Papers

High-fidelity (HF) simulations of parametric partial differential equations are expensive, whereas low-fidelity (LF) models such as coarse grids or simplified physics are cheap but biased. Multi-fidelity physics-informed neural networks combine the two, yet it remains unclear when cheap physics actually reduces the number of HF solves, and existing methods silently fail when the LF model is misleading and offer no guaranteed uncertainty. We answer the first question with a sharp sample-complexity bound: learning the HF field through its discrepancy from the LF model reduces the number of HF samples needed for accuracy $\varepsilon$ by the factor $\kappa^{2\gamma}$, where $\kappa$ is the ratio of the complexity of the discrepancy to that of the HF field and $\gamma$ is the effective-dimension exponent, and we confirm the predicted scaling with exact risk computations in a kernel model. Guided by the analysis, we propose GaMF-PINN, a gated multi-fidelity PINN that learns where to trust the LF model and falls back to physics-only learning where it does not, together with a function-level conformal procedure that returns uncertainty bands containing the entire HF solution with probability at least $1-\alpha$ in finite samples. We release MFPDE-Bench, an open benchmark of paired LF/HF solvers for four parametric PDEs with coarse-grid and simplified-physics LF models. Across MFPDE-Bench, GaMF-PINN reaches the accuracy of a standard HF-PINN with up to 8x fewer HF solves, remains robust when the LF model is deliberately corrupted, and attains the nominal coverage where Bayesian PINNs and deep ensembles under-cover.

Deep, high-resolution imaging is essential for unraveling biological complexity and advancing medical diagnostics, yet scattering fundamentally limits optical methods. Among the most promising approaches, photoacoustic imaging achieves penetration into deep tissue but with coarse resolution, while fluorescence provides subcellular detail but is confined to shallow depths. This depth-resolution trade-off remains a central barrier to biomedical imaging. To bridge this fundamental gap, we present a hybrid dual-modal strategy that combines the benefits of photoacoustic and fluorescence modalities. Our approach leverages hybrid opto-acoustic feedback for wavefront shaping and computational imaging through scattering media. By combining these complementary signals into a nonlinear feedback metric, we achieve robust optical focusing even under signal degradation. In particular, we show that photoacoustic-guided wavefront shaping inherently generates fluorescence that can be harvested for computational high-resolution imaging even within highly scattering biological tissues, thereby leveraging the complementary strengths of both modalities in a single framework. Proof-of-concept experiments demonstrate this synergistic approach, paving the way for optical imaging techniques that fully leverage the potential of such dual-modalities for large depth penetration and high resolution in complex biological tissues.

Viscoelastic rate-type fluids represent a popular class of non-Newtonian fluid models due to their ability to describe phenomena such as stress relaxation, non-linear creep, and normal stress differences. The presence of normal stress differences in a simple shear flow gives rise to forces acting in directions orthogonal to the primary flow direction. The rod climbing effect, i.e. the rise of a fluid along a rod rotating about its axis, is associated with this phenomenon. Within the class of viscoelastic rate-type fluids that includes the Oldroyd-B and Giesekus models with Gordon–Schowalter convected derivatives, we show – by means of thermodynamical analysis and numerical simulations – that a thermodynamically consistent variant of the Johnson–Segalman model captures experimental data exceedingly well and is therefore superior to other models in this class, including the standard Johnson–Segalman model, which is widely used in engineering applications but is shown here to be incompatible with the second law of thermodynamics. We release a robust and computationally efficient higher-order finite-element implementation as open-source software on GitHub. The implementation is based on an arbitrary Lagrangian–Eulerian (ALE) formulation of the governing equations and is developed using the Firedrake library.

