Correlations in sensory neural networks have both extrinsic and intrinsic origins. Extrinsic or stimulus correlations arise from shared inputs to the network and, thus, depend strongly on the stimulus ensemble. Intrinsic or noise correlations reflect biophysical mechanisms of interactions between neurons, which are expected to be robust to changes in the stimulus ensemble. Despite the importance of this distinction for understanding how sensory networks encode information collectively, no method exists to reliably separate intrinsic interactions from extrinsic correlations in neural activity data, limiting our ability to build predictive models of the network response. In this paper we introduce a general strategy to infer population models of interacting neurons that collectively encode stimulus information. The key to disentangling intrinsic from extrinsic correlations is to infer the couplings between neurons separately from the encoding model and to combine the two using corrections calculated in a mean-field approximation. We demonstrate the effectiveness of this approach in retinal recordings. The same coupling network is inferred from responses to radically different stimulus ensembles, showing that these couplings indeed reflect stimulus-independent interactions between neurons. The inferred model predicts accurately the collective response of retinal ganglion cell populations as a function of the stimulus.

We investigate the short-, medium-, and long-range structure of soft-disk configurations for a wide range of area fractions and simulation protocols by converting the real-space spectrum of volume fraction fluctuations for windows of width $L$ to the distance $h\left(L\right)$ from the window boundary over which fluctuations occur. Rapidly quenched unjammed configurations exhibit size-dependent super-Poissonian long-range features that surprisingly approach the totally random limit even close to jamming. Above and just below jamming, the spectra exhibit a plateau $h\left(L\right)=h_e$ for $L$ larger than particle size and smaller than a cutoff $L_c$ beyond which there are long-range fluctuations. The value of $h_e$ is independent of protocol and characterizes the putative hyperuniform limit. This behavior is compared with that for Einstein solids, with and without hyperuniformity-destroying defects. We find that key structural features of the particle configurations are more evident, as well as easier and more intuitive to quantify, using the real-space spectrum of hyperuniformity lengths rather than the spectral density.

Using event-driven kinetic Monte Carlo simulations, we investigate the early stage of nonequilibrium surface growth in a generic model with anisotropic interactions among the adsorbed particles. Specifically, we consider a two-dimensional lattice model of spherical particles where the interaction anisotropy is characterized by a control parameter $\eta$ measuring the ratio of interaction energy along the two lattice directions. The simplicity of the model allows us to study systematically the effect and interplay between $\eta$, the nearest-neighbor interaction energy $E_n$, and the flux rate $F$, on the shapes and the fractal dimension $D_f$ of clusters before coalescence. At finite particle flux $F$ we observe the emergence of rodlike and needle-shaped clusters whose aspect ratio $R$ depends on $\eta , E_n$, and $F$. In the regime of strong interaction anisotropy, the cluster aspect ratio shows power-law scaling as function of particle flux, $R\sim F^{-\alpha }$. Furthermore, the evolution of the cluster length and width also exhibit power-law scaling with universal growth exponents for all considered values of $F$. We identify a critical cluster length $L_c$ that marks a transition from one-dimensional to self-similar two-dimensional cluster growth. Moreover, we find that the cluster properties depend markedly on the critical cluster size $i^{*}$ of the isotropically interacting reference system ($\eta =1$).

We investigate the deformation of a longitudinally stretched rectangular sheet which is clamped at two opposite boundaries and free otherwise with experiments, numerical analysis, and asymptotic analysis of the biharmonic elastic equation governing their planar equilibrium configurations. The displacement field of the sheet is measured by tracking embedded fluorescent tracers with a digital image correlation technique. The experiments and numerical finite-element analysis are found to be in overall good agreement except at the very corners where large deformations occur. We find that the deformed sheet can be broadly divided into a uniaxially stretched central region and two clamp-dominated side regions. A subregion characterized by a diverging stress can be identified at each of the four clamped-free corners within the clamp-dominated region. We postulate that the divergence at the corners is regularized by nonlinear elastic deformations occurring in this subregion at the very corners and provide a nontrivial scaling for its size. Within the intermediate corner-dominated subregion, measured displacements grow with distance $r$ from the corners as $r^{\alpha }$, with power $\alpha <1$ consistent with the development of stress singularities at the intersection of the free and clamped edges.

