We study a two-species Vicsek model with intraspecies alignment and asymmetric interspecies couplings, where one species aligns with the other while the latter antialigns. Motivated by recent results showing that globally coherent chiral motion is not a generic large-scale state of finite-range nonreciprocal flocking, we ask whether a chiral state can nevertheless be stabilized in the discrete-time, metric, nonreciprocal two-species Vicsek model, and if so, under what conditions. For equal populations and motilities, we find that the global chiral state is a long-lived finite-time state rather than an asymptotically stable phase at nonzero motility. Its breaking time increases rapidly as the self-propulsion speed is reduced or the strength of the nonreciprocal coupling is enhanced, explaining why systems with very low motility can appear stably chiral over conventional simulation timescales. This finite-time chiral regime is further limited to high-density systems and to system sizes that are small relative to the interaction range. Within this window, we also find that chirality appears primarily when aligning interactions dominate over antialignment, whereas stronger antialignment leads to species segregation and suppresses chirality. Conversely, introducing species asymmetry through population imbalance drives transitions from the finite-time chiral regime to porous parallel-flocking or antiparallel-flocking liquids; motility imbalance induces asynchronous oscillations and, in extreme cases, leads to segregation into moving clusters of the faster species within a more dispersed background of slower particles. Overall, these results indicate that chirality in the nonreciprocal two-species Vicsek model arises within a restricted regime set by density, motility, interspecies coupling, and system size, rather than being a generic outcome of nonreciprocal interactions.

Numerical implementation of a theory yields acoustic wave packets whose peak-to-peak speeds from source to receiver are supersonic in a dispersionless medium due to temporal interference between direct and boundary-reflected paths. The effect occurs when the source and receiver are near each other and at least one is within $c\widetilde{\delta t}/2$ of the boundary, where $c$ is the phase speed of propagation in the medium, and $\widetilde{\delta t}$ is the smallest temporal separation between the paths at which interference first occurs. This $\mathrm{direct}+\mathrm{reflected}$ path mechanism is distinct from mechanisms yielding superluminal speeds for electromagnetic waves (EM) including quantum tunneling and anomalous dispersion. For temporally interfering $\mathrm{direct}+\mathrm{reflected}$ acoustic paths, simulations yield a speed of information less than $c$. The speed of information from the interfering paths can exceed the speed derived from propagation only along the direct path. We conjecture these results will also hold for EM waves. If so, we prove the speed of information is less than or equal to the speed of light in a vacuum, so the effect does not violate special relativity. These theoretical and simulation results, as well as their conjectured EM extension, should be readily accessible to experimental verification.

The diffusion of ideas and language represents a typical example of collective dynamics in complex systems, conventionally described by S-shaped models such as the logistic function and its generalizations. However, the role of subexponential growth—a slower-than-exponential pattern known in epidemiology—has been largely overlooked in social diffusion processes. Here, we present a piecewise power-law model to characterize complex growth curves with a few parameters. We systematically analyzed a large-scale dataset of approximately one billion Japanese blog articles linked to Wikipedia vocabulary, and observed consistent patterns in web search trend data (English, Spanish, and Japanese). Our analysis of 2963 items, selected for reliable estimation (e.g., sufficient duration/peak, monotonic growth), reveals that 1625 (55%) diffusion patterns without abrupt level shifts were adequately described by one or two segments. For single-segment curves, we found that (i) the mode of the shape parameter $\alpha$ was near 0.5, indicating prevalent subexponential growth; (ii) the peak diffusion scale is primarily determined by the growth rate $R$, with minor contributions from $\alpha$ or the duration $T$; and (iii) $\alpha$ showed a tendency to vary with the nature of the topic, being smaller for niche/local topics and larger for widely shared ones. Furthermore, a microbehavioral model of outward (stranger) versus inward (community) contact suggests that $\alpha$ can be interpreted as an index of the preference for outward-oriented communication. These findings suggest that subexponential growth is a common pattern of social diffusion, and our model provides a practical framework for consistently describing, comparing, and interpreting complex and diverse growth curves.

