Early light curves of many core-collapse supernovae (SNe) are thought to be powered by the interaction of the shock wave with optically thick extended material, either a bound envelope or preexplosion ejected circumstellar matter (CSM). We analytically analyze the early emission produced by a shock with velocity v traversing a material of mass M_\mathrm{e} and opacity κextending to radius R_\mathrm{e}, and show the emission varies qualitatively with varying τ_\mathrm{e}=κ\!M_\mathrm{e}/(4π\!R_\mathrm{e}^2): For τ_\mathrm{e}\gg\!c/v a shock breakout occurs near R_\mathrm{e} producing an ``edge breakout" -- a UV-dominated breakout burst followed by ``cooling emission" of the shock-heated material; for τ_\mathrm{e}\lesssim\!c/v a ``wind breakout" occurs -- the breakout pulse is prolonged and followed by extended emission shifting from UV to X-ray as the shock becomes collisionless. We derive the dependence on \{v,κ,M_\mathrm{e},R_\mathrm{e}\} of the duration and luminosity characterizing the different emission phases, and show that current observations typically do not allow inference of all parameters. In particular, since the optical bands lie in the Rayleigh-Jeans tail of radiation emitted during the cooling phase, the observed cooling luminosity depends weakly on radius, \propto\!R_\mathrm{e}^{1/4}, leading to 1-2 orders of magnitude uncertainty in its inferred value. This suggests, e.g., that the common day-scale light curve features in Stripped-Envelope SNe do not necessarily imply material extending to R_\mathrm{e}\sim10^3\!R_\odot and are often consistent with low-mass R_\mathrm{e}\sim\!10^2\!R_\odot bound envelopes. Early multiband coverage (especially in UV/X-ray) can break these degeneracies; the forthcoming \emph{ULTRASAT} UV mission will allow inferring the properties of extended material around the population of SNe progenitors.

As climate change intensifies extreme weather events, water disasters pose growing threats to global communities, making adaptive reservoir management critical for protecting vulnerable populations and ensuring water security. Modern water resource management faces unprecedented challenges from cascading uncertainties propagating through interconnected reservoir networks. These uncertainties, rooted in physical water transfer losses and environmental variability, make precise control difficult. For example, sending 10 tons downstream may yield only 8-12 tons due to evaporation and seepage. Traditional centralized optimization approaches suffer from exponential computational complexity and cannot effectively handle such real-world uncertainties, while existing multi-agent reinforcement learning (MARL) methods fail to achieve effective coordination under uncertainty. To address these challenges, we present MARLIN, a decentralized reservoir management framework inspired by starling murmurations intelligence. Integrating bio-inspired alignment, separation, and cohesion rules with MARL, MARLIN enables individual reservoirs to make local decisions while achieving emergent global coordination. In addition, a LLM provides real-time reward shaping signals, guiding agents to adapt to environmental changes and human-defined preferences. Experiments on USGS data show that MARLIN improves uncertainty handling by 23\%, cuts computation by 35\%, and accelerates flood response by 68\%, exhibiting super-linear coordination, with complexity scaling 5.4x from 400 to 10,000 nodes. These results demonstrate MARLIN's potential for disaster prevention and protecting communities through intelligent, scalable water resource management.

Modern data-driven applications that make real-time decisions increasingly depend on advanced sensors which use pre-stored calibration data. In such applications, accurate characterization of sensor output uncertainty is important for reliable data interpretation. Here, we present a method for real-time on-device dynamic uncertainty quantification for sensor outputs which depend on pre-stored calibration data. We show how sensor calibration compensation equations (essential in advanced sensing systems) propagate uncertainties resulting from the quantization of calibration parameters to the sensor output. We use a low-cost thermal sensor as a motivating example and show these ideas are practical and possible on actual embedded sensor systems by prototyping them on two commercially-available uncertainty tracking hardware platforms. One has average power dissipation 16.7 mW and achieves 42.9x speedup compared to the equal-accuracy Monte Carlo computation (the status quo), and the other 147.15 mW and achieves 94.4x speedup. We present a proof-of-usefulness application using the quantified uncertainty in edge detection over ten test scenes where we show accuracy and precision average improvement by 4.97 and 40.25 percentage points, respectively, trading off sensitivity. Another application example examines uncertainty quantification for four different calibration-data storage scenarios and compute that a 48% increase in memory yields 75% smaller uncertainty metrics over the baseline.

