Learning from experience is a key feature of decision-making in cognitively complex organisms. Strategic interactions involving Bayesian inferential strategies can enable us to better understand how evolving individual choices to be altruistic or selfish can affect collective outcomes in social dilemmas. Bayesian strategies are distinguished, from their reactive opponents, in their ability to modulate their actions in the light of new evidence. We investigate whether such strategies can be resilient against reactive strategies when actions not only determine the immediate payoff but can affect future payoffs by changing the state of the environment. We use stochastic games to mimic the change in environment in a manner that is conditioned on the players' actions. By considering three distinct rules governing transitions between a resource-rich and a resource-poor state, we ascertain the conditions under which Bayesian tit-for-tat strategy can resist being invaded by reactive strategies. We find that the Bayesian strategy is resilient against a large class of reactive strategies and is more effective in fostering cooperation leading to sustenance of the resource-rich state. However, the extent of success of the Bayesian strategies depends on the other strategies in the pool and the rule governing transition between the two different resource states.

Network science has significantly advanced our understanding of complex systems by representing them as graphs. Vertices correspond to system components, and edges capture pairwise interactions. However, many real-world systems (e.g., chemical reactions, brain networks, scientific collaborations) involve higher-order interactions that graphs fail to capture fully. Hypergraphs offer a more suitable framework, allowing interactions among multiple components, with each hyperedge connecting an arbitrary number of vertices. While significant progress has been made in studying the spectral properties of the matrix representation of a hypergraph, less attention has been given to efficiently computing its spectral density. Existing approaches primarily rely on direct diagonalization, which scales cubically with the number of vertices and is thus computationally prohibitive for large hypergraphs. In this work, we develop an efficient method for computing the spectral density of the signless Laplacian, adjacency, and Laplacian matrices of weighted hypergraphs using the cavity method. The cavity method is based on the incidence matrix, the most common way to represent hypergraphs. We further refine this approach to derive a more efficient method for unweighted hypergraphs that requires only the degree and order sequences. Finally, we validate the effectiveness of our processes demonstrating their computational efficiency and accuracy.

A shell model can be considered as a self-similar chain of interacting triads, where each triad can be interpreted as a nonlinear oscillator that can be mapped to a spinning top. Investigating the relation between phase dynamics and intermittency in such a chain of nonlinear oscillators, it is found that synchronization is linked to increased energy transfer. In particular, our results indicate that the observed systematic increase of intermittency, as the shell spacing is decreased, is associated with strong phase alignment among consecutive triadic phases, facilitating the energy cascade. It is shown that while the overall level of synchronization can be quantified using a Kuramoto order parameter for the global phase coherence in the inertial range, a local, weighted Kuramoto parameter can be used for the detection of burstlike events propagating across shells in the inertial range. This analysis reveals how locally phase-locked states are associated with the passage of extreme events of energy flux. Applying this method to helical shell models (i.e., for a class of helical interactions that couple the two helicities in a nonseparable topology) reveals that a reduction in phase coherence correlates with suppression of intermittency. When inverse cascade scenarios are considered using two different shell models including a nonlocal helical shell model, and a local standard shell model with a modified conservation law, it was shown that a particular phase organization is needed in order to sustain the inverse energy cascade. It was also observed that the PDFs of the triadic phases were peaked in accordance with the basic considerations of the form of the flux, which suggests that a triadic phase of $\pi /2$ and $-\pi /2$ maximizes the forward and the inverse energy cascades respectively.

