Papers

The multiplex network paradigm has been instrumental in revealing many unexpected phenomena and dynamical regimes in complex interacting systems. Nevertheless, most of the current research focuses on undirected multiplex structures, whereas real-world systems predominantly involve directed interactions. Here, we present an analytical framework for attaining optimal synchronization in directed multiplex networks composed of phase oscillators, considering both frustrated and non-frustrated regimes. A multiplex synchrony alignment function (MSAF) is introduced for this purpose, whose formulation integrates structural properties and dynamical characteristics of the individual directed layers. Using this function, we derive two classes of frequency distributions: one that yields perfect synchronization at a prescribed coupling strength in the presence of phase-lag, and another that optimizes synchronization over a broad range of coupling strengths. Numerical simulations on various directed duplex topologies demonstrate that both frequency sets substantially outperform conventional distributions. We also explore network optimization through a directed link rewiring strategy aimed at minimizing the MSAF, along with a swapping algorithm for optimally assigning fixed frequencies on both layers of a given directed duplex network. Examination of synchrony-optimized directed networks uncovers three notable correlations: a positive relationship between frequency and out-degree, a negative correlation between neighboring frequencies, and an anti-correlation between mirror node frequencies across directed layers.

Applications of quantum mechanics have led to many successful predictions and explanations of puzzling phenomena, and we now apply quantum mechanics to gain, process, and communicate information in novel ways. We can understand quantum mechanics by understanding how we have applied it. We should not seek agreement on the nature of the world it represents, because this theory does not itself represent the physical world (though its applications do help us to represent it better). When applied to a quantum state, quantum mechanics yields probabiities for physical events: both state and probability are objective–not because they represent elements of phyiscal reality, but because each exerts norrmative authority over the beliefs of anyone who accepts quantum mechanics and applies it relative to a physical situation they may (but need not) occupy. These events may be described by statements that are meaningful in an appropriate environmental context, and quantum mechanics can help one to say when that is. Measurement creates an appropriate context, so here the Born rule indirectly yields probabilities of measurement outcomes. The quantum state of a system does not "collapse" on measurement: a new state must be assigned relative to a physical situation in which information about the outcome is accessible. Understood this way, there is no measurement problem, and violations of Bell inequalities does not demonstrate "spooky" non-local action. Quantum field theories have no physical ontology of their own: a quantum field is a mathematical object in a model whose application helps us to improve and extend our descriptions of the world in other terms. We cannot realise the scenario of Wigner's friend and its recent extensions: but the data that provide overwhelming evidence for quantum mechanics are objective in the same sense as the relative measurement outcomes described in those scenarios.

Probabilistic forecasts must sum to unity and cannot express “I don't know.” Possibility theory relaxes this constraint: a subnormal distribution explicitly measures how much of the plausibility budget remains unassigned, ignorance signal that probability cannot represent. This paper develops a verification framework for such forecasts, centred on a five-number scorecard that separately diagnoses whether the forecast pointed at the right outcome (depth-of-truth), how sharply (diffuseness, support margin), how confidently (ignorance), and how dominantly (conditional necessity). A possibility-to-probability conversion preserves ignorance for familiar frequency-based scoring; categorical threshold scores (POD, FAR, CSI, etc.) connect to operational practice. Together, these three complementary facets – possibilistic, probabilistic, and categorical – expose failure modes invisible to any single metric. Storm Prediction Center convective outlook categories serve as the running example throughout; a synthetic reforecast demonstrates diagnostic visualisations and scorecard interpretation. Ignorance is better expressed than repressed.

A relaxed baseline case, based on the Primary Reference Discharge (PRD) design point, is used to conduct a first dedicated investigation for the most unstable low-$n$ MHD instabilities in SPARC baseline-like scenarios. The simulations use the high-fidelity 3D extended-MHD code \simcode{}, focusing on a qualitative understanding of potential sawtooth crashes. The linear simulation, by scanning over the resistivity, identifies a dominant internal kink mode at the $q=1$ surface with a toroidal mode number $n=1$. Both the current and the pressure profiles are strongly affecting the kink instability in the baseline case. The linear growth rate is sensitive to the keV-level temperature profile and the on-axis $q_0$ around unity. A simplified 1D eigenvalue solver provides additional support for elucidating the physical mechanisms of the 1/1 mode and qualitative interpretations for the M3D-C1 results. In 3D nonlinear simulations, the marginally unstable case gives a moderate sawtooth crash when $q_0$ is below unity. When both the current and the pressure drives exist (the baseline case), a strong sawtooth crash is obtained, which features a magnetic reconnection event and a hollowed pressure profile. These are consistent with features from both the Kadomtsev and Wesson models. The sawtooth oscillations shown in low-$\beta_0$ simulations also provide an initial effort to study sawtooth evolution in SPARC. However, several important physical effects are not yet included, such as two-fluid effects, kinetic alpha particles, and the associated heating sources, limiting quantitative predictions of crash amplitude and timescales. The present work therefore provides a qualitative physics basis for future studies of particle and heat transport during MHD activity in SPARC and future fusion pilot plants.

