yields caveolae with cuplike shapes similar to those observed experimentally. We find that the caveola shape and its sensitivity to changes in membrane tension can depend strongly on the caveola spontaneous curvature and on the size of caveola domains. Our results suggest that heterogeneity in caveola shape produces a staggered response of caveolae to mechanical perturbations of the cell membrane, which may facilitate regulation of membrane tension over the wide range of scales thought to be relevant for cell membranes.

How different are the results of constant-rate resetting of anomalous-diffusion processes in terms of their ensemble-averaged versus time-averaged mean-squared displacements (MSDs versus TAMSDs) and how does stochastic resetting impact nonergodicity? We examine, both analytically and by simulations, the implications of resetting on the MSD- and TAMSD-based spreading dynamics of particles executing fractional Brownian motion (FBM) with a long-time memory, heterogeneous diffusion processes (HDPs) with a power-law space-dependent diffusivity $D\left(x\right)=D_0{\left|x\right|}^{\gamma }$ and their “combined” process of HDP-FBM. We find, inter alia, that the resetting dynamics of originally ergodic FBM for superdiffusive Hurst exponents develops disparities in scaling and magnitudes of the MSDs and mean TAMSDs indicating weak ergodicity breaking. For subdiffusive HDPs we also quantify the nonequivalence of the MSD and TAMSD and observe a new trimodal form of the probability density function. For reset FBM, HDPs and HDP-FBM we compute analytically and verify by simulations the short-time MSD and TAMSD asymptotes and long-time plateaus reminiscent of those for processes under confinement. We show that certain characteristics of these reset processes are functionally similar despite a different stochastic nature of their nonreset variants. Importantly, we discover nonmonotonicity of the ergodicity-breaking parameter EB as a function of the resetting rate $r$. For all reset processes studied we unveil a pronounced resetting-induced nonergodicity with a maximum of EB at intermediate $r$ and $\mathrm{EB}\sim (1/r)$-decay at large $r$. Alongside the emerging MSD-versus-TAMSD disparity, this $r$-dependence of EB can be an experimentally testable prediction. We conclude by discussing some implications to experimental systems featuring resetting dynamics.

The survival of natural populations may be greatly affected by environmental conditions that vary in space and time. We look at a population residing in two locations (patches) coupled by migration, in which the local conditions fluctuate in time. We report on two findings. First, we find that, unlike rare events in many other systems, here the histories leading to a rare extinction event are not dominated by a single path. We develop the appropriate framework, which turns out to be a hybrid of the standard saddle-point method, and the Donsker-Varadhan formalism which treats rare events of atypical averages over a long time. It provides a detailed description of the statistics of histories leading to the rare event and the mean time to extinction. The framework applies to rare events in a broad class of systems driven by non-Gaussian noise. Second, applying this framework to the population-dynamics model, we find a phase transition in its extinction behavior. Strikingly, a patch which is a sink (where individuals die more than are born) can nonetheless reduce the probability of extinction, even if it lowers the average population's size and growth rate.

We investigate the role of bistability in the synchronization of a network of identical bursting neurons coupled through an generic electrical mean-field scheme. These neurons can exhibit distinct multistable states and, in particular, bistable behavior is observed when their sodium conductance is varied. With this, we consider three different initialization compositions: (i) the whole network is in the same periodic state; (ii) half of the network periodic, half chaotic; (iii) half periodic, and half in a different periodic state. We show that (i) and (ii) reach phase synchronization (PS) for all coupling strengths, while for (iii) small coupling regimes do not induce PS, and instead, there is a coexistence of different frequencies. For stronger coupling, case (iii) synchronizes, but after (i) and (ii). Since PS requires all neurons being in the same state (same frequencies), these different behaviors are governed by transitions between the states. We find that, during these transitions, (ii) and (iii) have transient chimera states and that (iii) has breathing chimeras. By studying the stability of each state, we explain the observed transitions. Therefore, bistability of neurons can play a major role in the synchronization of generic networks, with the simple initialization of the system being capable of drastically changing its asymptotic space.

