Daily Papers

A one-parameter family of Emden-Fowler equations defined by Lampariello's parameter p which, upon using Thomas-Fermi boundary conditions, turns into a set of generalized Thomas-Fermi equations comprising the standard Thomas-Fermi equation for p=1 is studied in this paper. The entire family is shown to be non integrable by reduction to the corresponding Abel equations whose invariants do not satisfy a known integrability condition. We also discuss the equivalent dynamical system of equations for the standard Thomas-Fermi equation and perform its phase-plane analysis. The results of the latter analysis are similar for the whole class.

The Saint-Venant shallow water equations (SWE) govern depth-integrated free-surface flows arising in dam-break inundation, flood routing, tsunami runup, and estuarine tidal dynamics. Closed-form analytical solutions exist only for highly idealized Riemann configurations, making rigorously verified numerical solvers essential. This work presents amerta, an open-source Python library that solves the one-dimensional frictionless Saint-Venant system on a uniform Cartesian grid using Monotone Upstream-centered Schemes for Conservation Laws (MUSCL) reconstruction with a minmod slope limiter, the Harten-Lax-van Leer-Contact (HLLC) approximate Riemann solver, and two-stage strong-stability-preserving Runge-Kutta (SSP-RK) time integration. Numba just-in-time (JIT) compilation accelerates the performance-critical kernels. The solver is verified end-to-end against the four canonical Riemann configurations: wet-bed dam break, dry-bed dam break, double rarefaction, and double shock. A six-component post-processing pipeline quantifies space-time topology, final-time error norms with empirical quantile decomposition, self-similarity collapse onto the analytical Riemann fan, integral-norm evolution, boundary-flux-corrected mass and energy diagnostics, and phase-plane analysis against analytical wave curves. The implementation conserves discrete mass to floating-point precision, satisfies discrete entropy admissibility identically, and reproduces all four analytical wave-curve geometries to within sub-centimetre accuracy in the depth-velocity phase plane. The complete source code, analytical-solution evaluators, post-processing scripts, and Network Common Data Format (NetCDF) archives are released under the MIT license.

The use of machine learning algorithms to investigate phase transitions in physical systems is a valuable way to better understand the characteristics of these systems. Neural networks have been used to extract information of phases and phase transitions directly from many-body configurations. However, one limitation of neural networks is that they require the definition of the model architecture and parameters previous to their application, and such determination is itself a difficult problem. In this paper, we investigate for the first time the relationship between the accuracy of neural networks for information of phases and the network configuration (that comprises the architecture and hyperparameters). We formulate the phase analysis as a regression task, address the question of generating data that reflects the different states of the physical system, and evaluate the performance of neural architecture search for this task. After obtaining the optimized architectures, we further implement smart data processing and analytics by means of neuron coverage metrics, assessing the capability of these metrics to estimate phase transitions. Our results identify the neuron coverage metric as promising for detecting phase transitions in physical systems.

Sonification -- the mapping of data to non-speech audio -- offers an underexplored channel for representing complex dynamical systems. We treat El Niño-Southern Oscillation (ENSO), a canonical example of low-dimensional climate chaos, as a test case for culturally-situated sonification evaluated through complex systems diagnostics. Using parameter-mapping sonification of the Niño 3.4 sea surface temperature anomaly index (1870--2024), we encode ENSO variability into two traditional Javanese gamelan pentatonic systems (pelog and slendro) across four composition strategies, then analyze the resulting audio as trajectories in a two-dimensional acoustic phase space. Recurrence-based diagnostics, convex hull geometry, and coupling analysis reveal that the sonification pipeline preserves key dynamical signatures: alternating modes produce the highest trajectory recurrence rates, echoing ENSO's quasi-periodicity; layered polyphonic modes explore the broadest phase space regions; and the two scale families induce qualitatively distinct coupling regimes between spectral brightness and energy -- predominantly anti-phase in pelog but near-independent in slendro. Phase space trajectory analysis provides a rigorous geometric framework for comparing sonification designs within a complex systems context. Perceptual validation remains necessary; we contribute the dynamical systems methodology for evaluating such mappings.

Strategies for the generation of periodic discrete structures with identical two-point correlation are developed. Starting from a pair of root structures, which are not related by translation, phase inversion or axis reflections, child structures of arbitrary resolution (i.e., pixel or voxel numbers) and number of phases (i.e., material phases/species) can be generated by means of trivial embedding based phase extension, application of kernels and/or phase coalescence, such that the generated structures inherit the two-point-correlation equivalence. Proofs of the inheritance property are provided by means of the Discrete Fourier Transform theory. A Python 3 implementation of the results is offered by the authors through the Github repository https://github.com/DataAnalyticsEngineering/EQ2PC in order to make the provided results reproducible and useful for all interested readers. Examples for the generation of structures are demonstrated, together with applications in the homogenization theory of periodic media.

The acute phase of the Covid-19 pandemic has made apparent the need for decision support based upon accurate epidemic modeling. This process is substantially hampered by under-reporting of cases and related data incompleteness issues. In this article we adopt the Bayesian paradigm and synthesize publicly available data via a discrete-time stochastic epidemic modeling framework. The models allow for estimating the total number of infections while accounting for the endemic phase of the pandemic. We assess the prediction of the infection rate utilizing mobility information, notably the principal components of the mobility data. We evaluate variational Bayes in this context and find that Hamiltonian Monte Carlo offers a robust inference alternative for such models. We elaborate upon vector analysis of the epidemic dynamics, thus enriching the traditional tools used for decision making. In particular, we show how certain 2-dimensional plots on the phase plane may yield intuitive information regarding the speed and the type of transmission dynamics. We investigate the potential of a two-stage analysis as a consequence of cutting feedback, for inference on certain functionals of the model parameters. Finally, we show that a point mass on critical parameters is overly restrictive and investigate informative priors as a suitable alternative.

While deep learning has advanced speech enhancement (SE), effective phase modeling remains challenging, as conventional networks typically operate within a flat Euclidean feature space, which is not easy to model the underlying circular topology of the phase. To address this, we propose a manifold-aware magnitude-phase dual-stream framework that aligns the phase stream with its intrinsic circular geometry by enforcing Global Rotation Equivariance (GRE) characteristic. Specifically, we introduce a Magnitude-Phase Interactive Convolutional Module (MPICM) for modulus-based information exchange and a Hybrid-Attention Dual-FFN (HADF) bottleneck for unified feature fusion, both of which are designed to preserve GRE in the phase stream. Comprehensive evaluations are conducted across phase retrieval, denoising, dereverberation, and bandwidth extension tasks to validate the superiority of the proposed method over multiple advanced baselines. Notably, the proposed architecture reduces Phase Distance by over 20\% in the phase retrieval task and improves PESQ by more than 0.1 in zero-shot cross-corpus denoising evaluations. The overall superiority is also established in universal SE tasks involving mixed distortions. Qualitative analysis further reveals that the learned phase features exhibit distinct periodic patterns, which are consistent with the intrinsic circular nature of the phase. The source code is available at https://github.com/wangchengzhong/RENet.

Image-to-Video diffusion models leverage input images to generate visually stunning content, yet frequently produce motion that violates physical laws. We reveal a surprising finding: a 2-step generation often exhibits better physical consistency than a 50-step output from the same model. Through spectral analysis, we trace this to phase erosion during denoising; the phase degrades significantly (dropping by approx 18% from step 2 to step 50), whereas the magnitude remains relatively stable. Building on this insight, we propose PhaseLock, a training-free framework that preserves the valid motion priors from few-step inference throughout the denoising trajectory. Rather than relying on full-step inference for physical consistency, PhaseLock extracts a motion prior from just 2 steps and enforces it onto high-fidelity generation via Latent Delta Guidance. Our approach effectively mitigates phase degradation, improving physical consistency by an average of 6.2 points across diverse models while largely maintaining visual fidelity, with negligible overhead (1.06times time, 1.02times memory) and reduced reliance on expensive external guidance methods (sim5times time).

Deep learning has become an area of interest in most scientific areas, including physical sciences. Modern networks apply real-valued transformations on the data. Particularly, convolutions in convolutional neural networks discard phase information entirely. Many deterministic signals, such as seismic data or electrical signals, contain significant information in the phase of the signal. We explore complex-valued deep convolutional networks to leverage non-linear feature maps. Seismic data commonly has a lowcut filter applied, to attenuate noise from ocean waves and similar long wavelength contributions. Discarding the phase information leads to low-frequency aliasing analogous to the Nyquist-Shannon theorem for high frequencies. In non-stationary data, the phase content can stabilize training and improve the generalizability of neural networks. While it has been shown that phase content can be restored in deep neural networks, we show how including phase information in feature maps improves both training and inference from deterministic physical data. Furthermore, we show that the reduction of parameters in a complex network outperforms larger real-valued networks.

We consider the solvable neural scaling model with three parameters: data complexity, target complexity, and model-parameter-count. We use this neural scaling model to derive new predictions about the compute-limited, infinite-data scaling law regime. To train the neural scaling model, we run one-pass stochastic gradient descent on a mean-squared loss. We derive a representation of the loss curves which holds over all iteration counts and improves in accuracy as the model parameter count grows. We then analyze the compute-optimal model-parameter-count, and identify 4 phases (+3 subphases) in the data-complexity/target-complexity phase-plane. The phase boundaries are determined by the relative importance of model capacity, optimizer noise, and embedding of the features. We furthermore derive, with mathematical proof and extensive numerical evidence, the scaling-law exponents in all of these phases, in particular computing the optimal model-parameter-count as a function of floating point operation budget.

Singularity Theory is used to comprehensively investigate the bifurcations of the steady-states of the traveling wave ODEs of the cubic-quintic Ginzburg-Landau equation (CGLE). These correspond to plane waves of the PDE. In addition to the most general situation, we also derive the degeneracy conditions on the eight coefficients of the CGLE under which the equation for the steady states assumes each of the possible quartic (the quartic fold and an unnamed form), cubic (the pitchfork and the winged cusp), and quadratic (four possible cases) normal forms for singularities of codimension up to three. Since the actual governing equations are employed, all results are globally valid, and not just of local applicability. In each case, the recognition problem for the unfolded singularity is treated. The transition varieties, i.e. the hysteresis, isola, and double limit curves are presented for each normal form. For both the most general case, as well as for various combinations of coefficients relevant to the particular cases, the bifurcations curves are mapped out in the various regions of parameter space delimited by these varieties. The multiplicities and interactions of the plane wave solutions are then comprehensively deduced from the bifurcation plots in each regime, and include features such as regimes of hysteresis among co-existing states, domains featuring more than one interval of hysteresis, and isola behavior featuring dynamics unrelated to the primary solution branch in limited ranges of parameter space.

Holographic Metasurface Transceivers (HMTs) are emerging as cost-effective substitutes to large antenna arrays for beamforming in Millimeter and TeraHertz wave communication. However, to achieve desired channel gains through beamforming in HMT, phase-shifts of a large number of elements need to be appropriately set, which is challenging. Also, these optimal phase-shifts depend on the location of the receivers, which could be unknown. In this work, we develop a learning algorithm using a {\it fixed-budget multi-armed bandit framework} to beamform and maximize received signal strength at the receiver for far-field regions. Our algorithm, named \Algo exploits the parametric form of channel gains of the beams, which can be expressed in terms of two {\it phase-shifting parameters}. Even after parameterization, the problem is still challenging as phase-shifting parameters take continuous values. To overcome this, {\it\HB} works with the discrete values of phase-shifting parameters and exploits their unimodal relations with channel gains to learn the optimal values faster. We upper bound the probability of {\it\HB} incorrectly identifying the (discrete) optimal phase-shift parameters in terms of the number of pilots used in learning. We show that this probability decays exponentially with the number of pilot signals. We demonstrate that {\it\HB} outperforms state-of-the-art algorithms through extensive simulations.

Reliable clinical deployment of deep medical image models is hindered by distribution shifts across scanners, sites, and acquisition protocols. Existing domain generalization (DG) methods often focus on style or intensity diversification, but they can still leave networks dependent on domain-specific texture correlations. Inspired by evidence that Fourier phase encodes semantic structure, we introduce PhaseAT, a phase-aware adversarial training framework for medical DG. PhaseAT forms phase-perturbed training views in the Fourier domain by iteratively updating a bounded phase perturbation while keeping the amplitude spectrum unchanged, thereby stressing spatial organization under matched appearance statistics. Perturbations are applied only to the luminance channel in YCbCr color space to avoid chromatic artifacts. Additionally, a simple phase-saliency mask concentrates updates on the most influential frequencies. The model is trained with a weighted combination of losses on clean and phase-perturbed samples, supporting both single-source and multi-source DG. We validate our method on two challenging medical datasets and demonstrate that PhaseAT achieves over 20% improvement in single-source domain generalization, outperforming several state-of-the-art DG methods. The code implementation is available at: https://github.com/ahmed-sharshar/PhaseAT.

A fully differential calculation in perturbative quantum chromodynamics is presented for the production of massive photon pairs at hadron colliders. All next-to-leading order perturbative contributions from quark-antiquark, gluon-(anti)quark, and gluon-gluon subprocesses are included, as well as all-orders resummation of initial-state gluon radiation valid at next-to-next-to-leading logarithmic accuracy. The region of phase space is specified in which the calculation is most reliable. Good agreement is demonstrated with data from the Fermilab Tevatron, and predictions are made for more detailed tests with CDF and DO data. Predictions are shown for distributions of diphoton pairs produced at the energy of the Large Hadron Collider (LHC). Distributions of the diphoton pairs from the decay of a Higgs boson are contrasted with those produced from QCD processes at the LHC, showing that enhanced sensitivity to the signal can be obtained with judicious selection of events.

Music source separation in the time-frequency domain is commonly achieved by applying a soft or binary mask to the magnitude component of (complex) spectrograms. The phase component is usually not estimated, but instead copied from the mixture and applied to the magnitudes of the estimated isolated sources. While this method has several practical advantages, it imposes an upper bound on the performance of the system, where the estimated isolated sources inherently exhibit audible "phase artifacts". In this paper we address these shortcomings by directly estimating masks in the complex domain, extending recent work from the speech enhancement literature. The method is particularly well suited for multi-instrument musical source separation since residual phase artifacts are more pronounced for spectrally overlapping instrument sources, a common scenario in music. We show that complex masks result in better separation than masks that operate solely on the magnitude component.

We report an optical method of generating arbitrary polarization states by manipulating the thicknesses of a pair of uniaxial birefringent plates, the optical axes of which are set at a crossing angle of {\pi}/4. The method has the remarkable feature of being able to generate a distribution of arbitrary polarization states in a group of highly discrete spectra without spatially separating the individual spectral components. The target polarization-state distribution is obtained as an optimal solution through an exploration. Within a realistic exploration range, a sufficient number of near-optimal solutions are found. This property is also reproduced well by a concise model based on a distribution of exploration points on a Poincar\'e sphere, showing that the number of near-optimal solutions behaves according to a power law with respect to the number of spectral components of concern. As a typical example of an application, by applying this method to a set of phase-locked highly discrete spectra, we numerically demonstrate the continuous generation of a vector-like optical electric field waveform, the helicity of which is alternated within a single optical cycle in the time domain.

