Finding self-similarity is a key step for understanding the governing law behind complex physical phenomena. Traditional methods for identifying self-similarity often rely on specific models, which can introduce significant bias. In this paper, we present a neural network-based approach that discovers self-similarity directly from observed data, without presupposing any models. The presence of self-similar solutions in a physical problem signals that the governing law contains a function whose arguments are given by power-law monomials of physical parameters, which are characterized by power-law exponents. The basic idea is to enforce such particular forms structurally in a neural network in a parametrized way. We train the neural network model using the observed data, and when the training is successful, we can extract the power exponents that characterize scale-transformation symmetries of the physical problem. We demonstrate the effectiveness of our method with both synthetic and experimental data, validating its potential as a robust, model-independent tool for exploring self-similarity in complex systems.

This study deals with polymer looping, an important process in many chemical and biological systems. We investigate basic questions on the looping dynamics of a polymer under tension using the freely jointed chain (FJC) model. Previous theoretical approaches to polymer looping under tension have relied on barrier escape methods, which assume local equilibrium, an assumption that may not always hold. As a starting point, we use an analytical expression for the equilibrium looping probability as a function of the number of monomers and applied force, predicting an inverse relationship between looping time and looping probability. Using molecular dynamics simulations, the predictions of this theoretical approach are validated within the numerical precision achieved. We compare our predictions to those of the barrier escape approach by way of a calculation of the mean first passage time (MFPT) for the ends of a polymer to cross. For this purpose, we derive the exact free energy landscape, but the resulting temporal predictions do not agree with the observed inverse scaling. We conclude that the traditional barrier escape approach does not provide satisfactory predictions for polymer looping dynamics and that the inverse scaling with looping probability offers a more reliable alternative.

We investigate the statistics of the first-passage time (FPT) to a fractal self-similar boundary of the Koch snowflake. When the starting position is fixed near the absorbing boundary, the FPT distribution exhibits an apparent power-law decay over a broad range of timescales, culminated by an exponential cutoff. By extensive Monte Carlo simulations, we compute the local persistence exponent of the survival probability and reveal its log-periodic oscillations in time due to self-similarity of the boundary. The effect of the starting point on this behavior is analyzed in depth. Theoretical bounds on the survival probability are derived from the analysis of diffusion in a circular sector. Physical rationales for the refined structure of the survival probability are presented.

We investigate a large ensemble of quadratic integrate-and-fire neurons with heterogeneous input currents and adaptation variables. Our analysis reveals that, for a specific class of adaptation, termed quadratic spike-frequency adaptation, the high-dimensional system can be exactly reduced to a low-dimensional system of ordinary differential equations, which describes the dynamics of three mean-field variables: the population's firing rate, the mean membrane potential, and a mean adaptation variable. The resulting low-dimensional firing rate equations (FREs) uncover a key generic feature of heterogeneous networks with spike-frequency adaptation: Both the center and width of the distribution of the neurons' firing frequencies are reduced, and this largely promotes the emergence of collective synchronization in the network. Our findings are further supported by the bifurcation analysis of the FREs, which accurately captures the collective dynamics of the spiking neuron network, including phenomena such as collective oscillations, bursting, and macroscopic chaos.

The folding of cellular monolayers pervades embryonic development and disease, and is often caused by cell shape changes such as cell wedging. However, the function and mechanical role of different active cellular changes in different regions of folding tissues remain unclear in many cases, at least partially because the quantification of out-of-plane mechanical stresses in complex three-dimensional tissues has proved challenging. The gastrulationlike inversion process of the green alga Volvox provides a unique opportunity to overcome this difficulty: Combining laser ablation experiments and a mechanical model, we infer the mechanical properties of the curved tissue from its unfurling on ablation. We go on to reproduce the tissue shapes at different developmental timepoints quantitatively using our mechanical model. Strikingly, this reveals out-of-plane stresses associated with additional cell shape changes away from those regions where cell wedging bends the tissue. Moreover, the fits indicate an adaptive response of the tissue to these stresses. In this way, our paper provides not only the experimental and theoretical framework to quantify out-of-plane stresses in tissue folding, but it also shows how additional cell shape changes can provide another source of out-of-plane stresses in development complementing cell wedging.