Classifying astrophysical bodies like stars, galaxies, and black holes plays an underlying role in understanding the evolution of the universe. Effective analysis of a huge number of astronomical objects captured by telescopes is a challenge. For the classification of astronomical objects, quantum computing coupled with artificial intelligence proposes a good solution. Quantum machine learning (QML) utilizes the concepts of quantum computing to process huge datasets with greater accuracy and efficiency. In the current study, quantum features extraction with a convolutional neural network (CNN), named the AstroNet model, is proposed for the classification of astronomical objects. Quantum features extraction involves the conversion of raw images of astrophysical objects into quantum states for further processing. This is achieved by encoding the values of pixels in the amplitudes of quantum states using qubits. The AstroNet model consists of two phases. We first construct a quantum circuit. Entanglement is introduced by randomlayers, which employ cnot gates along with parameterized rotations. All quantum operations are implemented using the pennylane library in Python on a simulator. This enables efficient representation and processing of complex image data, setting the stage for quantum-powered classification in the second phase. These quantum features are passed to the proposed CNN model, which is designed from scratch, having seven layers, including two convolutional, two dense, two max pooling, and one flatten. The AstroNet is trained, based on the selected hyperparameters like the Adam optimizer, Sparse Categorical Cross-entropy, 32 batch-size, 0.0001 learning rate, and 10 epochs. The capability of the AstroNet model is examined based on the five top astrophysical object classification datasets including Galaxy Zoo, Galaxy Zoo 2, SpaceNet, Star-galaxy, and six classes of astronomical objects. The AstroNet model achieves up to 0.99 classification performance, which is much better than the previously reported methods in this field.

We derive a multiscale framework that combines contributions from the lattice symmetry, shape, and interfacial effects to calculate the total magnetostatic energy and effective susceptibility of crystalline paramagnetic particle aggregates. Demagnetizing tensor fields are calculated through a Fourier-space method developed by Beleggia and M. De Graef [M. Beleggia and M. De Graef, J. Magn. Magn. Mater. 263, L1 (2003)] to account for shape anisotropy. A planewise Ewald summation method developed by Massidda [V. Massidda and J. Hernando, Physica B + C 101, 159 (1980)] supplies local field factors in the constant dipole approximation which account for the effect of crystal structure on internal fields, while explicitly accounting for field perturbations at surfaces. The effective energy and susceptibility scales illustrate the dependence of magnetic properties on both aggregate shape and internal organization and successfully predicts the occurrence of giant susceptibility in structured aggregates of paramagnetic particles.

We study the trapping of charged particles and macromolecules (such as DNA) in salt gradients in aqueous solutions. The source for the salt gradient can be as simple as a dissolving ionic crystal, as shown by McDermott et al. [Langmuir 28, 15491 (2012)]. Trapping is due to a competition between localization due to diffusiophoresis in the salt gradient, and spreading out by diffusion. The size of the trap is typically 1–$100\mu \mathrm{m}$. We further predict that, at steady state, the particle (macromolecule) number density is a power law of the salt concentration, with an exponent that is the ratio of the diffusiophoretic mobility to the diffusion coefficient of the trapped species. This ratio increases with size and typically becomes $\gg 1$ for particles or macromolecules with hydrodynamic radii of hundreds of nanometers and above. Thus, large particles or macromolecules are easily caught and trapped at steady state by salt gradients.

We analyze the universal conformational properties of comblike polymer topologies in the dilute-solution regime. To this end, we evaluate the effective radii of gyration of polymer structures across a range of parameters, including the number of branching points $n$, the functionality $f$ (the number of grafted side chains in addition to the backbone), and the relative polymerization degree $a$, defined as the ratio between the degrees of polymerization of the backbone spacer and the grafted side chains. We combine an analytical approach based on the continuous-chain model and direct polymer renormalization with coarse-grained molecular dynamics simulations and comparison with available experimental data. In particular, we quantitatively estimate the increase in the effective size of comb structures with increasing relative polymerization degree $a$. Our analytical results show good qualitative agreement with both the simulations and the available experimental data for monodisperse homopolymer combs.

Conventional phase segregation is controlled by a positive interfacial tension, which implies that the system relaxes towards a state in which the interfacial area (or length) is minimized, typically manifesting as a single droplet that grows with the system size. Intriguingly, the extension of the underlying Model B paradigm by two nonpotential terms (Active Model $\mathrm{B}+$) is able to describe the stable coexistence of many finite droplets. Here we numerically study Active Model $\mathrm{B}+$ in the vicinity of the transition between a single droplet (macrophase segregation) and multiple droplets (microphase segregation). Our results show that, although noise shifts transitions, the overall agreement with the mean-field theoretical predictions is very good. We find a strong correlation of droplet properties with a single parameter that determines the number, density, and fractal dimension of droplets. Deeper inside the domain of microphase segregation we observe another transition to a hexagonal lattice of regular droplets.