A theoretical model based on the method of super transition arrays (STA) is used to compute the emissivities, opacities, and average ionization states of carbon (C) and polystyrene (CH) plasmas in the warm-dense matter regime in which the coupling constant varies between 0.02 to 2.0. The accuracy of results of STA calculations is assessed by benchmarking against the available experimental data and results obtained using other theoretical methods, assuming that a state of local thermodynamic equilibrium exists in the plasma. In the case of a carbon plasma, the STA method yields spectral features that are in reasonably good agreement with Dirac-Fock and Hartree-Fock-Slater theories; in the case of CH, we find that STA-derived opacities are very similar to those derived using quantum-molecular-dynamics density-functional theory and Hartree-Fock method down to plasma temperature of about 20 eV. Our calculations also compare favorably with available experimental measurements of Gamboa et al. [High Energy Density Phys. 11, 75 (2014)] of the plasma temperature and average ionization state behind a blast wave in a pure carbon foam. Although the STA-computed average-ionization charge state in the rarefaction region appears to be lower than the experimental data, it is within the experimental uncertainty and the discrepancy is nevertheless consistent with results reported using an atomic kinetic model. In addition, we further predict the temperature dependence of average ionization states of CH plasma in the same temperature range as for the carbon plasma.

We developed a general framework for simulating multicomponent and multiphase systems using the lattice Boltzmann framework. Despite the fact that there is no restriction on the number of components in principle, in this article we focus an application to two-component mixtures, but we also demonstrate that the algorithm works for larger numbers of components. To validate our algorithm we separately minimized this underlying free energy to generate theoretical phase diagrams for mixtures of fluids with a van der Waals–like free energy. Our phase diagrams and lattice Boltzmann simulation results are presented in a density-density plane, which best matches with lattice Boltzmann simulations performed at constant volume and temperature. All the theoretical phase diagrams are well recovered by our lattice Boltzmann method.

We consider nonlocally coupled oscillators on the surface of a sphere. We analyze the existence and stability of a variety of symmetry-broken states, including the well-known spot and spiral chimeras as well as a new type of symmetry-breaking, the modulated coherent state. The stabilities of different stationary solutions along the Ott-Antonsen invariant manifold are explored and a complete bifurcation diagram is presented. Our bifurcation analysis reveals that the modulated coherent state bifurcates from a uniformly coherent state and coexists with the spiral chimera. We find that the spiral chimera could appear via an inverse Hopf bifurcation and a transcritical bifurcation. Unlike the spot chimera that coexists with uniform coherence, the spiral chimera could occur exclusively for a large parameter region. It is demonstrated numerically that the modulated coherent and spiral chimera states occur even for a finite-size system.

Properties of solitary waves in precompressed Hertzian chains of particles are studied in the long-wavelength limit using a well-known continuum model. Several main results are obtained by parametrizing the solitary waves in terms of their wave speed and their asymptotic amplitude. First, the asymptotic amplitude is shown to be directly related to the continuum sound speed, and the ratio of asymptotic amplitude to peak amplitude is shown to describe the degree of dynamical nonlinearity in the underlying discrete system. Second, an algebraic relation is derived that determines the dynamical nonlinearity ratio in terms of the ratio of the solitary wave speed to the sound speed. In particular, highly supersonic solitary waves correspond to highly nonlinear propagating pulses in weakly compressed systems, and slightly supersonic solitary waves correspond to weakly nonlinear propagating pulses in strongly compressed systems. Third, explicit formulas for the physical height, width, impulse, and energy of the solitary waves are obtained in both the strongly nonlinear regime and the weakly nonlinear regime. Asymptotic expansions are used to show that in the strongly nonlinear regime, solitary waves are well approximated by Nesterenko's compacton (having the same wave speed), while in the weakly nonlinear regime, solitary waves coincide with solitons of the Korteweg–de Vries equation, with the same wave speed. All of these results are illustrated by means of exact solitary wave solutions, including the physically important case that models a chain of spherical particles.