Autocatalysis, the ability of a chemical system to make more of itself, is a crucial feature in metabolism and is speculated to have played a decisive role in the origin of life. Nevertheless, how autocatalytic systems behave far from equilibrium remains unexplored. In this work, we elaborate on recent advances regarding the stoichiometric characterization of autocatalytic networks, particularly their absence of mass-like conservation laws, to study how this topological feature influences their nonequilibrium behavior. Building upon the peculiar topology of autocatalytic networks, we derive a decomposition of the chemical fluxes, which highlights the existence of productive modes in their dynamics. These modes produce the autocatalysts in net excess and require the presence of external fuel/waste species to operate. Relying solely on topology, the flux decomposition holds under broad conditions and, in particular, does not require steady state or elementary reactions. Additionally, we show that once externally controlled, the nonconservative forces brought by the external species do not act on these productive modes. This must be considered when one is interested in the thermodynamics of open autocatalytic networks. Specifically, we show that an additional term must be added to the semigrand free energy. Finally, from the thermodynamic potential, we derive the thermodynamic cost associated with the production of autocatalysts.

Our goal is to develop a design framework for multifunctional mechanical metamaterials that can tune their rigidity while optimizing other desired properties. Towards this goal, we first demonstrate that underconstrained central-force networks possess a critical rigidity manifold of codimension 1 in the space of their physical constraints. We describe how the geometry of this manifold generates a natural parametrization in terms of the states of self-stress, and then use this parametrization to numerically generate disordered network structures that are on the critical rigidity manifold and also optimize various objective functions, such as maximizing the bulk stiffness under dilation, or minimizing length variance to find networks that can be self-assembled from equal-length parts. This framework can be used to design mechanical metamaterials that can tune their rigidity and also exhibit other desired properties.

The cold shock domain (CSD) protein acts as a nucleic acid-binding protein and exhibits a strong affinity for the Y-box core motif ATTGG segment on gene promoter regions, playing a significant role in gene regulation. Given the moderate folding and unfolding rates of the cold shock protein from Bacillus caldolyticus (BcCsp) observed in previous magnetic tweezers studies, it is a suitable choice for investigating the interaction between CSD protein and single-stranded DNA containing ATTGG. While earlier studies utilizing single molecule force spectroscopy delved into the mechanical characteristics of BcCsp, the impact of ssDNA on its folding and unfolding dynamic behaviors has yet to be investigated. Here, utilizing stable magnetic tweezers, we compared the force-dependent folding and unfolding rates of BcCsp in the presence of different concentrations of TGATTGG ssDNA. We found that folding rate of BcCsp keeps the same, while unfolding rate decreases as the concentration of TGATTGG increases. Detailed unfolding free energy landscape analysis revealed that ssDNA not only binds to the native state of BcCsp, but also binds to the partially unfolded conformation to change the unfolding barrier. Our study demonstrates the coupling between protein folding or unfolding and ligand association/dissociation dynamics.

Gradient-based meta-learning algorithms have gained popularity for their ability to train models on new tasks using limited data. Empirical observations indicate that such algorithms are able to learn a shared representation across tasks, which is regarded as a key factor in their success. However, the in-depth theoretical understanding of the learning dynamics and the origin of the shared representation remains underdeveloped. In this work, we investigate the meta-learning dynamics of nonlinear two-layer neural networks trained on streaming tasks in the teacher-student scenario. Through the lens of statistical physics analysis, we characterize the macroscopic behavior of the meta-training processes, the formation of the shared representation, and the generalization ability of the model on new tasks. The analysis also points to the importance of the choice of certain hyperparameters of the learning algorithms.

We report on record brightness from Ag x-ray emission obtained using a novel laser-produced plasma source. The reported K-shell conversion efficiency of nearly 1% with a radiant energy of $\approx 0.6$ kJ/sr from Ag ions is the highest presently recorded and is about twofold greater than more conventional metal-lined cavity targets. He-like Ag ions are the dominant radiators at $\approx 22.7$ keV, which contrast the x-ray sources from other pulse power facilities that produce K-shell x-rays from Auger processes in near-neutral ions driven by the nonthermal hot electrons produced in the Z-pinch implosion. The reported x-ray emission was produced from a 4-mm-diameter, 4-mm-long underdense silver nanowire target at $10\mathrm{mg}/{\mathrm{cm}}^3$. The National Ignition Facility laser beams deposited $\approx 1000$ kJ of $3\omega$ light into the target with a $\approx 400$ TW, 2.5 ns square pulse. Finally, we show via comparisons of data with radiation-hydrodynamics simulations that flux-limited classical thermal energy transport models are inadequate in correctly modeling the behavior of these non-local thermodynamic equilibrium plasmas.

Chromosome organization can be modeled using various approaches, ranging from mechanistic bottom-up models to models inferred directly from experimental data. Many such models can recapitulate experimental Hi-C data for pairwise contact probabilities, meaning that these data cannot always be used to distinguish different models. Here, we consider two illustrative example models for bacterial chromosome organization: one a bottom-up model for loop extrusion, the other a data-driven maximum entropy model inferred from Hi-C data. We find that despite predicting similar pairwise contact frequencies, the models predict qualitatively different features on three-point contact maps. We explain these differences by constructing analytical approximations for three-point contact probabilities in each model. Finally, we apply our analytical approximations to previously published experimental multicontact data from human chromosomes, and find that these data are well described by the loop extruder approximation. Our work illustrates how multicontact statistics can be used to compare and test models for chromosome organization.

