Papers

Full-waveform inversion (FWI) requires accurate initial velocity models to avoid cycle-skipping, but constructing such models remains challenging in practice. Building on the depth-progressive diffusion framework introduced in Part~I, which relied on idealized reflectivity constraints, this work adapts the methodology to realistic exploration scenarios. We replace perfect structural information with migration-derived attributes extracted from seismic images, and introduce smooth background velocity models from tomography as additional conditioning inputs. The framework jointly leverages background/migration velocity, migrated structural information, and sparse well measurements to synthesize high-resolution velocity models through depth-progressive generation. Validation on synthetic examples demonstrates superior accuracy compared to conventional interpolation and alternative deep learning methods, with generated models successfully initializing FWI and mitigating cycle-skipping even in complex geological structures. Field data confirms practical applicability: despite training on synthetic data, the method generalizes effectively to field conditions, producing velocity models with synthetic data response that nearly match observed seismic data. As a result, this framework establishes a practical pathway to deploy generative diffusion models for velocity model building under realistic constraints.

In classical general relativity, it is well known that radially moving massless particles in the exterior region take infinite coordinate time to reach the event horizon in black hole spacetimes. In this short paper, we use two stochastic versions of ingoing radial null geodesic equation to study the stochastic radial motion of massless particles in Schwarzschild and Reissner-Nordström spacetimes. We show that the probability that a radially moving massless particle enters the black hole in finite coordinate time remains zero. This indicates the stochastic perturbations of quantum effects preserve certain properties of classical black holes.

Galaxy asymmetry is an efficient way to characterize galaxy morphology in atomic hydrogen 21 cm emission detections. We propose a novel Bayesian approach to calculate the probability of an underlying squared differences asymmetry in a noisy detection. This approach has a number of advantages, including the recovery of low asymmetry values where prior noise corrections failed. More importantly, our approach provides robust uncertainties on the asymmetry, enabling a wide variety of statistical studies of galaxy populations. This method is generalized for convolved noise measures. We validate our method using a convergence test. Finally, we show how, when applied to the untargeted HI survey WALLABY, our method nearly triples the number of reliable measurements relatively to the previous state-of-the-art technique. This Bayesian approach to measure asymmetry will therefore further unlock the statistical power of widefield galaxy surveys.

Myelin membranes are tightly connected to the axon, forming an electrical route for rapid saltatory conduction of action potentials from node to node. Beneath the myelin, adjacent to the node, lie voltage-gated potassium (K$^+$) channels, whose fundamental role in conduction remains poorly understood. Constrained by biological data, we developed a finite element model of a node of Ranvier encompassing an adaxonal membrane separating oligodendrocyte cytoplasm from the periaxonal space, and solved the full coupled set of physical equations governing electrodiffusion and voltage profiles at the nanoscale. Remarkably, we find that nodal action potentials invert at the inner adaxonal myelin membrane. The hyperpolarization-driven opening of myelinic Kir4.1 channels produces an instantaneous, powerful K$^+$ prebuffering, clamping the periaxonal K$^+$ concentration and enabling high-frequency action potential generation. Together, these findings indicate that the periaxon maintains an electrical feedback loop with the node, and suggest a key evolutionary advantage of juxtaparanodal K$^+$ channel positioning.