Benoit Mandelbrot's scientific legacy spans an extraordinary range of disciplines, from linguistics and fluid turbulence to cosmology and finance, suggesting the intellectual temperament of a "fox" in Isaiah Berlin's famous dichotomy of thinkers. This essay argues, however, that Mandelbrot was, at heart, a "hedgehog": a thinker unified by a single guiding principle. Across his diverse pursuits, the concept of scaling – manifested in self-similarity, power laws, fractals, and multifractals – served as the central idea that structured his work. By tracing the continuity of this scaling paradigm through his contributions to mathematics, physics, and economics, the paper reveals a coherent intellectual trajectory masked by apparent eclecticism. Mandelbrot's enduring insight in the modeling of natural and social phenomena can be understood through the lens of the geometry and statistics of scale invariance.

Magnetic fields play a central role in accretion physics around black holes, yet their physical origin within accretion flows remains an open problem. In this work, we investigate the generation and subsequent evolution of magnetic fields triggered by anisotropic radiation fields in black hole accretion discs with compact rotating inner corona. We self-consistently evolve the magnetic field using the generalized field evolution MHD equation, including advection, shear-driven induction, and Hall effects. The radiation field acts as a primary field generator, while azimuthal rotation in the magnetized plasma provides rapid amplification. We find that radiation-generated fields efficiently reach a dominant toroidal component by Keplerian rotation, leading to magnetic field strengths of order $\sim 10^{8}\,\mathrm{G}$ in the vicinity of a 10 solar mass black hole and accretion disc-corona emitting at luminosity equivalent to the Eddington unit. These magnetic fields are achieved within viscous timescales and reach or exceed local equipartition estimates based on gas pressure. When vertical outflows are included, the amplified magnetic fields are advected into the corona, magnetizing disc-launched winds and jet precursors with field strengths of similar order. Our results demonstrate that radiation is not merely a passive component of accretion flows, but provides a robust and unavoidable trigger for the generation of dynamically significant magnetic fields. Our results provide a physically grounded explanation for the origin of large-scale, structured magnetic fields in and around accretion discs. This mechanism offers a pathway for magnetizing accretion discs and their outflows without invoking externally supplied magnetic flux, with broad implications for X-ray binaries, active galactic nuclei and other transients such as gamma-ray bursts (GRBs).

Intelligent routing plays a key role in modern communication infrastructure, including data centers, computing networks, and future 6G networks. Although reinforcement learning (RL) has shown great potential for intelligent routing, its practical deployment remains constrained by high energy consumption and decision latency. Here, we propose a photonic spiking RL architecture that implements a proximal policy optimization (PPO)-based intelligent routing algorithm. The performance of the proposed approach is systematically evaluated on a software-defined network (SDN) with a fat-tree topology. The results demonstrate that, under various baseline traffic rate conditions, the PPO-based routing strategy significantly outperforms the conventional Dijkstra algorithm in several key performance metrics. Furthermore, a hardware-software collaborative framework of the spiking Actor network is realized for three typical baseline traffic rates, utilizing a photonic synapse chip based on a Mach-Zehnder interferometer (MZI) array and a photonic spiking neuron chip based on distributed feedback lasers with a saturable absorber (DFB-SAs). Experimental validation on 640 state-action pairs shows that the inference accuracy of the hardware-software collaborative framework is consistent with that of the pure algorithmic implementation. The impacts of different hidden-layer scales in the spiking Actor network and varying network size of fat-tree topology are further analyzed. The integration of photonic spiking RL with SDN-based routing establishes a novel paradigm for intelligent routing optimization, featuring ultra-low latency and high energy efficiency. This approach exhibits broad application prospects in real-time network optimization scenarios, including large-scale data centers, computing networks, satellite Internet systems, and future 6G networks.