High-throughput solid-state nanopore experiments generate continuous MHz-rate data streams in which only a small fraction of data contains informative molecular information. This creates storage and processing bottlenecks that limit experimental scalability. We introduce Data Sieving, a GPU-accelerated acquisition framework that integrates real-time event detection directly into the measurement pipeline and selectively stores and allows real-time analysis of snapshots around molecular translocations. The system employs a lightweight rolling-average and min-max trigger to identify event candidates in parallel across channels. This architecture reduces stored data volume by up to 98% while preserving complete molecular signatures across a wide temporal range, from microsecond-scale protein dynamics to second-scale nucleic acid nanoparticle events. Continuous baseline monitoring enables autonomous closed-loop actuation; in high-concentration DNA experiments, automatic declogging restored pore conductance, reducing the time spent in a non-productive clogged state to near-zero and without interrupting parallel measurements. Validated across DNA, protein, and nucleic acid nanoparticle measurements, Data Sieving links data storage directly to molecular information content rather than experiment duration, enabling scalable, real-time operation of parallel nanopore sensors. The approach provides a hardware-agnostic foundation for long-duration, high-bandwidth single-molecule experiments and other event-driven sensing platforms. By using algorithms intrinsically compatible with low-latency digital architectures, this framework provides a clear path toward high-bandwidth, highly multiplexed recording across hundreds of individual nanopore channels in both solid-state and biological pores.

Accuracy, variationality, and convergence underpin the reliability of modern electronic structure methods, yet definitive benchmarks in the relativistic regime remain elusive due to the absence of numerically exact full configuration interaction (CI) references. Recent algorithmic advances in the CI framework, enabled by the small-tensor-product (STP) decomposition approach, have dramatically extended the tractable size of the configuration space, making numerically exact CI calculations feasible in large active spaces previously beyond reach. In this work, we employ the recently developed STP-CI framework to perform large-scale numerically exact CI calculations and directly benchmark relativistic coupled cluster and density matrix renormalization group methods. Definitive benchmarking of approximate relativistic electronic structure methods is ensured through the application of the gap theorem, which provides rigorous error bounds on the CI reference and establishes a controlled standard for assessing accuracy, variationality, and convergence.

Some algorithms for the numerically exact treatment of fermion determinants are summarised. This is not supposed to be a review, rather a concise handbook. The audience is expected to have a basic understanding of how to put fermions on a computer. We primarily discuss different ways to work with the fermion matrix in the "sausage" (Green's function) formulation for quantum Monte Carlo (QMC). We emphasise the need for varied approaches in different space-time volume regimes. In particular, for small spatial volumes we describe a numerically stable method based on dense matrix operations. It is designed specifically to deal with very low temperature regimes. On the other hand, for (relatively) large volumes we describe a highly efficient and scalable sparse matrix approach.

The Variationally Mimetic Operator Network (VarMiON) approach is a machine learning technique, originally developed to predict the solution of elliptic differential problems, that combines operator networks with a structure inherited from the variational formulation of the equations. We investigate the capabilities of this method in the context of viscous flows, by extending its formulation to vector-valued unknown fields and with a particular emphasis on the space-time approximation context necessary to deal with transient flows. As a first step, we restrict attention to the regime of low-to-moderate Reynolds numbers, in which the Navier–Stokes equations can be linearized to give the time-dependent Stokes problem for incompressible fluids. The details of the method as well as its performance are illustrated in three paradigmatic flow geometries where we obtain a very good agreement between the VarMiON predictions and reference finite-element solutions.