In this study, we examine how orbital degrees of freedom and Majorana surface states influence the magnetic penetration depth in the superconductor UTe$_2$. Using a two-orbital model, we analyze pairing states belonging to the irreducible representations of the $D_{2h}$ crystal symmetry: $A_u$, $B_{1u}$, $B_{2u}$, and $B_{3u}$. For bulk nodal states such as $B_{2u}$, we find that the penetration depth for screening currents along the antinodal direction and the cylindrical axis scales as $T^2$, in strong contrast to the conventional $T^4$ law. This behavior originates from quasiparticles near the point nodes contributing to the interorbital paramagnetic current. We further show that Majorana surface states can dominate the low-temperature response. The fully gapped $A_u$ state hosts Majorana cones, which produce a $T^3$ dependence of the penetration depth when the ratio of penetration depth to coherence length ($κ$) is small. In contrast, the other pairing states exhibit Majorana Fermi arcs: the exponent is $n=2$ along the dispersive direction, while along the dispersionless direction it depends on whether the arcs terminate at endpoints. The exponent $n=2$ in the dispersive direction is robust, while it in the dispersionless direction relies on the presence or absence of the endpoints of the arcs and deviates from $n=2$ when endpoints are absent. Our results demonstrate that penetration-depth measurements provide a direct probe of Majorana surface states in low-$κ$ superconductors. For larger $κ$, the surface contribution becomes negligible and the temperature dependence is governed by bulk quasiparticles.

In this work, we investigate the discrete Calderón problem on grid graphs of dimension three or higher, formed by hypercubic structures. The discrete Calderón problem is concerned with determining whether the discrete Dirichlet-to-Neumann (DtN) operator, which links boundary potentials to boundary current responses, can uniquely identify the conductivity values on the graph edges. We provide an affirmative answer to the question, thereby extending the classical uniqueness result of Curtis and Morrow for two-dimensional square lattices. The proof employs a novel slicing technique that decomposes the problem into lower-dimensional components. Additionally, we support the theoretical finding with numerical experiments that illustrate the effectiveness of the approach.

Multi-centre studies increasingly rely on distributed inference, where sites share only centre-level summaries. Homogeneity of parameters across centres is often violated, motivating methods that both \emph{test} for equality and \emph{learn} centre groupings before estimation. We develop multivariate Cochran-type tests that operate on summary statistics and embed them in a sequential, test-driven \emph{Clusters-of-Centres (CoC)} algorithm that merges centres (or blocks) only when equality is not rejected. We derive the asymptotic $χ^2$-mixture distributions of the test statistics and provide plug-in estimators for implementation. To improve finite-sample integration, we introduce a multi-round bootstrap CoC that re-evaluates merges across independently resampled summary sets; under mild regularity and a separation condition, we prove a \emph{golden-partition recovery} result: as the number of rounds grows with $n$, the true partition is recovered with probability tending to one. We also give simple numerical guidelines, including a plateau-based stopping rule, to make the multi-round procedure reproducible. Simulations and a real-data analysis of U.S.\ airline on-time performance (2007) show accurate heterogeneity detection and partitions that change little with the choice of resampling scheme.

A model-independent determination of the CKM angle $γ$ is presented, using the $B^\pm\to[K^+K^-π^+π^-]_D h^\pm$ and $B^\pm\to[π^+π^-π^+π^-]_D h^\pm$ decays, with $h=K,π$. This measurement is the first phase-space-binned study of these decay modes, and uses a sample of proton-proton collision data collected by the LHCb experiment, corresponding to an integrated luminosity of $9$fb$^{-1}$. The phase-space bins are optimised for sensitivity to $γ$, and in each bin external inputs from the BESIII experiment are used to constrain the charm strong-phase parameters. The result of this binned analysis is $γ= (53.9_{-8.9}^{+9.5})^\circ$, where the uncertainty includes both statistical and systematic contributions. Furthermore, when combining with existing phase-space-integrated measurements of the same decay modes, a value of $γ= (52.6_{-6.4}^{+8.5})^\circ$ is obtained, which is one of the most precise determinations of $γ$ to date.