We present a non-perturbative framework for the quantum treatment of vibrational excitation in molecular systems driven by electric fields with arbitrary time dependence. For harmonic potentials with linear dipole coupling, the field-induced dynamics is exactly described by a displaced coherent state, whose evolution is completely determined by a complex phase-space coordinate. Closed-form expressions for this coordinate reveal a clear distinction between resonant and non-resonant regimes. The resulting vibrational populations follow a Poisson distribution determined by a dimensionless time-dependent phase-space displacement, for both resonant and non-resonant driving. Resonant driving results in an enhanced phase-space displacement, whereas finite detuning between the driving and vibrational frequencies leads to an exponential suppression of the phase-space displacement and vibrational excitation. While the approach reduces to the standard time-dependent perturbation theory in the weak-field limit, it remains valid in the strong-field regime, where perturbative treatments fail. Our results provide a transparent phase-space picture of vibrational control and enable non-perturbative state preparation in ultrafast spectroscopy.

We present 1d-qt-ideal-solver, an open-source Python library for simulating one-dimensional quantum tunneling dynamics under idealized coherent conditions. The solver implements the split-operator method with second-order Trotter-Suzuki factorization, utilizing FFT-based spectral differentiation for the kinetic operator and complex absorbing potentials to eliminate boundary reflections. Numba just-in-time compilation achieves performance comparable to compiled languages while maintaining code accessibility. We validate the implementation through two canonical test cases: rectangular barriers modeling field emission through oxide layers and Gaussian barriers approximating scanning tunneling microscopy interactions. Both simulations achieve exceptional numerical fidelity with machine-precision energy conservation over femtosecond-scale propagation. Comparative analysis employing information-theoretic measures and nonparametric hypothesis tests reveals that rectangular barriers exhibit moderately higher transmission coefficients than Gaussian barriers in the over-barrier regime, though Jensen-Shannon divergence analysis indicates modest practical differences between geometries. Phase space analysis confirms complete decoherence when averaged over spatial-temporal domains. The library name reflects its scope: idealized signifies deliberate exclusion of dissipation, environmental coupling, and many-body interactions, limiting applicability to qualitative insights and pedagogical purposes rather than quantitative experimental predictions. Distributed under the MIT License, the library provides a deployable tool for teaching quantum mechanics and preliminary exploration of tunneling dynamics.

We present AERO, a audio super-resolution model that processes speech and music signals in the spectral domain. AERO is based on an encoder-decoder architecture with U-Net like skip connections. We optimize the model using both time and frequency domain loss functions. Specifically, we consider a set of reconstruction losses together with perceptual ones in the form of adversarial and feature discriminator loss functions. To better handle phase information the proposed method operates over the complex-valued spectrogram using two separate channels. Unlike prior work which mainly considers low and high frequency concatenation for audio super-resolution, the proposed method directly predicts the full frequency range. We demonstrate high performance across a wide range of sample rates considering both speech and music. AERO outperforms the evaluated baselines considering Log-Spectral Distance, ViSQOL, and the subjective MUSHRA test. Audio samples and code are available at https://pages.cs.huji.ac.il/adiyoss-lab/aero

We present anyakrakusuma, an open-source Python library that solves the discrete static Schrödinger bridge problem, the entropically regularized counterpart of optimal transport, through a log-domain Sinkhorn--Knopp iteration and reconstructs the entropic interpolation between two empirical point clouds. The solver is paired with a diagnostic pipeline that characterizes the optimal coupling and the intermediate distributions through information-theoretic and geometric measures. We exercise the library on four idealized planar cases spanning a circle-to-circle dilation, a spiral-to-mixture fragmentation, a rigid reorientation of two moons, and a Lissajous-to-trefoil deformation. The log-domain formulation is necessary rather than merely convenient at the parameters studied, where the cost-to-regularization ratio reaches four hundred and the Gibbs kernel underflows double precision across most of its range; the iteration nonetheless attains a marginal residual of 10^{-9} and unit marginal fidelity in every case. Residual histories decay geometrically over approximately eight decades at per-iteration contraction factors between 0.966 and 0.976, which are local rates near the fixed point that lie many orders of magnitude below the worst-case Hilbert-metric bound. The covariance analysis recovers an imposed ninety-degree reorientation to within 0.07^circ, roughly forty times smaller than its uncertainty, across a masked interval of near-isotropy on which the principal axis is unobservable. The diagnostics are reported with explicit attention to the regimes in which each is well defined, including the differential entropy, which is meaningful only on the open interpolation interval. The presented cases are constructed rather than measured; quantitative application to empirical point clouds requires further study.

We present a comprehensive analysis of how two-layer neural networks learn features to solve the modular addition task. Our work provides a full mechanistic interpretation of the learned model and a theoretical explanation of its training dynamics. While prior work has identified that individual neurons learn single-frequency Fourier features and phase alignment, it does not fully explain how these features combine into a global solution. We bridge this gap by formalizing a diversification condition that emerges during training when overparametrized, consisting of two parts: phase symmetry and frequency diversification. We prove that these properties allow the network to collectively approximate a flawed indicator function on the correct logic for the modular addition task. While individual neurons produce noisy signals, the phase symmetry enables a majority-voting scheme that cancels out noise, allowing the network to robustly identify the correct sum. Furthermore, we explain the emergence of these features under random initialization via a lottery ticket mechanism. Our gradient flow analysis proves that frequencies compete within each neuron, with the "winner" determined by its initial spectral magnitude and phase alignment. From a technical standpoint, we provide a rigorous characterization of the layer-wise phase coupling dynamics and formalize the competitive landscape using the ODE comparison lemma. Finally, we use these insights to demystify grokking, characterizing it as a three-stage process involving memorization followed by two generalization phases, driven by the competition between loss minimization and weight decay.

Chirality plays an important role in many optical phenomena, and it is crucial to have efficient and accurate numerical algorithms to simulate solutions in this setting. In this paper, we discuss a High-Order Spectral method coupled to geometric regular perturbation theory, which results in just such a method. We view the chirality of the laterally periodic, constant permittivity/permeability structure as deviating from a background value, and demonstrate analyticity of the field scattered by a plane electromagnetic wave with respect to this deformation. This analyticity is not only with respect to chirality deformations of arbitrarily large real size, but also joint in the spatial variables. We also show how the High--Order Perturbation of Envelopes (HOPE) recursions, which we used to establish these results, can be implemented as a rapid, robust, and reliable numerical algorithm.

Phase-field models provide a versatile framework for simulating fracture nucleation and propagation without explicit crack tracking. Their principal computational challenge is the need to resolve a small regularization length with a sufficiently fine finite element mesh. This requirement can render uniform-mesh simulations prohibitively expensive, particularly for three-dimensional problems, problems involving distributed crack nucleation, and soft nearly incompressible materials. Adaptive mesh refinement offers a natural means of reducing this cost, but existing approaches often rely on heuristic refinement indicators, are primarily designed for problems containing pre-existing cracks, and retain increasingly large refined regions as cracks grow in size. This work presents an adaptive mesh coarsening framework along with adaptive mesh refinement for phase-field fracture. The coarsening strategy replaces the fractured region in the crack wake with a coarse crack band that preserves the essential mechanical behavior of a crack, making it necessary to have a refined mesh only in a small region near the tip of the growing crack. The method introduces a physics-based refinement indicator derived from the violation of the material strength surface, which is a necessary condition for fracture evolution. The indicator therefore robustly identifies regions where crack nucleation or propagation is imminent and can be applied across arbitrary materials, geometries, and loading conditions. The framework is implemented in parallel within FEniCSx; the supporting finite element codes are made available. Its generality and substantial computational benefit are demonstrated through benchmark problems involving crack propagation and nucleation under quasi-static and dynamic loading, for soft and hard materials, and for thermomechanical fracture.

Topical observations of the thermosphere at altitudes below 200 , km are of great benefit in advancing the understanding of the global distribution of mass, composition, and dynamical responses to geomagnetic forcing, and momentum transfer via waves. The perceived risks associated with such low altitude and short duration orbits has prohibited the launch of Discovery-class missions. Miniaturization of instruments such as mass spectrometers and advances in the nano-satellite technology, associated with relatively low cost of nano-satellite manufacturing and operation, open an avenue for performing low altitude missions. The time dependent coefficients of a second order non-homogeneous ODE which describes the motion have a double periodic shape. Hence, they will be approximated using Jacobi elliptic functions. Through a change of variables the original ODE will be converted into Hill's ODE for stability analysis using Floquet theory. We are interested in how changes in the coefficients of the ODE affect the stability of the solution. The expected result will be an allowable range of parameters for which the motion is dynamically stable. A possible extension of the application is a computational tool for the rapid evaluation of the stability of entry or re-entry vehicles in rarefied flow regimes and of satellites flying in relatively low orbits.

Synchronization in one dimension displays generic scale invariance with universal properties previously observed in surface kinetic roughening and the wider context of the Kardar-Parisi-Zhang (KPZ) universality class. This has been established for phase oscillators and also for some limit-cycle oscillators, both in the presence of columnar (quenched) disorder and of time-dependent noise, by extensive numerical simulations, and has been analytically motivated by continuum approximations in the strong oscillator coupling limit. The robustness and the precise boundaries in parameter space for such critical behavior remain unclear, however, which may preclude further developments, including the extension of these results to higher dimensions and the experimental observation of nonequilibrium criticality in synchronizing (e.g.~electronic or chemical) oscillators. We here present complete numerical phase diagrams of one-dimensional synchronization, including saturation times and values, but, most importantly, also dynamical features giving insight into the gradual emergence of synchronous dynamics, based on systems of phase oscillators with either type of randomness. In the absence of synchronization, the dynamics evolves as expected for random deposition (for time-dependent noise) or linear growth (for columnar disorder), while a crossover from Edwards-Wilkinson to Kardar-Parisi-Zhang behavior (with the corresponding type of randomness) is observed as the randomness strength, or the nonoddity of the coupling among oscillators, is increased in the synchronous region -- their combined effect being partially captured by the so-called KPZ coupling. The distortion of scaling due to phase slips near the desynchronization boundary, a feature that is likely to play a role in experimental contexts, is also discussed.

Standard diffusion corrupts data using Gaussian noise whose Fourier coefficients have random magnitudes and random phases. While effective for unconditional or text-to-image generation, corrupting phase components destroys spatial structure, making it ill-suited for tasks requiring geometric consistency, such as re-rendering, simulation enhancement, and image-to-image translation. We introduce Phase-Preserving Diffusion φ-PD, a model-agnostic reformulation of the diffusion process that preserves input phase while randomizing magnitude, enabling structure-aligned generation without architectural changes or additional parameters. We further propose Frequency-Selective Structured (FSS) noise, which provides continuous control over structural rigidity via a single frequency-cutoff parameter. φ-PD adds no inference-time cost and is compatible with any diffusion model for images or videos. Across photorealistic and stylized re-rendering, as well as sim-to-real enhancement for driving planners, φ-PD produces controllable, spatially aligned results. When applied to the CARLA simulator, φ-PD improves CARLA-to-Waymo planner performance by 50\%. The method is complementary to existing conditioning approaches and broadly applicable to image-to-image and video-to-video generation. Videos, additional examples, and code are available on our https://yuzeng-at-tri.github.io/ppd-page/{project page}.

Materials that undergo internal transformations are usually described in solid mechanics by multi-well energy functions that account for both elastic and transformational behavior. In order to separate the two effects, physicists use instead phase-field-type theories where conventional linear elastic strain is quadratically coupled to an additional field that describes the evolution of the reference state and solely accounts for nonlinearity. In this paper we propose a systematic method allowing one to split the non-convex energy into harmonic and nonharmonic parts and to convert a nonconvex mechanical problem into a partially linearized phase-field problem. The main ideas are illustrated using the simplest framework of the Peierls-Nabarro dislocation model.

Generative Adversarial Networks (GANs) are a popular formulation to train generative models for complex high dimensional data. The standard method for training GANs involves a gradient descent-ascent (GDA) procedure on a minimax optimization problem. This procedure is hard to analyze in general due to the nonlinear nature of the dynamics. We study the local dynamics of GDA for training a GAN with a kernel-based discriminator. This convergence analysis is based on a linearization of a non-linear dynamical system that describes the GDA iterations, under an isolated points model assumption from [Becker et al. 2022]. Our analysis brings out the effect of the learning rates, regularization, and the bandwidth of the kernel discriminator, on the local convergence rate of GDA. Importantly, we show phase transitions that indicate when the system converges, oscillates, or diverges. We also provide numerical simulations that verify our claims.

We consider dense, associative neural-networks trained by a teacher (i.e., with supervision) and we investigate their computational capabilities analytically, via statistical-mechanics of spin glasses, and numerically, via Monte Carlo simulations. In particular, we obtain a phase diagram summarizing their performance as a function of the control parameters such as quality and quantity of the training dataset, network storage and noise, that is valid in the limit of large network size and structureless datasets: these networks may work in a ultra-storage regime (where they can handle a huge amount of patterns, if compared with shallow neural networks) or in a ultra-detection regime (where they can perform pattern recognition at prohibitive signal-to-noise ratios, if compared with shallow neural networks). Guided by the random theory as a reference framework, we also test numerically learning, storing and retrieval capabilities shown by these networks on structured datasets as MNist and Fashion MNist. As technical remarks, from the analytic side, we implement large deviations and stability analysis within Guerra's interpolation to tackle the not-Gaussian distributions involved in the post-synaptic potentials while, from the computational counterpart, we insert Plefka approximation in the Monte Carlo scheme, to speed up the evaluation of the synaptic tensors, overall obtaining a novel and broad approach to investigate supervised learning in neural networks, beyond the shallow limit, in general.

We prove a weighted Wasserstein spectral gap for the three-dimensional primitive equations on mathscr E={uin H^1cap L^8: partial_zuin L^4} under finite-rank additive Brownian forcing that is phase-complete finite Fourier and satisfies a quantitative quadratic saturation condition. In particular, four real forcing directions suffice and this number is optimal within the phase-complete class. Consequently, the system is uniquely ergodic and exponentially mixing in the H^1 topology. The main difficulties stem from the lack of sufficiently strong moment bounds and the highly degenerate nature of the noise, placing the problem outside the direct reach of standard methods. We introduce a new quantitative stable--compact asymptotic coupling criterion that captures the delicate balance between the available control of the growth of initial perturbations and the accuracy--cost of compensating them by perturbing the noise. For the primitive equations, this leads to a quantitative infinite-dimensional Hörmander analysis requiring tracking the degree and coefficient cost of Lie-bracket polynomials with the Fourier frequency.