Stochastic kinetic models are ubiquitous in physics, yet inferring their parameters from experimental data remains challenging. For deterministic models, parameter inference often relies on gradients, which can be obtained efficiently through automatic differentiation (AD). However, AD cannot be applied directly to the Gillespie stochastic simulation algorithm (SSA), since sampling from a discrete set of reactions introduces non-differentiable operations. In this work, we adopt three gradient estimators from machine learning for the Gillespie SSA: the Gumbel-Softmax Straight-Through (GS-ST) estimator, the Score Function estimator, and the Alternative Path estimator. We use the estimators to evaluate gradients of steady-state and time-dependent observables, and compare their performance in representative biophysical systems with relaxation dynamics (bimolecular association) and oscillatory dynamics (repressilator). We find that the GS-ST estimator generally yields well-behaved gradient estimates, but exhibits diverging variance in challenging parameter regimes, which can cause parameter inference to fail. In these cases, other estimators provide more robust, lower variance gradients. Our results demonstrate that gradient-based parameter inference can be effectively combined with the Gillespie SSA, with different estimators offering complementary advantages.

A lithium droplet transport and evaporation model has been developed within the Direct Simulation Monte Carlo code OpenEdge. This model integrates gravity, collisional ion drag, orbital-motion-limited charging, energy-balance evaporation, and an anisotropic rocket recoil force using a Strang-split integrator. Validation against analytical drag-gravity solutions and independent RK45 evaporation integration demonstrates relative errors below 0.00001 for droplet radii of 1.5, 2.5, and 3.5 mm. Simulations of ensembles containing 100000 droplets, launched from inner and outer divertor surfaces in SOLPS-ITER plasma background for the CAT tokamak reactor concept, indicate that transport outcomes are determined by initial size, velocity, and launch location. Outer-divertor droplets predominantly redeposit locally, whereas inner-divertor droplets reach the low-field-side wall. Smaller droplets lose most of their mass to evaporation before reaching the core, while larger droplets retain their mass and redeposit on nearby tiles. Both one-way and iterative two-way coupling frameworks map the evaporated lithium onto the SOLPS-ITER mesh as volumetric sources, facilitating self-consistent evaluation of lithium droplet impacts on edge-plasma performance.

Near-surface wind fields on Mars are profoundly modulated by complex topography, yet fine-scale wind field characteristics remain poorly resolved for key geomorphological units such as deltas, valleys, and impact craters, due to the spatial constraints of lander-based wind observations. To address this, we identified three dominant wind directions using measured near-surface wind data from the Perseverance rover at Jezero Crater and then integrated in-situ wind measurements with high-resolution numerical modeling. We established a high-resolution three-dimensional (3D) terrain model encompassing key local geomorphic units, including the delta, an impact crater, and nearby mesas, and performed Computational Fluid Dynamics (CFD) simulations under the above-mentioned three dominant wind directions. The results reveal a robust coupling mechanism between local topography and near-surface wind field structures. We demonstrate that wind speed is significantly enhanced over windward slopes but evidently attenuated within depressions and crater floors. Crucially, significant wind direction deflection angles were particularly evident in areas characterized by steeper slopes. For instance, wind flow exhibited a symmetrical deflection pattern along the opposing inner walls of the modeled impact crater, but stabilizing on the crater floor. Spatial comparisons indicate that wind deflection is most pronounced over steeper slopes, while sector-based distributions within the impact crater reveal a consistent symmetry between opposing wall and floor regions. These findings offer new and critical insights into the intimate connection between Martian surface aeolian erosion/deposition processes and local topographic evolution, which is vital for interpreting the sedimentary history of Jezero Crater.

Analytical theories of polymer dynamics typically focus on the linear response around some steady state obtained via perturbative calculations. The present study derives a dynamical, nonlinear mean-field theory that yields unified access to the evolution of conformations, contact probabilities, and fluctuations of active polymers within a single analytical framework. As in previous mean-field descriptions of passive polymers, the object of interest is the two-point correlator, which is the lowest-order relevant observable in the general Langevin equation of a polymer. In contrast, the present focus is on active polymers driven by heterogeneous monomer-level kicks and spatially correlated active flows, while allowing nonreciprocal couplings, in the presence of hydrodynamic and contact interactions. Using a Gaussian closure to truncate higher-order correlations leads to a self-consistent diffusion equation for the chain correlations. In some cases, this can be further simplified to the dynamics of pairwise squared separations in closed form. In the continuum limit, the theory reveals useful analogies to similar mean-field approximations for reaction-diffusion systems, as well as fractional diffusion in different scale-free regimes. Deriving asymptotic solutions in different parameter regimes of the continuum limit recovers the scalings of coiled, globular, and self-avoiding polymers, thus validating the theory. Applied to hydrodynamically coupled active polymers, such as chromatin, the framework predicts a sequence of crossover scalings between coiled, swollen, and hyper-compacted fractal states.