Detecting parity violation on cosmological scales would provide a striking clue to new physics. Large-scale structure offers the raw statistical power -- many three-dimensional modes -- to make such tests. However, for scalar observables, like galaxy clustering, the leading parity-sensitive observable is the trispectrum, whose high dimensionality makes the measurement and noise estimation challenging. We present two late-time parity-odd kurto spectra that compress the parity-odd scalar trispectrum into one-dimensional, power-spectrum-like observables. They are built by correlating (i) two appropriately weighted quadratic composite fields, or (ii) a linear and cubic composite field, constructed from dark matter (DM) or galaxy overdensity fields. We develop an FFTLog pipeline for efficient theoretical predictions of the two observables. We then validate the estimators for a specific parity-odd primordial template on perturbative DM field, and on DM and halo fields in full N-body \texttt{Quijote} simulations, with and without parity-odd initial conditions, in real and redshift space. For DM, the variance is dominated by the parity-even contribution -- i.e., the gravitationally induced parity-even trispectrum -- and is efficiently suppressed by phase-matched fiducial subtraction. For halos, discreteness-driven stochasticity dominates and is not appreciably reduced by subtraction; however, optimal weighting and halo-matter cross kurto spectra considerably mitigate this noise and enhance the signal. Using controlled down-sampling of the matter field, we empirically calibrate how the parity-even variance scales with number density and volume, and provide an illustrative forecast for the detectability of parity-odd kurto spectra in a Euclid-like spectroscopic galaxy survey.

We present a comprehensive analysis of super-Eddington black hole accretion simulations that solve the GRMHD equations coupled with angle-discretized radiation transport. The simulations span a range of accretion rates, two black hole spins, and two magnetic field topologies, and include resolution studies as well as comparisons with non-radiative models. Super-Eddington accretion flows consistently develop geometrically thick disks supported by radiation pressure, regardless of magnetic field configuration. Radiation generated in the inner disk drives substantial outflows, forming conical funnel regions that limit photon escape and result in very low radiation efficiency. The accretion flows are highly turbulent with thermal energy transport dominated by radiation advection rather than diffusion. Angular momentum is primarily carried outward by Maxwell stress, with turbulent Reynolds stress playing a subdominant role. Both strong and weak jets are produced. Strong jets arise from sufficient net vertical magnetic flux and rapid black hole spin and can effectively evacuate the funnel, enabling radiation to escape through strong geometric beaming. In contrast, weak jets fail to clear the funnel, which becomes obscured by radiation-driven outflows and leads to distinct observational signatures. Spiral structures are observed in the plunging region, behaving like density waves. These super-Eddington models are applicable to a variety of astronomical systems, including ultraluminous X-ray sources, little red dots, and black hole transients.

Strong, symmetrically focusing plasma lenses are promising for accommodating the small beams associated with plasma-based accelerators and collider final foci. However, while focusing with active and passive plasma lenses has been experimentally demonstrated, compatibility with high-brightness beams relevant for applications has not. In this Letter, we show experimentally that passive plasma lenses can preserve free-electron-laser-quality slice emittance while focusing two orders of magnitude more strongly than quadrupole magnets, and that the focal parameters can be controlled.

In this work, we investigate the coupling between a strong impurity and the topological boundary of an SSH heterojunction, composed of two SSH chains belonging to different topological classes. We show that impurity boundary coupling gives rise to bonding and antibonding states within the SSH bulk gap. This coupling produces an interference effect in the local density of states, as the impurity approaches the boundary the LDOS evolves from a single sharp peak to a characteristic double peak structure. Moreover, the interference strength can be quantified by the decay length of the bonding or antibonding wavefunction and by the energy splitting of the LDOS resonance peaks near the Fermi energy.

A particularly compelling aspect of the GW190521 event detected by the LIGO--Virgo--KAGRA (LVK) collaboration is that it has an extremely short duration, and lacks a clearly identifiable inspiral phase usually observed in the binary black holes (BBHs) coalescence. In this work, we hypothesize that GW190521 might represent a single, isolated gravitational wave (GW) echo pulse from the wormhole, which is the postmerger remnant of BBHs in another universe and connected to our universe through a throat. The ringdown signal after BBHs merged in another universe can pass through the throat of wormhole and be detected in our universe as a short-duration echo pulse. Our analysis results indicate that our model yields a network signal-to-noise ratio comparable to that of the standard BBHs merger model reported by the LVK collaboration. For GW190521, Bayesian model selection yields $\ln \mathcal{B}^{\text{Echo}}_{\text{BBH}} \simeq -2.9$, indicating that the data favor the BBH hypothesis over our echo-for-wormhole model.