The prediction of phase diagrams in the search for new phases is a complex and computationally intensive task. Density functional theory provides, in many situations, the desired accuracy, but its throughput becomes prohibitively limited as the number of species involved grows, even when used with local and semi-local functionals. Here, we explore the possibility of integrating machine-learning models in the workflow for the construction of ternary convex hull diagrams. In particular, we train a set of spectral neighbour-analysis potentials (SNAPs) over readily available binary phases and we establish whether this is good enough to predict the energies of novel ternaries. Such a strategy does not require any new calculations specific for the construction of the model, but just avails of data stored in binary-phase-diagram repositories. We find that a so-constructed SNAP is capable of accurate total-energy estimates for ternary phases close to the equilibrium geometry but, in general, is not able to perform atomic relaxation. This is because during a typical relaxation path a given phase traverses regions in the parameter space poorly represented by the training set. Different metrics are then investigated to assess how an unknown structure is well described by a given SNAP model, and we find that the standard deviation of an ensemble of SNAPs provides a fast and non-specie-specific metric.

The phase evolution of gravitational waves encodes critical information about the orbital dynamics of binary systems. In this work, we test the robustness of parameterized tests against unmodeled deviations from general relativity. We demonstrate that these parameterized tests are flexible and sensitive in detecting generic deviations in the waveform using the Cutler-Vallisneri bias formalism. This universality arises from examining the inherent geometry of the waveform signal and understanding how biases manifest. We show how Bayes factors are governed by the intrinsic geometry of the waveform signal manifold when parameterized tests are used to approximate generic violations of GR. We use the singular value decomposition to propose templates that are orthogonal to parameterized tests, identifying degeneracies and enhancing the detection of potential deviations. More broadly, the geometric framework developed here clarifies -- at a fundamental level -- how subtle waveform effects (including orbital eccentricity, spin precession, waveform systematics, and instrumental glitches) can mimic one another in data, and when they are intrinsically distinguishable.

We consider dense, associative neural-networks trained with no supervision and we investigate their computational capabilities analytically, via a statistical-mechanics approach, and numerically, via Monte Carlo simulations. In particular, we obtain a phase diagram summarizing their performance as a function of the control parameters such as the quality and quantity of the training dataset and the network storage, valid in the limit of large network size and structureless datasets. Moreover, we establish a bridge between macroscopic observables standardly used in statistical mechanics and loss functions typically used in the machine learning. As technical remarks, from the analytic side, we implement large deviations and stability analysis within Guerra's interpolation to tackle the not-Gaussian distributions involved in the post-synaptic potentials while, from the computational counterpart, we insert Plefka approximation in the Monte Carlo scheme, to speed up the evaluation of the synaptic tensors, overall obtaining a novel and broad approach to investigate neural networks in general.

As the number of seismic sensors grows, it is becoming increasingly difficult for analysts to pick seismic phases manually and comprehensively, yet such efforts are fundamental to earthquake monitoring. Despite years of improvements in automatic phase picking, it is difficult to match the performance of experienced analysts. A more subtle issue is that different seismic analysts may pick phases differently, which can introduce bias into earthquake locations. We present a deep-neural-network-based arrival-time picking method called "PhaseNet" that picks the arrival times of both P and S waves. Deep neural networks have recently made rapid progress in feature learning, and with sufficient training, have achieved super-human performance in many applications. PhaseNet uses three-component seismic waveforms as input and generates probability distributions of P arrivals, S arrivals, and noise as output. We engineer PhaseNet such that peaks in probability provide accurate arrival times for both P and S waves, and have the potential to increase the number of S-wave observations dramatically over what is currently available. This will enable both improved locations and improved shear wave velocity models. PhaseNet is trained on the prodigious available data set provided by analyst-labeled P and S arrival times from the Northern California Earthquake Data Center. The dataset we use contains more than seven million waveform samples extracted from over thirty years of earthquake recordings. We demonstrate that PhaseNet achieves much higher picking accuracy and recall rate than existing methods.

The spectral smoothness properties of the low-frequency array of the Square Kilometer Array (SKA), namely SKA-Low, are an important issue for its scientific objectives to be attainable. A large array of 256 log-periodic dipole antennas, installed on top of a 42~m circular ground plane, will work as an SKA-Low station in the frequency range 50-350 MHz. In this article, the ground plane induced effects are examined in terms of antenna beam spectral characteristics, while different antenna placements are considered. Results are produced both at isolated antenna and at array level in the band 50-100 MHz, by employing an approximate method for the speeding-up of array simulations. We attempt to distinguish the ground plane effect from that of mutual coupling among antennas, which appears to be more severe at specific frequencies, using 2 figures of merit. The Discrete Fourier Transform (DFT) components of gain pattern ratios identify the fundamental spatial components of the ripple, while the Envelope Correlation Coefficient quantifies the penalty to considering an infinite ground plane.

Online surgical phase recognition (SPR) underpins context-aware operating-room systems and requires committing to a prediction at every frame from past context alone. Surgical video poses three demands that natural-video recognizers do not jointly address: procedures span tens of thousands of frames, time flows non-uniformly as long routine stretches are punctuated by brief phase-defining transitions, and the visual domain is narrow so backbone features are strongly correlated across channels. Existing recognizers either let per-frame cost grow with elapsed length, or hold cost bounded but advance state at a uniform rate with channel-independent dynamics, leaving the latter two demands unaddressed. We present SurgicalMamba, a causal SPR model built on Mamba2's structured state-space duality (SSD) that holds per-frame cost at O(d). It introduces three SSD-compatible components, each targeting one demand: a dual-path SSD block that separates long- and short-term regimes at the level of recurrent state; intensity-modulated stepping, a continuous-time time-warp that adapts the slow path's effective rate to phase-relevant information; and state regramming, a per-chunk Cayley rotation that opens cross-channel mixing in the otherwise axis-aligned SSM recurrence. The learned rotation planes inherit a phase-aligned structure without any direct supervision, offering an interpretable internal signature of surgical workflow. Across seven public SPR benchmarks, SurgicalMamba reaches state-of-the-art accuracy and phase-level Jaccard under strict online evaluation: 94.6%/82.7% on Cholec80 (+0.7 pp/+2.2 pp over the strongest prior) and 89.5%/68.9% on AutoLaparo (+1.7 pp/+2.0 pp), at 119 fps on a single GPU. Ablations isolate the contribution of each component. The code is publicly available at https://github.com/sukjuoh/Surgical-Mamba.

The energy levels of hydrogen-like atoms are obtained from the phase-space quantization, one of the pillars of the old quantum theory, by three different methods - (i) direct integration, (ii) Sommerfeld's original method, and (iii) complex integration. The difficulties come from the imposition of elliptical orbits to the electron, resulting in a variable radial component of the linear momentum. Details of the calculation, which constitute a recurrent gap in textbooks that deal with phase-space quantization, are shown in depth in an accessible fashion for students of introductory quantum mechanics courses.

The "theoretical limit of time-frequency resolution in Fourier analysis" is thought to originate in certain mathematical and/or physical limitations. This, however, is not true. The actual origin arises from the numerical (technical) method deployed to reduce computation time. In addition, there is a gap between the theoretical equation for Fourier analysis and its numerical implementation. Knowing the facts brings us practical benefits. In this case, these related to boundary conditions, and complex integrals. For example, replacing a Fourier integral with a complex integral brings a hybrid method for the Laplace and Fourier transforms, and reveals another perspective on time-frequency analysis. We present such a perspective here with a simple demonstrative analysis.

Fourier Neural Operators (FNO) learn solution operators of partial differential equations by parameterizing global convolutions in the complex Fourier domain. For real-valued PDE solutions, the complex FFT carries representational redundancy through conjugate symmetry. We introduce the Hartley Neural Operator (HNO), the exact real-valued mirror of FNO: it replaces the FFT with the purely real Discrete Hartley Transform and learns a single real multiplier per retained spectral mode, with no complex arithmetic. Because the real Hartley spectrum is not halved by conjugate symmetry, HNO retains twice as many frequency corners as FNO but one real weight where FNO carries a complex pair, so the two operators are iso-parametric at equal width and differ only in spectral basis. Our central thesis is that the best basis is a property of the operator. Self-adjoint elliptic operators (Poisson, biharmonic) have real, symmetric Green's functions that the real Hartley multiplier diagonalizes exactly, and HNO is favored there. Time-dependent operators carry phase, from oscillation in the wave equation to transport in advection, Burgers, and Navier-Stokes, which a real diagonal multiplier cannot represent, so FNO is favored there, and increasingly so with the operator's phase content, leaving the phaseless heat equation as the borderline case. Training both operators identically and benchmarking across PDE classes, initial-condition families, and boundary conditions, we find an elliptic-versus-time-dependent split that is monotone in operator phase content and matches the Green's-function theory we develop. Rather than a universal winner, our findings give a predictive rule: match the spectral basis to the symmetry of the solution operator.

We study the sparse phase retrieval problem, which seeks to recover a sparse signal from a limited set of magnitude-only measurements. In contrast to prevalent sparse phase retrieval algorithms that primarily use first-order methods, we propose an innovative second-order algorithm that employs a Newton-type method with hard thresholding. This algorithm overcomes the linear convergence limitations of first-order methods while preserving their hallmark per-iteration computational efficiency. We provide theoretical guarantees that our algorithm converges to the s-sparse ground truth signal x^{natural} in R^n (up to a global sign) at a quadratic convergence rate after at most O(log (Vertx^{natural} Vert /x_{min}^{natural})) iterations, using Omega(s^2log n) Gaussian random samples. Numerical experiments show that our algorithm achieves a significantly faster convergence rate than state-of-the-art methods.

Indirect Time of Flight LiDARs can indirectly calculate the scene's depth from the phase shift angle between transmitted and received laser signals with amplitudes modulated at a predefined frequency. Unfortunately, this method generates ambiguity in calculated depth when the phase shift angle value exceeds 2pi. Current state-of-the-art methods use raw samples generated using two distinct modulation frequencies to overcome this ambiguity problem. However, this comes at the cost of increasing laser components' stress and raising their temperature, which reduces their lifetime and increases power consumption. In our work, we study two different methods to recover the entire depth range of the LiDAR using fewer raw data sample shots from a single modulation frequency with the support of sensor's gray scale output to reduce the laser components' stress and power consumption.

In this paper, we study the problem of principal component analysis with generative modeling assumptions, adopting a general model for the observed matrix that encompasses notable special cases, including spiked matrix recovery and phase retrieval. The key assumption is that the underlying signal lies near the range of an L-Lipschitz continuous generative model with bounded k-dimensional inputs. We propose a quadratic estimator, and show that it enjoys a statistical rate of order frac{klog L{m}}, where m is the number of samples. We also provide a near-matching algorithm-independent lower bound. Moreover, we provide a variant of the classic power method, which projects the calculated data onto the range of the generative model during each iteration. We show that under suitable conditions, this method converges exponentially fast to a point achieving the above-mentioned statistical rate. We perform experiments on various image datasets for spiked matrix and phase retrieval models, and illustrate performance gains of our method to the classic power method and the truncated power method devised for sparse principal component analysis.

In this paper we revisit the classical problem of polynomial interpolation, with a slight twist; namely, polynomial evaluations are available up to a group action of the unit circle on the complex plane. It turns out that this new setting allows for a phaseless recovery of a polynomial in a polynomial time.

Gastrointestinal malignancies constitute a leading cause of cancer-related mortality worldwide, with advanced-stage prognosis remaining particularly dismal. Originating as a groundbreaking technique for early gastric cancer treatment, Endoscopic Submucosal Dissection has evolved into a versatile intervention for diverse gastrointestinal lesions. While computer-assisted systems significantly enhance procedural precision and safety in ESD, their clinical adoption faces a critical bottleneck: reliable surgical phase recognition within complex endoscopic workflows. Current state-of-the-art approaches predominantly rely on multi-stage refinement architectures that iteratively optimize temporal predictions. In this paper, we present Clinical Prior Knowledge-Constrained Diffusion (CPKD), a novel generative framework that reimagines phase recognition through denoising diffusion principles while preserving the core iterative refinement philosophy. This architecture progressively reconstructs phase sequences starting from random noise and conditioned on visual-temporal features. To better capture three domain-specific characteristics, including positional priors, boundary ambiguity, and relation dependency, we design a conditional masking strategy. Furthermore, we incorporate clinical prior knowledge into the model training to improve its ability to correct phase logical errors. Comprehensive evaluations on ESD820, Cholec80, and external multi-center demonstrate that our proposed CPKD achieves superior or comparable performance to state-of-the-art approaches, validating the effectiveness of diffusion-based generative paradigms for surgical phase recognition.

Fracture is one of the main causes of failure in engineering structures. Phase field methods coupled with adaptive mesh refinement (AMR) techniques have been widely used to model crack propagation due to their ease of implementation and scalability. However, phase field methods can still be computationally demanding making them unfeasible for high-throughput design applications. Machine learning (ML) models such as Graph Neural Networks (GNNs) have shown their ability to emulate complex dynamic problems with speed-ups orders of magnitude faster compared to high-fidelity simulators. In this work, we present a dynamic mesh-based GNN framework for emulating phase field simulations of crack propagation with AMR for different crack configurations. The developed framework - ADAPTive mesh-based graph neural network (ADAPT-GNN) - exploits the benefits of both ML methods and AMR by describing the graph representation at each time-step as the refined mesh itself. Using ADAPT-GNN, we predict the evolution of displacement fields and scalar damage field (or phase field) with high accuracy compared to conventional phase field fracture model. We also compute crack stress fields with high accuracy using the predicted displacements and phase field parameter. Finally, we observe speed up of 15-36x compared to serial execution of the phase field model.

Four-dimensional computed tomography (4DCT) captures the full respiratory cycle of thoracic anatomy, yet current Internal Target Volume contouring workflows process each phase in isolation, discarding temporal coherence and leaving contours vulnerable to phase-specific artifacts. We present a lightweight framework that applies parameter-efficient fine-tuning to the Segment Anything Model 3 (SAM 3) via low-rank adaptation (LoRA) to align its text-prompted segmentation with the medical domain using only seven annotated 3D CT volumes. Furthermore, the framework incorporates a hard negative mining strategy to improve boundary discrimination in low-contrast thoracic regions. At inference, phase-wise predictions are refined through phase-coherent temporal filtering and spatial connectivity analysis. Since respiratory motion is continuous and periodic, genuine anatomy appears in contiguous blocks of phases, whereas transient artifacts appear sporadically and are thus effectively suppressed. Experiments on pulmonary and cardiac structures yield median Dice scores of 0.968 and 0.910 with 95th-percentile Hausdorff distances of 0.998 mm and 2.931 mm, respectively. The proposed framework effectively eliminates the severe false-positive predictions inherent in the zero-shot inference of the unadapted SAM 3. With only seven annotated volumes, the framework retains over 95% of full-data accuracy, and the entire pipeline is trainable on a single consumer-grade GPU, demonstrating a scalable, data-efficient solution for adaptive radiotherapy.