Reinforcement learning (RL) is a core technology enabling the transition of artificial intelligence (AI) from perception to decision-making, but its deployment on conventional electronic hardware suffers from high latency and energy consumption imposed by the von Neumann architecture. Here, we propose a photonic spiking twin delayed deep deterministic policy gradient (TD3) reinforcement learning architecture for neuromorphic autonomous navigation and experimentally validate it on a distributed feedback laser with a saturable absorber (DFB-SA) array. The hybrid architecture integrates a photonic spiking Actor network with dual continuous-valued Critic networks, where the final nonlinear spiking activation layer of the Actor is deployed on the DFB-SA laser array. In autonomous navigation tasks, the system achieves an average reward of 58.22 plus-minus 17.29 and a success rate of 80% plus-minus 8.3%. Hardware-software co-inference demonstrates an estimated energy consumption of 0.78 nJ/inf and an ultra-low latency of 191.20 ps/inf, with co-inference error rates of 0.051% and 0.059% in task scenarios with and without obstacle interference, respectively. Simulations for error-activated channels show full agreement with the expected responses, validating the dynamic characteristics of the DFB-SA laser. The architecture shows strong potential for integration with large-scale photonic linear computing chips, enabling fully-functional photonic computation and low-power, low-latency neuromorphic autonomous navigation.

We present a new inverse-time formulation of vortex stretching in the Navier-Stokes equations, based on a PDE framework inspired by score-based diffusion models. By absorbing the ill-posed backward Laplacian arising from time reversal into a drift term expressed through a score function, the inverse-time dynamics are formulated in a Lagrangian manner. Using a discrete Lagrangian flow of an axisymmetric vortex-stretching field, the score function is learned with a neural network and employed to construct backward-time particle trajectories. Numerical results demonstrate that information about initial positions is rapidly lost in the compressive direction, whereas it is relatively well preserved in the stretching direction.

We investigate the role of feature superposition in the emergence of power-law training dynamics using a teacher-student framework. We first derive an analytic theory for training without superposition, establishing that the power-law training exponent depends on both the input data statistics and channel importance. Remarkably, we discover that a superposition bottleneck induces a transition to a universal power-law exponent of $\sim 1$, independent of data and channel statistics. This one over time training with superposition represents an up to tenfold acceleration compared to the purely sequential learning that takes place in the absence of superposition. Our finding that superposition leads to rapid training with a data-independent power law exponent may have important implications for a wide range of neural networks that employ superposition, including production-scale large language models.

Why does quantum theory need the complex numbers? With a view toward answering this question, I argue that the usual Hilbert-space formalism is a special case of the general method of Markovian embeddings. I then describe the `indivisible interpretation' of quantum theory, according to which a quantum system can be regarded as an `indivisible' stochastic process unfolding in an old-fashioned configuration space, with wave functions and other exotic Hilbert-space ingredients demoted from having an ontological status. The complex numbers end up being necessary to ensure that the Hilbert-space formalism is indeed a Markovian embedding.

We provide a local probabilistic description of the limiting statistics of large preferential attachment trees in terms of the ordinary degree (number of neighbors) but augmented with information on leafdegree (number of neighbors that are leaves). The full description is the joint degree-leafdegree distribution $n_{k,\ell}$, which we derive from its associated multivariate generating function. From $n_{k,\ell}$ we obtain the leafdegree distribution, $m_{\ell}$, as well as the fraction of vertices that are protected (nonleaves with leafdegree zero) as a function of degree, $n_{k,0}$, among numerous other results. We also examine fluctuations and concentration of joint degree-leafdegree empirical counts $N_{k,\ell}$. Although our main findings pertain to the preferential attachment tree, the approach we present is highly generalizable and can characterize numerous existing models, in addition to facilitating the development of tractable new models. We further demonstrate the approach by analyzing $n_{k,\ell}$ in two other models: the random recursive tree, and a redirection-based model.