Natural killer cells (NKCs) can distinguish the difference between normal and abnormal cells, and kill the latter. Nevertheless, regardless of the past intensive studies on the intracellular crosstalk via extracellular vesicles, the generic dynamical behaviors of the NKCs around its co-cultured cells in their attacking process remains an elusive intriguing issue. Here, using the binary mixtures of NKCs and normal fibroblast/cancer cells, we experimentally reveal the above unexplored issue. It is found that, NKCs initially assess and identify the type of co-cultured cells. For cancer cells, NKCs attach to them, recruit neighboring NKCs to form clusters, and exhibit anchored fluctuating motion around the cancer cells in the killing process, until the death of cancer cells. In response, CCs also aggregate into larger clusters than those of the NKC free case, until their death, to avoid NKC attacking. In contrast, when interacting with normal fibroblasts, NKCs continuously scout around the cells, without forming large clusters. They cause little effect on fibroblast motion.

In business, politics, and life, folk wisdom encourages people to aim for above-average results, but not to let the perfect be the enemy of the good. Here, we mathematically formalize and extend this folk wisdom. We model a time-limited search for strategies having uncertain rewards. At each time step, the searcher is either satisfied with their current reward or continues searching. We prove that the optimal satisfaction threshold is both finite and strictly larger than the mean of available rewards—matching folk wisdom. This result is robust to search costs, unless they are high enough to prohibit all search. We show that being too ambitious has a higher expected cost than being too cautious. We show that the optimal satisfaction threshold increases if the search time is longer, or if the reward distribution is rugged (i.e., has low autocorrelation) or left-skewed. The skewness result reveals counterintuitive contrasts between optimal ambition and optimal risk-taking. We show that using upward social comparison to assess the reward landscape substantially harms expected performance. We show how these insights can be applied qualitatively to real-world settings, using examples from entrepreneurship, economic policy, political campaigns, online dating, and college admissions. We discuss implications of several possible extensions of our model, including intelligent search, reward landscape uncertainty, and risk aversion.

Collective motion in biological swarms emerges from local interactions among individuals with limited sensing and cognition, offering valuable insights for decentralized engineered systems. This study presents a systematic framework for extracting interaction graphs from multiagent trajectory data. Three graph identification methods, sparse regression, Granger causality, and cross-correlation, together with geometric anisotropy analysis, are applied to experimental recordings of honey bees during scattered and focused return-to-hive behaviors, aggregations of midges, and flocking passerine jackdaws. Connectivity analysis reveals task-dependent interaction structures: scattered honey bees exhibit causal interactions with up to ten neighbors, whereas focused bees interact with only two to three agents, with midges showing slightly lower connectivity. Cross-correlation analysis indicated honey bees exhibit distance-sensitivity in close proximity, while flocking birds exhibit a distance-dependent correlation decline. These results highlight diverse coordination mechanisms relevant to bio-inspired networked systems.

Analyzing and modeling the mobility process with tour behavior is fundamental to understanding a wide range of complex systems, including animal foraging, human mobility, and freight transportation. However, despite their importance, the distribution of tour length has long been neglected in individual human mobility models. To fill this gap, we analyze Foursquare users' check-in data and find that the distribution of urban tour length follows a truncated power-law distribution. To reproduce the universal scaling law for human mobility in urban areas, we introduce a tour terminate-continue model. Our model reproduces not only the urban tour length distribution, but also Heaps' law, Zipf's law, and the distribution of the radius of gyration, providing an additional perspective for characterizing individual human mobility.

In this work, molecular-dynamics simulations were performed on the ionic liquid 1-butyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide ([BMIM][TFSI]) to investigate the influence of external electric fields on the ion-transport properties. In the low-field regime (0–0.2 V/nm), the two-state model effectively analyzes the deviation from the Nernst-Einstein relation by quantifying the contribution of bound ions to self-diffusion and estimating the range of the free-ion fraction. In the high-field regime (0.2–1.8 V/nm), both mobility and diffusivity exhibit nonlinear growth, accompanied by ionic dipole alignment and field-induced local redistribution of counterions, as revealed by normal and angular-dependent radial-distribution functions (RDFs and ARDFs). We observed saturation of both dipole alignment and radial-distribution functions in the highest fields, which contrasts with the continued increase in mobility and diffusivity. In further analysis of ionic dynamics, we found that the mean residence time of bound ions decreases exponentially with the field strength. This suggests that accelerated ion dynamics might be the key factor driving the continued enhancement of diffusivity and mobility.