We present a multi-epoch Very Long Baseline Array (VLBA) survey of radio sources in the Orion Nebula Cluster (ONC), updating the detection statistics and investigating inter-epoch variability. The dataset comprises eight C-band (4-8 GHz) epochs targeting 575 radio sources previously identified in deep Very Large Array surveys. VLBA observations result in resolutions of milliarcseconds and are only sensitive to high brightness temperatures meaning only non-thermal emission is observed. We detect 226 unique radio sources corresponding to a detection fraction of 39 per cent. The majority of sources (~83 per cent) are detected only once indicating that non-thermal emission associated with Young Stellar Objects (YSOs) is highly intermittent. To quantify variability, we use per-epoch peak flux densities and the variability factor (VF) defined as the ratio between the maximum and minimum fluxes. We identify 21 sources (~9 per cent of detected sources) that exhibit high variability defined as a change of flux density by at least a factor of five. We crossmatch with the COUP Chandra survey to identify sources as YSOs. We identify COUP counterparts for ~56 per cent of the detected sources. The remaining population cannot be explained solely by variability or background contamination, suggesting a population of radio detected YSOs without X-ray counterparts. We find a clear correlation between radio and X-ray luminosities consistent with the Güdel-Benz relation, the empirical relation between non-thermal radio and thermal X-ray emission for magnetically active stars.

Driven-dissipative many-body quantum systems can be exploited in quantum enhanced sensing protocols. Here, non-classical correlations may allow one to reach a measurement precision that surpasses the standard quantum limit. The relevant figure of merit for assessing such quantum advantage is the quantum Fisher information (QFI). In a many-body setting its computation is challenging as it requires knowledge of the full system-environment state. Here we make use of a field-theoretical approach, which is particularly well suited for systems with many degrees of freedom. In particular, we exploit that the QFI can be linked to a Keldysh path-integral. This route leads to a semiclassical expression of the QFI, which is obtained through a controlled expansion in the so-called quantum fields. We benchmark the framework on three systems of increasing complexity: the driven-dissipative harmonic oscillator, the boundary time crystal - which becomes semiclassical at large system sizes - and a two-dimensional array of collectively emitting atoms. We assess in which parameter regimes the semiclassical description holds and gives access to system sizes beyond the reach of exact methods.

Seismic velocity model building (VMB) is fundamental for understanding subsurface structures. Traditional methods demand high-quality starting models and, also, remain limited in resolution in coverage and computationally intensive. Recent generative diffusion model-based approaches capture statistical priors to support traditional inversion methods, but these approaches do not account for the top to bottom progression of information (layer stripping) involved in surface recorded data, where deep velocity information depends on the shallow. To address this issue, we propose a depth-progressive diffusion framework that constructs velocity models incrementally from shallow to deep by propagating prior information. Our method trains on paired shallow-deep velocity patches with variable overlap and explicit depth encoding, integrating multiple geophysical constraints including well logs and seismic images (representing structural information). During inference, we synthesize overlapping depth slices using a progressive algorithm and merge them with Gaussian-weighted blending to eliminate boundary artifacts. This approach leverages both learned geological distributions and observed shallow priors while providing uncertainty quantification. Extensive numerical experiments on in-distribution tests and an out-of-distribution test demonstrate excellent VMB accuracy with a strong correlation between predicted uncertainty and actual errors. As a proof of concept, this part I employs idealized structural constraints derived from vertical reflectivity to validate the methodological framework. The companion paper (Part II) extends the approach to realistic structural constraints relying on migrated images with field data applications.

Strong-to-weak spontaneous symmetry breaking (SWSSB) can occur in a maximally mixed charge sector even when ordinary charged correlations vanish. We study this order when a charge sector splits into dynamically disconnected fragments. In a one-dimensional $t$-$J_z$ chain with species-resolved dephasing, each fragment is labeled by a conserved spin word. A charged transfer between separated finite intervals preserves that word only if the intervening spins satisfy a periodicity constraint. In the full-state two-point sense, we use this constraint to prove the absence of long-range fidelity and Rényi-1 order in typical fixed-composition fragments, uniformly over all norm-bounded charged operators in any prescribed finite interval. A fragment with primitive spin-word period $k$ supports a $k$-particle channel with exact long-distance value $\nu^k(1-\nu)^k/k^2$, and no charged operator on fewer than $k$ sites can carry this order. A transverse exchange connects the fragments while preserving the global charges and restores the full-sector steady state at finite size. The conserved spin word therefore selects the local channels that can support mixed-state order.

