Quantum information scrambling and chemical reactions.

The ultimate regularity of quantum mechanics creates a tension with the assumption of classical chaos used in many of our pictures of chemical reaction dynamics. Out-of-time-order correlators (OTOCs) provide a quantum analog to the Lyapunov exponents that characterize classical chaotic motion. Maldacena, Shenker, and Stanford have suggested a fundamental quantum bound for the rate of information scrambling, which resembles a limit suggested by Herzfeld for chemical reaction rates. Here, we use OTOCs to study model reactions based on a double-well reaction coordinate coupled to anharmonic oscillators or to a continuum oscillator bath. Upon cooling, as one enters the tunneling regime where the reaction rate does not strongly depend on temperature, the quantum Lyapunov exponent can approach the scrambling bound and the effective reaction rate obtained from a population correlation function can approach the Herzfeld limit on reaction rates: Tunneling increases scrambling by expanding the state space available to the system. The coupling of a dissipative continuum bath to the reaction coordinate reduces the scrambling rate obtained from the early-time OTOC, thus making the scrambling bound harder to reach, in the same way that friction is known to lower the temperature at which thermally activated barrier crossing goes over to the low-temperature activationless tunneling regime. Thus, chemical reactions entering the tunneling regime can be information scramblers as powerful as the black holes to which the quantum Lyapunov exponent bound has usually been applied.

Chaotic turnover of rare and abundant species in a strongly interacting model community.

The composition of ecological communities varies not only between different locations but also in time. Understanding the fundamental processes that drive species toward rarity or abundance is crucial to assessing ecosystem resilience and adaptation to changing environmental conditions. In plankton communities in particular, large temporal fluctuations in species abundances have been associated with chaotic dynamics. On the other hand, microbial diversity is overwhelmingly sustained by a "rare biosphere" of species with very low abundances. We consider here the possibility that interactions within a species-rich community can relate both phenomena. We use a Lotka-Volterra model with weak immigration and strong, disordered, and mostly competitive interactions between hundreds of species to bridge single-species temporal fluctuations and abundance distribution patterns. We highlight a generic chaotic regime where a few species at a time achieve dominance but are continuously overturned by the invasion of formerly rare species. We derive a focal-species model that captures the intermittent boom-and-bust dynamics that every species undergoes. Although species cannot be treated as effectively uncorrelated in their abundances, the community's effect on a focal species can nonetheless be described by a time-correlated noise characterized by a few effective parameters that can be estimated from time series. The model predicts a nonunitary exponent of the power-law abundance decay, which varies weakly with ecological parameters, consistent with observation in marine protist communities. The chaotic turnover regime is thus poised to capture relevant ecological features of species-rich microbial communities.

Chaotic neural dynamics facilitate probabilistic computations through sampling.

Cortical neurons exhibit highly variable responses over trials and time. Theoretical works posit that this variability arises potentially from chaotic network dynamics of recurrently connected neurons. Here, we demonstrate that chaotic neural dynamics, formed through synaptic learning, allow networks to perform sensory cue integration in a sampling-based implementation. We show that the emergent chaotic dynamics provide neural substrates for generating samples not only of a static variable but also of a dynamical trajectory, where generic recurrent networks acquire these abilities with a biologically plausible learning rule through trial and error. Furthermore, the networks generalize their experience in the stimulus-evoked samples to the inference without partial or all sensory information, which suggests a computational role of spontaneous activity as a representation of the priors as well as a tractable biological computation for marginal distributions. These findings suggest that chaotic neural dynamics may serve for the brain function as a Bayesian generative model.

CAPE: a deep learning framework with Chaos-Attention net for Promoter Evolution.