Guided mode resonance (GMR), the resonant coupling of free-space light into leaky waveguide modes, is traditionally achieved with periodic patterned structures. However, this approach makes its key properties such as quality factor (Q-factor) fabrication-dependent and non-tunable. Here, we introduce a time grating platform, i.e., a homogeneous waveguide whose refractive index is modulated periodically in time, that allows tunable GMRs through temporal modulation engineering rather than spatial structural redesign. We show that the Q-factors of these GMRs diverge as the modulation depth vanishes. Furthermore, unconstrained by energy conservation, the resonances exhibit near-unity reflection for fundamental harmonics and values exceeding 40 for first-order harmonics. Our findings not only apply to yield a giant Goos-Hänchen shift over 103 times wavelength without sacrificing the reflection magnitude, but also open new avenues for related phenomena such as bound states in the continuum, unidirectional GMRs and beyond.

We investigate the conditions for triggering the plasmoid instability in a dynamically forming current sheet in the resistive magnetohydrodynamic framework, using a pseudo-spectral code applied to the Orszag-Tang vortex at Lundquist number $S \sim 10^5$. Following García Morillo & Alexakis (2025), we use the power spectrum of the current density $E_J(k)$, complemented by the vorticity spectrum $E_\omega(k)$, to assess the convergence of our simulations, and show that this diagnostic remains valid even in the presence of physical plasmoids, allowing us to unambiguously distinguish them from spurious ones. We then show that physical plasmoids can be triggered in a well-resolved spectral simulation when three conditions are simultaneously met: a perturbation applied near the time of maximum current density, with amplitude above a critical threshold $\varepsilon_c \sim 10^{-5}$ for our numerical scheme, and with spectral content containing the unstable wavenumbers. These conditions are confirmed using continuous noise injection, which yields similar results at amplitudes one to two orders of magnitude lower. The resulting growth rates and plasmoid numbers are in good agreement with the theory of \citet{Comisso2017}. These results resolve the apparent paradox raised by García Morillo & Alexakis (2025) and also clarify the role of numerical noise in the triggering of the plasmoid instability.

We demonstrate that strong-field ionization of atoms in circularly polarized laser fields generates a photoelectron spin texture with toroidal topology in momentum space. Using time-dependent Schrödinger equation simulations, spin-resolved classical-trajectory Monte Carlo calculations, and an extended spin-resolved strong-field approximation including intermediate excitation pathways, we show that the rotation angle of this spin torus provides access to attosecond relative time delays associated with photoelectron wave packets released by tunneling from the counter-rotating and co-rotating \(p\)-orbital channels. When intermediate-state dynamics become significant, the torus develops a clear splitting. These results establish photoelectron spin textures as a complementary source of dynamical information beyond conventional momentum spectroscopy, and identify spin polarization as a robust internal degree of freedom for self-referenced attosecond metrology.

The widespread use of digital devices has raised growing concerns about its impact on sustained attention at the population level. In this work, we propose a minimal dynamical framework to describe the collective evolution of attention under continuous exposure to screen-mediated environments. We introduce a macroscopic variable representing the population-level sustained attention and model its dynamics as the result of competing mechanisms: intrinsic cognitive recovery and degradation induced by digital stimulation. The digital environment is treated as an external control parameter that continuously perturbs the system, leading to a relaxational dynamics. The proposed mechanisms are consistent with empirical findings on attentional dynamics under digital exposure. We first analyze a linear formulation, which provides an analytically tractable baseline, and then extend the model by incorporating a nonlinear degradation term that captures amplification effects under high-intensity stimulation. We derive an explicit expression for the stationary state and show that the equilibrium attention level decreases monotonically with increasing exposure. An effective potential formulation is introduced, revealing that digital overstimulation progressively deforms the dynamical landscape, shifting the stable state toward regimes of reduced attention without generating multiple equilibria. Importantly, the model does not rely on social contagion or interaction-driven bistability, but instead describes a continuous displacement of the collective cognitive regime under environmental pressure. Our results suggest that the impact of digital technologies on attention may be understood as a gradual macroscopic effect emerging from persistent external stimulation, rather than as a transition between competing behavioral states.