We report the first measurements of two-particle transverse momentum correlations for mid-rapidity charged particles in Au+Au collisions at $\sqrt{s_{\rm NN}} =$ 3.0, 3.2, 3.5, 3.9, 4.5, 5.2 and 7.7 GeV recorded by the STAR experiment. The results are compared with previous STAR measurements from the Beam Energy Scan Phase I (BES-I) and with transport model calculations. The measured two-particle $p_{\rm T}$ correlators exhibit an approximate power-law scaling with the number of participating nucleons ($N_{\rm part}$), consistent with expectations from an independent-source scenario. This scaling is least well described at the lowest collision energy, $\sqrt{s_{\rm NN}} = 3.0$~GeV. Furthermore, a non-monotonic energy dependence of the $p_{\rm T}$ correlations is observed in central collisions, representing the first systematic observation of such behavior as a function of collision energy.

Secure multiparty computation (MPC) enables mutually distrustful parties to compute on private digital inputs. We initiate the study of spatiotemporal MPC, extending this paradigm to functionalities whose inputs additionally depend on physical facts such as the parties' locations, times, or trajectories. Such protocols must simultaneously hide spatiotemporal information and ensure its physical consistency: a malicious party should not be able to make the functionality operate on a spatiotemporal input inconsistent with its actual physical state. The main conceptual challenge is to formulate extraction of spatiotemporal information within the simulation-based security framework. We introduce arguments of spatiotemporal knowledge, following the principle "I prove, therefore I am:" rather than defining physical presence directly through a mathematical relation, we define it operationally through the ability to complete a sound spatiotemporal verification protocol. Accordingly, an extractor recovers a spatiotemporal point from a successful prover and certifies its physical validity by using the extracted prover to succeed in an auxiliary spatiotemporal verification protocol. Building on this notion, we define universally composable (UC) security for spatiotemporal MPC, capturing privacy, physical consistency, and composability. We provide constructions achieving this new MPC notion. We first construct UC-secure commit-and-prove of spatiotemporal knowledge: in the CRS model under LWE against quantum provers without pre-shared entanglement, and in the QROM against quantum provers with unbounded pre-shared entanglement. Using these protocols, we obtain UC-secure spatiotemporal MPC from semi-honest post-quantum MPC. We also extend our framework to support quantum functionalities with classical spatiotemporal input.

Young stellar systems provide key insights into the processes governing star/planet formation, often exhibiting complex and evolving photometric variability. In this paper, we present an analysis of the object around NOI 105872, observed by the Next Generation Transit Survey (NGTS) to eclipse a young ($4.1\pm0.4$ Myr) M-type star in the Orion Nebula Cluster. The system displays deep, asymmetric eclipses with a period of $\sim0.69$ days, alongside variability in morphology. We combine photometric observations spanning approximately a decade from multiple ground- and space-based facilities to investigate the nature of this system. We explore a range of physical scenarios to reproduce the eclipse profiles and their evolution. After analysis, our preferred explanation is a circumsecondary disk surrounding a companion in orbit around the M-type primary. We adopt a six-parameter disk model and fit the eclipse profiles independently to each dataset. The best-fitting solution yields a disk radius of $\sim 0.005 \mathrm{au}$ or $0.98 R_{*}$, with broadly consistent orientations across epochs, but with variations that may be attributed to disk precession or intrinsic stellar variability. Constraints from the Hill radius imply a companion mass consistent with a very low-mass stellar companion. These results establish NOI 105872 as a candidate for a circumsecondary disk system in a young stellar environment. Continued photometric monitoring and spectroscopic follow-up will be essential to confirm this interpretation. If confirmed, systems such as NOI 105872 provide valuable benchmarks for understanding disk dynamics, companion formation, and the origin of complex eclipse phenomena in young stars.