Compressed ultrafast photography (CUP) is applied to laser breakdown in argon and xenon under pressures up to 40 bars to obtain two-dimensional images of the plasma dynamics of single events with a spatial resolution of $250\times 100$ pixels and an equivalent frame rate of 500 GHz. Light emission as a function of position and time is measured through red, green, blue, and broadband filters. The spatially encoded and temporally sheared image normally used in CUP is now enhanced by the introduction of a constraint given by a spatially integrated and temporally sheared unencoded signal. The data yield insights into the temperature, opacity, the plasma formation process, and heat flow within the plasma and to the surrounding ambient gas. Contours of constant emission indicate that plasmas formed from sufficiently dense gas contract rather than expand despite having a temperature of a few eV. Plasmas formed from relatively low pressure gases such as 7-bar argon can radiate with emissivity near unity. Modeling transport and opacity as arising from inverse Bremsstrahlung requires a degree of ionization that strongly exceeds expectations based on Saha's equation even as customarily modified to include density and screening. According to this model, both electrons and ions are strongly coupled with a plasma coefficient $\gtrsim 1$. During the first few nanoseconds after formation, Stefan-Boltzmann radiation and thermal conduction to ambient gas are too weak to explain the observed cooling rates, suggesting that transport within the plasma dominates its evolution. Yet, thermal conduction within the plasma itself is also small as indicated by the persistence of thermal inhomogeneities for far longer timescales. The fact that plasma is isolated from the surroundings makes it an excellent system for the study of the equation of state and hydrodynamics of such dense plasmas via the systems and techniques described.

How do neural language models acquire a language's structure when trained for next-token prediction? We address this question by deriving theoretical scaling laws for neural network performance on synthetic datasets generated by the random hierarchy model (RHM)—an ensemble of probabilistic context-free grammars designed to capture the hierarchical structure of natural language while remaining analytically tractable. Previously, we developed a theory of representation learning based on data correlations that explains how deep learning models capture the hierarchical structure of the data sequentially, one layer at a time. Here, we extend our theoretical framework to account for architectural differences. In particular, we predict and empirically validate that convolutional networks, whose structure aligns with that of the generative process through locality and weight sharing, enjoy a faster scaling of performance compared to transformer models, which rely on global self-attention mechanisms. This finding clarifies the architectural biases underlying neural scaling laws and highlights how representation learning is shaped by the interaction between model architecture and the statistical properties of data.

Mutually repelling particles spontaneously form ordered clusters when forced into confinement. The clusters may adopt similar spatial arrangements even if the underlying particle interactions are contrastingly different. Here, we demonstrate with both simulations and experiments that it is possible to induce particles of very different types to self-assemble into the same ordered geometric structure by simply regulating the ratio between the repulsive and confining forces. This is the case for both long- and short-ranged potentials. This property is initially explored in systems with two-dimensional circular symmetry and subsequently demonstrated to be valid throughout the transition to one-dimensional structures through continuous elliptical deformations of the confining field. We argue that this feature can be utilized to manipulate the spatial structure of confined particles, thereby paving the way for the design of clusters with specific functionalities.