We study Hopf bifurcation of stationary activity bumps to localized, spatially coherent oscillations in a family of elementary neural field models involving nonlocal synaptic excitation and inhibition with Heaviside firing rate nonlinearity and local linear adaption, both with and without a localized input inhomogeneity, on the one-dimensional spatial domain $(-\infty ,\infty )$, including cases of interacting pairs of neural fields. (We treat the same neural fields on two-dimensional spatial domain ${\mathbb{R}}^2$ separately.) A main focus is to categorize how the underlying symmetries of the nonlinear operators in this family of equations give rise to a related set of spatially coherent time-periodic solutions that bifurcate via Hopf bifurcation with respect to different spatial eigenmodes, each with different spatial structures being selected as a result of the relative balance of synaptic inhibition to excitation. A general framework is constructed to analyze stationary bump solutions in a neural field model containing $N$ neural fields with $M$ linear gating variables that modulate different neural fields. Under a basic set of symmetry assumptions on the synaptic weight functions and the input homogeneity, we show that all such neural fields have two broad classes of eigenmodes with either even or odd spatial symmetry. When these eigenmodes destabilize via Hopf bifurcation, it leads to various types of spatially coherent, time-periodic oscillations that can take the form of breathing bumps or breathers that expand and contract and sloshing bumps or sloshers which move side-to-side. Analytical treatments combined with numerical simulations provide a more complete picture of the emergence of these periodic activity patterns and novel secondary bifurcations are found to occur, including torus, period-doubled, and Rossler band-like dynamics. Interacting pairs of neural fields that support bumps, breathers, and sloshers can lead to novel spatially coherent oscillations with different patterns of synchrony and spatial positioning depending on the type of synaptic interactions between the neural fields including novel in-phase and antiphase breathers and sloshers. A novel transition from a slosher to a spatially localized, traveling periodic wave is also found. The approach is extended to the case of multibump solutions and bifurcations leading to various multibump breathers and sloshers are observed.

We study the bifurcation of stationary activity bumps to localized, spatially coherent oscillations in a family of elementary neural field models involving nonlocal synaptic excitation and inhibition with Heaviside firing rate nonlinearity and local linear adaption, both with and without a localized input inhomogeneity, on two-dimensional spatial domain ${\mathbb{R}}^2$, including two cases of interacting pairs of neural fields. [We treat the same neural fields on the one-dimensional spatial domain $(-\infty ,\infty )$ separately.] A general framework is constructed to analyze stationary bump solutions in a neural field model containing $N$ neural fields with $M$ linear gating variables that modulate different neural fields. A main focus is to demonstrate how underlying symmetries in this family of equations give rise to a related set of spatially coherent time-periodic solutions that bifurcate via Hopf bifurcation with respect to different spatial eigenmodes, each with different spatial structures being selected as a result of the relative balance of synaptic inhibition to excitation. A Hopf bifurcation with $\text{O}\left(2\right)$ symmetry for radially symmetric stationary bumps is relevant for bifurcation with respect to higher-order spatial modes in these neural fields due to the geometric multiplicity of these eigenvalues resulting from the symmetries of the synaptic connections and input inhomogeneity. Hopf bifurcation of stationary bumps in these neural fields thereby produce either breather (standing wave) type of solutions with $D_n$ dihedral symmetry or rotor (rotating wave) type of solutions with $Z_n$ rotational symmetry when a stationary bump destabilizes in a supercritical Hopf bifurcation. Interacting pairs of symmetric neural fields that support bumps lead to different types of in-phase and antiphase breather and rotor solutions when stationary bumps destabilize in a Hopf bifurcation with respect to different eigenmodes. Stability of ring solutions is also studied and Hopf bifurcation is found to lead to different ring breathers and ring rotors with analogous $n$-fold symmetry. Secondary and subcritical bifurcations also occur in these neural fields on two-dimensional domains which can produce a diverse set of spatiotemporal patterns, particularly in the presence of an input inhomogeneity; however, this is beyond the scope of this study and will be treated in more depth separately.