When two photonic structures of different topology are joined, an optical mode appears at their junction. Its existence depends only on this topological difference and not on the precise dimensions of either structure. Here we realize the photonic analogue of a Jackiw-Rebbi (JR) state in hexagonal boron nitride (hBN) hosting negatively charged boron vacancies, optically addressable spin defects. Two partially etched gratings, in which the order of the radiating and dark band-edge modes is reversed, are joined side by side. Angle-resolved reflectivity and photoluminescence reveal this reversal and a non-dispersive JR state at the junction. The state proves remarkably tolerant: despite fabrication errors of up to 20 nm, its wavelength lies within a 1 nm of the design, as predicted by a systematic numerical tolerance analysis. JR gratings therefore offer a robust, monolithic platform for controlling the emission of luminescent defects.

Water's anomalous properties have been hypothesized to originate from a liquid-liquid critical point in the supercooled regime, separating high- and low-density liquid states. Experimental verification remains challenging due to rapid crystallization under these conditions. A recent study reported evidence for such a transition, based primarily on a pronounced increase in the heat capacity of rapidly heated low-density amorphous ice. Here, we show that this heat capacity increase can be explained without invoking a liquid-liquid transition. By combining simulations using a machine-learning potential trained on the state-of-the-art MB-pol water model, combined with the Tool-Narayanaswamy-Moynihan (TNM) model of the glass transition, we demonstrate that the observed signal can arise instead from a dynamical effect induced by the mobilization of rotational and translational molecular degrees of freedom during ultrafast heating. We further show that our findings are fully consistent with recent electron diffraction measurements showing structural arrest of supercooled water close to our predicted glass-transition temperature. These results provide an alternative interpretation of the experimental observations and highlight the importance of nonequilibrium glassy dynamics in the interpretation of the behavior of supercooled water on ultra-short time scales.

Appell functions are a large class of multi-variable quasi-elliptic functions, which are also instances of higher depth mock modular forms. A central aspect of these functions is their non-holomorphic modular completion. Our previous work developed Appell functions for a general positive definite lattice $\Lambda$, and expressed the non-holomorphic completion in terms of the generalized error functions $M_P$, which are integrals over a $P$-dimensional hyperplane in $\Lambda\otimes \mathbb{C}$. In this sequel, we express $M_P$ as a $P$-dimensional iterated integral of variables $w_j\in \mathbb{H}$, such that the completion of the Appell function takes the form of an iterated Eichler integral of modular forms. We apply this to the case of the root lattice of the $A_N$ Lie algebra, which is of particular interest because of their appearance in partition functions of topological twisted Yang-Mills theories.

Neutrino astronomy at high energies is an emerging field but still in a state of infancy. It is barely a dozen years ago that a diffuse flux of extraterrestrial neutrinos with energies in the TeV and PeV ranges was detected and even fewer that first individual sources could be identified. A new window to the universe has been opened after four decades of efforts to realize the gigantic instruments that made that breakthrough possible. This review describes the road towards the present, reviews the actual status of the field and sketches future developments.

The inner disk of the T Tauri star HD 143006 is inclined and casts a broad shadow on a large portion of the outer disk. We use this extraordinary geometry to study the impact of stellar ultraviolet (UV) irradiation on disk chemistry, temperature, and line formation. We present new ALMA observations of this disk in CO, $^{13}$CO, C$^{18}$O, CN, HCN, HCO$^+$, CS and C$_3$H$_2$ and combine these with previously-published data to get a rich dataset, which is modeled with ProDiMo models for the illuminated and shadowed side by including an optional inclined inner disk to partially block stellar illumination of the outer disk. The observed line flux contrasts between the illuminated and the shadowed disk sides are small. We explain this by introducing “equilibrated models” which consider a slow heating/cooling relaxation of gas parcels orbiting in and out of the shadow. We fit the radial line intensity profiles of all 14 ALMA lines for both halves of the disk, the SED beyond 20$\,\mu$m, and two ALMA continuum images, with an overall reduced $\chi$ of about 2.3, in one combined model. Line intensities only increase slightly on the illuminated side because the gas warms up slowly, although fast UV photochemistry significantly reduces the observable molecular concentrations. For the lines of N$_2$H$^+$ and CS, which probe deeper layers where the gas and dust temperatures are coupled, slow UV-desorption of ices such as NH$_3$ and H$_2$S plays a crucial role. This can result in a brightening of these lines on the shadowed side. The carbon-to-oxygen ratio in the outer disk of HD 143006 is slightly greater than one ($\sim 1.05$). The disk mass is fitted to be as low as $0.0012 M_{\odot}$, but almost equally well-fitting models with a fixed disk mass of $0.021 M_\odot$ can be obtained after re-adjusting the disk shape, dust, and gas heating/cooling parameters. (abridged)