Neural communication operates on both fast synaptic transmission and slower, diffusive extrasynaptic signaling, yet how these two modes jointly organize brain function remains unclear. Here, using the complete synaptic and neuropeptidergic connectomes of Caenorhabditis elegans, we develop a unified multiplex framework linking anatomical wiring to functional communication. We infer structure-derived functional connectivity from the synaptic connectome using equilibrium principles from statistical physics, yielding a probabilistic map of information flow across all synaptic pathways, and compare this functional layer directly with the extrasynaptic connectome. This reveals a principled functional specialization across four communication regimes: (i) a topology-dependent layer that reinforces and stabilizes synaptic motor circuits, (ii) a topology-resilient modulatory layer supporting global regulation and behavioral state control, (iii) a purely extrasynaptic network sustaining survival and homeostasis, and (iv) a purely synaptic regime mediating rapid, low-latency sensorimotor processing. Together, these findings reveal that synaptic and extrasynaptic signaling form complementary architectures optimized for speed, modulation, robustness, and survival, and provide a general strategy for integrating structural and modulatory connectomes to understand how distinct communication modes cooperate to sustain coherent brain function.

Auxiliary Field Quantum Monte Carlo (AFQMC) has emerged as a powerful framework for treating strongly correlated electronic systems, offering a favorable balance between computational cost and accuracy. In this paper, we present a novel AFQMC method that uses the isometric tensor hypercontraction (ITHC) technique to diagonalize the two-body Coulomb interaction of molecular electronic Hamiltonians by introducing additional fictitious fermionic modes. Our method shows reduced theoretical complexity and better practical performance for both propagation and local energy evaluation compared to the standard AFQMC method. We demonstrate the efficacy of this approach by computing the ground-state energies of a linear $\ce{H10}$-chain and the benzene molecule. Our results show that the extended-basis AFQMC recovers many-body correlations with a precision comparable to that of high-level wavefunction methods such as Coupled Clusters (CC) or Density Matrix Renormalization Group (DMRG), while offering significantly improved scaling.

Introduction: Terbium-149 ($^{149}$Tb) is a promising radionuclide for targeted $\alpha$ therapy that has a non-zero branching ratio (BR) for positron decay. However, its relatively low positron branching fraction and multiple prompt $\gamma$ emissions may challenge quantitative imaging. This study evaluates, for the first time, the imaging performance and quantitative accuracy of $^{149}$Tb using a clinical long axial field-of-view (LAFOV) PET/CT system. Methods: Quantitative accuracy of $^{149}$Tb was assessed with a NEMA IEC body phantom, which was filled with about 45 MBq $^{149}$Tb and a sphere-to-background ration of 10:1. The phantom was scanned for 20 min and shorter scan times and lower activities were simulated. Recovery coefficients, coefficient of variation, and lung residual error were evaluated for different reconstruction settings and compared to the EARL standard 2 for $^{18}$F. Results: High-quality PET images of $^{149}$Tb were obtained, even with a simulated total activity of 4.5 MBq. The 20 min and full activity scan yielded a mean recovery coefficient $RC_\textit{mean}$ of $0.55$, $0.69$, $0.73$, $0.76$, $0.79$, and $0.81$ for the six phantom spheres. Despite the low count statistics, the coefficient of variation stays mostly below $15\,\%$. Relative scatter correction combined with prompt $\gamma$ modeling provided robust quantification. Conclusion: $^{149}$Tb can be imaged using a commercial LAFOV PET/CT with a quantitative accuracy comparable to the EARL standard 2 for $^{18}$F. These findings demonstrate the feasibility of PET-based treatment verification and dosimetry for targeted $\alpha$ therapy with $^{149}$Tb.