Thin flame dynamics in a turbulent flow remains debated, with various parameterizations proposed for the typical flame propagation velocity. According to the classical Damköhler's model based on Huygens' principle, a flame front should advance at a constant velocity normal to the interface between reactants and products, with a turbulent acceleration induced by the wrinkling and surface increase of the interface. However, combustion experiments often deviate from this model due to intertwined thermal and turbulent effects, complicating flame acceleration characterization. In this study, we use an autocatalytic reaction that generates a thin reactive front in an aqueous medium, enabling clearer isolation of turbulence effects. Using oscillating grids to generate turbulence in a closed tank, we examine two configurations: a single-grid setup with a spatially decaying turbulence and a dual-grid system with in the middle, a nearly homogeneous, isotropic turbulence. Particle Image Velocimetry and Laser Induced Fluorescence measurements capture both the velocity field and the front propagation, revealing two different regimes: the expected Huygens' propagation regime, but also a reactive mixing regime, where the turbulent advection of the products inside the reactants initiates multiple, dispersed reaction locations. Additionally, we show that even the small density difference between reactants and products plays a crucial role in the front dynamics. This work advances our understanding of autocatalytic fronts in turbulence, emphasizing the critical interplay between chemical kinetics and flow dynamics.

We conduct an indirect dark matter (DM) search in the Galactic Center, focusing on a square region within $\pm 9^{\circ}$ in Galactic longitude and latutide, using 2,865 days of data ($\sim$8 years) from the High-Altitude Water Cherenkov (HAWC) Observatory. We explore DM particles within the Weakly Interacting Massive Particles framework with masses from 1 TeV to 10 PeV. Analyzing three annihilation channels ($b\bar{b}$, $τ^{+}τ^{-}$, $W^{+}W^{-}$) and three density profiles (Navarro-Frenk-White, Einasto, Burkert), we find no significant excess and set 95\% confidence-level upper limits on the velocity-weighted annihilation cross section. Our results provide the first constraints on DM particles well above 100 TeV using gamma-ray data from the Galactic Center, with the strongest limits $\mathcal{O}(10^{-24})$~cm$^{3}$/s, from the $τ^{+}τ^{-}$ channel and the Einasto profile.

We introduce and analyse the kinetic random-field nonreciprocal Ising model, which incorporates bimodal (double-delta) diffusive disorder along with pairwise nonreciprocal interactions between two different species. Using mean-field and effective-field theory, in combination with kinetic Monte Carlo simulations (3D Glauber dynamics), we identify a nonequilibrium tricritical (Bautin) point separating Hopf-type transitions (continuous) from saddle-node-of-limit-cycle (SNLC) transitions (discontinuous). For a weak random field which is less than a critical value, the onset of collective oscillations (the "swap" phase) occurs via a supercritical Hopf bifurcation, whereas for fields greater than the critical value, the transition is first-order (SNLC), exhibiting hysteresis and Binder-cumulant signatures. The finite-size scaling of the susceptibility is consistent with the distinct critical and discontinuous behaviour shown in the Hopf and SNLC regimes, respectively (effective exponents $\approx1.96$ in the Hopf regime and $\approx3.0$ in the SNLC regime). Additionally, in the first-order regime, the swap phase is sustained only above a threshold nonreciprocity, and this threshold increases monotonically with the disorder strength. We further identify a new droplet-induced swap phase in the larger field-strength region, which cycles eight different metastable states. A dynamical free-energy picture rationalises droplet nucleation as the mechanism for these cyclic jumps. Together, these results demonstrate how disorder and nonreciprocity combined generate rich nonequilibrium criticality, with implications for driven and active systems.

We investigate charge balance functions for pion, kaon, and proton pairs in proton-proton (pp) collisions at $\sqrt{s}=13$ TeV using Monte Carlo models, PYTHIA8 and EPOS-LHC, with transverse spherocity to classify event topology and charged-particle multiplicity to select system size. Simulations with PYTHIA8 and EPOS-LHC reveal that balance-function widths in rapidity and azimuthal angle depend on multiplicity and event shape. In PYTHIA8, widths decrease monotonically with multiplicity, consistent with local charge conservation in a fragmentation-dominated scenario. In contrast, the EPOS-LHC model, especially when using the core corona implementation, exhibits a more intricate response, where the combined effects of hydrodynamic radial flow and longitudinal diffusion result in narrower azimuthal correlations and broader rapidity correlations. These features are characteristic signatures of collective dynamics, similar to those observed in heavy-ion collisions. Events with low spherocity, which are jet-like in nature, exhibit significantly narrower balance function widths compared to isotropic events with high spherocity, illustrating that event-shape selection provides clear sensitivity to the underlying dynamics of particle production in pp collisions. The species dependence and event-shape sensitivity of the balance-function widths provide information about the hadronization dynamics and collectivity in small systems. These results demonstrate that multidimensional, particle species dependent balance function measurements can disentangle the underlying mechanisms of charge correlations and medium-like behavior in high-multiplicity pp collisions.