Orbital angular momentum (OAM) multiplexing provides an infinite-dimensional discrete Hilbert space ideally suited for high-capacity free-space quantum key distribution (QKD). Nevertheless, pure scalar spatial modes carrying topological charge (|ell| ge 1) undergo severe decoherence when transmitted through terrestrial atmospheric turbulence. Turbulent refractive-index eddies split high-order vortex singularities, induce catastrophic intermodal crosstalk across adjacent topological channels, and rapidly drive the quantum bit error rate (QBER) well above the unconditional 11% security threshold associated with individual cloning attacks. Here, we demonstrate that hybrid polarization-OAM entangled states, known as vector vortex beams (VVBs), provide intrinsic, hardware-free immunity against turbulent perturbations. Because the optical anisotropy of terrestrial air is exceedingly small (Δn < 10^{-9}), refractive-index fluctuations couple symmetrically to orthogonal circular polarization modes as an identical common-mode scalar phase screen that cancels in the relative polarization-phase degree of freedom. By numerically propagating modal fields through modified power-spectral phase screens over turbulence strengths ranging from D/r_0 = 0 to 3.0, we show that the VVB encoding protocol suppresses the asymptotic QBER from 42.0% to 4.8%, yielding an error-suppression factor of approximately 11.6 without requiring active adaptive optics or deformable mirrors.

Intelligent robots need to interact with diverse objects across various environments. The appearance and state of objects frequently undergo complex transformations depending on the object properties, e.g., phase transitions. However, in the vision community, segmenting dynamic objects with phase transitions is overlooked. In light of this, we introduce the concept of phase in segmentation, which categorizes real-world objects based on their visual characteristics and potential morphological and appearance changes. Then, we present a new benchmark, Multi-Phase, Multi-Transition, and Multi-Scenery Video Object Segmentation (M^3-VOS), to verify the ability of models to understand object phases, which consists of 479 high-resolution videos spanning over 10 distinct everyday scenarios. It provides dense instance mask annotations that capture both object phases and their transitions. We evaluate state-of-the-art methods on M^3-VOS, yielding several key insights. Notably, current appearance-based approaches show significant room for improvement when handling objects with phase transitions. The inherent changes in disorder suggest that the predictive performance of the forward entropy-increasing process can be improved through a reverse entropy-reducing process. These findings lead us to propose ReVOS, a new plug-andplay model that improves its performance by reversal refinement. Our data and code will be publicly available at https://zixuan-chen.github.io/M-cube-VOS.github.io/.

The relationship between material properties and independent variables such as temperature, external field or time, is usually represented by a curve or surface in a multi-dimensional space. Determining such a curve or surface requires a series of experiments or calculations which are often time and cost consuming. A general strategy uses an appropriate utility function to sample the space to recommend the next optimal experiment or calculation within an active learning loop. However, knowing what the optimal sampling strategy to use to minimize the number of experiments is an outstanding problem. We compare a number of strategies based on directed exploration on several materials problems of varying complexity using a Kriging based model. These include one dimensional curves such as the fatigue life curve for 304L stainless steel and the Liquidus line of the Fe-C phase diagram, surfaces such as the Hartmann 3 function in 3D space and the fitted intermolecular potential for Ar-SH, and a four dimensional data set of experimental measurements for BaTiO3 based ceramics. We also consider the effects of experimental noise on the Hartmann 3 function. We find that directed exploration guided by maximum variance provides better performance overall, converging faster across several data sets. However, for certain problems, the trade-off methods incorporating exploitation can perform at least as well, if not better than maximum variance. Thus, we discuss how the choice of the utility function depends on the distribution of the data, the model performance and uncertainties, additive noise as well as the budget.

In recent years, the neural radiance field (NeRF) model has gained popularity due to its ability to recover complex 3D scenes. Following its success, many approaches proposed different NeRF representations in order to further improve both runtime and performance. One such example is Triplane, in which NeRF is represented using three 2D feature planes. This enables easily using existing 2D neural networks in this framework, e.g., to generate the three planes. Despite its advantage, the triplane representation lagged behind in its 3D recovery quality compared to NeRF solutions. In this work, we propose TriNeRFLet, a 2D wavelet-based multiscale triplane representation for NeRF, which closes the 3D recovery performance gap and is competitive with current state-of-the-art methods. Building upon the triplane framework, we also propose a novel super-resolution (SR) technique that combines a diffusion model with TriNeRFLet for improving NeRF resolution.

Modeling and re-rendering dynamic 3D scenes is a challenging task in 3D vision. Prior approaches build on NeRF and rely on implicit representations. This is slow since it requires many MLP evaluations, constraining real-world applications. We show that dynamic 3D scenes can be explicitly represented by six planes of learned features, leading to an elegant solution we call HexPlane. A HexPlane computes features for points in spacetime by fusing vectors extracted from each plane, which is highly efficient. Pairing a HexPlane with a tiny MLP to regress output colors and training via volume rendering gives impressive results for novel view synthesis on dynamic scenes, matching the image quality of prior work but reducing training time by more than 100times. Extensive ablations confirm our HexPlane design and show that it is robust to different feature fusion mechanisms, coordinate systems, and decoding mechanisms. HexPlane is a simple and effective solution for representing 4D volumes, and we hope they can broadly contribute to modeling spacetime for dynamic 3D scenes.

This project focuses on a method to extract a frequency comb in mechanical means, for general interest and numerous practical applications in MEMS. The method of execution is the implementation of a beam that is exhibiting non-linear dynamics that is perturbed and analyzed for its transverse vibrations. The perturbation is an external harmonic driver with a chosen small amplitude and frequency (which is slightly detuned from the beam eigenfrequency), that when engaged with the unperturbed beam oscillations, causes it reach a state of "injection pulling" - an effect that occurs when one harmonic oscillator is coupled with a second one and causes it to oscillate in a frequency near its own. This causes the beam to reach SNIC bifurcation, rendering a frequency comb as desired. Theoretical analysis showed that the problem can be modelled using a non-linear equation of the beam, that translates to a form of the non-linear Duffing equation. While a solution to the dynamics function of the beam is hard to obtain in practice due to mathematical difficulties, a slow evolution model is suggested that is composed of functions of a amplitude and phase. Using several additional mathematical assumptions, the amplitude is seen to be related to the phase, while the phase equation solution is seen to be of the form of Adler's equation. These assumptions ultimately reduce the entire behaviour of the beam to a relatively simple solution to the Adler equation, which has a known analytical solution. Computerized numerical simulations are run on it to check the results and compare them to the theory and desired outcome. The results agreed with the theory and produce the expected frequency comb, showing the assumptions to be valid in extracting the comb.

We introduce a data-driven diagnostic that combines the singular value decomposition (SVD) with an information-theoretic entropy to quantify the phase-space complexity of perturbed distribution functions in gyrokinetic turbulence. Applying this framework to nonlinear flux-tube simulations that solve the time evolution of the ion distribution function represented by Fourier modes with the wavenumber for real space, we define the von Neumann entropy (vNE) to analyze the velocity-space structure. A global survey in the wavenumber space reveals a wavenumber-dependent variation of the vNE in velocity-space structure: the vNE remains low at low wavenumber but increases across k_perpρ_{ti}sim 1. Hermite/Laguerre decompositions revealed that the finite Larmor radius (FLR) phase mixing in the perpendicular (magnetic-moment) direction is active. Simultaneously, the systematic increase in vNE for k_perpρ_{ti} correlates with the broadening of the Hermite spectrum, suggesting enhanced parallel phase mixing (Landau resonance) as the primary mechanism for the observed wave number dependence. These results demonstrate that the SVD-based vNE provides a compact measure of kinetic complexity without assuming a predefined basis and enables a global mapping of its wavenumber dependence of phase-mixing processes in gyrokinetic turbulence.

Post-merger gravitational wave echoes provide a unique opportunity to probe the near-horizon structure of astrophysical black holes, that may be modified due to non-perturbative quantum gravity phenomena. However, since the waveform is subject to large theoretical uncertainties, it is necessary to develop model-agnostic search methods for detecting echoes from observational data. A promising strategy is to identify the characteristic quasinormal modes (QNMs) associated with echoes, {\it in frequency space}, which complements existing searches of quasiperiodic pulses in time. In this study, we build upon our previous work targeting these modes by incorporating relative phase information to optimize the Bayesian search algorithm. Using a new phase-marginalized likelihood, the performance can be significantly improved for well-resolved QNMs. This enables an efficient model-agnostic search for QNMs of different shapes by using a simple search template. To demonstrate the robustness of the search algorithm, we construct four complementary benchmarks for the echo waveform that span a diverse range of different theoretical possibilities for the near-horizon structure. We then validate our Bayesian search algorithms by injecting the benchmark models into different realizations of Gaussian noise. Using two types of phase-marginalized likelihoods, we find that the search algorithm can efficiently detect the corresponding QNMs. Therefore, our search strategy provides a concrete Bayesian and model-agnostic approach to "quantum black hole seismology".

We present a continuous variable tomography scheme that reconstructs the Husimi Q-function (Wigner function) by Lagrange interpolation, using measurements of the Q-function (Wigner function) at the Padua points, the optimal sampling points for two dimensional reconstruction. Our approach drastically reduces the number of measurements required compared to using equidistant points on a regular grid, although reanalysis of such experiments is possible. The reconstruction algorithm produces a reconstructed function with exponentially decreasing error and quasi-linear runtime in the number of Padua points. Moreover, using the interpolating polynomial of the Q-function, we present a technique to directly estimate the density matrix elements of the continuous variable state, with only linear propagation of input measurement error. Furthermore, we derive a state-independent analytical bound on this error, such that our estimate of the density matrix is accompanied by a measure of its uncertainty.

Next-generation nano and quantum devices have increasingly complex 3D structure. As the dimensions of these devices shrink to the nanoscale, their performance is often governed by interface quality or precise chemical or dopant composition. Here we present the first phase-sensitive extreme ultraviolet imaging reflectometer. It combines the excellent phase stability of coherent high-harmonic sources, the unique chemical- and phase-sensitivity of extreme ultraviolet reflectometry, and state-of-the-art ptychography imaging algorithms. This tabletop microscope can non-destructively probe surface topography, layer thicknesses, and interface quality, as well as dopant concentrations and profiles. High-fidelity imaging was achieved by implementing variable-angle ptychographic imaging, by using total variation regularization to mitigate noise and artifacts in the reconstructed image, and by using a high-brightness, high-harmonic source with excellent intensity and wavefront stability. We validate our measurements through multiscale, multimodal imaging to show that this technique has unique advantages compared with other techniques based on electron and scanning-probe microscopies.

We introduce a theoretical framework for differentiable surface evolution that allows discrete topology changes through the use of topological derivatives for variational optimization of image functionals. While prior methods for inverse rendering of geometry rely on silhouette gradients for topology changes, such signals are sparse. In contrast, our theory derives topological derivatives that relate the introduction of vanishing holes and phases to changes in image intensity. As a result, we enable differentiable shape perturbations in the form of hole or phase nucleation. We validate the proposed theory with optimization of closed curves in 2D and surfaces in 3D to lend insights into limitations of current methods and enable improved applications such as image vectorization, vector-graphics generation from text prompts, single-image reconstruction of shape ambigrams and multi-view 3D reconstruction.

Recent space-borne and ground-based observations provide photometric measurements as time series. The effect of interstellar dust extinction in the near-infrared range is only 10% of that measured in the V band. However, the sensitivity of the light curve shape to the physical parameters in the near-infrared is much lower. So, interpreting these types of data sets requires new approaches like the different large-scale surveys, which create similar problems with big data. Using a selected data set, we provide a method for applying routines implemented in R to extract most information of measurements to determine physical parameters, which can also be used in automatic classification schemes and pipeline processing. We made a multivariate classification of 131 Cepheid light curves (LC) in J, H, and K colors, where all the LCs were represented in 20D parameter space in these colors separately. Performing a Principal Component Analysis (PCA), we got an orthogonal coordinate system and squared Euclidean distances between LCs, with 6 significant eigenvalues, reducing the 20-dimension to 6. We also estimated the optimal number of partitions of similar objects and found it to be equal to 7 in each color; their dependence on the period, absolute magnitude, amplitude, and metallicity are also discussed. We computed the Spearman rank correlations, showing that periods and absolute magnitudes correlate with the first three PCs significantly. The first two PC are also found to have a relationship with the amplitude, but the metallicity effects are only marginal. The method shown can be generalized and implemented in unsupervised classification schemes and analysis of mixed and biased samples. The analysis of our Classical Cepheid near-infrared LC sample showed that the J, H, K curves are insufficient for determination of stellar metallicity, with mass being the key factor shaping them.

We study the emergence of multi-step reasoning in deep Transformer language models through a geometric and statistical-physics lens. Treating the hidden-state trajectory as a flow on an implicit Riemannian manifold, we analyze the layerwise covariance spectrum of activations, where C^{(ell)}=E[h^{(ell)}h^{(ell)top}], and track deviations from a random-matrix bulk. Across model scales (1.5B--30B), we observe a sharp reduction in effective dimensionality consistent with a phase transition: an order parameter based on sparsity/localization, Ω(h)=1-|h|_1/(d|h|_2), exhibits a discontinuity near a critical normalized depth γ_capprox 0.42 in sufficiently large models. We formalize the forward pass as a discrete coarse-graining map and relate the appearance of stable "concept basins" to fixed points of this renormalization-like dynamics. The resulting low-entropy regime is characterized by a spectral tail collapse and by the formation of transient, reusable object-like structures in representation space, which we call Transient Class Objects (TCOs). We provide theoretical conditions connecting logical separability to spectral decay and validate the predicted signatures with layerwise probes on multiple open-weight model families.

Diffusion models (DMs) represent state-of-the-art generative models for continuous inputs. DMs work by constructing a Stochastic Differential Equation (SDE) in the input space (ie, position space), and using a neural network to reverse it. In this work, we introduce a novel generative modeling framework grounded in phase space dynamics, where a phase space is defined as {an augmented space encompassing both position and velocity.} Leveraging insights from Stochastic Optimal Control, we construct a path measure in the phase space that enables efficient sampling. {In contrast to DMs, our framework demonstrates the capability to generate realistic data points at an early stage of dynamics propagation.} This early prediction sets the stage for efficient data generation by leveraging additional velocity information along the trajectory. On standard image generation benchmarks, our model yields favorable performance over baselines in the regime of small Number of Function Evaluations (NFEs). Furthermore, our approach rivals the performance of diffusion models equipped with efficient sampling techniques, underscoring its potential as a new tool generative modeling.