Understanding semantic relationships within complex networks derived from lexical resources is fundamental for network science and language modeling. While network embedding methods capture contextual similarity, quantifying semantic distance based directly on explicit definitional structure remains challenging. Accurate measures of semantic similarity allow for navigation on lexical networks based on maximizing semantic similarity in each navigation jump (Semantic Navigation, SN). This work introduces Ontological Differentiation (OD), a formal method for measuring divergence between concepts by analyzing overlap during recursive definition expansion. The methodology is applied to networks extracted from the Simple English Wiktionary, comparing OD scores with other measures of semantic similarity proposed in the literature (cosine similarity based on random-walk network exploration). We find weak correlations between direct pairwise OD scores and cosine similarities across 2 million word pairs, sampled from a pool representing over 50% of the entries in the Wiktionary lexicon. This establishes OD as a largely independent, definition-based semantic metric, whose orthogonality to cosine similarity becomes more pronounced when low-semantic-content terms were removed from the dataset. Additionally, we use cumulative OD scores to evaluate paths generated by vector-based SN and structurally optimal Shortest Paths (SP) across networks. We find SN paths consistently exhibit significantly lower cumulative OD scores than shortest paths, suggesting that SN produces trajectories more coherent with the dictionary's definitional structure, as measured by OD. Ontological Differentiation thus provides a novel, definition-grounded tool for analyzing, validating, and potentially constructing navigation processes in lexical networks.

Human behavior plays a critical role in shaping epidemic trajectories. During health crises, people respond in diverse ways in terms of self-protection and adherence to recommended measures, largely reflecting differences in how individuals assess risk. This behavioral variability induces effective heterogeneity into key epidemic parameters, such as infectivity and susceptibility. We introduce a minimal extension of the susceptible-infected-removed (SIR) model, denoted HeSIR, that captures these effects through a simple bimodal scheme, where individuals may have higher- or lower-transmission-related traits. We derive a closed-form expression for the epidemic threshold in terms of the model parameters, and the network's degree distribution and homophily, defined as the tendency of like-risk individuals to preferentially interact. We identify a resurgence regime just beyond the classical threshold, where the number of infected individuals may initially decline before surging into large-scale transmission. Through simulations on homogeneous and heterogeneous network topologies we corroborate the analytical results and highlight how variations in susceptibility and infectivity influence the epidemic dynamics. We further show that, under suitable assumptions, the HeSIR model maps onto a standard SIR process on an appropriately modified contact network, providing a unified interpretation in terms of structural connectivity. Our findings quantify the effect of heterogeneous behavioral responses, especially in the presence of homophily, and caution against underestimating epidemic potential in fragmented populations, which may undermine timely containment efforts. The results also extend to heterogeneity arising from biological or other nonbehavioral sources.

We study the out-of-equilibrium scaling behavior of two-dimensional and three-dimensional Ising systems, when they are slowly driven across their magnetic first-order transitions at low temperature $T<T_c$, where $T_c$ is the temperature of their continuous transition. We consider Kibble-Zurek (KZ) protocols in which a spatially homogenous magnetic field $h$ varies as $h\left(t\right)=t/t_s$ with a timescale $t_s$. The KZ dynamics starts from negatively magnetized configurations equilibrated at $h_i<0$ and stops at a positive value of $h$ where the configurations acquire a positive average magnetization. We consider the Metropolis and the heat-bath dynamics, which are two specific examples of a purely relaxational dynamics. We focus on two different dynamic regimes. We consider the out-equilibrium finite-size scaling (OFSS) limit in which the system size $L$ and the timescale $t_s$ diverge simultaneously, keeping an appropriate combination fixed. Then, we analyze the KZ dynamics in the thermodynamic limit (TL), obtained by taking first the $L\to \infty$ limit at fixed $t$ and $t_s$, and then considering the scaling behavior in the large-$t_s$ limit. Our numerical results provide evidence of OFSS, as predicted by general scaling arguments. The results in the TL show the emergence of spinodal-like behaviors: The passage from the negatively magnetized phase to the positively magnetized one occurs at positive values $h_{*}>0$ of the magnetic field, which decrease as $h_{*}\sim 1/{(ln{t}_s)}^{\kappa }$, with $\kappa =2$ and $\kappa =1$ in two and three dimensions, respectively, for $t_s\to \infty$. We identify $\sigma \equiv t{(lnt)}^{\kappa }/t_s$ as the relevant scaling variable associated with the KZ dynamics in the TL.