I take a pragmatist perspective on quantum theory. This is not a view of the world described by quantum theory. In this view quantum theory itself does not describe the physical world, nor our observatons, experiences or opinions of it. Instead, the theory offers reliable advice on when to expect an event of one kind or another, and on how strongly to expect each possible outcome of that event. The actual outcome is a perspectival fact: a fact relative to a physical context of assessment. Measurement outcomes and quantum states are both perspectival. By noticing that each must be relativized to an appropriate physical context one can resolve the measurement problem and the problem of nonlocal action. But if the outcome of a quantum measurement is not an absolute fact, then why shoud the statistics of such outcomes give us any objective reason to accept quantum theory? One can describe extensions of the scenario of Wigner's friend in which a statement expressing the outcome of a quantum measurement would be true relative to one such context but not relative to another. However, physical conditions in our world prevent us from realizing such scenarios. Since the outcome of every actual quantum measurement is certified at what is essentially a single context of assessment, the outcome relative to that context is an objective fact in the only sense that matters for science. We should accept quantum theory because the statistics these outcomes display are just those it leads us to expect.

We investigate the role of stochastic resetting in non-Markovian systems, where memory effects arise due to slow relaxation, rugged energy landscapes, disordered environments, and molecular crowding. Using the celebrated continuous-time random walk (CTRW) framework, we analyze first-passage processes with multiple competing outcomes and examine how resetting can selectively enhance desired events. We characterize the efficiency of resetting through conditional mean first-passage times (MFPTs) and demonstrate that its impact is highly sensitive to the underlying waiting-time statistics. Furthermore, we derive an inequality that quantifies how resetting controls fluctuations in conditional first-passage times (FPTs), revealing regimes where variability is significantly suppressed. Our results provide a systematic understanding of how long-term memory influences competitive first-passage outcomes and establish resetting as a powerful control mechanism beyond the conventional Markovian setting.

We present a large-scale experimental study of quantum-computing-based molecular simulation carried out on IQM's Sirius 24-qubit superconducting processor, utilizing up to 16 operational qubits. The work employs Sample-based Quantum Diagonalization (SQD) together with the Local Unitary Cluster Jastrow (LUCJ) ansatz to estimate ground-state energies for a set of benchmark molecules, including H$_2$, LiH, BeH$_2$, H$_2$O, and NH$_3$. In addition, we introduce a Linear-CNOT variant of the Unitary Coupled-Cluster Singles and Doubles (LCNot-UCCSD) ansatz within the SQD workflow, trading higher circuit depth for reduced classical preprocessing. A comparison between these ansätze is provided, clarifying their respective strengths, limitations, and suitability for near-term quantum hardware. We further explore potential energy landscapes through 1D scans for H$_2$ and HeH$^+$ using both STO-3G and 6-31G basis sets, and for LiH and BeH$_2$ in STO-3G. Extending beyond this, we demonstrate the experimental construction of a full 2D potential energy surface for the water molecule on quantum hardware, mapped over a 32 $\times$ 32 grid in bond length and bond angle. To move beyond small benchmark systems, we combine SQD(LUCJ) with Density Matrix Embedding Theory (DMET) to compute active-space energies for a set of ligand-like molecules, as well as the pharmacologically relevant amantadine system. Across all studies, the majority of quantum-computed energies agree with reference FCI results, as well as with DMET-CASCI energies for embedded systems, to within chemical accuracy for the chosen basis sets. These results demonstrate the reliability of sample-based diagonalization approaches and underscore the potential of hybrid embedding strategies for extending quantum simulations to increasingly complex molecular systems, while also highlighting their practicality on current IQM quantum hardware.

Urban populations exhibit fractal organization and systematic scaling regularities, yet the scaling exponents reported across cities vary substantially, challenging existing theory. Using 100~m gridded population maps for 109 urban regions in the Netherlands (2000–2023) and 368 major world cities (1975–2020), we recursively coarse-grain each city and quantify how the mean and variance of inhabitants in square grid cells of side length $\ell$ scale with $\ell$. This yields two exponents, $\beta$ from $\langle N_\ell\rangle\sim \ell^{\beta}$ and $\gamma$ from $\mathrm{Var}(N_\ell)\sim \ell^{\gamma}$, where in the small-$\ell$ limit $\beta$ equals the planar fractal dimension of populated space. Across cities within a given year, $\gamma$ depends linearly on $\beta$. Compiling $>$10,000 exponent estimates over five decades shows that this hyperscaling relation is robust yet non-universal: its slope and intercept vary across continents and drift systematically in time, trending toward the limiting form $\gamma\simeq 2+\beta$. A mean-field (independent-cell) argument predicts a quadratic mean–variance mapping and cannot reproduce the observed $\beta$–$\gamma$ dependence, implying strong spatial correlations. We derive a correlation-aware variance decomposition in which $\gamma$ is controlled by a correlation dimension $D_c$; in the correlation-dominated regime $\gamma=2+D_c$. If large maturing cities, as are the ones selected in our dataset, evolve to effective monofractal ($D_c\simeq \beta$) cities, the asymptotic prediction becomes $\gamma\simeq 2+\beta$, consistent with the observed temporal drift. This interdependence links urban geometry and fluctuations, provides an empirical constraint for mechanistic models of urban growth, and implies scaling predictions for spatial indicators built from local means and variances.