Neural vocoders have recently advanced waveform generation, yielding natural and expressive audio. Among these approaches, iSTFT-based vocoders have recently gained attention. They predict a complex-valued spectrogram and then synthesize the waveform via iSTFT, thereby avoiding learned upsampling stages that can increase computational cost. However, current approaches use real-valued networks that process the real and imaginary parts independently. This separation limits their ability to capture the inherent structure of complex spectrograms. We present ComVo, a Complex-valued neural Vocoder whose generator and discriminator use native complex arithmetic. This enables an adversarial training framework that provides structured feedback in complex-valued representations. To guide phase transformations in a structured manner, we introduce phase quantization, which discretizes phase values and regularizes the training process. Finally, we propose a block-matrix computation scheme to improve training efficiency by reducing redundant operations. Experiments demonstrate that ComVo achieves higher synthesis quality than comparable real-valued baselines, and that its block-matrix scheme reduces training time by 25%. Audio samples and code are available at https://hs-oh-prml.github.io/ComVo/.

Vision Transformers operate on fixed patch grids, which can introduce phase-dependent instability for dense prediction: changing the patch partition can change the token evidence available to a pixel, especially near boundaries. We formalize patch-grid phase as a nuisance variable and propose Phase Marginalization, a post-hoc marginalization method that evaluates structured patch-grid phases, inverse-aligns dense outputs, and aggregates them in the original image coordinate system. The central variant, Uniform Phase Marginalization with K = 4, is training-free and improves over the canonical K = 1 baseline across measured segmentation, depth, and local matching settings. In a controlled Cityscapes experiment, Uniform Phase Marginalization provides a modest compute-matched advantage over generic shift-based four-forward test-time augmentation (TTA) (+0.31 mean Intersection-over-Union over the strongest tested generic row). A scaling study further shows that K = 4 is a practical cost-accuracy trade-off: K = 8 is essentially unchanged and K = 16 adds little accuracy at much higher latency. These results position patch-grid phase as a measurable nuisance variable and Phase Marginalization as a simple diagnostic and post-hoc marginalization baseline for dense ViT prediction.

Scaling laws predict loss from compute but not how capabilities interact. We measure the coupling between reasoning and truthfulness across 63 base models from 16 families and find a regime change invisible to loss curves: below a family-dependent critical scale N_c, capabilities anticorrelate; above it, they cooperate. N_c approx 3.5B parameters [2.9B, 13.4B] (bootstrap 95% CI), but model size is not the only variable that determines phase. Architecture, data curation, and training recipe each shift N_c independently: curated training eliminated the coupling dip between Qwen generations (0.025 to 0.830 at matched scale), Gemma-4 at 4B achieves coupling 0.871, characteristic of 13B+ standard-trained models, through distillation and architectural innovation, and Phi at 1B matches web-trained coupling at 10B through data curation alone. Width normalization eliminates the anticorrelation across all tested families, supporting an output-projection bottleneck. Internally, 38 of 40 models show zero competing attention heads. A sparse-regression ODE cross-predicts held-out Llama-2 at 5.6% error. The diagnostic requires no model internals -- only public benchmark scores across a model family. The cooperative regime extends to the frontier (r = +0.72, 34 models, 10 labs). Code, data, and an open-source activation-steering tool for any open-weight model are released alongside an interactive dashboard that diagnoses any model's coupling phase, suggests concrete interventions (data curation, width, benchmark rotation), and provides ODE scaling predictions, frontier diagnostics, and eigenstructure analysis: https://zehenlabs.com/cape/.

We revisit quantum phase estimation algorithms for the purpose of obtaining the energy levels of many-body Hamiltonians and pay particular attention to the statistical analysis of their outputs. We introduce the mean phase direction of the parent distribution associated with eigenstate inputs as a new post-processing tool. By connecting it with the unknown phase, we find that if used as its direct estimator, it exceeds the accuracy of the standard majority rule using one less bit of resolution, making evident that it can also be inverted to provide unbiased estimation. Moreover, we show how to directly use this quantity to accurately find the energy levels when the initialized state is an eigenstate of the simulated propagator during the whole time evolution, which allows for shallower algorithms. We then use IBM Q hardware to carry out the digital quantum simulation of three toy models: a two-level system, a two-spin Ising model and a two-site Hubbard model at half-filling. Methodologies are provided to implement Trotterization and reduce the variability of results in noisy intermediate scale quantum computers.

Data-driven surrogate models are an alternative to numerical homogenization of heterogeneous materials. In this contribution, a supervised learning approach is presented for predicting effective Lamé parameters of hyperelastic composites from low-dimensional microstructural descriptors. The data set is based on previously published numerical homogenization results for ensembles of two-phase stochastic microstructures generated by planar Boolean models, covering variations of inclusion shape, phase contrast, and area fraction; see Brändel, Brands, Maike, Rheinbach, Schröder, Schwarz and Stoyan (2022). A neural network is trained on combinations of scalar and curve-valued statistical descriptors, including the area fraction, a derived scalar shape descriptor τ, the two-point correlation function S_2(r), and the lineal-path function ell(z). Additional data representing limiting cases of the parameter space are incorporated to stabilize training and improve extrapolation behavior. The surrogate is evaluated by leave-one-grain-type-out cross-validation in order to assess generalization to unseen grain geometries. Numerical results demonstrate that additional descriptors can reduce relative errors. A predictor trained with τ and S_2(r) provides a compact representation with good quantitative accuracy and regular dense response behavior. Adding the lineal-path function ell(z) further reduces the error at the available data points, indicating that it is a promising additional descriptor; however, dense post-training response evaluations show that improved pointwise accuracy does not automatically guarantee physically admissible behavior between sampled parameter values. This motivates future work on physically constrained surrogate models, loss formulations, bounded output parametrizations, and a more systematic representation of curve-valued geometric descriptors.

Hidden-state probes effectively detect LLM hallucinations, but the geometry of the signal remains poorly characterized, driving increasingly complex probe architectures. Across three 7B-scale models and three datasets in a paired-example paradigm, we find the signal overwhelmingly dominated by a single mean-shift component, and removing this direction collapses detection to chance. Shrinkage linear discriminant analysis closes about 73% of the gap between 1D and full-dimensional classifiers, so apparent architectural complexity largely reflects high-dimensional covariance estimation difficulty rather than exploitable non-linearity. A simple L2-regularized logistic regression (0.952 AUROC) bounds or outperforms twelve controlled architectural alternatives, and our multi-layer aggregation exceeds CLAP cross-layer attention probing under matched paradigm. Because the signal spans a contiguous layer band, LayerMix aggregates it to match oracle-layer performance without oracle access. Our claims characterize the geometry within the controlled paired-example paradigm. Our code is available at https://github.com/js-lee-AI/LayerMix.

Extracting the London penetration depth, λ(T), from the measured magnetic susceptibility, χ(T), of a superconducting platelet in a perpendicular magnetic field requires knowing the function χ(λ) computed for the actual sample geometry. Thin films are increasingly important in quantum computing and superconducting electronics, most of which operate at ultra-low excitation fields in the vortex-free regime. Understanding their electromagnetic response in the Meissner--London (finite-λ, no vortices) state is therefore essential for extracting intrinsic properties such as the London penetration depth and superfluid phase stiffness. While numerous prior works have addressed different aspects of this problem, here we focus on providing an analytical semi-empirical representation of χ(λ) based on the 2D sheet-current model and establishing the limits of its applicability using two independent full 3D numerical solutions: finite-element modeling and a volume-current integral equation. As a result, we provide χ(λ) for a disc of radius a and thickness d in closed form, valid for all λ and for aspect ratios δequiv d/(2a)le0.05, and accurate to 0.1%. The two-dimensional sheet description with Pearl length Λ=2λ^2/d is adequate for δlesssim10^{-4} and λgtrsim 4d. Thicker films require the full closed form, which includes the three-dimensional corrections. Using the same numerical analysis, we provide an empirical formula that maps rectangular samples---the geometry most commonly used in experiments---onto a disc with an ``effective radius'' for subsequent calculation of χ(λ), and formulate a complete calibration protocol for whole-sample susceptibility measurements.

Surgical workflow recognition has numerous potential medical applications, such as the automatic indexing of surgical video databases and the optimization of real-time operating room scheduling, among others. As a result, phase recognition has been studied in the context of several kinds of surgeries, such as cataract, neurological, and laparoscopic surgeries. In the literature, two types of features are typically used to perform this task: visual features and tool usage signals. However, the visual features used are mostly handcrafted. Furthermore, the tool usage signals are usually collected via a manual annotation process or by using additional equipment. In this paper, we propose a novel method for phase recognition that uses a convolutional neural network (CNN) to automatically learn features from cholecystectomy videos and that relies uniquely on visual information. In previous studies, it has been shown that the tool signals can provide valuable information in performing the phase recognition task. Thus, we present a novel CNN architecture, called EndoNet, that is designed to carry out the phase recognition and tool presence detection tasks in a multi-task manner. To the best of our knowledge, this is the first work proposing to use a CNN for multiple recognition tasks on laparoscopic videos. Extensive experimental comparisons to other methods show that EndoNet yields state-of-the-art results for both tasks.

Outer-learning algorithms use infinitesimal sensitivities to propose finite changes to initialization or training parameters. For hard-ReLU training, the derivative of the finite program and the derivative of its flow limit do not by themselves specify the response at a chosen radius. We characterize the intervening regime in which the perturbation radius is proportional to the GD step. Integer event rounding then survives at leading order: smooth Euler bias shifts each discrete phase, and upstream rounding moves downstream branch boundaries. We derive the crossing indices and a uniform endpoint expansion for finitely many separated transverse events in piecewise-C^2 dynamics, away from recursive phase boundaries. In contractive affine regions, an explicit remainder and complete branch verification certify finite candidate comparisons. Scalar phase frequencies and a coupled feedback ablation test the mechanism; frozen nonlinear-network experiments show radius-dependent prediction accuracy, including incomplete branch matches and failed-word tails. Together with local AD and uniform flow consistency, the result identifies sufficient response regimes: differentiating training is a choice of perturbation resolution as well as a choice of derivative.

One technique to visualize the training of neural networks is to perform PCA on the parameters over the course of training and to project to the subspace spanned by the first few PCA components. In this paper we compare this technique to the PCA of a high dimensional random walk. We compute the eigenvalues and eigenvectors of the covariance of the trajectory and prove that in the long trajectory and high dimensional limit most of the variance is in the first few PCA components, and that the projection of the trajectory onto any subspace spanned by PCA components is a Lissajous curve. We generalize these results to a random walk with momentum and to an Ornstein-Uhlenbeck processes (i.e., a random walk in a quadratic potential) and show that in high dimensions the walk is not mean reverting, but will instead be trapped at a fixed distance from the minimum. We finally compare the distribution of PCA variances and the PCA projected training trajectories of a linear model trained on CIFAR-10 and ResNet-50-v2 trained on Imagenet and find that the distribution of PCA variances resembles a random walk with drift.

We reformulate the Landau analysis of Feynman integrals with the aim of advancing the state of the art in modern particle-physics computations. We contribute new algorithms for computing Landau singularities, using tools from polyhedral geometry and symbolic/numerical elimination. Inspired by the work of Gelfand, Kapranov, and Zelevinsky (GKZ) on generalized Euler integrals, we define the principal Landau determinant of a Feynman diagram. We illustrate with a number of examples that this algebraic formalism allows to compute many components of the Landau singular locus. We adapt the GKZ framework by carefully specializing Euler integrals to Feynman integrals. For instance, ultraviolet and infrared singularities are detected as irreducible components of an incidence variety, which project dominantly to the kinematic space. We compute principal Landau determinants for the infinite families of one-loop and banana diagrams with different mass configurations, and for a range of cutting-edge Standard Model processes. Our algorithms build on the Julia package Landau.jl and are implemented in the new open-source package PLD.jl available at https://mathrepo.mis.mpg.de/PLD/.

Bound states in the continuum (BIC) metasurfaces are typically described by geometry-specific parameters, hindering cross-geometry comparison, while ultranarrow qBIC features are easily diluted in full-spectrum learning. Here, 2015 samples from seven dielectric metasurface families are mapped to a shared reciprocal-lattice grid, where two frozen low-order Fourier channels capture resonance shifts with mean within-branch R^2 values of 0.871-0.999. Field-level analysis of two representative branches further confirms that these shifts are consistent with the Maxwell-Fourier perturbation picture. A five-channel K-space backbone models the broadband spectrum, while a local complex K-space expert parameterizes the qBIC resonance through a differentiable Fano layer. The expert reduces resonance-position mean absolute error (MAE) from 3.2 to 0.95 nm and the resonance-depth error by 14-fold on a geometry-blocked test set. The same coordinate supports spectrum-to-structure reconstruction.

Predicting the microstructural and morphological evolution of materials through phase-field modelling is computationally intensive, particularly for high-throughput parametric studies. While neural operators such as the Fourier neural operator (FNO) show promise in accelerating the solution of parametric partial differential equations (PDEs), the lack of explicit physical constraints, may limit generalisation and long-term accuracy for complex phase-field dynamics. Here, we develop a physics-informed neural operator framework to learn parametric phase-field PDEs, namely PF-PINO. By embedding the residuals of phase-field governing equations into the data-fidelity loss function, our framework effectively enforces physical constraints during training. We validate PF-PINO against benchmark phase-field problems, including electrochemical corrosion, dendritic crystal solidification, and spinodal decomposition. Our results demonstrate that PF-PINO significantly outperforms conventional FNO in accuracy, generalisation capability, and long-term stability. This work provides a robust and efficient computational tool for phase-field modelling and highlights the potential of physics-informed neural operators to advance scientific machine learning for complex interfacial evolution problems.

This study introduces amangkurat, an open-source Python library designed for the robust numerical simulation of relativistic scalar field dynamics governed by the nonlinear Klein-Gordon equation in (1+1)D spacetime. The software implements a hybrid computational strategy that couples Fourier pseudo-spectral spatial discretization with a symplectic Størmer-Verlet temporal integrator, ensuring both exponential spatial convergence for smooth solutions and long-term preservation of Hamiltonian structure. To optimize performance, the solver incorporates adaptive timestepping based on Courant-Friedrichs-Lewy (CFL) stability criteria and utilizes Just-In-Time (JIT) compilation for parallelized force computation. The library's capabilities are validated across four canonical physical regimes: dispersive linear wave propagation, static topological kink preservation in phi-fourth theory, integrable breather dynamics in the sine-Gordon model, and non-integrable kink-antikink collisions. Beyond standard numerical validation, this work establishes a multi-faceted analysis framework employing information-theoretic entropy metrics (Shannon, Rényi, and Tsallis), kernel density estimation, and phase space reconstruction to quantify the distinct phenomenological signatures of these regimes. Statistical hypothesis testing confirms that these scenarios represent statistically distinguishable dynamical populations. Benchmarks on standard workstation hardware demonstrate that the implementation achieves high computational efficiency, making it a viable platform for exploratory research and education in nonlinear field theory.