In this paper, we take a step toward characterizing the physics of the hovering phenomenon in flapping insects and hummingbirds as a class of extremum seeking (ES) feedback systems. By characterizing hovering flight in insects and hummingbirds as a natural hovering ES system, we achieve (1) very simple, (2) stable, (3) model-free, and (4) real-time hovering. More importantly, our hovering ES characterization only needs the natural oscillations of the wing as the ES input. That is, unlike other control techniques in the literature, the natural hovering ES system only needs the natural flapping action built in the system and feedback of local sensations (measurements) related to the altitude where the insect seeks to stabilize itself. Said ES characterization can become an important initial step in starting a new line of research that may succeed in resolving the long-standing gap between model-based control theory and the biologically observed mechanisms that stabilize hovering flight. We provide simulation trials, including comparisons with some approaches from literature, to demonstrate the effectiveness and robustness of our results. We used literature data for hawkmoth, cranefly, bumblebee, dragonfly, hoverfly, and a hummingbird.

Dropout is a regularization technique widely used in training artificial neural networks to mitigate overfitting. It consists of dynamically deactivating subsets of the network during training to promote more robust representations. Despite its widespread adoption, dropout rates are often selected heuristically, and theoretical explanations of its success remain sparse. Here we analytically study dropout in two-layer neural networks trained with online stochastic gradient descent. In the high-dimensional limit, we derive a set of ordinary differential equations that fully characterize the evolution of the network during training and capture the effects of dropout. We obtain a number of exact results describing the generalization error and the optimal dropout probability at short, intermediate, and long training times. Our analysis shows that dropout reduces detrimental correlations between hidden nodes and mitigates the impact of label noise and that the optimal dropout probability increases with the level of noise in the data. Our results are validated by extensive numerical simulations.

Maximum tolerated dose (MTD) and low-dose metronomic (LDM) schedules are widely used clinical strategies in cancer chemotherapy despite the fact that both approaches have inherent limitations. MTD often leads to drug resistance in tumors, whereas LDM usually results in the predominance of drug-sensitive or drug-resistant cancer cells, depending on the specific dose applied. To circumvent these unfavorable outcomes, we propose in this work a promising adaptive therapy strategy that alternates MTD and LDM schemes across the treatment cycles. By studying a three-component tumor system with replicator equations, we find that alternate administration of MTD and LDM at different lengths of the treatment cycle can significantly delay the development of drug-resistant phenotypes compared to when the two schemes are operated separately. This outcome recapitulates the weak form of the Parrondo's paradox, where appropriate combinations of two individually suboptimal strategies can produce an even more superior outcome (a more favorable therapeutic effect in our case). We also validate the feasibility of the proposed adaptive therapy strategy in spatially distributed tumor ecosystems by implementing agent-based simulations. Our findings offer potential clues to the challenges in state-of-the-art adaptive therapy methods, which often require precise regulation of drug dose and timing based on the proportions of drug-sensitive and drug-resistant cancer cells within a tumor.

A key problem in deep learning and computational neuroscience is relating the geometrical properties of neural representations to task performance. Here, we consider this problem for continuous decoding tasks where neural variability may affect task precision. Using methods from statistical mechanics, we study the average-case learning curves for $\varepsilon$-insensitive support vector regression and discuss its capacity as a measure of linear decodability. Our analysis reveals a phase transition in training error at a critical load, capturing the interplay between the tolerance parameter $\varepsilon$ and neural variability. We uncover a double-descent phenomenon in the generalization error, showing that $\varepsilon$ acts as a regularizer, both suppressing and shifting these peaks. Theoretical predictions are validated both with toy models and deep neural networks, extending the theory of support vector machines to continuous tasks with inherent neural variability.

We report a quantitative study of the onset of dawn choruses of cicadas in several natural habitats. A time-frequency analysis of the acoustical signals is used to define an order parameter for the development of collective singing. The ensemble of recordings reveals that the chorus onset times accurately track the changing sunrise times over the course of many weeks, occurring at a solar elevation of $-3.8^{\circ }\pm 0.2^{\circ }$. Despite day-to-day variations in the amplitude of fully developed choruses, the order parameter data collapse to a common sigmoidal curve when scaled by those amplitudes and shifted by the onset time, revealing a characteristic rise time of $\approx 60$ s for a chorus to reach saturation amplitude. The results are used to obtain the cumulative distribution function of singing as a function of ground illumination, from which is obtained a generalized susceptibility which exhibits a narrow peak with a half width of $\approx 12\%$. The variance of the order parameter exhibits a similar peak, suggesting that a generalized fluctuation-dissipation theorem holds for this system. A model of decision making under ramps of a control parameter is developed and can achieve a quantitative match to the data. It suggests that sharpness of the susceptibility peak reflects cooperative decision making arising from acoustic communication.