The choice between conservative and non-conservative formulations is a fundamental dilemma in CFD. While non-conservative forms offer intuitive modeling in primitive variables, they typically produce erroneous shock speeds. This paper critically analyzes these formulations, contrasting classical failures against the capabilities of Physics-Informed Neural Networks (PINNs). Using the Adaptive Weight and Viscosity (PINNs-AWV) architecture, we evaluate cases ranging from shallow water equations to unsteady 1D and 2D Euler equations. Results reveal a significant dichotomy: while PINNs-AWV restores physical fidelity in scalar and steady systems, standard non-conservative PINNs fail in unsteady systems like the Sod shock tube. We demonstrate this failure stems from non-vanishing source terms introduced by viscous regularization, which violate the Rankine–Hugoniot jump conditions. To resolve this, we implement a path-integral framework based on Dal Maso–LeFloch–Murat (DLM) theory. By incorporating path-consistent losses in PINNs (PI-PINN) and using path-conservative numerical schemes, we successfully recover correct shock speeds within non-conservative frameworks. Our results prove the path-integral approach provides a rigorous mathematical bridge for physical accuracy in both classical and machine learning solvers, enabling primitive-variable formulations in transient, high-speed simulations.

Position-dependent diffusivities are central parameters in reduced stochastic descriptions of molecular transport in heterogeneous environments, but their reliable estimation from molecular dynamics simulations remains challenging. We present a residence-time approach (RTA) that extracts local diffusivities from first-exit statistics measured in biased simulations after compensation of the mean free-energy gradient. We apply the method to oxygen diffusion across a hexadecane/water slab, water permeation across a POPC lipid bilayer, and transport of water and volatile organic compounds through a model skin-barrier membrane. In the slab system, RTA diffusivities agree with independently determined bulk reference values. In the membrane systems, propagator predictions based on RTA-derived diffusivities reproduce unbiased molecular dynamics propagators over substantial lag-time ranges, while also revealing that, in some cases, no single lag-time-independent diffusivity profile captures the dynamics across all timescales. These results support residence-time statistics as a practical route for determining effective position-dependent diffusivities from biased molecular simulations.

The structure of all the permutations of a sequence can be represented as a permutohedron, a graph where vertices are permutations and two vertices are linked if a swap of adjacent elements in the permutation of one of the vertices produces the permutation of the other vertex. It has been hypothesized that word orders in languages minimize the swap distance in the permutohedron: given a source order, word orders that are closer in the permutohedron should be less costly and thus more likely. Here we explain how to measure the degree of optimality of word order variation with respect to swap distance minimization. We illustrate the power of our novel mathematical framework by examining spontaneous gestures produced by speakers from four languages (two SVO languages and two VSO languages, which represent two linguistic families). We show that crosslinguistic gestures are at least $77\%$ optimal. It is unlikely that the multiple times where crosslinguistic gestures hit optimality are due to chance. We establish the theoretical foundations for research on the optimality of word or gesture order with respect to swap distance minimization in communication systems. Finally, we introduce the quadratic assignment problem (QAP) into language research as an umbrella for multiple optimization problems and, accordingly, postulate a general principle of optimal assignment that unifies various linguistic principles including swap distance minimization.

Thin-film lithium niobate (TFLN) has emerged as a versatile integrated photonics platform, combining strong electro-optic and nonlinear effects. Among TFLN devices, ring resonators play a central role in filtering, modulation, and nonlinear optical processes. However, intrinsic loss, which ultimately limits ring performance, is most often summarized by single-valued metrics, and its statistical variability across resonances has received limited attention. Here, we show that intrinsic loss rates in monolithic TFLN ring resonators follow a statistical distribution, comprising a baseline loss and a tail arising from discrete loss events. This behavior is revealed by characterizing 2233 resonances, using an adiabatic waveguide-ring coupling architecture that selectively excites the fundamental mode and yields clean spectra in the ultra-high-Qi regime. We find the most probable intrinsic loss rate ki = 2 pi x 10.4 MHz, indicating operation in a low-loss regime comparable to state-of-the-art thick silicon nitride platforms.