Interactions between the planetary magnetic field of a hot Jupiter and the winds within its atmosphere are moderated by the electron and ion abundances. For a solar metallicity atmosphere at pressures between 10 and $10^{-4}$ bar, the primary sources for these charged species are expected to be the potassium and sodium atoms, and models of magnetic effects in hot Jupiter atmospheres have typically assumed that charged species exist within the atmosphere in their equilibrium abundances. In this work, we investigate the thermochemical kinetics of alkali species within a hot Jupiter atmosphere, thus allowing for the thermal ionisation fraction to depart from equilibrium, and demonstrate that quenching of ions occurs between 1 and 10 mbar. This increase in ionisation fraction on the nightside and at mid-latitudes results in stronger magnetic interaction, here modelled using the magnetic drag approximation, further slowing the jet and altering the global circulation. We additionally show that while quenching occurs, large magnetic resistivities resulting from low electron abundances continue to exist on the nightside between 10 and 100 mbar, in tension with magnetohydrodynamic models that assume horizontally uniform magnetic resistivities to simplify the explicit integration of the induction equation. At lower pressures ($\sim$ 0.1 mbar) where the electrons have become horizontally homogenised, the magnetic Reynolds number approaches or exceeds unity, signalling the breakdown of the magnetic drag approximation. We thus stress that chemical kinetics represents a dynamically important component of modelling hot Jupiter atmospheres while at the same time further complicating the treatment of magnetic effects.

Active microrheology is an effective tool to determine the rheological properties of viscous, viscoelastic, or elastic materials on microscopic length scales. The positional response of an embedded probe particle to an externally applied oscillating driving force allows to indirectly characterize the properties of the surrounding media. We aim to explore the linear and nonlinear response of probe particles in a microrheological setup of planar geometry. For this purpose, we extend the computational method of fluid particle dynamics from viscous fluid-like to viscoelastic and elastic media, including nonlinear regimes. We consider a system confined by solid walls. In this case, we validate the approach by quantifying the linear response in terms of a Jeffreys model. Increasing the amplitude of the driving force, we observe distinct nonlinear effects. They include distorted stress-strain curves and a gradual net drift of probe particles initially positioned close to a wall. This drift vanishes in the viscous fluid-like and elastic solid-like limits, but is manifest for intermediate viscoelastic systems. We further address a setup of two probe particles in the absence of walls. They experience reciprocal pairwise oscillatory forcing. Here, nonlinearities in viscoelastic systems induce a net drift gradually moving the particles further apart from each other. Comparing with real setups, our implementation of the driving force is in line with experimental setups of optical tweezers or active magnetic microrheology.

In this paper we analyze the performance of photonic CZ gates based on N waveguide-coupled cavities containing two-level emitters. We derive single- and two-photon scattering matrices for one cavity using the input-output formalism of quantum optics and for N>1 cavities using the SLH formalism, allowing us to compute the CZ gate fidelity. We consider two input Gaussian wave packets that are centered on a two-photon transition of the emitter-cavity system, and find a trade-off between optimizing the single-photon and two-photon wave packet shape. While the single-photon wave packet is preserved for large emitter-cavity coupling rates, where there is little overlap with the single-photon transitions, the two-photon wave packet acquires the necessary $\pi$ phase shift for smaller coupling rates, comparable to the cavity decay rate multiplied by the number of cavities. We find that this trade-off limits the CZ gate fidelity to approximately 60% when averaging over all input states.