We present a combined imaginary-time/real-time time-dependent (TD) approach for evaluating linear absorption spectra of open-shell systems at the electron attachment (EA) and ionization potential (IP) equation-of-motion coupled-cluster (EOMCC) levels of theory and within the exact two-component relativistic framework. The absorption lineshape is given by the Fourier transform of the electric dipole autocorrelation function, which is obtained from a real-time simulation. Approximations of the lowest-energy EA- and IP-EOMCC eigenstates, which are required as initial states for the real-time simulation, are generated by propagating a Koopmans EA/IP state in imaginary time. TD-EA/IP-EOMCC linear absorption spectra of open-shell atomic (Na, K, Rb, F, Cl, and Br) and diatomic (SiH and ClO) systems closely reproduce those obtained from standard TD-EA/IP procedures carried out in the frequency domain. We find that the existence of low-lying states with non-negligible overlap with the Koopmans determinant impacts the length of the imaginary-time propagation required to obtain an initial state that produces correct absolute energies and peak height intensities in spectra extracted from the subsequent real-time TD-EA/IP-EOMCC calculations.

The mid-infrared spectral window is essential for molecular fingerprinting and atmospheric sensing, yet unlocking its full potential is currently constrained by a fundamental instrumental trade-off: existing systems cannot simultaneously deliver broad bandwidth, high photon flux, and metrological frequency fidelity. Here, we resolve this bottleneck by demonstrating a metrology-grade spectroscopic system based on difference frequency generation, driven by widely tunable, near-infrared diode lasers traceable to atomic standards. Our system achieves continuous tunability across the 3-3.7 $\mu$m atmospheric window and delivers output power exceeding 45 mW with an absolute frequency accuracy of 7.2 MHz. We harness this convergence to overcome a critical barrier in integrated photonics, unambiguously identifying and eliminating hydrogen-induced absorption in silicon nitride microresonators to achieve an 88-fold reduction in optical loss. We further reveal multi-phonon absorption in the silica cladding as the fundamental limit to mid-infrared integrated photonics. Finally, we demonstrate the system's versatility through scattering-resilient LiDAR capable of penetrating optically dense fog, and dual-modality sensing that simultaneously retrieves target distance and chemical composition. By unifying the rigor of frequency metrology with the versatility of broadband sensing, this architecture establishes a new paradigm for multi-dimensional perception in complex environments.

Conventional financial strategy evaluation relies on isolated backtests in static environments. Such evaluations assess each policy independently, overlook correlations and interactions, and fail to explain why strategies ultimately persist or vanish in evolving markets. We shift to an ecological perspective, where trading strategies are modeled as adaptive agents that interact and learn within a shared market. Instead of proposing a new strategy, we present FinEvo, an ecological game formalism for studying the evolutionary dynamics of multi-agent financial strategies. At the individual level, heterogeneous ML-based traders-rule-based, deep learning, reinforcement learning, and large language model (LLM) agents-adapt using signals such as historical prices and external news. At the population level, strategy distributions evolve through three designed mechanisms-selection, innovation, and environmental perturbation-capturing the dynamic forces of real markets. Together, these two layers of adaptation link evolutionary game theory with modern learning dynamics, providing a principled environment for studying strategic behavior. Experiments with external shocks and real-world news streams show that FinEvo is both stable for reproducibility and expressive in revealing context-dependent outcomes. Strategies may dominate, collapse, or form coalitions depending on their competitors-patterns invisible to static backtests. By reframing strategy evaluation as an ecological game formalism, FinEvo provides a unified, mechanism-level protocol for analyzing robustness, adaptation, and emergent dynamics in multi-agent financial markets, and may offer a means to explore the potential impact of macroeconomic policies and financial regulations on price evolution and equilibrium.