Predicting the strength of promoters and guiding their directed evolution is a crucial task in synthetic biology. This approach significantly reduces the experimental costs in conventional promoter engineering. Previous studies employing machine learning or deep learning methods have shown some success in this task, but their outcomes were not satisfactory enough, primarily due to the neglect of evolutionary information. In this paper, we introduce the Chaos-Attention net for Promoter Evolution (CAPE) to address the limitations of existing methods. We comprehensively extract evolutionary information within promoters using merged chaos game representation and process the overall information with modified DenseNet and Transformer structures. Our model achieves state-of-the-art results on two kinds of distinct tasks related to prokaryotic promoter strength prediction. The incorporation of evolutionary information enhances the model's accuracy, with transfer learning further extending its adaptability. Furthermore, experimental results confirm CAPE's efficacy in simulating in silico directed evolution of promoters, marking a significant advancement in predictive modeling for prokaryotic promoter strength. Our paper also presents a user-friendly website for the practical implementation of in silico directed evolution on promoters. The source code implemented in this study and the instructions on accessing the website can be found in our GitHub repository https://github.com/BobYHY/CAPE.

Unveiling order from chaos by approximate 2-localization of random matrices.

Quantum many-body systems are typically endowed with a tensor product structure. A structure they inherited from probability theory, where the probability of two independent events is the product of the probabilities. The tensor product structure of a Hamiltonian thus gives a natural decomposition of the system into independent smaller subsystems. It is interesting to understand whether a given Hamiltonian is compatible with some particular tensor product structure. In particular, we ask, is there a basis in which an arbitrary Hamiltonian has a 2-local form, i.e., it contains only pairwise interactions? Here we show, using analytical and numerical calculations, that a generic Hamiltonian (e.g., a large random matrix) can be approximately written as a linear combination of two-body interaction terms with high precision; that is, the Hamiltonian is 2-local in a carefully chosen basis. Moreover, we show that these Hamiltonians are not fine-tuned, meaning that the spectrum is robust against perturbations of the coupling constants. Finally, by analyzing the adjacency structure of the couplings [Formula: see text], we suggest a possible mechanism for the emergence of geometric locality from quantum chaos.

Analytical study of the Lorenz system: Existence of infinitely many periodic orbits and their topological characterization.

We consider the Lorenz equations, a system of three-dimensional ordinary differential equations modeling atmospheric convection. These equations are chaotic and hard to study even numerically, and so a simpler "geometric model" has been introduced in the seventies. One of the classical problems in dynamical systems is to relate the original equations to the geometric model. This has been achieved numerically by Tucker for the classical parameter values and remains open for general values. In this paper, we establish analytically a relation to the geometric model for a different set of parameter values that we prove must exist. This is facilitated by finding a way to apply topological tools developed for the study of surface dynamics to the more intricate case of three-dimensional flows.

Emergent programmable behavior and chaos in dynamically driven active filaments.

How the behavior of cells emerges from their constituent subcellular biochemical and physical parts is an outstanding challenge at the intersection of biology and physics. A remarkable example of single-cell behavior occurs in the ciliate Lacrymaria olor, which hunts for its prey via rapid movements and protrusions of a slender neck, many times the size of the original cell body. The dynamics of this cell neck is powered by a coat of cilia across its length and tip. How a cell can program this active filamentous structure to produce desirable behaviors like search and homing to a target remains unknown. Here, we present an active filament model that allows us to uncover how a "program" (time sequence of active forcing) leads to "behavior" (filament shape dynamics). Our model captures two key features of this system-time-varying activity patterns (extension and compression cycles) and active stresses that are uniquely aligned with the filament geometry-a "follower force" constraint. We show that active filaments under deterministic, time-varying follower forces display rich behaviors including periodic and aperiodic dynamics over long times. We further show that aperiodicity occurs due to a transition to chaos in regions of a biologically accessible parameter space. We also identify a simple nonlinear iterated map of filament shape that approximately predicts long-term behavior suggesting simple, artificial "programs" for filament functions such as homing and searching space. Last, we directly measure the statistical properties of biological programs in L. olor, enabling comparisons between model predictions and experiments.

Instantons and the quantum bound to chaos.