Ecosystems persist over geological timescales by continuously cycling nutrients. However, we lack a quantitative model of how diverse organisms organize with respect to one another. We observe these dynamics in a quasi-two-dimensional microbial ecosystem, in which all microbes live within the penetration depths of oxygen and light. This community is composed of both photosynthetic bacteria, which produce sugars and oxygen, and aerobic bacteria, which consume oxygen and sugars. Shinning a light on the community drives a nutrient cycle between these two groups of microbes. Illuminating a spot, we measure the resulting distribution of oxygen. Under normal conditions, diffusion alone stabilizes oxygen gradients. However, at freezing temperatures or low atmospheric oxygen concentration, the kinetics of microbial oxygen production and consumption dominate. Surprisingly, after three weeks, the initially uniform distribution of oxygen in the spot becomes an annulus. We present a robust method to invert the measured oxygen concentration for the distribution of oxygen sources and sinks.

We use the method of recurrence relations to investigate the dynamics of the one-dimensional spin-$1/2$ Heisenberg model with Dzyaloshinskii-Moriya (DM) interaction in a magnetic field perpendicular to the DM axis. Our results are valid in the high-temperature limit. We determine exactly the first four recurrants, which produce the time-dependent correlation functions. In order to extend our results to longer times, we introduce a new extrapolation procedure for obtaining higher-order recurrants. Our extrapolation mechanism produces good results when compared to the well-known behavior of the relaxation function in the limit of the $\mathit{XY}$ and isotropic Heisenberg models. The relaxation function and the spectral density function are then analyzed for several values of the external field $B$ for the Heisenberg model with DM interactions in one dimension, in the $T\to \infty$ limit. We find that the external field produces stronger and faster oscillations in relaxation functions and a suppression of the central peak in the spectral density. That is accompanied by the appearance of a peak centered at a finite frequency, due to enhancement of the collective mode of spins precessing about the external field.

By quenched-randomly mixing local units of different spatial dimensionalities, we have studied Ising spin-glass systems on hierarchical lattices continuously in dimensionalities $1\le d\le 3$. The global phase diagram in temperature, antiferromagnetic bond concentration, and spatial dimensionality is calculated. We find that, as dimension is lowered, the spin-glass phase disappears to zero temperature at the lower-critical dimension $d_c=2.431$. Our system being a physically realizable system, this sets an upper limit to the lower-critical dimension in general for the Ising spin-glass phase. As dimension is lowered towards $d_c$, the spin-glass critical temperature continuously goes to zero, but the spin-glass chaos fully subsists to the brink of the disappearance of the spin-glass phase. The Lyapunov exponent, measuring the strength of chaos, is thus largely unaffected by the approach to $d_c$ and shows a discontinuity to zero at $d_c$.

We investigate how the dimensionality of the embedding space affects the microscopic crackling dynamics and the macroscopic response of heterogeneous materials. Using a fiber bundle model with localized load sharing, computer simulations are performed from one to eight dimensions slowly increasing the external load up to failure. Analyzing the constitutive curve, fracture strength, and avalanche statistics of bundles we demonstrate that a gradual crossover emerges from the universality class of localized behavior to the mean field class of fracture as the embedding dimension increases. The evolution between the two universality classes is described by an exponential functional form. Simulations revealed that the average temporal profile of crackling avalanches evolves with the dimensionality of the system from a strongly asymmetric shape to a symmetric parabola characteristic for localized stresses and homogeneous stress fields, respectively.