The intrusion of single passive intruders into granular particles has been studied in detail. However, the intrusion force produced by multiple intruders separated at a distance from one another, and hence the effect of their presence in close proximity to one another, is less explored. Here, we used numerical simulations and laboratory experiments to study the force response of two parallel rods intruding vertically into granular media while varying the gap spacing between them. We also explored the effect of variations in friction, intruder size, and particle size on the force response. The total work ($W$) of the two rods over the depth of intrusion was measured, and the instantaneous velocities of particles over the duration of intrusion were calculated by simulations. We found that the total work done by the intruders changes with distance between them. We observed a peak in $W$ at a gap spacing of $\sim 3$ particle diameters, which was up to 25% greater than $W$ at large separation (>11 particle diameters), beyond which the total work plateaued. This peak was likely due to reduced particle flow between intruders as we found a larger number of strong forces—identified as force chains—in the particle domain at gaps surrounding the peak force. Although higher friction caused greater force generation during intrusion, the gap spacing between the intruders at which the peak total work was generated remained unchanged. Larger intruder sizes resulted in greater total work with the peak in $W$ occurring at slightly larger intruder separations. Taken together, our results show that peak total work done by two parallel intruders remained within a narrow range, remaining robust to most other tested parameters.

Pressurized elastic shells are ubiquitous in nature and technology, from the outer walls of yeast and bacterial cells to artificial pressure vessels. Indentation measurements simultaneously probe the internal pressure and elastic properties of thin shells and serve as a useful tool for strength testing and for inferring internal biological functions of living cells. We study the effects of geometry and pressure-induced stress on the indentation stiffness of ellipsoidal and cylindrical elastic shells using shallow-shell theory. We show that the linear indentation response reduces to a single integral with two dimensionless parameters that encode the asphericity and internal pressure. This integral can be numerically evaluated in all regimes and is used to generate compact analytical expressions for the indentation stiffness in various regimes of technological and biological importance. Our results provide theoretical support for previous scaling and numerical results describing the stiffness of ellipsoids, reveal a new pressure scale that dictates the large-pressure response, and give new insights to the linear indentation response of pressurized cylinders.

Micro- and nanoscale systems driven by rapid changes in control parameters (control protocols) dissipate significant energy. In the fast-protocol limit, we find that protocols that minimize dissipation at fixed duration are universally given by a two-step process, jumping to and from a point that balances jump size with fast relaxation. Jump protocols could be exploited by molecular machines or thermodynamic computing to improve energetic efficiency, and implemented in nonequilibrium free-energy estimation to improve accuracy.

We study the Kuramoto model with attractive sine coupling. We introduce a complex-valued matrix formulation whose argument coincides with the original Kuramoto dynamics. We derive an exact solution for the complex-valued model, which permits analytical insight into individual realizations of the Kuramoto model. The existence of a complex-valued form of the Kuramoto model provides a key demonstration that, in some cases, reformulations of nonlinear dynamics in higher-order number fields may provide tractable analytical approaches.

Conserved surface roughening represents a special case of interface dynamics where the total height of the interface is conserved. Recently, it was suggested [Caballero et al., Phys. Rev. Lett. 121, 020601 (2018)] that the original continuum model known as the Conserved Kardar-Parisi-Zhang (CKPZ) equation is incomplete, as additional nonlinearity is not forbidden by any symmetry in $d>1$. In this work, we perform detailed field-theoretic renormalization group (RG) analysis of a general stochastic model describing conserved surface roughening. Systematic power counting reveals additional marginal interaction at the upper critical dimension, which appears also in the context of molecular beam epitaxy. Depending on the origin of the surface particle's mobility, the resulting model shows two different scaling regimes. If the particles move mainly due to the gravity, the leading dispersion law is $\omega \sim k^2$, and the mean-field approximation describing a flat interface is exact in any spatial dimension. On the other hand, if the particles move mainly due to the surface curvature, the interface becomes rough with the mean-field dispersion law $\omega \sim k^4$, and the corrections to scaling exponents must be taken into account. We show that the latter model consist of two subclasses of models that are decoupled in all orders of perturbation theory. Moreover, our RG analysis of the general model reveals that the universal scaling is described by a rougher interface than the CKPZ universality class. The universal exponents are derived within the one-loop approximation in both fixed $d$ and $\varepsilon$-expansion schemes, and their relation is discussed. We point out all important details behind these two schemes, which are often overlooked in the literature, and their misinterpretation might lead to inconsistent results.