The rate at which information scrambles in a quantum system can be quantified using out-of-time-ordered correlators. A remarkable prediction is that the associated Lyapunov exponent [Formula: see text] that quantifies the scrambling rate in chaotic systems obeys a universal bound [Formula: see text]. Previous numerical and analytical studies have indicated that this bound has a quantum-statistical origin. Here, we use path-integral techniques to show that a minimal theory to reproduce this bound involves adding contributions from quantum thermal fluctuations (describing quantum tunneling and zero-point energy) to classical dynamics. By propagating a model quantum-Boltzmann-conserving classical dynamics for a system with a barrier, we show that the bound is controlled by the stability of thermal fluctuations around the barrier instanton (a delocalized structure which dominates the tunneling statistics). This stability requirement appears to be general, implying that there is a close relation between the formation of instantons, or related delocalized structures, and the imposition of the quantum-chaos bound.

Two-dimensional constrained chaos and industrial revolution cycles.

Since the 1760s, at least three industrial revolutions have occurred. To explain this phenomenon, we introduce two-dimensional (2D) constrained chaos. Using a model of innovation dynamics, we show that an industrial-revolution-like technology burst, driven by investment/saving motives for R&D activities, recurs about every one hundred years if the monopolistic use of a new technology lasts about 8 y.

Predicting chromosomal compartments directly from the nucleotide sequence with DNA-DDA.

Three-dimensional (3D) genome architecture is characterized by multi-scale patterns and plays an essential role in gene regulation. Chromatin conformation capturing experiments have revealed many properties underlying 3D genome architecture, such as the compartmentalization of chromatin based on transcriptional states. However, they are complex, costly and time consuming, and therefore only a limited number of cell types have been examined using these techniques. Increasing effort is being directed towards deriving computational methods that can predict chromatin conformation and associated structures. Here we present DNA-delay differential analysis (DDA), a purely sequence-based method based on chaos theory to predict genome-wide A and B compartments. We show that DNA-DDA models derived from a 20 Mb sequence are sufficient to predict genome wide compartmentalization at the scale of 100 kb in four different cell types. Although this is a proof-of-concept study, our method shows promise in elucidating the mechanisms responsible for genome folding as well as modeling the impact of genetic variation on 3D genome architecture and the processes regulated thereby.

Light chaotic dynamics in the transformation from curved to flat surfaces.

Light propagation on a two-dimensional curved surface embedded in a three-dimensional space has attracted increasing attention as an analog model of four-dimensional curved spacetime in the laboratory. Despite recent developments in modern cosmology on the dynamics and evolution of the universe, investigation of nonlinear dynamics of light on non-Euclidean geometry is still scarce, with fundamental questions, such as the effect of curvature on deterministic chaos, challenging to address. Here, we study classical and wave chaotic dynamics on a family of surfaces of revolution by considering its equivalent conformally transformed flat billiard, with nonuniform distribution of the refractive index. We prove rigorously that these two systems share the same dynamics. By exploring the Poincaré surface of section, the Lyapunov exponent, and the statistics of eigenmodes and eigenfrequency spectrum in the transformed inhomogeneous table billiard, we find that the degree of chaos is fully controlled by a single, curvature-related geometric parameter of the curved surface. A simple interpretation of our findings in transformed billiards, the "fictitious force," allows us to extend our prediction to other classes of curved surfaces. This powerful analogy between two a priori unrelated systems not only brings forward an approach to control the degree of chaos, but also provides potentialities for further studies and applications in various fields, such as billiards design, optical fibers, or laser microcavities.

Intrinsic nonlinear dynamics drive single-species systems.

The importance of oscillations and deterministic chaos in natural biological systems has been discussed for several decades and was originally based on discrete-time population growth models (May 1974). Recently, all types of nonlinear dynamics were shown for experimental communities where several species interact. Yet, there are no data exhibiting the whole range of nonlinear dynamics for single-species systems without trophic interactions. Up until now, ecological experiments and models ignored the intracellular dimension, which includes multiple nonlinear processes even within one cell type. Here, we show that dynamics of single-species systems of protists in continuous experimental chemostat systems and corresponding continuous-time models reveal typical characteristics of nonlinear dynamics and even deterministic chaos, a very rare discovery. An automatic cell registration enabled a continuous and undisturbed analysis of dynamic behavior with a high temporal resolution. Our simple and general model considering the cell cycle exhibits a remarkable spectrum of dynamic behavior. Chaos-like dynamics were shown in continuous single-species populations in experimental and modeling data on the level of a single type of cells without any external forcing. This study demonstrates how complex processes occurring in single cells influence dynamics on the population level. Nonlinearity should be considered as an important phenomenon in cell biology and single-species dynamics and also, for the maintenance of high biodiversity in nature, a prerequisite for nature conservation.