Incorporation of machine learning (ML) techniques into atomic-scale modeling has proven to be an extremely effective strategy to improve the accuracy and reduce the computational cost of simulations. It also entails conceptual and practical challenges, as it involves combining very different mathematical foundations, as well as software ecosystems that are very well developed in their own right, but do not share many commonalities. To address these issues and facilitate the adoption of ML in atomistic simulations, we introduce two dedicated software libraries. The first one, metatensor, provides multi-platform and multi-language storage and manipulation of arrays with many potentially sparse indices, designed from the ground up for atomistic ML applications. By combining the actual values with metadata that describes their nature and that facilitates the handling of geometric information and gradients with respect to the atomic positions, metatensor provides a common framework to enable data sharing between ML software -- typically written in Python -- and established atomistic modeling tools -- typically written in Fortran, C or C++. The second library, metatomic, provides an interface to store an atomistic ML model and metadata about this model in a portable way, facilitating the implementation, training and distribution of models, and their use across different simulation packages. We showcase a growing ecosystem of tools, including low-level libraries, training utilities, and interfaces with existing software packages that demonstrate the effectiveness of metatensor and metatomic in bridging the gap between traditional simulation software and modern ML frameworks.

A finite relational structure A is called compact if for any infinite relational structure B of the same type, the existence of a homomorphism from B to A is equivalent to the existence of homomorphisms from all finite substructures of B to A. We show that if A has width one, then the compactness of A can be proved in the axiom system of Zermelo and Fraenkel, but otherwise, the compactness of A implies the existence of non-measurable sets in 3-space.

The scotogenic model provides a minimal and elegant framework that simultaneously explains neutrino masses and accommodates a viable dark matter (DM) candidate. In this work, we investigate the phenomenology of fermionic DM in the scotogenic model, with a particular emphasis on the effects of a non-standard cosmological history characterized by a low reheating temperature. We demonstrate that entropy injection from inflaton decay can significantly dilute the DM abundance, thereby relaxing the annihilation cross section required to reproduce the observed relic density and opening new regions of viable parameter space. We further analyze the complementarity between current and future direct detection experiments and charged lepton flavour violation (cLFV) searches in probing this scenario. Our results show that next-generation direct detection experiments such as DARWIN and XLZD, together with upcoming cLFV searches (in particular the future sensitivity of $μ\rightarrow 3e$ and $μ\rightarrow e$ conversion experiments), will be capable of testing substantial regions of the parameter space, including those associated with low reheating temperatures.

Blockchain networks offer decentralization, transparency, and immutability for managing critical data but encounter scalability problems as the number of network members and transaction issuers grows. Sharding is considered a promising solution to enhance blockchain scalability. However, most existing blockchain sharding techniques prioritize performance at the cost of availability (e.g., a failure in a few servers holding a shard leads to data unavailability). In this paper, we propose PyloChain, a hierarchical sharded blockchain that balances availability and performance. PyloChain consists of multiple lower-level local chains and one higher-level main chain. Each local chain speculatively executes local transactions to achieve high parallelism across multiple local chains. The main chain leverages a directed-acyclic-graph (DAG)-based mempool to guarantee local block availability and to enable efficient Byzantine Fault Tolerance (BFT) consensus to execute global (or cross-shard) transactions within a collocated sharding. PyloChain speculatively executes local transactions across multiple local chains to achieve high parallelism. In order to reduce the number of aborted local transactions, PyloChain applies a simple scheduling technique to handle global transactions in the main chain. PyloChain provides a fine-grained auditing mechanism to mitigate faulty higher-level members by externalizing main chain operations to lower-level local members. We implemented and evaluated PyloChain, demonstrating its performance scalability with 1.49x higher throughput and 2.63x faster latency compared to the state-of-the-art balanced hierarchical sharded blockchain.