We study the parameter dependence and transversality properties of trajectories of the controlled ODE $ U_x = P, qquad P_x = - f(U) - βP + tilde α(x)U, arising from traveling-wave solutions of a bistable reaction-diffusion equation with control. Optimal profiles minimizing the L^1-norm of the control \tilde α are determined by the unstable and stable manifolds Γ_u, Γ_s, the critical curve P^*(U) = Uf(U), and the associated function F(U) = dP^*{dU} + f(U){P^*(U)}. We establish generic transversality properties for these objects with respect to perturbations of the speed β and the nonlinear source f, together with quantitative estimates on the first- and second-order dependence of the invariant manifolds on these parameters. We also analyze the loss of regularity at the critical speed β^{**}, where the unstable manifold approaches the strongly stable manifold of the equilibrium (U^*,0)$. These results provide the ODE ingredients used in the analysis of the structure and regularity of optimal profiles in paper [S. Bianchini and C. Trifone. Traveling profiles and control cost for a PDE describing the evolution of invasive species. 2026. arXiv: 2606.23979 [math.OC]].

Using the weights of trained Neural Network (NN) models as data modality has recently gained traction as a research field - dubbed Weight Space Learning (WSL). Multiple recent works propose WSL methods to analyze models, evaluate methods, or synthesize weights. Weight space learning methods require populations of trained models as datasets for development and evaluation. However, existing collections of models - called `model zoos' - are unstructured or follow a rudimentary definition of diversity. In parallel, work rooted in statistical physics has identified phases and phase transitions in NN models. Models are homogeneous within the same phase but qualitatively differ from one phase to another. We combine the idea of `model zoos' with phase information to create a controlled notion of diversity in populations. We introduce 12 large-scale zoos that systematically cover known phases and vary over model architecture, size, and datasets. These datasets cover different modalities, such as computer vision, natural language processing, and scientific ML. For every model, we compute loss landscape metrics and validate full coverage of the phases. With this dataset, we provide the community with a resource with a wide range of potential applications for WSL and beyond. Evidence suggests the loss landscape phase plays a role in applications such as model training, analysis, or sparsification. We demonstrate this in an exploratory study of the downstream methods like transfer learning or model weights averaging.

We present an open-source Python implementation of an idealized high-order pseudo-spectral solver for the one-dimensional nonlinear Schr\"odinger equation (NLSE). The solver combines Fourier spectral spatial discretization with an adaptive eighth-order Dormand-Prince time integration scheme to achieve machine-precision conservation of mass and near-perfect preservation of momentum and energy for smooth solutions. The implementation accurately reproduces fundamental NLSE phenomena including soliton collisions with analytically predicted phase shifts, Akhmediev breather dynamics, and the development of modulation instability from noisy initial conditions. Four canonical test cases validate the numerical scheme: single soliton propagation, two-soliton elastic collision, breather evolution, and noise-seeded modulation instability. The solver employs a 2/3 dealiasing rule with exponential filtering to prevent aliasing errors from the cubic nonlinearity. Statistical analysis using Shannon, R\'enyi, and Tsallis entropies quantifies the spatio-temporal complexity of solutions, while phase space representations reveal the underlying coherence structure. The implementation prioritizes code transparency and educational accessibility over computational performance, providing a valuable pedagogical tool for exploring nonlinear wave dynamics. Complete source code, documentation, and example configurations are freely available, enabling reproducible computational experiments across diverse physical contexts where the NLSE governs wave evolution, including nonlinear optics, Bose-Einstein condensates, and ocean surface waves.

Radio interferometric imaging aims to estimate an unknown sky intensity image from degraded observations, acquired through an antenna array. In the theoretical case of a perfectly calibrated array, it has been shown that solving the corresponding imaging problem by iterative algorithms based on convex optimization and compressive sensing theory can be competitive with classical algorithms such as CLEAN. However, in practice, antenna-based gains are unknown and have to be calibrated. Future radio telescopes, such as the SKA, aim at improving imaging resolution and sensitivity by orders of magnitude. At this precision level, the direction-dependency of the gains must be accounted for, and radio interferometric imaging can be understood as a blind deconvolution problem. In this context, the underlying minimization problem is non-convex, and adapted techniques have to be designed. In this work, leveraging recent developments in non-convex optimization, we propose the first joint calibration and imaging method in radio interferometry, with proven convergence guarantees. Our approach, based on a block-coordinate forward-backward algorithm, jointly accounts for visibilities and suitable priors on both the image and the direction-dependent effects (DDEs). As demonstrated in recent works, sparsity remains the prior of choice for the image, while DDEs are modelled as smooth functions of the sky, i.e. spatially band-limited. Finally, we show through simulations the efficiency of our method, for the reconstruction of both images of point sources and complex extended sources. MATLAB code is available on GitHub.

We present a new approach for understanding the periodicity structure and semantics of motion datasets, independently of the morphology and skeletal structure of characters. Unlike existing methods using an overly sparse high-dimensional latent, we propose a phase manifold consisting of multiple closed curves, each corresponding to a latent amplitude. With our proposed vector quantized periodic autoencoder, we learn a shared phase manifold for multiple characters, such as a human and a dog, without any supervision. This is achieved by exploiting the discrete structure and a shallow network as bottlenecks, such that semantically similar motions are clustered into the same curve of the manifold, and the motions within the same component are aligned temporally by the phase variable. In combination with an improved motion matching framework, we demonstrate the manifold's capability of timing and semantics alignment in several applications, including motion retrieval, transfer and stylization. Code and pre-trained models for this paper are available at https://peizhuoli.github.io/walkthedog.

Quantum computers provide new avenues to access ground and excited state properties of systems otherwise difficult to simulate on classical hardware. New approaches using subspaces generated by real-time evolution have shown efficiency in extracting eigenstate information, but the full capabilities of such approaches are still not understood. In recent work, we developed the variational quantum phase estimation (VQPE) method, a compact and efficient real-time algorithm to extract eigenvalues on quantum hardware. Here we build on that work by theoretically and numerically exploring a generalized Krylov scheme where the Krylov subspace is constructed through a parametrized real-time evolution, which applies to the VQPE algorithm as well as others. We establish an error bound that justifies the fast convergence of our spectral approximation. We also derive how the overlap with high energy eigenstates becomes suppressed from real-time subspace diagonalization and we visualize the process that shows the signature phase cancellations at specific eigenenergies. We investigate various algorithm implementations and consider performance when stochasticity is added to the target Hamiltonian in the form of spectral statistics. To demonstrate the practicality of such real-time evolution, we discuss its application to fundamental problems in quantum computation such as electronic structure predictions for strongly correlated systems.

The annealing phase is a pivotal convergence stage in LLM pre-training that ultimately determines final model quality. However, effectively selecting training data during this phase remains a key challenge. Current strategies rely on empirical heuristics, such as domain filtering or context extension, which lack a principled grounding in optimization theory. In this work, we characterize the annealing phase through the lens of the loss landscape's spectral geometry. We argue that optimal convergence requires gradient updates to satisfy heterogeneous constraints across different eigen-directions. Building on this insight, we formulate data selection as a problem of satisfying these directional constraints. To this end, we propose DiReCT (Directionally-Restrained Constrained Training), a novel framework that reformulates sample selection in the annealing stage as a constrained optimization problem. By imposing explicit directional constraints on per-sample gradients based on the spectral properties of the Hessian, DiReCT identifies samples that align with the optimal curvature-aware descent path. Extensive experiments across various model scales demonstrate that DiReCT consistently achieves state-of-the-art performance. For future research, code is available at https://github.com/xuyj233/Direct.

The analytical formulae for the phase space factors and the three-momenta of three- and four-body final states are derived for all sets of independent kinematic variables containing invariant mass variables. These formulae will help experimental physicist to perform the data analysis. As an example, we show how to use these formulae to distinguish the different mechanisms of e+pto e+J/ψ+ p process for searching the signals of P_c states at the energy region of Electron-Ion collider at China (EicC).

In the present article we study diffuse interface models for two-phase biomembranes. We will do so by starting off with a diffuse interface model on R^n defined by two coupled phase fields u,v. The first phase field u is the diffuse approximation of the interior of the membrane; the second phase field v is the diffuse approximation of the two phases of the membrane. We prove a compactness result and a lower bound in the sense of Gamma-convergence for pairs of phase functions (u_varepsilon,v_varepsilon). As an application of this first result, we consider a diffuse approximation of a two-phase Willmore functional plus line tension energy.

The task of synthesizing novel views from a single image has useful applications in virtual reality and mobile computing, and a number of approaches to the problem have been proposed in recent years. A Multiplane Image (MPI) estimates the scene as a stack of RGBA layers, and can model complex appearance effects, anti-alias depth errors and synthesize soft edges better than methods that use textured meshes or layered depth images. And unlike neural radiance fields, an MPI can be efficiently rendered on graphics hardware. However, MPIs are highly redundant and require a large number of depth layers to achieve plausible results. Based on the observation that the depth complexity in local image regions is lower than that over the entire image, we split an MPI into many small, tiled regions, each with only a few depth planes. We call this representation a Tiled Multiplane Image (TMPI). We propose a method for generating a TMPI with adaptive depth planes for single-view 3D photography in the wild. Our synthesized results are comparable to state-of-the-art single-view MPI methods while having lower computational overhead.

In an unbounded plane, straight lines are used extensively for mathematical analysis. They are tools of convenience. However, those with high slope values become unbounded at a faster rate than the independent variable. So, straight lines, in this work, are made to be bounded by introducing a parametric nonlinear term that is positive. The straight lines are transformed into bounded nonlinear curves that become unbounded at a much slower rate than the independent variable. This transforming equation can be expressed as a continued fraction of straight lines. The continued fraction is real-valued and converges to the solutions of the transforming equation. Following Euler's method, the continued fraction has been reduced into an infinite series. The usefulness of the bounding nature of continued fraction is demonstrated by solving the problem of image classification. Parameters estimated on the Fashion-MNIST dataset of greyscale images using continued fraction of regression lines have less variance, converge quickly and are more accurate than the linear counterpart. Moreover, this multi-dimensional parametric estimation problem can be expressed on xy- plane using the parameters of the continued fraction and patterns emerge on planar plots.

MRI reconstruction from undersampled k-space measurements is an ill-posed inverse problem. Physics-driven deep learning (PD-DL) methods have shown strong performance for this task by combining the MRI forward model with learned image regularization within algorithm-unrolling frameworks. However, most existing PD-DL methods reconstruct complex-valued images directly, thereby implicitly coupling magnitude and phase within a single learned representation. This coupled regularization may be suboptimal in reconstruction settings where accurate phase modeling plays an important role, such as partial Fourier (PF) imaging, where recovery of the omitted asymmetric k-space measurements depends on the underlying image phase. In such scenarios, explicit modeling of magnitude and phase as separate components may reduce the reliance on externally estimated or predefined phase information. To this end, we propose UMPIRE-Net (Unrolled Magnitude-Phase In REgularization Network), a PD-DL method that introduces separate learned regularizers for magnitude and phase components, together with a novel data-fidelity formulation that enforces measurements consistency. We evaluate UMPIRE-Net for accelerated MRI with PF across different datasets and acceleration factors. Experimental results demonstrate that our proposed method improves reconstruction quality compared with a conventional complex-valued PD-DL baseline, yielding sharper images and reduced artifacts. Code available at: https://github.com/MahdiSaberii/UMPIRE-Net

Drones equipped with cameras are emerging as a powerful tool for large-scale aerial 3D scanning, but existing automatic flight planners do not exploit all available information about the scene, and can therefore produce inaccurate and incomplete 3D models. We present an automatic method to generate drone trajectories, such that the imagery acquired during the flight will later produce a high-fidelity 3D model. Our method uses a coarse estimate of the scene geometry to plan camera trajectories that: (1) cover the scene as thoroughly as possible; (2) encourage observations of scene geometry from a diverse set of viewing angles; (3) avoid obstacles; and (4) respect a user-specified flight time budget. Our method relies on a mathematical model of scene coverage that exhibits an intuitive diminishing returns property known as submodularity. We leverage this property extensively to design a trajectory planning algorithm that reasons globally about the non-additive coverage reward obtained across a trajectory, jointly with the cost of traveling between views. We evaluate our method by using it to scan three large outdoor scenes, and we perform a quantitative evaluation using a photorealistic video game simulator.

Subspace representation is a fundamental technique in various fields of machine learning. Analyzing a geometrical relationship among multiple subspaces is essential for understanding subspace series' temporal and/or spatial dynamics. This paper proposes the second-order difference subspace, a higher-order extension of the first-order difference subspace between two subspaces that can analyze the geometrical difference between them. As a preliminary for that, we extend the definition of the first-order difference subspace to the more general setting that two subspaces with different dimensions have an intersection. We then define the second-order difference subspace by combining the concept of first-order difference subspace and principal component subspace (Karcher mean) between two subspaces, motivated by the second-order central difference method. We can understand that the first/second-order difference subspaces correspond to the velocity and acceleration of subspace dynamics from the viewpoint of a geodesic on a Grassmann manifold. We demonstrate the validity and naturalness of our second-order difference subspace by showing numerical results on two applications: temporal shape analysis of a 3D object and time series analysis of a biometric signal.

A comparative analysis of the special shapes (patterns, profiles) of the eclipses applied for the phenomenological modeling of the light curves of eclipsing binary stars is conducted. Families of functions are considered, generalizing local approximations (Andronov, 2010, 2012) and the functions theoretically unlimited in a width, based on a Gaussian (Mikulasek, 2015). For an analysis, the light curve of the star V0882 Car = 2MASS J11080308 - 6145589 of the classic Algol - subtype (\beta Persei) is used. By analyzing dozens of modified functions with additional parameters, it was chosen the 14 best ones according to the criterion of the least sum of squares of deviations. The best are the functions with an additional parameter, describing profiles, which are limited in phase.

Radiotherapy often involves a prolonged treatment period. During this time, patients may experience organ motion due to breathing and other physiological factors. Predicting and modeling this motion before treatment is crucial for ensuring precise radiation delivery. However, existing pre-treatment organ motion prediction methods primarily rely on deformation analysis using principal component analysis (PCA), which is highly dependent on registration quality and struggles to capture periodic temporal dynamics for motion modeling.In this paper, we observe that organ motion prediction closely resembles an autoregressive process, a technique widely used in natural language processing (NLP). Autoregressive models predict the next token based on previous inputs, naturally aligning with our objective of predicting future organ motion phases. Building on this insight, we reformulate organ motion prediction as an autoregressive process to better capture patient-specific motion patterns. Specifically, we acquire 4D CT scans for each patient before treatment, with each sequence comprising multiple 3D CT phases. These phases are fed into the autoregressive model to predict future phases based on prior phase motion patterns. We evaluate our method on a real-world test set of 4D CT scans from 50 patients who underwent radiotherapy at our institution and a public dataset containing 4D CT scans from 20 patients (some with multiple scans), totaling over 1,300 3D CT phases. The performance in predicting the motion of the lung and heart surpasses existing benchmarks, demonstrating its effectiveness in capturing motion dynamics from CT images. These results highlight the potential of our method to improve pre-treatment planning in radiotherapy, enabling more precise and adaptive radiation delivery.