Many of the existing approaches to assess and predict the performance of players, teams, or products in competitive contests rely on the assumption that comparisons occur between pairs of such entities. There are, however, several real contests where more than two entities are part of each comparison, e.g., sports tournaments, multiplayer board and card games, and preference surveys. The Plackett-Luce (PL) model provides a principled approach to infer the ranking of entities involved in such contests characterized by multibody comparisons. Unfortunately, traditional algorithms used to compute PL rankings suffer from slow convergence, which limits the application of the PL model to relatively small-scale systems. Here, we present an alternative implementation that allows for significant speed-ups and validate its efficiency in both synthetic and real-world sets of data. Further, we perform systematic cross-validation tests concerning the ability of the PL model to predict unobserved comparisons. We find that a PL model trained on a set composed of multibody comparisons is more predictive than a PL model trained on a set of projected pairwise comparisons derived from the very same training set, emphasizing the need of properly accounting for the true multibody nature of real-world systems whenever such information is available.

Models of opinion dynamics describe how opinions are shaped in various environments. While these models are able to replicate general opinion distributions observed in real-world scenarios, their capacity to align with data at the user level remains mostly untested. We evaluate the capacity of the multistate voter model with zealots to capture individual opinions in a fine-grained Twitter dataset collected during the 2017 French presidential elections. Our findings reveal a strong correspondence between individual opinion distributions in the equilibrium state of the model and ground-truth political leanings of the users. Additionally, we demonstrate that discord probabilities accurately identify pairs of like-minded users. These results emphasize the validity of the voter model in complex settings and advocate for further empirical evaluations of opinion dynamics models at the user level.

Crystallization through vapor deposition is ubiquitous and is inevitably influenced by impurities that often impact the local structure. Interestingly, the effect of immobilizing some of the depositing particles themselves, which would preserve local structural symmetry, remains largely unexplored. Herein, we perform colloidal vapor deposition on a substrate with a few pinned adcolloids, termed “mobility impurities.” Through thermodynamic and kinematic measurements, we demonstrate that these pinned adcolloids, even though they share identical geometry and interaction with depositing particles, are disfavored as nucleation centers. Our experimental findings, supported by molecular dynamics simulations and a simple theoretical model, reveal that entropic contributions, rather than energetic ones, govern nucleation physics in the presence of mobility impurities. Moreover, tuning the mobility of colloids on the substrate adjusts the nucleation likelihood at pinned sites. In later stages of growth, pinning induces mode localization and alters the thin film's vibrational spectrum. Our work thus underscores the potential of strategically incorporating mobility impurities to engineer material properties.

Graph-theoretical methods have proven valuable for investigating alterations in both anatomical and functional brain connectivity networks during Alzheimer's disease (AD). Recent studies suggest that representing brain networks in a suitable geometric space can better capture their connectivity structure. This study introduces a novel approach to characterize brain connectivity changes using low-dimensional, informative representations of networks in a latent geometric space. Specifically, the networks are embedded in a polar representation of the hyperbolic plane, the hyperbolic disk. Here, we used a geometric score, entirely based on the computation of distances between nodes in the latent space, to measure the effect of a perturbation on the nodes. Precisely, the score is a local measure of distortion in the geometric neighborhood of a node following a perturbation. The method is applied to a brain network dataset of patients with AD and healthy participants, derived from diffusion-weighted (DWI) and functional magnetic resonance (fMRI) imaging scans. We show that, compared with standard graph measures, our method more accurately identifies the brain regions most affected by neurodegeneration. Notably, the abnormalities detected in memory-related and frontal areas are robust across multiple brain parcellation scales. Finally, our findings suggest that the geometric perturbation score could serve as a potential biomarker for characterizing the progression of the disease.