This paper provides an empirical study of the Social Sphere Model for influence prediction, previously introduced by the authors, combining link prediction with top-k centrality-based selection. We apply the model to the temporal arXiv General Relativity and Quantum Cosmology collaboration network, evaluating its performance under varying edge sampling rates and prediction horizons to reflect different levels of initial data completeness and network evolution. Accuracy is assessed using mean squared error in both link prediction and influence maximization tasks. The results show that the model effectively identifies latent influencers, i.e., nodes that are not initially central but later influential, and performs best with denser initial graphs. Among the similarity measures tested, the newly introduced RA-2 metric consistently yields the lowest prediction errors. These findings support the practical applicability of the model to predict real-world influence in evolving networks.

Background and Objective: The electrocardiogram (ECG) plays a crucial role in the diagnosis and treatment of various cardiac diseases. ECG signals suffer from low-resolution (LR) due to the use of convenient acquisition devices, as well as internal and external noises and artifacts. Classical ECG super-resolution (ECGSR) methods adopt an open-loop architecture that converts LR ECG signals to super-resolution (SR) ones. According to the theory of automatic control, a closed-loop framework exhibits superior dynamic and static performance compared with its open-loop counterpart. Methods: This paper proposes a closed-loop approach, termed circular ECGSR (CECGSR), which models the degradation process from SR ECG signals to LR ones. The negative feedback mechanism of the closed-loop system is based on the differences between the LR ECG signals. A mathematical loop equation is constructed to characterize the closed-loop infrastructure. The Taylor series expansion is employed to demonstrate the near-zero steady-state error of the proposed method. A Plug-and-Play strategy is considered to establish the SR unit of the proposed architecture, leveraging any existing advanced open-loop ECGSR methods. This paper also presents Transformer model based open-loop ECGSR and closed-loop CECGSR algorithms. Results: Simulation experiments on both noiseless and noisy subsets of the Physikalisch-Technische Bundesanstalt-Extra Large (PTB-XL) datasets demonstrate that the proposed CECGSR outperforms state-of-the-art open-loop ECGSR algorithms in the reconstruction performance of ECG signals. Conclusions: The proposed method will efficiently enrich ECG signal details and remove ECG signal artifacts in clinical applications.

Decoded Quantum Interferometry (DQI) is a recently proposed quantum optimization algorithm that exploits sparsity in the Fourier spectrum of objective functions, with the potential for exponential speedups over classical algorithms on suitably structured problems. While highly promising in idealized settings, its resilience to noise has until now been largely unexplored. To address this, we conduct a rigorous analysis of DQI under noise, focusing on local depolarizing noise. For the maximum linear satisfiability problem, we prove that, in the presence of noise, performance is governed by a noise-weighted sparsity parameter of the instance matrix, with solution quality decaying exponentially as sparsity decreases. We demonstrate this decay through numerical simulations on two special cases: the Optimal Polynomial Intersection problem and the Maximum XOR Satisfiability problem. The Fourier-analytic methods we develop can be readily adapted to other classes of random Pauli noise, making our framework applicable to a broad range of noisy quantum settings and offering guidance on preserving DQI's potential quantum advantage under realistic noise.

Kernel methods are versatile tools for function approximation and surrogate modeling. In particular, greedy techniques offer computational efficiency and reliability through inherent sparsity and provable convergence. Inspired by the success of deep neural networks and structured deep kernel networks, we consider deep, multilayer kernels for greedy approximation. This multilayer structure, consisting of linear kernel layers and optimizable kernel activation function layers in an alternating fashion, increases the expressiveness of the kernels and thus of the resulting approximants. Compared to standard kernels, deep kernels are able to adapt kernel intrinsic shape parameters automatically, incorporate transformations of the input space and induce a data-dependent reproducing kernel Hilbert space. For this, deep kernels need to be pretrained using a specifically tailored optimization objective. In this work, we not only introduce deep kernel greedy models, but also present numerical investigations and comparisons with neural networks, which clearly show the advantages in terms of approximation accuracies. As applications we consider the approximation of model problems, the prediction of breakthrough curves for reactive flow through porous media and the approximation of solutions for parameterized ordinary differential equation systems.