Two-dimensional (2D) Potts model is a classical example when the symmetry of the order parameter controls the order of a phase transition: on a square lattice with nearest-neighbors interaction, when the number of states $q$ is less than or equal to 4, the second-order phase transition is observed, while for $q>4$ the first-order phase transition occurs. Recent research shows that even when the number of states is fixed, increasing the interaction range allows one to reach the point where the order of the phase transition changes. I focus on a $q=3$ 2D Potts model and, from the analysis of the partition-function zeros, locate the number of interacting neighbors that change the order of the phase transition.

Traveling waves (TWs) are a fundamental mechanism of large-scale spatiotemporal coordination in the cortex, yet how their directionality originates from microscale circuit properties remains an open question. To address this, we introduce a multiscale model that reveals a dual emergence process underlying cortical TW dynamics. We show that local nonreciprocal excitation-inhibition (E-I) coupling generically produces sustained collective oscillations. These oscillations serve as building blocks for macroscopic waves: when spatially coupled, they give rise to large-scale spatiotemporal patterns whose propagation direction is determined by emergent frequency gradients. Crucially, these frequency gradients—and therefore the wave propagation direction—can be controlled by intrinsic network properties (e.g., E-I coupling gradients) and extrinsic input. Our model reproduces the diversity of experimentally observed TW behaviors, including both fixed-direction and task-responsive propagation. Furthermore, the system exhibits robust wave formation even under fluctuating external input, mirroring biological reliability. By linking synaptic-level architecture to large-scale wave dynamics, our work establishes a mechanistic, multiscale foundation for the emergence and control of cortical TWs, with broader implications for neural computation and nonreciprocal wave-metamaterials.

Ultraintense laser interactions with near-critical density (NCD) targets have emerged as a promising approach to enhance proton energy and flux. In this study, we used three-dimensional particle-in-cell simulations to investigate proton acceleration by a linearly polarized 100 TW, 40-fs laser beam interacting with near-critical-density targets. Four target types were compared: log-pile foam structure, spongelike foam structure, uniform plasma, and solid foil. The results indicate that log-pile foam targets enhance proton yield by up to a factor of 9 and increase total energy by up to a factor of 10, compared to the other target types. This improvement is attributed to the efficient laser absorption (more than twice the absorption of other targets) into the log-pile structure and the multitarget normal sheath acceleration mechanism, which occurs between the surfaces of the log-pile structure within the target. Additionally, the self-generated radial magnetic field, arising from the low-density plasma, collimates the electrons, while the strong quasistatic transverse electric field focuses the proton beams along the laser axis. These improvements in proton generation, coupled with the practically feasible additive fabrication, make the log-pile foam target more advantageous than other NCD target types.

We investigate the transport behavior of tungsten impurities with finite inertia in drift-wave turbulence using the Hasegawa-Wakatani model. Unlike previous tracer-based models, our simulations reveal a transition to nondiffusive dynamics for a range of charge states. This mechanism offers a turbulence-driven route to core impurity accumulation. This finding underscores the nontrivial role of particle inertia in impurity dynamics and has strong implications for impurity control in future fusion devices such as ITER.

Single-chain elasticity is of fundamental importance in polymer physics, as it underlies many of the unique properties of polymer systems. Recently, there has been interest in characterizing the elastic properties of catenanes, molecular architectures composed of linked molecular rings. To date most studies have focused on the force-extension behavior of polycatenane and catenane dimers. In this study, we employ Monte Carlo computer simulations to investigate the elastic properties of a collection of catenane chains. In addition to polycatenane, we also examine the properties of catenane ribbons constructed by connecting two or three polycatenane chains together with a variable number of side-link rings. After first characterizing the behavior of free polycatenane chains and catenane ribbons, we examine their mechanical response to both an elongational force and a torque applied to the end rings of the chain. We find that the stretching induced by the force is counterbalanced by increasing the torque, which tends to twist the chains and in so doing reduce the extension length. At low torque, the twist angle of the end rings of the chain varies linearly with torque, and the associated torsional spring constant, characterizing the resistance of the chain to twist with the applied torque, tends to increase with stretching force. Relative to polycatenane, ribbons tend to be more elongated at low force and less elongated at strong force. In addition, increasing the ribbon width dramatically increases the torsional stiffness of the chain. Finally, decreasing the degree of side-linking in ribbons tends to decrease slightly the extension length at moderate force and to increase the torsional stiffness for sufficiently large gaps.