Atomistic simulations provide valuable insights into the physical processes governing material behavior. However, their applicability is fundamentally constrained by the limited time scales accessible to brute-force simulations. This bottleneck often stems from complex energy landscapes where the systems stay trapped in metastable states for long periods of time. Yet, the long-term evolution is controlled by the transitions between the metastable states, which are rare events and difficult to observe. We present an importance sampling method designed to accelerate the time scale of Markov chain Monte Carlo (MCMC) simulations. By employing a bias potential, our approach enhances the sampling of rare transition events while preserving the relative probabilities of distinct transition pathways. The bias potential is represented by a neural network which enables the flexibility needed for high-dimensional systems. We propose a rigorous formulation to obtain the original transition rates between metastable states using transition paths obtained from the biased simulation. We further use a branching random walk (BRW) technique to enhance efficiency and to reduce variance. The proposed methodology is validated on 2-dimensional and 14-dimensional systems, demonstrating its accuracy and scalability.

In this work, we derive a new model for immiscible two-layer gas-liquid stratified flows in pipes with general cross sections. The bottom layer is occupied by an incompressible fluid in liquid phase with hydrodynamics based on a hydrostatic pressure, following a shallow water approximation. The top layer is occupied by a compressible gas, following an ideal gas law leading to conservation of mass, momentum and energy. The two subsystems are linked through non-conservative products, representing momentum and energy exchanges between layers. The hyperbolic properties of the resulting model are analyzed, including the derivation of entropy inequalities, and the approximations of eigenvalues of the corresponding coefficient matrix. Numerical tests are included to demonstrate the merits of the model and the numerical approximations, including well-balancedness, Riemann problems, and perturbations and convergence toward steady states at rest. Besides simulations of water and air where the density difference between layers is significant, a case where such difference is not so pronounced (like gas and liquid hydrogen) is also shown.

This work provides a comprehensive theoretical framework for understanding the symmetry properties of High-Resolution NMR spectra. We analyze the conditions under which a spectrum exhibits mirror symmetry (palindromicity). We demonstrate that such symmetry can arise from two distinct mechanisms: (1) the direct geometric bisymmetry of the Hamiltonian matrix in a generalized canonical basis (typical for balanced systems like $A_nB_n$ or $A_nX_n$), and (2) a more fundamental property of topological isospectrality (similarity) under parameter exchange induced by the internal symmetry of the spin system, which applies even when the matrix lacks geometric symmetry (as observed in $AA'BB'$ systems).

The derivation of the equations of motion for nonholonomic systems remains a central issue in analytical mechanics, primarily due to the tension between the d'Alembert-Lagrange differential principle and integral variational approaches. This study investigates the validity of the commutation relation between the variational operator and the time derivative, which is a geometric identity in holonomic manifolds but becomes problematic when dealing with velocity-dependent constraints. By analyzing the transposition rule, we define a formal relationship between the Chetaev variation and the total variation of the constraints. We show that the simultaneous requirement of kinematically admissible variations and the fulfillment of the Chetaev condition is generally incompatible with the standard commutation rule, unless a specific geometric condition - encoded through a skew-symmetric algebraic structure and the Lagrangian derivative of the constraints - is satisfied. Furthermore, this work extends the analysis to systems with multiple constraints introducing the concept of dynamic compensation. While Frobenius' Theorem provides a static criterion for integrability based on individual vector fields, our results suggest that dynamic consistency according to Chetaev's principle emerges as a collective phenomenon. We demonstrate that even when individual constraints are intrinsically non-integrable, their interactions can cancel out deviations from holonomy, maintaining global consistency. Notably, we show that for systems with high constraints this property is satisfied regardless of the constraints' form. These findings broaden the class of analyzable physical systems, suggesting that dynamic consistency is a resilient property that persists even in the absence of simple geometric integrability.

I present the results from a spatial model of the prisoner's dilemma, played on a toroidal lattice. Each individual has a default strategy of either cooperating ($C$) or defecting ($D$). Two strategies were tested, including “tit-for-tat” (TFT), in which individuals play their opponent's last play, or simply playing their default play. Each individual also has a probability of telling the truth ($0 \leq P_{truth} \leq 1$) about their last play. This parameter, which can evolve over time, allows individuals to be, for instance, a defector but present as a cooperator regarding their last play. This leads to interesting dynamics where mixed populations of defectors and cooperators with $P_{truth} \geq 0.75$ move toward populations of truth-telling cooperators. Likewise, mixed populations with $P_{truth} < 0.7$ become populations of lying defectors. Both such populations are stable because they each have higher average scores than populations with intermediate values of $P_{truth}$. Applications of this model are discussed with regards to both humans and animals.