We examine the geometry of neural network training using the Jacobian of trained network parameters with respect to their initial values. Our analysis reveals low-dimensional structure in the training process which is dependent on the input data but largely independent of the labels. We find that the singular value spectrum of the Jacobian matrix consists of three distinctive regions: a "chaotic" region of values orders of magnitude greater than one, a large "bulk" region of values extremely close to one, and a "stable" region of values less than one. Along each bulk direction, the left and right singular vectors are nearly identical, indicating that perturbations to the initialization are carried through training almost unchanged. These perturbations have virtually no effect on the network's output in-distribution, yet do have an effect far out-of-distribution. While the Jacobian applies only locally around a single initialization, we find substantial overlap in bulk subspaces for different random seeds. Our code is available at https://github.com/EleutherAI/training-jacobian

In applications such as social, energy, transportation, sensor, and neuronal networks, high-dimensional data naturally reside on the vertices of weighted graphs. The emerging field of signal processing on graphs merges algebraic and spectral graph theoretic concepts with computational harmonic analysis to process such signals on graphs. In this tutorial overview, we outline the main challenges of the area, discuss different ways to define graph spectral domains, which are the analogues to the classical frequency domain, and highlight the importance of incorporating the irregular structures of graph data domains when processing signals on graphs. We then review methods to generalize fundamental operations such as filtering, translation, modulation, dilation, and downsampling to the graph setting, and survey the localized, multiscale transforms that have been proposed to efficiently extract information from high-dimensional data on graphs. We conclude with a brief discussion of open issues and possible extensions.

Sagnac interferometers are important tools for precision measurements. Cancellation of common-path noise ensures a high degree of stability against external perturbations, while their sensitivity to rotations provides the basis of laser gyroscopes. Here we highlight another, less explored feature of Sagnac interferometers: the fact that optical elements are traversed in reverse order for clockwise and counterclockwise propagating light components. This provides the opportunity to explore a classical realization of indefinite causal order, where the order of events within a sequence is not fixed. We explore this concept to identify the geometric phase associated with two non-commuting polarization operations with a single measurement. This idea may have applications for the rapid determination of polarization manipulations or optical activity within chiral media, but foremost it provides a geometric illustration of indefinite causal order.

Motivated by topologically protected states in wave physics, we study localised eigenmodes in one-dimensional periodic media with defects. The Su-Schrieffer-Heeger model (the canonical example of a one-dimensional system with topologically protected localised defect states) is used to demonstrate the method. Our approach can be used to describe two broad classes of perturbations to periodic differential problems: those caused by inserting a finite-sized piece of arbitrary material and those caused by creating an interface between two different periodic media. The results presented here characterise the existence of localised eigenmodes in each case and, when they exist, determine their eigenfrequencies and provide concise analytic results that quantify the decay rate of these modes. These results are obtained using both high-frequency homogenisation and transfer matrix analysis, with good agreement between the two methods.

The 3D Gaussian Splatting (3DGS) gained its popularity recently by combining the advantages of both primitive-based and volumetric 3D representations, resulting in improved quality and efficiency for 3D scene rendering. However, 3DGS is not alias-free, and its rendering at varying resolutions could produce severe blurring or jaggies. This is because 3DGS treats each pixel as an isolated, single point rather than as an area, causing insensitivity to changes in the footprints of pixels. Consequently, this discrete sampling scheme inevitably results in aliasing, owing to the restricted sampling bandwidth. In this paper, we derive an analytical solution to address this issue. More specifically, we use a conditioned logistic function as the analytic approximation of the cumulative distribution function (CDF) in a one-dimensional Gaussian signal and calculate the Gaussian integral by subtracting the CDFs. We then introduce this approximation in the two-dimensional pixel shading, and present Analytic-Splatting, which analytically approximates the Gaussian integral within the 2D-pixel window area to better capture the intensity response of each pixel. Moreover, we use the approximated response of the pixel window integral area to participate in the transmittance calculation of volume rendering, making Analytic-Splatting sensitive to the changes in pixel footprint at different resolutions. Experiments on various datasets validate that our approach has better anti-aliasing capability that gives more details and better fidelity.

We review the method NAV (New Algol Variable) first introduced in 2012Ap.....55..536A, which uses the locally-dependent shapes of eclipses in an addition to the trigonometric polynomial of the second order (which typically describes the "out-of-eclipse" part of the light curve with effects of reflection, ellipticity and O'Connell). Eclipsing binary stars are believed to show distinct eclipses only if belonging to the EA type. With a decreasing eclipse width, the statistically optimal value of the trigonometric polynomial s (2003ASPC..292..391A) drastically increases from ~2 for elliptic (EL) variables without eclipses, ~6-8 for EW and up to ~30-50 for some EA with narrow eclipses. In this case of large number of parameters, the smoothing curve becomes very noisy and apparent waves (the Gibbs phenomenon) may be seen. The NAV set of the parameters may be used for classification in the GCVS, VSX and similar catalogs. The maximal number of parameters is m=12, which corresponds to s=5, if correcting both the period and the initial epoch. We have applied the method to few stars, also in a case of multi-color photometry (2015JASS...32..127A), when it is possible to use the phenomenological parameters from the NAV fit to estimate physical parameters using statistical dependencies. We conclude that the NAV approximation is better than the TP one even for the case of EW-type stars with much wider eclipses. It may also be used to determine timings (see 2005ASPC..335...37A for a review of methods) or to determine parameters in the case of variable period, using a complete light curve modeling the phase variations. The method is illustrated on 2MASS J11080447-6143290 (EA-type), USNO-B1.0 1265-0306001 and USNO-B1.0 1266-0313413 (EW-type) and compared to various other methods from the literature.

We put forward the dynamical study of a novel higher-order small network of Chialvo neurons arranged in a ring-star topology, with the neurons interacting via linear diffusive couplings. This model is perceived to imitate the nonlinear dynamical properties exhibited by a realistic nervous system where the neurons transfer information through higher-order multi-body interactions. We first analyze our model using the tools from nonlinear dynamics literature: fixed point analysis, Jacobian matrix, and bifurcation patterns. We observe the coexistence of chaotic attractors, and also an intriguing route to chaos starting from a fixed point, to period-doubling, to cyclic quasiperiodic closed invariant curves, to ultimately chaos. We numerically observe the existence of codimension-1 bifurcation patterns: saddle-node, period-doubling, and Neimark Sacker. We also qualitatively study the typical phase portraits of the system and numerically quantify chaos and complexity using the 0-1 test and sample entropy measure respectively. Finally, we study the collective behavior of the neurons in terms of two synchronization measures: the cross-correlation coefficient, and the Kuramoto order parameter.

Forecasting seismic waveforms beyond observed data remains challenging due to the nonlinear, dispersive, and multi-scale nature of seismic wave propagation. In this work, we introduce SeismoGPT, a transformer-based autoregressive model designed to forecast three-component seismic waveforms directly in the time domain. Forecasting is formulated as a physically constrained continuation problem in which the model receives waveform context beginning at the P-wave arrival and extending a defined time beyond the S-wave arrival, after which future motion is generated recursively without access to ground-truth samples. Evaluation is performed on synthetic seismograms spanning source depths of 5--100\,km, epicentral distances of 10--90^circ, and magnitudes 3 leq M_w leq 7. To disentangle the effects of context length and prediction horizon, we define three evaluation configurations using a distance-normalized context ratio and fixed prediction horizons of 120 and 240\,s. Across all configurations, the model achieves median normalized cross correlation above 0.93. Analysis of representative forecasts shows that successful predictions preserve both phase coherence and spectral energy distribution. Where failure cases arise, this is primarily due to gradual phase drift during autoregressive rollout rather than unphysical signal generation. These results demonstrate that transformer-based sequence models can learn stable dynamical continuation of seismic wavefields, highlighting the potential of foundation-model approaches for physics-driven time-series forecasting. There are potential applications of this methodology in seismic warning and hazard mitigation, particularly for next-generation gravitational-wave observatories, such as the Einstein Telescope.

I introduce a novel mathematical framework integrating topological dynamics, operator algebras, and ergodic geometry to study lattices of asynchronous metric dynamical systems. Each node in the lattice carries an internal flow represented by a one-parameter family of operators, evolving on its own time scale. I formalize stratified state spaces capturing multiple levels of synchronized behavior, define an asynchronous evolution metric that quantifies phase-offset distances between subsystems, and characterize emergent coherent topologies arising when subsystems synchronize. Within this framework, I develop formal operators for the evolution of each subsystem and give precise conditions under which phase-aligned synchronization occurs across the lattice. The main results include: (1) the existence and uniqueness of coherent (synchronized) states under a contractive coupling condition, (2) stability of these coherent states and criteria for their emergence as a collective phase transition in a continuous operator topology, and (3) the influence of symmetries, with group-invariant coupling leading to flow-invariant synchrony subspaces and structured cluster dynamics. Proofs are given for each theorem, demonstrating full mathematical rigor. In a final section, I discuss hypothetical applications of this framework to symbolic lattice systems (e.g. subshifts), to invariant group actions on dynamical lattices, and to operator fields over stratified manifolds in the spirit of noncommutative geometry. Throughout, I write in the first person to emphasize the exploratory nature of this work. The paper avoids any reference to cosmology or observers, focusing instead on clean, formal mathematics suitable for a broad array of dynamical systems.

The nonlinear pseudo-oscillator recently tackled by Gadella and Lara is mapped to an Emden-Fowler (EF) equation that is written as an autonomous two-dimensional ODE system for which we provide the phase-space analysis and the parametric solution. Through an invariant transformation we find periodic solutions to a certain class of EF equations that pass an integrability condition. We show that this condition is necessary to have periodic solutions and via the ODE analysis we also find the sufficient condition for periodic orbits. EF equations that do not pass integrability conditions can be made integrable via an invariant transformation which also allows us to construct periodic solutions to them. Two other nonlinear equations, a zero-frequency Ermakov equation and a positive power Emden-Fowler equation are discussed in the same context

Simulation-to-reality translation must bridge the appearance gap between synthetic and real domains while preserving structural and semantic consistency. Conditioning-based methods achieve spatial alignment but introduce computationally expensive control modules. Paired-data methods achieve realism but rely on complex synthesis pipelines, often altering scene geometry and semantics. Training-free editing methods avoid both constraints but lack a learned appearance prior, limiting their perceptual quality. Recently proposed phase-preserving diffusion presents a promising alternative, but Fourier-domain formulations are constrained by global spectral coupling. This coupling induces spatial artifacts such as ringing and boundary leakage, thereby degrading structural and semantic consistency. We introduce Wavelet Phase Diffusion, which addresses this through two components. First, we operate in the Dual-Tree Complex Wavelet Packet Transform domain, whose localized wavelet packets enable spatially adaptive phase injection without global spectral interference. Second, Low-Frequency Randomization (LFR) replaces the low-frequency packet, decoupling the model from the synthetic illumination prior and enabling in-distribution real-world appearance. Both components train on unpaired open-domain data, and introduce negligible inference overhead. The spatial locality further enables instance-level translation, where individual objects or regions are translated to photorealistic appearance independently while the surrounding scene remains untranslated. On vKITTI to KITTI image translation, ours outperforms prior methods in realism and semantic consistency while maintaining competitive structural alignment. For CARLA video translation, ours approaches the realism of paired-data methods while reducing VLM planner ADE and FDE by 5.4% and 5.1%, respectively.

Spectral analysis provides one of the most effective paradigms for information-preserving dimensionality reduction, as simple descriptions of naturally occurring signals are often obtained via few terms of periodic basis functions. In this work, we study deep neural networks designed to harness the structure in frequency domain for efficient learning of long-range correlations in space or time: frequency-domain models (FDMs). Existing FDMs are based on complex-valued transforms i.e. Fourier Transforms (FT), and layers that perform computation on the spectrum and input data separately. This design introduces considerable computational overhead: for each layer, a forward and inverse FT. Instead, this work introduces a blueprint for frequency domain learning through a single transform: transform once (T1). To enable efficient, direct learning in the frequency domain we derive a variance-preserving weight initialization scheme and investigate methods for frequency selection in reduced-order FDMs. Our results noticeably streamline the design process of FDMs, pruning redundant transforms, and leading to speedups of 3x to 10x that increase with data resolution and model size. We perform extensive experiments on learning the solution operator of spatio-temporal dynamics, including incompressible Navier-Stokes, turbulent flows around airfoils and high-resolution video of smoke. T1 models improve on the test performance of FDMs while requiring significantly less computation (5 hours instead of 32 for our large-scale experiment), with over 20% reduction in average predictive error across tasks.

Schrödinger operators with nonlocal δ-interaction are studied with the use of the Lax-Phillips scattering theory methods. The condition of applicability of the Lax-Phillips approach in terms of non-cyclic functions is established. Two formulas for the S-matrix are obtained. The first one deals with the Krein-Naimark resolvent formula and the Weyl-Titchmarsh function, whereas the second one is based on modified reflection and transmission coefficients. The S-matrix S(z) is analytical in the lower half-plane C_- when the Schrödinger operator with nonlocal δ-interaction is positive self-adjoint. Otherwise, S(z) is a meromorphic matrix-valued function in C_- and its properties are closely related to the properties of the corresponding Schrödinger operator. Examples of S-matrices are given.

Endoscopic Submucosal Dissection (ESD) is a minimally invasive procedure initially developed for early gastric cancer treatment and has expanded to address diverse gastrointestinal lesions. While computer-assisted surgery (CAS) systems enhance ESD precision and safety, their efficacy hinges on accurate real-time surgical phase recognition, a task complicated by ESD's inherent complexity, including heterogeneous lesion characteristics and dynamic tissue interactions. Existing video-based phase recognition algorithms, constrained by inefficient temporal context modeling, exhibit limited performance in capturing fine-grained phase transitions and long-range dependencies. To overcome these limitations, we propose SPRMamba, a novel framework integrating a Mamba-based architecture with a Scaled Residual TranMamba (SRTM) block to synergize long-term temporal modeling and localized detail extraction. SPRMamba further introduces the Hierarchical Sampling Strategy to optimize computational efficiency, enabling real-time processing critical for clinical deployment. Evaluated on the ESD385 dataset and the cholecystectomy benchmark Cholec80, SPRMamba achieves state-of-the-art performance (87.64% accuracy on ESD385, +1.0% over prior methods), demonstrating robust generalizability across surgical workflows. This advancement bridges the gap between computational efficiency and temporal sensitivity, offering a transformative tool for intraoperative guidance and skill assessment in ESD surgery. The code is accessible at https://github.com/Zxnyyyyy/SPRMamba.