We introduce new invariants of smooth complex projective varieties, called Hodge atoms. Their construction combines rational Gromov-Witten invariants with classical Hodge theory and relies on the notion of an F-bundle, which is a non-archimedean version of a non-commutative Hodge structure. The Hodge atoms arise from the spectral decomposition of the F-bundle under the Euler vector field action, and behave additively under blowups, in accordance with Iritani's blowup theorem. We compute several examples and demonstrate applications to birational geometry. In particular, we prove that a very general cubic fourfold is not rational. We also obtain a new proof of the equality of Hodge numbers of birational Calabi-Yau manifolds in any dimension. Furthermore, we show that the framework naturally extends to representations of other motivic Galois groups. This enables the theory of atoms to produce new obstructions to rationality over non-algebraically closed fields of characteristic zero as well.

Let $F$ be a totally real number field, and $g,f,h$ be Hilbert modular forms over $F$ that are Hecke eigenforms satisfying $g=f\cdot h$. We characterize such product identities among all real quadratic fields of narrow class number one, proving they occur only for $F=\mathbb Q(\sqrt{5})$, with precisely two such identities. We also shed some light on the general totally real case by showing that no such identity exists when both $f$ and $h$ are Eisenstein series of distinct weights.

First-order phase transitions in the early Universe are a well-motivated source of gravitational waves (GWs). In this Letter, we identify a previously overlooked GW production mechanism: gravitational transition radiation, arising from graviton emission by particles whose mass changes as they pass through expanding bubble walls. Unlike conventional sources such as bubble collisions or sound waves, this mechanism operates at the microscopic scale set by the Lorentz-contracted wall thickness, leading to GW emission at significantly higher frequencies. The resulting spectrum features a distinctive shape with a peak frequency redshifting to $f_{\rm peak}\sim T_0\sim 10^{10}\,{\rm Hz}$ where $T_0$ is the current temperature of the Universe. This mechanism is generic and is expected to operate similarly for domain walls and other relativistic interfaces.

We investigate the advantage of using squeezed input light for generating gravity-induced entanglement (GIE) through Fourier-domain analysis. Based on the findings of Ref.~\cite{Miki2024}, which demonstrated the feasibility of detecting GIE in optomechanical systems under quantum control, we further demonstrate that squeezed input light can reduce the optical noise in the mechanical conditional state and enhance GIE. Furthermore, we estimate the systematic and statistical errors in the measurement of GIE using the Fourier transformation over a finite measurement time. Based on the error estimations using the signal-to-noise ratio (SNR) in GIE detection, we find that a total measurement time of $10^6\,\mathrm{s}$ is required to achieve ${\rm SNR} = 1$ when using squeezed input light, whereas $10^{6.8}\,\mathrm{s}$ is needed without squeezed input light. This result highlights the effectiveness of optomechanical systems and the critical role of squeezed input light in enhancing the detectability of GIE.

Non-Hermitian quantum many-body systems exhibit a rich array of physical phenomena, including non-Hermitian skin effects and exceptional points, that remain largely inaccessible to existing numerical techniques. In this work, we investigate the application of variational Monte Carlo and neural network wavefunction representations to examine their ground-state (the eigenstate with the smallest real part energy) properties. Due to the breakdown of the Rayleigh-Ritz variational principle in non-Hermitian settings, we develop a self-consistent symmetric optimization framework based on variance minimization with a dynamically updated energy estimate. Our approach respects the biorthogonal structure of left and right eigenstates, and is further strengthened by exploiting system symmetries and pseudo-Hermiticity. Tested on a two-dimensional non-Hermitian transverse field Ising model endowed with a complex longitudinal field, our method achieves high accuracy across both parity-time symmetric and broken phases. Moreover, we propose novel optimization routines that address the challenges posed by exceptional points and provide reliable convergence to the ground state in regimes where standard variational techniques fail. Lastly, we show, through extensive numerical evidence, that our method offers a scalable and flexible computational tool to investigate non-Hermitian quantum many-body systems, beyond the reach of conventional numerical techniques such as the density-matrix renormalization group algorithm.

For integer $n$, the $n$-iterated line graph $L^n(G)$ of an undirected graph $G$ is defined to be $L(L^{n-1}(G))$, where $L^1(G)$ is the line graph $L(G)$ of $G$. In this paper we introduce hamiltonian path index. Hamiltonian path index, denoted by $h_p(G)$, is the minimum number $n$ such that $L^n(G)$ contains a hamiltonian path. We show that hamiltonian path index of $G$ exists for any graph $G$ and we set the exact value of hamiltonian path index for trees and discuss the problem about graphs with hamiltonian 2-connected blocks.