Recently, numerical examples of stable soap bubble clusters with multiple torus bubbles have been presented. The geometry of these clusters is based on the Platonic solids whose vertices have valence $3$ (in order to fulfill Plateau's laws): the tetrahedron, the cube, the dodecahedron. The clusters respectively contain a bubble of genus $3, 5, 11$. The construction is quite generic and can be used with any convex polyhedron. If stable, the cluster obtained using a polyhedron with $n$ faces has $3n+2$ bubbles and one of these bubbles has genus $n-1$. We propose here to show that is it possible to get stable soap bubble clusters with multiple torus bubbles using a geometry based on prisms and Archimedean solids as well.

On-chip integration of 2D materials provides a promising route towards next-generation integrated optical devices with performance beyond existing limits. Here, significantly enhanced spectral broadening induced by self-phase modulation (SPM) is experimentally demonstrated in silicon nitride (Si3N4) waveguides integrated with 2D monolayer molybdenum disulfide (MoS2) films. Monolayer MoS2 films with ultrahigh optical nonlinearity are synthesized via low-pressure chemical vapor deposition (LPCVD) and subsequently transferred onto Si3N4 waveguides, with precise control of the film coating length and placement achieved by selectively opening windows on the chip silica upper cladding. Detailed SPM measurements at telecom wavelengths are performed using fabricated waveguides with various MoS2 film coating lengths. Compared to devices without MoS2, increased spectral broadening of sub-picosecond optical pulses is observed for the hybrid devices, achieving a broadening factor of up to ~ 2.4 for a device with a 1.4-mm-long MoS2 film. Theoretical fitting of the experimental results further reveals an increase of up to ~27 fold in the nonlinear parameter ({\gamma}) for the hybrid MoS2 / Si3N4 waveguides and an equivalent Kerr coefficient (n2) of MoS2 nearly 5 orders of magnitude higher than Si3N4. These results confirm the effectiveness of on-chip integration of 2D MoS2 films to enhance the nonlinear optical performance of integrated photonic devices.

People learn about opportunities and actions by observing the experiences of their friends. We model how homophily – the tendency to associate with similar others – affects both the endogenous quality and diversity of the information accessible to decision makers. Homophily provides higher-quality information, since observing the payoffs of another person is more informative the more similar that person is to the decision maker. However, homophily can lead people to take actions that generate less information. We show how network connectivity influences the tradeoff between the endogenous quantity and quality of information. Although homophily hampers learning in sparse networks, it enhances learning in sufficiently dense networks.

In this paper, we demonstrate the ultra-high-power handling capability and DC bias stability of optical microring and electro-optic (EO) coupling resonators on the thin-film lithium tantalate (TFLT) platform. We show that, with annealing, oxide-cladded TFLT resonators can handle several watts (4W) of circulating power with minimal frequency shift and no observable photo-refractive effect. Furthermore, we demonstrate a compact 2mm coupling modulator achieving a low Vpi of 3V with stable bias and phase control in the telecom C-band.

In soil physics, saturated hydraulic conductivity, K_sat, is among the most important hydraulic properties with broad applications to modeling flow and transport under saturated conditions. Its accurate estimation, however, is challenging and requires precise characterization of pore space. In this study, we applied concepts of critical path analysis (CPA) to estimate K_sat from soil water retention curve. To evaluate the CPA, we used 313 undisturbed soil samples from the Kansas Mesonet database in which the value of K_sat spans over five orders of magnitude in variation. We found that the CPA estimated K_sat reasonably well with root mean square log-transformed error RMSLE = 0.87. For most samples, the predicted values were around the 1:1 line within a factor of 10 of the measurements. We also estimated K_sat using five other methods but none was more accurate than the CPA.