In this work, we develop a new framework for computing atom-resolved contributions to optical properties based on atoms-in-molecules (AIM) schemes. The formalism is independent of the specific AIM method and is made rigorous by partitioning momentum matrix elements into atomic contributions while exactly satisfying the relevant sum rules. Zincblende GaP provides a two-atom demonstration of the atom-resolved second-harmonic-generation (SHG) analysis using five AIM partitioning methods. The two-center Ga–P channels account for $80.6$–$82.2\%$ of the SHG response, despite the pronounced partition dependence of the atomic charges. We then apply the framework to six representative ultraviolet nonlinear-optical crystals: $\beta$-BaB$_2$O$_4$ (BBO), LiB$_3$O$_5$ (LBO), CsB$_3$O$_5$ (CBO), CsLiB$_6$O$_{10}$ (CLBO), KBe$_2$BO$_3$F$_2$ (KBBF), and LiCs$_2$PO$_4$ (LCPO). The atom-triplet decomposition shows that two-center channels dominate the principal SHG components, while on-site terms are smaller and multicenter terms provide an important secondary contribution. Although the AIM charges, detailed local percentages, and exact pathway ranks depend on the partition, the physical interpretation remains stable across the tested AIM methods. B/O-only pathways dominate the leading responses of KBBF and LBO. Mixed pathways involving B/O or P/O atoms and cations make substantial contributions to the leading responses of BBO, CBO, CLBO, and LCPO. The decomposition framework therefore establishes a quantitative connection between local response pathways and the bulk nonlinear-optical response.

The X-ray brightness delivered by fourth-generation light sources strongly depends on the electron beam current and transverse emittance. Reaching higher brilliance and lower emittances are increasingly limited by intra beam scattering, particularly at low and medium beam energies, where low emittances combined with high beam currents result in large phase-space densities. Increasing the vertical emittance through betatron coupling is commonly employed to mitigate intra beam scattering by relaxing the phase-space density. However, the redistribution of damping partition numbers due to coupling, the presence of vertical dispersion, and consequently their impact on the balance between synchrotron radiation and intra beam scattering are often neglected. In this work, we develop a self-consistent Ordinary Differential Equations-based framework to describe both the steady-state and time evolution of three-dimensional beam emittances in the simultaneous presence of synchrotron radiation, quantum excitation, betatron coupling, vertical dispersion, and intra beam scattering; allowing for realistic damping partition numbers. The model consistently accounts for the modification of synchrotron radiation damping rates and intra beam scattering growth rates arising from betatron coupling. Application to the BESSY III lattice demonstrates that damping partition redistribution and optics modifications significantly influence the equilibrium emittances. A systematic comparison of vertical emittance generation via a transverse feedback-generated excitation, betatron coupling, and vertical dispersion highlights the trade-offs between horizontal emittance reduction and operational constraints.

Protein rotational kinetics are essential for understanding macromolecular behavior in crowded environments, yet measuring these dynamics at solid-liquid interfaces remains a significant challenge due to low signal strengths. Here, we experimentally demonstrate a label-based optical technique for measuring rotational diffusion kinetics using an all-dielectric multilayer stack that sustains both transverse electric and transverse magnetic polarized surface electromagnetic waves. We introduce the concept of Fluorescence Recovery after Orientational Photobleaching, a rotational analogue to the standard translatory fluorescence recovery after photobleaching technique, which utilizes anisotropic photobleaching via resonant transverse electric excitation followed by real-time monitoring of the orientational relaxation towards isotropy. Our ratiometric analysis of the transverse electric and magnetic polarized fluorescence components allows for a distance-independent estimation of the rotational friction coefficient. Applying this method to covalently bound neutravidin, we observe a rotational friction coefficient (about 5.8E-18 J s) significantly higher than in bulk solutions, highlighting the impact of surface anchoring and molecular crowding. The proposed approach provides a robust, high-sensitivity platform for resolving biomolecular dynamics in complex interfacial environments.