Adaptive regulation can itself perturb the state it is intended to stabilize. In replicated simulations of an adaptive agent, we compare external disturbance, persistent internally generated disturbance, and control-generated disturbance under regulation-first and disturbance-first ordering. Persistent internal disturbance produces the largest exposure and regulatory burden within the tested parameter grid. When positive controller updates generate an immediate disturbance cost, increasing that cost produces a nonmonotonic response: effective disturbance initially rises, variability across stochastic runs increases over an intermediate range, and corrective activity becomes strongly suppressed at higher costs. The results show how disturbance source and timing shape exposure and controller burden in this model. They motivate testing adaptive agents with distinct disturbance sources and assessing regulatory activity alongside exposure.

We consider a dilatonic dyon black hole solution with a gravitational radius of $2 \mu$ and two charges, $Q_1$ (electric) and $Q_2$ (magnetic), within the framework of a four-dimensional gravitational model comprising one scalar field and one 2-form. The dilaton coupling constant $\lambda$ is fixed by $\lambda^2 = \frac{3}{2}$. This solution is related to the $A_2$ Toda chain. The circular orbits of null geodesics are explored, and the fifth-order polynomial master equation governing the photon sphere radius $R_0$ is analyzed. It is shown to admit a unique solution satisfying $R_0 > 2 \mu$. The circular null geodesics are proven to be unstable. Finally, the black hole shadow is examined, yielding relations for the shadow angle and the critical impact parameter.

The induction region of a model wind farm is investigated experimentally as an adverse pressure gradient (APG) turbulent boundary layer problem, using hot-wire anemometry. An array of porous discs, with diameter $D=50$\,mm representing the farm, in multiple configurations across two turbulent boundary layers of different depths, with farm-present and farm-absent configurations compared throughout. The farm imposes a spatially developing adverse pressure gradient in the approach flow. Spanwise-averaged measurements reveal systematic farm-scale global blockage extending to at least $10D$ upstream in all cases. The farm-induced turbulence intensity increase, which reaches up to $7\%$ relative to the farm-absent reference for the shallowest boundary layer, is shown by cumulative variance decomposition to be carried predominantly by large-scale motions of the boundary layer, whilst the small-scale turbulence intensity is only weakly affected. This selective large-scale energisation is consistent with the outer-layer amplification driven by an adverse pressure gradient. The concentration of farm-induced turbulence energy at scales comparable to or larger than the rotor diameter has direct implications for turbine fatigue loading, preferentially exciting coherent rotor-scale load fluctuations at the frequencies most damaging under fatigue. The results establish a quantitative link between wind farm global blockage and APG boundary layer physics.

We construct the Super-Composite Higgs, a scenario designed to stabilize the Higgs mass and generate the flavor structure within a single dynamical framework. The basic idea is to combine supersymmetry and compositeness, where the Higgs mass is protected by supersymmetry and Yukawa couplings are generated through partial compositeness. This combination offers mutual advantages and ameliorates several drawbacks of each individual theory. The Super-Composite Higgs makes experimentally testable predictions across three different areas of fundamental physics. At the precision frontier, the electron EDM is predicted to be within reach of future experiments. At the observational cosmology frontier, measurable effects in CMB and large-scale structures are expected from an ultra-light gravitino. At the high-energy frontier, an upper bound on supersymmetric particle masses, derived from cosmological considerations, indicates that squarks should be lighter than about 10 TeV, which is within reach of the FCC-hh.