In the example of a lattice gas with “hole-particle” symmetry, a convincing confirmation is obtained for the direct relationship between the condensation phenomenon and the divergent behavior of the virial expansions for pressure and density in powers of activity. For such lattice-gas models of arbitrary geometry and dimensions, a general analytical expression is derived for the phase-transition activity (the convergence radius of activity expansions) that, in particular, exactly matches the well-known phase-transition activity of the Lee-Yang model. The study proves analytically the strict equality of pressure for the low-density and high-density virial expansions in powers of density (in terms of irreducible cluster integrals or virial coefficients) exactly at the symmetrical points, where their isothermal bulk modulus vanishes, as well as for the corresponding expansions in powers of activity (in terms of reducible cluster integrals) at the same points (the points of their divergence). It is also shown that Mayer's expansion with the constant (volume-independent) cluster integrals remains correct up to the condensation beginning, and the actual density dependence must be taken into account for the high-order integrals only in more dense regimes beyond the saturation point.

We investigate the evolutions of edge Majorana fermions (MFs), and we show that they can be used to characterize different topological phases and study topological phase transitions. For some limiting cases of the evolution process for the Kitaev chain model and the Su-Schrieffer-Heeger (SSH) model, we give analytical expressions of the survival probabilities (SPs) of the edge MFs. For a general case, we consider a dimerized Kitaev model as well as the Kitaev chain with disorder chemical potential, and we numerically calculate the SPs of two edge correlation MFs. Our results show that both of them are equal to zero, one of them is equal to zero at some times, or neither of them is equal to zero, which corresponds to the SSH-like topological, topological superconductor, and trivial phases, respectively.

The killing power of membrane-active antimicrobial peptides (AMPs) lies in their ability to disrupt the structures of pathogenic membranes. While understanding the AMPs’ mechanisms of action is key to realizing their therapeutic potentials, how the AMPs modulate membrane elasticity and thereby affect membrane structure remains an open question, even though the AMP-induced variations in membrane curvature are widely considered to be crucial. Here, we exploit the x-ray diffraction technique to examine how the dominant bacterial lipid, phosphatidylethanolamine, varies its monolayer elastic properties upon interacting with six artificial peptides mimicking the AMPs’ common amino acid content. Remarkably, the monolayer spontaneous curvature $C_0$ is unaffected by any of the peptides. In contrast, the peptides designated as ${\left(\mathrm{K}2\mathrm{W}\right)}^2$, K4W2, R6, and R9, mimicking the AMP mutants with microbicidal potency, are able to modify the monolayer bending moduli $K_{cp}$, while those derived from the impotent mutants cannot. The results are consistent with the scenario that the AMPs disrupt the structure of pathogenic monolayers by, additionally if not exclusively, modulating their $K_{cp}$’s, with stiffening and softening leading to two different modes of disruption, that is, toroidal pore formation and membrane micellation, respectively.

We derive the macroscopic stress tensor for plug-free dense granular flow, using a first-principles coarse-graining of the intergranular forces. The derivation is based on the assumption, which defines the da Vinci fluid model, that the intergranular interactions are dominated by normal contact forces and solid friction. An explicit form for the stress—strain rate relation in the slow flow regime is obtained, providing, together with previously derived equations for the formation and growth dynamics of plug regions, a full closure for the rheology of dense granular fluids, in terms of well-defined material parameters. This relation allows us to quantify the strain rate, at which the flow crosses over from solid-friction-dominated to viscosity-dominated flow.

We perform computational studies of repulsive, frictionless disks to investigate the development of stress anisotropy in mechanically stable (MS) packings at jamming onset. We focus on two protocols for generating MS packings at jamming onset: (1) isotropic compression and (2) applied simple or pure shear strain $\gamma$ at fixed packing fraction $\varphi$. MS packings of frictionless disks occur as geometric families (i.e., quasiparabolic segments with positive curvature) in the $\varphi \text{−}\gamma$ plane. MS packings from protocol 1 populate parabolic segments with both signs of the slope, $d\varphi /d\gamma >0$ and $d\varphi /d\gamma <0$. In contrast, MS packings from protocol 2 populate segments with $d\varphi /d\gamma <0$ only. For both simple and pure shear, we derive a relationship between the stress anisotropy and local dilatancy $d\varphi /d\gamma$ obeyed by MS packings along geometrical families. We show that for MS packings prepared using isotropic compression, the stress anisotropy distribution is Gaussian centered at zero with a standard deviation that decreases with increasing system size. For shear jammed MS packings, the stress anisotropy distribution is a convolution of Weibull distributions that depend on strain, which has a nonzero average and standard deviation in the large-system limit. We also develop a framework to calculate the stress anisotropy distribution for packings generated via protocol 2 in terms of the stress anisotropy distribution for packings generated via protocol 1.