While opinion dynamics models have been extensively studied as stylized models, there has been growing attention to the possibility of combining these models with empirical data. This attention seems to be driven by the many social issues that strongly depend on people's opinions (such as climate change and vaccination) and the need for empirically valid models to design related policy interventions. While different models have been combined in various ways with empirical data, standardised comparison of models against empirical data is still lacking. In this article, we test the validity of multiple opinion dynamics models–including both stylized and more realistic models. Our approach follows a "data science-like" validation procedure, where we first calibrate the model's free parameters using an initial range of years (e.g. 2010-2015), and then use data from one wave (e.g. 2016) to predict data in the following wave (e.g. 2017). We initially tested such a procedure using simulated data and then tested different models on various topics from the European Social Survey. Both toy models and empirical models perform well on the simulated data, but fail to predict future years in the empirical data. Furthermore, during the calibration phase on the empirical data, most models learned to "freeze"–meaning that their predictions for the following year are just a copy of the data from the previous year. This work advances the literature by offering a benchmark for comparing different opinion dynamics models. Furthermore, our tests show that real-world dynamics appear to be completely incompatible with the dynamics of the tested models. This calls for more effort in exploring what are the features that would improve validity and applications for opinion dynamics models.

The nuclear electric quadrupole moment (NQM) of $^{87}$Sr has recently been revisited using high-precision relativistic atomic calculations [B. Lu et al., Phys. Rev. A 100, 012504 (2019)], indicating that the currently accepted value should be revised and that their result may serve as a new reference. In the present work, we determine the NQM of $^{87}$Sr from the molecular method, by combining the experimentally measured nuclear quadrupole coupling constants (NQCCs) of SrO and SrS with highly accurate relativistic calculations of the electric field gradient (EFG) at the Sr nucleus. Electronic correlation is treated at the CCSD(T), CCSD-T and CCSD$\tilde{\text{T}}$ levels. The iterative T contribution of the latter, composite scheme was obtained using a newly implemented parallel scheme where the distributed memory tensor library Cyclops Tensor Framework (CTF) was made available to the DIRAC code for relativistic molecular calculations through TAPP, the new community standard for tensor operations. All correlated calculations are performed using the exact two-component molecular mean-field Hamiltonian (X2C$\mathrm{mmf}$). The Gaunt two-electron interaction is incorporated, an even-tempered optimized quadruple-$\zeta$ quality basis set is employed, and vibrational corrections are accounted for. Our best result is $Q($$^{87}$Sr$) = 0.33666 \pm 0.00258$ b, which is about 10% larger than currently accepted standard value, while it is in excellent agreement with recent determinations [Y.-B. Tang, arXiv:2512.07603 [physics.atom-ph] (2025)].

Natural selection for terrestrial locomotion has yielded unifying patterns in the body shape of legged animals, often manifesting as scaling laws. One such pattern appears in the frontal aspect ratio. Smaller animals like insects typically adopt a landscape frontal aspect ratio, with a wider side-to-side base of support than center of mass height. Larger animals like elephants, however, are taller than wide with a portrait aspect ratio. Known explanations for postural scaling are restricted to animal groups with similar anatomical and behavioural motifs, but the trend in frontal aspect ratio transcends such commonalities. Here we show that vertebrates and invertebrates with diverse body plans, ranging in mass from 28 mg to 22000 kg, exhibit size-dependent scaling of the frontal aspect ratio driven by the need for lateral stability on uneven natural terrain. Because natural terrain exhibit scale-dependent unevenness, and the frontal aspect ratio is important for lateral stability during locomotion, smaller animals need a wider aspect ratio for stability. This prediction is based on the fractal property of natural terrain unevenness, requires no anatomical or behavioural parameters, and agrees with the measured scaling despite vast anatomical and behavioural differences. Furthermore, a statistical phylogenetic comparative analysis found that shared ancestry and random trait evolution cannot explain the measured scaling. Thus, our findings reveal that terrain roughness, acting through natural selection for stability, likely drove the macroevolution of frontal shape in terrestrial animals.