We establish the large-$n$ asymptotics of Hankel determinants for unitary random matrix ensembles possessing a higher-order edge singularity. We focus on ensembles where the equilibrium measure is supported on a single interval and the limiting eigenvalue density vanishes to order $2k+\frac{1}{2}$ for $k \in \mathbb{N}$. Notably, we explicitly evaluate the constant term in the asymptotic expansion, which involves a regularized integral of the Hamiltonian associated with the Painlevé I ($P_{\rm I}^{2k}$) hierarchy. As a by-product, we also prove the universality of the eigenvalue correlation kernel near this singular edge and derive a limiting kernel expressed through functions related to a special solution of the $P_{\rm I}^{2k}$ equation. Our method relies on the Deift-Zhou nonlinear steepest descent analysis for the Riemann-Hilbert problem of orthogonal polynomials.

The Nernst effect, which converts a heat current into a charge current in the orthogonal direction, is generally classified into the ordinary effect due to an external magnetic field applied to conductors and the anomalous effect due to static magnetization in magnetic materials. Thus, one expects that the anomalous Nernst effect disappears at the Curie temperature following the magnetization. Here, we observe the Nernst effect which rather manifests around the Curie temperature. In a series of ferromagnetic (Mn,Cr)Sb samples, the Nernst coefficients exhibit finite values even across the Curie temperatures, whereas the anomalous Hall resistivity disappears, suggesting the breakdown of the Mott relation. These surviving Nernst and vanishing Hall effects result in a peak behavior of the transverse thermoelectric conductivity around the Curie temperature, which we theoretically reproduce by introducing longitudinal fluctuations of spins without accounting for an exotic spin texture, a non-trivial electronic structure, or magnon- and phonon-drag effects. The Nernst effect driven by the longitudinal spin fluctuations reveals that not only the static magnetic order but also the spin fluctuations can be a driving force of the Nernst effect in magnetic materials, opening another way for boosting transverse thermoelectric conversion.

Mass-conserving reaction-diffusion systems with two species correspond to a seemingly simple case where pattern formation occurs under the influence of a conservation law. Here, we first revisit their linear stability behavior and point out that generically two instabilities can occur: a stationary large-scale mass-conserving (Cahn-Hilliard) instability and an instability that combines features of a stationary large-scale non-mass-conserving (Allen-Cahn) instability and a oscillatory large-scale mass-conserving (conserved-Hopf) instability. We term it an Allen-Cahn-Hopf instability. Second, we investigate the nonlinear dynamics for a specific model related to the formation of cell polarization where only a Cahn-Hilliard instability can occur, i.e., all primary bifurcations are stationary. We analyze how secondary and further bifurcations subsequently give rise to various oscillatory states. The emerging rich spectrum of spatiotemporal behavior includes several period-doubling cascades related to different forms of spatial and temporal symmetry breaking. Beside regular states, three types of low-dimensional spatiotemporal chaos occur and involve transitions like fusion and an outer crises. Our results demonstrate the importance of nonlinear interactions in the dynamics of mass-conserving reaction-diffusion systems, and show that even a simple two-species system with primary bifurcations of Cahn-Hilliard type can show complex spatiotemporal behavior.

We present an extension of the Frenkel exciton model to incorporate exchange interactions between monomers in molecular aggregates in conjunction with {a multi-reference electronic structure approach}. Our derivation, {which combines the Frenkel exciton Hamiltonian and the single-electron pair exchange approximation}, yields a non-perturbative, variational expression for the exchange coupling that naturally excludes any basis set superposition error. The method has been implemented in OpenMolcas and enables combination with multi-reference electronic structure techniques. The main objective of the present study is to assess the role of exchange in systems with strong multi-configurational character. Illustrative examples demonstrate how the inclusion of exchange at different levels of approximation can substantially alter the magnitude and sign of intermonomer couplings and thus, for instance, potentially converting the predicted classification of the aggregate from H-type to J-type. Comparison with TDDFT-based couplings highlights significant discrepancies arising from multi-reference effects, double excitations, and Rydberg transitions. Overall, this approach advances the predictive modeling of photophysical and photochemical processes in aggregates of polyacenes, carotenoids, and other systems where multi-configurational and Rydberg states are essential.