The evolution of the defect microstructure in materials at high temperature is dominated by diffusion-mediated interactions between dislocations, cavities, and surfaces. This gives rise to complex nonlinear couplings between interstitial and vacancy-type dislocation loops, cavities, and the field of diffusing vacancies that adiabatically follows the evolution of microstructure. In our previous work, we developed a nonlocal model for the climb of curved dislocations and the morphological evolution of cavities during postirradiation annealing of structural components in nuclear reactors. We now expand the formalism to include the treatment of population of very small defects and dislocation loops that are below the experimental detection limit. These are taken into account through a mean field approach coupled with an explicit real-space treatment of larger-scale discrete defect clusters. We find that randomly distributed small defects screen diffusive interactions between larger discrete clusters, renormalizing the free diffusion Green's functions and transforming them into Yukawa-type propagators. The evolution of the coupled system is modelled self-consistently, showing how the defect microstructure evolves through a nonmonotonic variation of the distribution of sizes of dislocation loops and cavities, treated as discrete real-space objects.

The dynamics, instability, and pattern formation of thermally triggered thin liquid films are investigated numerically under a long-wave limit approximation. To determine the mechanisms responsible for instability growth and pattern formation in confined heated nanofilms, acoustic phonon (AP) and thermocapillary (TC) models are examined using both linear and nonlinear analyses. Under uniform heating conditions, both AP and TC models predict the formation of raised columnar structures (pillars) and bicontinuous structures for very low and high filling ratios defined as the ratio of the initial film thickness to the plate separation distance, $D^{-1}$. A transition threshold is observed when $D\approx 2.5$. However, the TC model predicts smaller features for larger $D$, whereas the opposite prediction applies for the AP model. Under spatially variable cooling conditions involving a patterned top plate, both TC and AP models exhibit similar predictions: pillars form under the top plate protrusions. When the heating is spatially variable, the lower plate is patterned; the AP model predicts pillar formation above ridges, whereas the TC model predicts pillar formation above the valleys.

The sample mean $\overline{X}$ is probably the most popular estimator of the expected value in all sciences and $\mathrm{var}\left(\overline{X}\right)$ measures the error (standard- and mean-square-errors). Here, an alternative approach to estimation of $\mathrm{var}\left(\overline{X}\right)$ for time series data is presented. The method has an accuracy similar to dependent bootstrapping, but scales in $O\left(n\right)$ time, and applies to stationary time series, including stationary Markov chains. The computational complexity is bounded by $12n$ floating point operations, but this can be reduced to $n+O\left(1\right)$ in large computations. Convergence in relative error squared is faster than $n^{-1/2}$ and the method is insensitive to the probability distribution of the observations. It is proven that a small part of the correlation structure is relevant to the convergence rate of the method. From this, proof of the Blocking method [Flyvbjerg and Petersen, J. Chem. Phys. 91, 461 (1989)] follows as a corollary. The result is also used to propose a hypothesis test surveying the relevant part of the correlation structure. It yields a fully automatic method which is sufficiently robust to operate without supervision. An algorithm and sample code showing the implementation is available for Python, C++, and R [www.github.com/computative/block]. Method validation using autoregressive AR(1) and AR(2) processes and physics applications is included. Method self-evaluation is provided by bias and mean-square-error statistics. The method is easily adapted to multithread applications and data larger than computing cluster memory, such as ultralong time series or data streams. This way, the paper provides a stringent and modern treatment of the Blocking method using rigorous linear algebra, multivariate probability theory, real analysis, and Fisherian statistical inference.