We investigate the location of the critical and tricritical points of the three-dimensional Blume-Capel model by analyzing the behavior of the first Lee-Yang zero, the density of partition function zeros, and higher-order cumulants of the magnetization. Our analysis is conducted through Monte-Carlo simulations, intentionally using only small system sizes. We demonstrate that this approach yields excellent results for studying the critical behavior of the model. Our findings indicate that, at the tricritical point, where logarithmic corrections are anticipated, the numerical results align closely with the theoretical exponents describing these corrections. These expected values are then employed to accurately determine the coordinates of the tricritical point. At the model's critical point, the corrections correspond to those of the three-dimensional Ising model criticality, which we also use to precisely ascertain the critical temperature at zero crystal field. Additionally, we utilize more traditional thermodynamic quantities to validate the self-consistency of our analysis.

We present a model of active Brownian particles for the process of jellyfish swarm formation. The motivation for our analysis is the phenomenon of jellyfish blooming in natural habitats and clustering of jellyfish in laboratory tanks which follow from an interplay of physical and behavioral mechanisms. We reach the conclusion that phase separation at low jellyfish density is induced by behavioral reactions to environmental conditions. Dense regions are then maintained by self-induced stimuli which result in a recruitment process. Our results agree with the biological fact that jellyfish exhibit an extreme sensitivity to stimuli in order to achieve favorable aggregations. Based on our model, we are able to provide a clear terminology for future experimental analysis of jellyfish swarming and we pinpoint potential limitations of tank experiments.

We postulate that waiting times between avalanches in self-organized critical systems are distributed according to a universal double power-law probability density. This density is defined by two critical exponents $\alpha$ and $\beta$ characterizing the distribution of short ($\sim {\delta }^{-\alpha }$) and long ($\sim {\delta }^{-\beta }$) waiting times, and a crossover parameter ${\delta }_0$ that separates the two behaviors in a sharp shoulder. This crossover parameter depends on the system properties as well as on the observation conditions. It can be used as a scaling factor that transforms the distributions into a universal scaling law as proposed by Per Bak. We use experimental data from labquake catalogs (acoustic emission events) obtained during the uniaxial compression of a number of charcoal samples with different hardnesses and different energy thresholds. To obtain good fits it is essential that the catalogs are long enough to include a representative critical mixture of periods with different avalanche rates. In all the cases studied, individual maximum likelihood analysis allows the exponents $\alpha$ and $\beta$ and the crossover parameter ${\delta }_0$ to be fitted. This parameter shows a clear dependence with the energy threshold that can be explained from the Gutenberg-Richter law for the avalanche energy distributions. The observed variations of the exponents $\alpha$ and $\beta$ fall within the sample-to-sample variability, which suggest that these values could be universal. We estimate mean values $\alpha =0.9\pm 0.1$ and $\beta =2.0\pm 0.3$ from the full set of recorded experimental data. These values are close to the combination $\alpha =1, \beta =2$, which exhibits a special mathematical cancellation of singularities.

Plasma is capable of mediating the conversion of two pump photons into two different photons through a relativistic four-wave mixing nonlinearity. Spontaneously created photon pairs are emitted at symmetric angles with respect to the colinear pump direction, and the emission rate is largest if they have identical frequency. Thus, two orthogonally polarized pumps can produce polarization-entangled photon pairs through a millimeter-long homogeneous plasma. The noise from Raman scattering can be avoided if the pump detuning differs from twice the plasma frequency. However, pump detuning exactly equal to twice the plasma frequency can significantly enhance the interaction rate, which allows for the production of strong two-mode squeezed states. Remarkably, the amplified noise from Raman scattering are correlated and hence can be suppressed in one of the output quadratures, thereby maintaining the squeezing magnitude.

A persistent public health challenge is identifying immunization schemes that are effective against highly mutable pathogens such as HIV and influenza viruses. To address this, we analyze a simplified model of affinity maturation, the Darwinian evolutionary process B cells undergo during immunization. The vaccination protocol determines the selection forces that steer affinity maturation to generate antibodies. We focus on identifying the optimal selection forces exerted by a generic time-dependent vaccination protocol to maximize the production of broadly neutralizing antibodies (bnAbs) that can protect against a broad spectrum of pathogen strains. The model utilizes a path integral representation and operator approximations within a mean-field limit and provides guiding principles for optimizing time-dependent vaccine-induced selection forces to enhance bnAb generation. We compare our analytical mean-field results with the outcomes of stochastic simulations, and we discuss their similarities and differences.