Conventional wisdom in deep learning holds that overparameterization—having more parameters $p$ than training samples $n$—is benign: larger models generalize better and, even without regularization, interpolating models generalize well, the test error following a double-descent curve. One might expect the same benign overfitting for diffusion models, whose training reduces to regression, i.e. to minimizing a quadratic score-matching loss. Yet the opposite is observed: overfitting here is catastrophic, driving the model into a memorization regime. We resolve this paradox by combining experiments on U-Nets trained on CelebA with a random-features model for which we derive closed-form learning curves. We show that with a fixed number $m$ of noise realizations per training sample, an interpolation peak does occur, but at $p\sim nm$ rather than at $p\sim n$ as in standard regression. The rise of the test loss, however, sets in much earlier, at $p\sim n$, independently of $m$. This overfitting is malign because, although the implicit regularization of training is fully at work, it drives the model toward the empirical score, which memorizes the training set, rather than toward the true score. A bias-variance decomposition pinpoints the mechanism: the bias of the score estimator starts to grow at $p\sim n$; past the peak the variance decays, as in regression, whereas the bias keeps growing and both saturate at a large value. Since diffusion models are trained with $m\gg1$, the peak is pushed to very large model sizes, and therefore sit on the rising branch that precedes it, where malign overfitting is already in play. Nevertheless, overparameterization remains beneficial when paired with regularization: in the random-features theory and in U-Net experiments, optimally regularized large models—via a ridge penalty or early stopping, respectively—outperform any unregularized models.

We analyze stationary, axisymmetric Einstein-Maxwell-dilaton theory with zero cosmological constant in the conformal Carter class, employing a generalized Ernst approach on the space of potentials. We begin by establishing a complete local correspondence between Plebański-Demiański principal coordinates and Weyl data, covering the electric, magnetic, and twist potentials as well as the 1-forms \(A\), \(B\), and \(C\). In the source-free Weyl reduction, requiring the invariant area density to be harmonic singles out the \(\Lambda=0\) sector, and the principal chiral splitting isolates both electromagnetic misalignment and the part due to acceleration. Next, we obtain the Einstein reconstruction equations for general local EMD configurations in this setting. In a physical Carter domain with an ordinary scalar, the bilinear factor \(\Om=1-\acc pq\) enforces \(C=0\) and \(B_-=0\). With fixed \(\alphao\neq0\), the scalar field equation further rules out the charged PD Coulomb-type 1-form. Lastly, assuming an exact quadratic Stäckel scalar 1-form, the conditions of exactness together with reconstruction restrict the system to a single aligned branch, but consistency with the full potential equations removes this branch for arbitrary smooth Carter structure functions. Consequently, within the quadratic Stäckel class studied here, there is no local nonconstant solution with an ordinary dilaton. This conclusion does not extend to phantom scalars, conformal factors of higher degree, or non-Stäckel 1-forms.

We demonstrate a laser-wakefield accelerator driven by a high-repetition-rate optical parametric chirped-pulse amplification (OPCPA) laser, producing stable, quasi-monoenergetic electron beams at 100 Hz. Using 70 mJ, 8.1 fs laser pulses, we obtain 47 MeV electron beams with 15 pC charge and an intrinsic energy spread below 10%. Measurements over 10,000 consecutive shots show rms fluctuations of only 1.4% in peak energy and 12% in charge, together with low pointing jitter. Principal-component analysis reveals that the beam fluctuations are described by five physically interpretable modes, dominated by slow variations below 1 Hz. Particle-in-cell simulations reproduce the measured spectrum and show that nonlinear self-focusing localizes ionization injection, resulting in the observed narrow energy distribution. The demonstrated combination of electron energy, charge, beam quality, and stability represents a significant step toward high-average-power laser-plasma accelerators.