Terminating spiral waves with a single designed stimulus: Teleportation as the mechanism for defibrillation.

We identify and demonstrate a universal mechanism for terminating spiral waves in excitable media using an established topological framework. This mechanism dictates whether high- or low-energy defibrillation shocks succeed or fail. Furthermore, this mechanism allows for the design of a single minimal stimulus capable of defibrillating, at any time, turbulent states driven by multiple spiral waves. We demonstrate this method in a variety of computational models of cardiac tissue ranging from simple to detailed human models. The theory described here shows how this mechanism underlies all successful defibrillation and can be used to further develop existing and future low-energy defibrillation strategies.

Adolescents' Perceptions of Household Chaos Predict Their Adult Mental Health: A Twin-Difference Longitudinal Cohort Study.

This study tested whether adolescents who perceived less household chaos in their family's home than their same-aged, same-sex sibling achieved more favorable developmental outcomes in young adulthood, independent of parent-reported household chaos and family-level confounding. Data came from 4,732 families from the Twins Early Development Study, a longitudinal, U.K.-population representative cohort study of families with twins born in 1994 through 1996 in England and Wales. Adolescents who reported experiencing greater household chaos than their sibling at the age of 16 years suffered significantly poorer mental-health outcomes at the age of 23 years, independent of family-level confounding. Mental-health predictions from perceived household chaos at earlier ages were not significant, and neither were predictions for other developmental outcomes in young adulthood, including socioeconomic status indicators, sexual risk taking, cannabis use, and conflict with the law. The findings suggest that altering children's subjective perceptions of their rearing environments may help improve their adult mental health.

Mean-field interacting multi-type birth-death processes with a view to applications in phylodynamics.

Multi-type birth-death processes underlie approaches for inferring evolutionary dynamics from phylogenetic trees across biological scales, ranging from deep-time species macroevolution to rapid viral evolution and somatic cellular proliferation. A limitation of current phylogenetic birth-death models is that they require restrictive linearity assumptions that yield tractable message-passing likelihoods, but that also preclude interactions between individuals. Many fundamental evolutionary processes - such as environmental carrying capacity or frequency-dependent selection - entail interactions, and may strongly influence the dynamics in some systems. Here, we introduce a multi-type birth-death process in mean-field interaction with an ensemble of replicas of the focal process. We prove that, under quite general conditions, the ensemble's stochastically evolving interaction field converges to a deterministic trajectory in the limit of an infinite ensemble. In this limit, the replicas effectively decouple, and self-consistent interactions appear as nonlinearities in the infinitesimal generator of the focal process. We investigate a special case that is rich enough to model both carrying capacity and frequency-dependent selection while yielding tractable message-passing likelihoods in the context of a phylogenetic birth-death model.

Uncertainty quantification for the random HIV dynamical model driven by drug adherence.

In HIV drug therapy, the high variability of CD4+ T cells and viral loads brings uncertainty to the determination of treatment options and the ultimate treatment efficacy, which may be the result of poor drug adherence. We develop a dynamical HIV model coupled with pharmacokinetics, driven by drug adherence as a random variable, and systematically study the uncertainty quantification, aiming to construct the relationship between drug adherence and therapeutic effect. Using adaptive generalized polynomial chaos, stochastic solutions are approximated as polynomials of input random parameters. Numerical simulations show that results obtained by this method are in good agreement, compared with results obtained through Monte Carlo sampling, which helps to verify the accuracy of approximation. Based on these expansions, we calculate the time-dependent probability density functions of this system theoretically and numerically. To verify the applicability of this model, we fit clinical data of four HIV patients, and the goodness of fit results demonstrate that the proposed random model depicts the dynamics of HIV well. Sensitivity analyses based on the Sobol index indicate that the randomness of drug effect has the greatest impact on both CD4+ T cells and viral loads, compared to random initial values, which further highlights the significance of drug adherence. The proposed models and qualitative analysis results, along with monitoring CD4+ T cells counts and viral loads, evaluate the influence of drug adherence on HIV treatment, which helps to better interpret clinical data with fluctuations and makes several contributions to the design of individual-based optimal antiretroviral strategies.