In this work, we propose a comprehensive theoretical framework combining percolation theory with nonlinear dynamics to study hypergraphs with a time-varying giant component. We consider in particular hypergraphs with higher-order triadic interactions. Higher-order triadic interactions occur when one or more nodes up-regulate or down-regulate a hyperedge. For instance, enzymes regulate chemical reactions involving multiple reactants. Here we propose and investigate higher-order triadic percolation on hypergraphs showing that the giant component can have a nontrivial dynamics. Specifically, we show that the fraction of nodes in the giant component undergoes a route to chaos in the universality class of the logistic map. In hierarchical higher-order triadic percolation, we extend this paradigm in order to treat hierarchically nested higher-order triadic interactions. We demonstrate the nontrivial effects of their increased combinatorial complexity on the critical phenomena and the dynamical properties of the process. Finally, we consider other generalizations of the model studying the effect of adopting interdependencies and node regulation instead of hyperedge regulation. The comprehensive theoretical framework presented here sheds light on possible scenarios for climate networks, biological networks, and brain networks, where the hypergraph connectivity changes over time.

A continuous-time projection quantum Monte Carlo algorithm is employed to simulate the ground state of a short-range quantum spin-glass model, namely, the two-dimensional Edwards-Anderson Hamiltonian with transverse field, featuring Gaussian nearest-neighbor couplings. We numerically demonstrate that guiding wave functions based on self-learned neural networks suppress the population control bias below modest statistical uncertainties, at least up to a hundred spins. By projecting a two-fold replicated Hamiltonian, the spin overlap is determined. A finite-size scaling analysis is performed to estimate the critical transverse field where the spin-glass transition occurs, as well as the critical exponents of the correlation length and the spin-glass susceptibility. For the latter two, good agreement is found with recent estimates from the literature for different random couplings. We also address the spin-overlap distribution within the spin-glass phase, finding that, for the workable system sizes, it displays a nontrivial double-peak shape with large weight at zero overlap.

We study the full distribution $P\left(E\right)$ of the ground-state energy of a single quantum particle in a potential $V\left(\mathit{x}\right)=V_0\left(\mathit{x}\right)+\sqrt{\epsilon }{v}_1\left(\mathit{x}\right)$, where $V_0\left(\mathit{x}\right)$ is a deterministic “background” trapping potential and $v_1\left(\mathit{x}\right)$ is the disorder. We consider arbitrary trapping potentials $V_0\left(\mathit{x}\right)$ and white-noise disorder $v_1\left(\mathit{x}\right)$, in arbitrary spatial dimension $d$. In the weak-disorder limit $\epsilon \to 0$, we find that $P\left(E\right)$ scales as $P\left(E\right)\sim e^{-s\left(E\right)/\epsilon }$. The large-deviation function $s\left(E\right)$ is obtained by calculating the most likely configuration of $V\left(\mathit{x}\right)$ conditioned on a given ground-state energy $E$. For infinite systems, we obtain $s\left(E\right)$ analytically in the limits $E\to \pm \infty$ and $E\simeq E_0$ where $E_0$ is the ground-state energy in the absence of disorder. We perform explicit calculations for the case of a harmonic trap $V_0\left(\mathit{x}\right)\propto x^2$ in dimensions $d\in \{1,2,3\}$. Next, we calculate $s\left(E\right)$ exactly for a finite, periodic one-dimensional system with a homogeneous background $V_0\left(x\right)=0$. We find that, remarkably, the system exhibits a sudden change of behavior as $E$ crosses a critical value $E_c<0$: At $E>E_c$, the most likely configuration of $V\left(x\right)$ is homogeneous, whereas at $E<E_c$ it is inhomogeneous, thus spontaneously breaking the translational symmetry of the problem. As a result, $s\left(E\right)$ is nonanalytic: Its second derivative jumps at $E=E_c$. We interpret this singularity as a second-order dynamical phase transition.

Backward stimulated Raman scattering is a three-wave coupling instability requiring the matching of an incoming pump light wave to a scattered light wave and an electron plasma wave. It can be harmful to laser-driven inertial confinement fusion because of the reflection of a part of the incident laser flux and the generation of suprathermal electrons that preheat the fuel. It is believed that by increasing the laser bandwidth, one can suppress the excitation of Raman scattering and mitigate its detrimental effects. It is demonstrated in this paper that using a broad bandwidth laser has little effect on stimulated Raman scattering in the kinetic inflation regime where Landau damping dominates, as the additional bandwidth allows the electron plasma wave to match a wider range of laser frequencies. As a result, plasma wave saturation and Raman backscattering levels remain high even when the laser bandwidth is much larger than the effective instability growth rate.