Canada, a Tier 1 nuclear nation involved in uranium mining and refining, operating nuclear power reactors, and with a Small Modular Reactor action plan, maintains a rigorous nuclear security infrastructure. The Nuclear Emergency Response team at Natural Resources Canada fulfills federal mandates in high-sensitivity air- and ground-based mobile survey for prevention, detection and response. A robust operational framework exists for deployment of traditional large-volume NaI(Tl)-based detection suites. At the same time, a research arm examines emerging non-nuclear technologies which can enhance the capabilities of the operational team. Herein, the potential for uncrewed mobile systems in nuclear security and emergency response operations is discussed. The impact of new technologies such as silicon photomultipliers, gamma imagers and self-shielding directional detectors is presented, and the use of high-performance computing in modelling of system response functions is discussed. Finally, a capability to extrapolate to the location of a source some distance away from a survey trajectory is shown. The extrapolation method includes propagation of the measurement error to the extrapolated region, essential information for nuclear response operators to know if a region is actually clear of radioactivity or not.

Optical resonances in nanostructures enable strong enhancement of nonlinear processes at the nanoscale, such as second-harmonic generation (SHG), with high-$Q$ modes providing intensified light–matter interactions and sharp spectral selectivity for applications in filtering, sensing, and nonlinear spectroscopy. Thanks to the recent advances in thin-film lithium niobate (TFLN) technology, these key features can be now translated to lithium niobate for realizing novel nanoscale nonlinear optical platforms. Here, we demonstrate a large-area metasurface, realized by scalable nanoimprint lithography, comprising a slanted titanium dioxide (TiO$_2$) nanograting on etchless TFLN for efficient narrowband SHG. This is enabled by the optimal coupling of quasi-bound state in the continuum (q-BIC) modes with a narrowband pulsed laser pump. The demonstrated normalized SHG efficiency is $0.15\%\,\mathrm{cm}^2/\mathrm{GW}$, which is among the largest reported for LN metasurfaces. The low pump peak intensity ($3.64~\mathrm{kW}/\mathrm{cm}^2$) employed, which enables SHG even by continuous-wave pumping, allows envisioning integrated and portable photonic applications. SHG wavelength tuning from $870$ to $920~\mathrm{nm}$ with stable output power as well as polarization control is also achieved by off-normal pump illumination. This versatile platform opens new opportunities for sensing, THz generation and detection, and ultrafast electro-optic modulation of nonlinear optical signals.

Disorder in photonic crystals and waveguides creates states inside the photonic band gap. These states are often described as Lifshitz tails despite exhibiting energy distributions inconsistent with Lifshitz statistics near the band edge. Here we show that in photonic-crystal waveguides with intentionally engineered anisotropic disorder, the band-edge tail accessible experimentally follows an Urbach law universally, with cumulative statistics $F(\Delta)=\exp[-(\Delta/\alpha)^\beta]$, where $\Delta$ is the spectral detuning from the band edge, and an exponent $\beta \approx 1$ independent of disorder strength and orientation. In contrast to Lifshitz behavior, the density of states is maximal at the band edge and decays into the gap. Crucially, we find that the Urbach energy $\alpha$ is anisotropic, with a pronounced directional splitting and qualitatively different scaling for disorder parallel and perpendicular to the waveguide axis. These conclusions are supported by quantitative agreement between optical measurements of GaAs photonic-crystal waveguides and full-vector simulations. The anisotropic Urbach energy emerges as a sensitive probe of disorder-mode coupling and a practical metric to characterize structural disorder in photonic devices.