Processionary Caterpillars at the Edge of Complexity.

This article deals with individuals moving in procession in real and artificial societies. A procession is a minimal form of society in which individual behavior is to go in a given direction and the organization is structured by the knowledge of the one ahead. This simple form of grouping is common in the living world, and, among humans, procession is a very circumscribed social activity whose origins are certainly very remote. This type of organization falls under microsociology, where the focus is on the study of direct interactions between individuals within small groups. In this article, we focus on the particular case of pine tree processionary caterpillars (Thaumetopoea pityocampa). In the first part, we propose a formal definition of the concept of procession and compare field experiments conducted by entomologists with agent-based simulations to study real caterpillars' processionaries as they are. In the second part, we explore the life of caterpillars as they could be. First, by extending the model beyond reality, we can explain why real processionary caterpillars behave as they do. Then we report on field experiments on the behavior of real caterpillars artificially forced to follow a circular procession; these experiments confirm that each caterpillar can either be the leader of the procession or follow the one in front of it. In the third part, by allowing variations in the speed of movement on an artificial circular procession, computational simulations allow us to observe the emergence of unexpected mobile spatial structures built from regular polygonal shapes where chaotic movements and well-ordered forms are intimately linked. This confirms once again that simple rules can have complex consequences.

Mixed uncertainty analysis on pumping by peristaltic hearts using Dempster-Shafer theory.

In this paper, we introduce the numerical strategy for mixed uncertainty propagation based on probability and Dempster-Shafer theories, and apply it to the computational model of peristalsis in a heart-pumping system. Specifically, the stochastic uncertainty in the system is represented with random variables while epistemic uncertainty is represented using non-probabilistic uncertain variables with belief functions. The mixed uncertainty is propagated through the system, resulting in the uncertainty in the chosen quantities of interest (QoI, such as flow volume, cost of transport and work). With the introduced numerical method, the uncertainty in the statistics of QoIs will be represented using belief functions. With three representative probability distributions consistent with the belief structure, global sensitivity analysis has also been implemented to identify important uncertain factors and the results have been compared between different peristalsis models. To reduce the computational cost, physics constrained generalized polynomial chaos method is adopted to construct cheaper surrogates as approximations for the full simulation.

Propagation of waves in high Brillouin zones: Chaotic branched flow and stable superwires.

We report unexpected classical and quantum dynamics of a wave propagating in a periodic potential in high Brillouin zones. Branched flow appears at wavelengths shorter than the typical length scale of the ordered periodic structure and for energies above the potential barrier. The strongest branches remain stable indefinitely and may create linear dynamical channels, wherein waves are not confined directly by potential walls as electrons in ordinary wires but rather, indirectly and more subtly by dynamical stability. We term these superwires since they are associated with a superlattice.

A Bayesian neural network predicts the dissolution of compact planetary systems.

We introduce a Bayesian neural network model that can accurately predict not only if, but also when a compact planetary system with three or more planets will go unstable. Our model, trained directly from short N-body time series of raw orbital elements, is more than two orders of magnitude more accurate at predicting instability times than analytical estimators, while also reducing the bias of existing machine learning algorithms by nearly a factor of three. Despite being trained on compact resonant and near-resonant three-planet configurations, the model demonstrates robust generalization to both nonresonant and higher multiplicity configurations, in the latter case outperforming models fit to that specific set of integrations. The model computes instability estimates up to [Formula: see text] times faster than a numerical integrator, and unlike previous efforts provides confidence intervals on its predictions. Our inference model is publicly available in the SPOCK (https://github.com/dtamayo/spock) package, with training code open sourced (https://github.com/MilesCranmer/bnn_chaos_model).