This work considers an extension of the Kuramoto model with run-and-tumble dynamics—a type of self-propelled motion. The difference between the extended and the original model is that in the extended version angular velocity of individual particles is no longer fixed but can change sporadically with a new velocity drawn from a distribution $g\left(\omega \right)$. Because the Kuramoto model undergoes phase transition, it offers a simple case study for investigating phase transition for a system with self-propelled particles.

We present exact solutions for the size of the giant connected component of complex networks composed of cliques following bond percolation. We use our theoretical result to find the location of the percolation threshold of the model, providing analytical solutions where possible. We expect the results derived here to be useful to a wide variety of applications including graph theory, epidemiology, percolation, and lattice gas models, as well as fragmentation theory. We also examine the Erdős-Gallai theorem as a necessary condition on the graphicality of configuration model networks comprising clique subgraphs.

The role of gravity in human motor control is at the same time obvious and difficult to isolate. It can be assessed by performing experiments in variable gravity. We propose that adiabatic invariant theory may be used to reveal nearly conserved quantities in human voluntary rhythmic motion, an individual being seen as a complex time-dependent dynamical system with bounded motion in phase space. We study an explicit realization of our proposal: An experiment in which we asked participants to perform $\infty -$ shaped motion of their right arm during a parabolic flight, either at self-selected pace or at a metronome's given pace. Gravity varied between 0 and $1.8$ $g$ during a parabola. We compute the adiabatic invariants in the participant's frontal plane assuming a separable dynamics. It appears that the adiabatic invariant in vertical direction increases linearly with $g$, in agreement with our model. Differences between the free and metronome-driven conditions show that participants' adaptation to variable gravity is maximal without constraint. Furthermore, motion in the participant's transverse plane induces trajectories that may be linked to higher-derivative dynamics. Our results show that adiabatic invariants are relevant quantities to show the changes in motor strategy in time-dependent environments.

An advection-diffusion-reaction model for autologous chemotaxis of two cells in an interstitial flow is analyzed. Each cell secretes ligands uniformly over its surface; the ligands are absorbed by surface receptors anisotropically due to the flow and interaction between ligand fields around each cell. The absorption is quantified in terms of a vectorial anisotropy parameter, $\mathit{A}$, which is proportional to the first moment of the ligand concentration field about the surface of each cell. We consider the physiologically relevant limit of a weak interstitial flow, where the Péclet number, $\text{Pe}$, which characterizes the relative importance of ligand transport via advection to diffusion, is small. We further assume that the cells are separated at a distance that is large compared to the sum of their radii. These conditions allow us to utilize a reciprocal theorem and the method of reflections to construct an asymptotic approximation for $\mathit{A}$ to first order in $\text{Pe}$ for widely separated cells. We find that interactions between the cells: (i) reduce the flow-aligned ligand anisotropy around each cell and (ii) lead to a component of $\mathit{A}$ that is perpendicular to the flow direction. The interaction is long ranged, decaying with the inverse distance between cells to leading order. We finally discuss how interactions between multiple cells could affect our findings.

Several neurodegenerative diseases impact the olfactory system, and in particular the olfactory bulb, early in disease progression. One mechanism by which damage occurs is via synaptic dysfunction. Here, we implement a computational model of the olfactory bulb and investigate the effect of weakened connection weights on network oscillatory behavior. Olfactory bulb network activity can be modeled by a system of equations that describes a set of coupled nonlinear oscillators. In this modeling framework, we propagate damage to synaptic weights using several strategies, varying from localized to global. Damage propagated in a dispersed or spreading manner leads to greater oscillatory power at moderate levels of damage. This increase arises from a higher average level of mitral cell activity due to a shift in the balance between excitation and inhibition. That this shift leads to greater oscillations depends critically on the nonlinearity of the activation function. Linearized analysis of the network dynamics predicts when this shift leads to loss of oscillatory activity. We thus demonstrate one potential mechanism involved in the increased gamma oscillations seen in some animal models of Alzheimer's disease, and we highlight the potential that pathological olfactory bulb behavior presents as an early biomarker of disease.