Weather Jiu-Jitsu is a control paradigm for extreme climatological events, inspired by chaos theory. As a proposition, small, precise, targeted, and cost-inexpensive perturbations can redirect trajectories of a large dynamical system. This strategy has been demonstrated analytically in the Lorenz-63 system, where a naturally chaotic trajectory switching between two attractors can be confined to a single attractor, indefinitely, via arbitrarily small perturbations. This paper examines the feasibility of Microsoft's Aurora -- a 1.3 billion parameter global atmospheric model -- as a test bed for this strategy. This paper explores three questions: (1) Is Aurora a reliable enough simulation environment to serve as a meaningful testbed? (2) Are the perturbations required to redirect its trajectories small enough to be physically plausible? (3) Does Aurora's learned latent space (the parametric estimators on climatological attributes) yield any apparent, structured, and/or perhaps interpretable features that can convey a geo/atmospheric response to initial conditions? We find evidence consistent with all three: Aurora's modeled trajectories respond to perturbations beyond measurement drift, the perturbation magnitudes required are small relative to the model's own forecast uncertainty, and its latent representations exhibit directional structure that responds to Jiu-Jitsu-type interventions, even though that structure does not separate extreme from normal states outright. These results should be read as feasibility diagnostics rather than a demonstration of control: we do not implement or test an actual steering intervention on Aurora, and several of our findings, particularly around the model's latent-space geometry, are exploratory.

Longitudinal medical imaging captures temporal evolution of lesions, yet extracting the underlying dynamical parameters governing this evolution remains challenging. We propose an inverse Bayesian framework for inferring lesion dynamics from longitudinal spectral CT. We decompose spectral feature (x) evolution into three components: equation* dx_i{dt} = A_i x_i + B \cdot n + C \cdot Δx_{sat} equation* where A_i captures intrinsic dynamics (lesion-autonomous evolution), B captures local environment tumour burden (organ tumour burden through satellite count coupling), and C captures environment/satellite state change (i.e., whether surrounding lesions move similarly or not). We demonstrate the framework on photon-counting NSCLC CT data from metastases, recovering distinct dynamical regimes: lung lesions exhibit significant satellite count coupling (B=-0.34, p<0.05) suggesting competitive dynamics, while liver lesions show synergistic satellite behaviour coupling (Capprox+1.0, p<0.05). Synthetic validation confirms parameter recovery, and cross-coupling analysis validates that our method detects non-zero coupling when present. This work establishes inverse dynamical inference as a principled methodology for extracting interpretable parameters from longitudinal imaging, moving beyond static feature extraction toward mechanistic characterisation of lesion behaviour. The code and data are available at: https://github.com/lukasf98/inverse-bayesian-inference

Over the last decades, progress in modal analysis has enabled increasingly routine use of modal parameters, including those extracted from in-situ measurements, for applications such as structural health monitoring and finite element model updating. For output-only identification, or Operational Modal Analysis (OMA), widely adopted approaches include Stochastic Subspace Identification (SSI) methods and the Natural Excitation Technique combined with the Eigensystem Realization Algorithm (NExT-ERA). Nevertheless, SSI-based techniques may become cumbersome on large systems, while NExT-ERA fitting can struggle when measurements are contaminated by noise. To alleviate these, this work investigates an OMA frequency-domain formulation for aeronautical structures by coupling the Loewner Framework (LF) with NExT, yielding the proposed NExT-LF method. The method exploits the computational efficiency of LF together with the impulse response function retrieval enabled by NExT. NExT-LF is assessed on two experimental benchmarks: the eXperimental BeaRDS 2 high-aspect-ratio wing main spar and an Airbus Helicopters H135 bearingless main rotor blade. The identified modal parameters are compared against available experimental references and results obtained via SSI with Canonical Variate Analysis and NExT-ERA. The results show that the modes identified by NExT-LF correlate well with benchmark data, particularly for high-amplitude tests and in the low-frequency range.

In this paper, a PDE-ODE model with discontinuity in the flux as well as a flux constraint is analyzed. A modified Riemann solution is proposed and the existence of a weak solution to the Cauchy problem is rigorously investigated using the wavefront tracking scheme.

This study investigates the dynamics of pedestrian crossing flows with varying crossing angles α to classify different scenarios and derive implications for crowd management. Probability density functions of four key features-velocity v, density ρ, avoidance number Av, and intrusion number In-were analyzed to characterize pedestrian behavior. Velocity-density fundamental diagrams were constructed for each α and fitted with functional forms from existing literature. Classification attempts using Av-In and v-ρ phase spaces revealed significant overlaps, highlighting the limitations of these metrics alone for scenario differentiation. To address this, machine learning models, including logistic regression and random forest, were employed using all four features. Results showed robust classification performance, with v and Av contributing most significantly. Insights from feature importance metrics and classification accuracy offer practical guidance for managing high-density crowds, optimizing pedestrian flow, and designing safer public spaces. These findings provide a data-driven framework for advancing pedestrian dynamics research.

Most single-channel separators estimate a source by applying a real gain to the mixture in each time-frequency bin. The optimum of that format, which the oracle masks used as bounds do not attain, is the orthogonal projection of the source onto the line spanned by the mixture, its residual set by the angle between them. Locating an estimator reduces to the block structure of a real-linear operator on stacked spectra, giving a chain of four nested classes whose three larger terms match three assumptions on the prior: zero means, circularity and absence of inter-frequency coupling. Held fixed the chain is a cascade of four orthogonal projections; refitted per frame it collapses onto its first term, attributing the whole residual to one missing real parameter per bin, the phase. When the phase posterior is symmetric about the mixture direction, the minimum mean-square estimate falls back onto the line, with gain the posterior mean of the oracle gain and excess error its variance. On MUSDB18 a posterior mean under a non-circular Gaussian-mixture prior leaves the class yet stays 11.44 dB under the per-frame ceiling, which four times as many components and 7.5x the data do not close; a closed-form gate attributes some 70% of it, in decibels, to the predicted variance. The widest fixed class stays 6.70 dB under the same ceiling. Leaving the class and minimising squared error are conflicting requests: the barrier lies in the criterion rather than in the prior.

Single-image piece-wise planar 3D reconstruction aims to simultaneously segment plane instances and recover 3D plane parameters from an image. Most recent approaches leverage convolutional neural networks (CNNs) and achieve promising results. However, these methods are limited to detecting a fixed number of planes with certain learned order. To tackle this problem, we propose a novel two-stage method based on associative embedding, inspired by its recent success in instance segmentation. In the first stage, we train a CNN to map each pixel to an embedding space where pixels from the same plane instance have similar embeddings. Then, the plane instances are obtained by grouping the embedding vectors in planar regions via an efficient mean shift clustering algorithm. In the second stage, we estimate the parameter for each plane instance by considering both pixel-level and instance-level consistencies. With the proposed method, we are able to detect an arbitrary number of planes. Extensive experiments on public datasets validate the effectiveness and efficiency of our method. Furthermore, our method runs at 30 fps at the testing time, thus could facilitate many real-time applications such as visual SLAM and human-robot interaction. Code is available at https://github.com/svip-lab/PlanarReconstruction.

We demonstrate a new computational illumination technique that achieves large space-bandwidth-time product, for quantitative phase imaging of unstained live samples in vitro. Microscope lenses can have either large field of view (FOV) or high resolution, not both. Fourier ptychographic microscopy (FPM) is a new computational imaging technique that circumvents this limit by fusing information from multiple images taken with different illumination angles. The result is a gigapixel-scale image having both wide FOV and high resolution, i.e. large space-bandwidth product (SBP). FPM has enormous potential for revolutionizing microscopy and has already found application in digital pathology. However, it suffers from long acquisition times (on the order of minutes), limiting throughput. Faster capture times would not only improve imaging speed, but also allow studies of live samples, where motion artifacts degrade results. In contrast to fixed (e.g. pathology) slides, live samples are continuously evolving at various spatial and temporal scales. Here, we present a new source coding scheme, along with real-time hardware control, to achieve 0.8 NA resolution across a 4x FOV with sub-second capture times. We propose an improved algorithm and new initialization scheme, which allow robust phase reconstruction over long time-lapse experiments. We present the first FPM results for both growing and confluent in vitro cell cultures, capturing videos of subcellular dynamical phenomena in popular cell lines undergoing division and migration. Our method opens up FPM to applications with live samples, for observing rare events in both space and time.

In this paper, we prove the existence of stationary pulse solutions for a bulk-surface reaction-diffusion system modeling cell polarization in two-dimensional domains. Using a singular perturbation method, we construct pulse solutions whose centers lie near non-degenerate critical points of a geometry-dependent potential expressed in terms of the Neumann Green's function, as formally predicted in watanabe2026. The main analytical difficulty arises from the half-Laplacian induced by the logarithmic singularity of the Green's function, resulting in algebraically rather than exponentially decaying inner solutions. Our analysis may also serve as a useful guide for applying singular perturbation methods to other bulk-surface type systems.

In order to study oscillators coupled by pulses emitted at discrete times, it is generally assumed that the effect of each pulse is an instantaneous phase shift, with a possible conduction delay between emission and receipt. However, we are interested in neural oscillators in which each pulse (action potential) activates a biexponential synapse, and at high frequencies, the duration of the synaptic conductance may be greater than the network period. Therefore, the effect of received pulses can summate over the course of several cycles. To overcome this limitation, we previously defined a mean field approach for a single synchronous population. Here, we extend it to two alternating synchronous populations by assuming a perturbation of a single oscillator from one of the synchronous populations which is represented by a single self-connected neural oscillator. The train of delayed biexponential synapses emitted by each oscillator is divided into a tonic and a phasic component. Because of the continuous rather than pulsatile nature of the input, we had to drop the concept of oscillator phase and derive self-consistent criteria for the existence and stability of an alternating firing pattern between two synchronous populations based solely on the perturbation of time intervals from their steady state values. Simulations showed that for high frequency oscillations as defined above, the mean field approach predicts the existence and stability of phase-locking between two synchronous populations better than the instantaneous phase shift approach. This approach may generalize to other forms of coupling amongst non-neural oscillators.

Correlative computational microscopy is accelerating the mapping of dynamic biological systems by integrating morphological and molecular measurements across spatial scales, from organelles to entire organisms. Visualization, measurement, and prediction of interactions among the components of biological systems can be accelerated by generalist computational imaging frameworks that relax the trade-offs imposed by multiplex dynamic imaging. This work reports a generalist framework for wave optical imaging of the architectural order (waveOrder) among biomolecules for encoding and decoding multiple specimen properties from a minimal set of acquired channels, with or without fluorescent labels. waveOrder expresses material properties in terms of elegant physically motivated basis vectors directly interpretable as phase, absorption, birefringence, diattenuation, and fluorophore density; and it expresses image data in terms of directly measurable Stokes parameters. We report a corresponding multi-channel reconstruction algorithm to recover specimen properties in multiple contrast modes. With this framework, we implement multiple 3D computational microscopy methods, including quantitative phase imaging, quantitative label-free imaging with phase and polarization, and fluorescence deconvolution imaging, across scales ranging from organelles to whole zebrafish. These advances are available via an extensible open-source computational imaging library, waveOrder, and a napari plugin, recOrder.

Based on a time-dependent Ginzburg-Landau system of equations and finite element modeling, we present novel results related with the physics of phase-slippage in superconducting wires surrounded by a non-superconductive environment. These results are obtained within our previously reported approach related to superconducting rings and superconductive gravitational wave detector transducers. It is shown that the phase-slip centers (PSCs) can be effective in originating not only positive but also negative thermal fluxes. With an appropriate design utilizing thermal diodes, PSCs can serve as cryocooling engines. Operating at Tsim 1 K cryostat cold-finger, they can achieve sub-Kelvin temperatures without using ^3He.

The Stokes V parameter characterizes asymmetry of amplitudes between right- and left-handed waves, and non-vanishing value of the V parameter yields a circularly polarized signal. Cosmologically, V parameter may be a direct probe for parity violation in the universe. In this paper, we theoretically investigate a measurement of this parameter, particularly focusing on the gravitational-wave backgrounds observed via ground-based interferometers. In contrast to the traditional analysis that only considers the total amplitude (or equivalently Omega_{GW}), the signal analysis including a circular-polarized mode has a rich structure due to the multi-dimensionality of target parameters. We show that, by using the network of next-generation detectors, separation between polarized and unpolarized modes can be performed with small statistical loss induced by their correlation.

Flow matching (FM) enables high-fidelity generation, while self-supervised learning (SSL) speech models provide hierarchical representations spanning acoustic and phonetic levels. However, existing FM-based speech enhancement (SE) methods operate primarily in the spectral domain, treating SSL features only as external conditions rather than modeling directly in the SSL latent space. To fully exploit the structural richness of SSL representations, we propose PhASE-Flow, an FM-based SE framework that operates entirely in the SSL space. It models the conditional distribution of clean acoustic representations given phonetic ones, reconstructing the waveform via a neural vocoder. Experiments show that PhASE-Flow outperforms state-of-the-art baselines in perceptual quality and intelligibility. Notably, it achieves competitive performance with only four sampling steps, enabling highly efficient inference. Audio demos are available at https://anonymous.4open.science/w/phase-flow_demo-E6E1/.

Artificial Intelligence (AI) weather models are improving rapidly, and their forecasts are already competitive with long-established traditional Numerical Weather Prediction (NWP). To build confidence in this new methodology, it is critical that we understand how these predictions are generated. This is a huge challenge as these AI weather models remain largely black boxes. In other areas of Machine Learning (ML), mechanistic interpretability has emerged as a framework for understanding ML predictions by analysing the building blocks responsible for them. Here we present an open-source, highly adaptable tool which incorporates concepts from mechanistic interpretability. The tool organises internal latent representations from the model processor and allows for initial analyses, including cosine similarity and Principal Component Analysis (PCA), enabling the user to identify directions in latent space potentially associated with meteorological features. Applying our tool to the graph neural network GraphCast, we present preliminary case studies for mid-latitude synoptic-scale waves and specific humidity. These demonstrate the tool's ability to identify linear combinations of latent channels that appear to correspond to interpretable features.

Using the supersymmetric method of random matrix theory within the Heidelberg approach framework we provide statistical description of stationary intensity sampled in locations inside an open wave-chaotic cavity, assuming that the time-reversal invariance inside the cavity is fully broken. In particular, we show that when incoming waves are fed via a finite number M of open channels the probability density {cal P}(I) for the single-point intensity I decays as a power law for large intensities: {cal P}(I)sim I^{-(M+2)}, provided there is no internal losses. This behaviour is in marked difference with the Rayleigh law {cal P}(I)sim exp(-I/I) which turns out to be valid only in the limit Mto infty. We also find the joint probability density of intensities I_1, ldots, I_L in L>1 observation points, and then extract the corresponding statistics for the maximal intensity in the observation pattern. For Lto infty the resulting limiting extreme value statistics (EVS) turns out to be different from the classical EVS distributions.