Metamaterials derive their unconventional properties from engineered microstructures, with periodic lattices providing a versatile framework for modeling wave propagation. Dispersion relations, obtained from Bloch-Floquet theory, govern how waves propagate, attenuate, or localize within such systems. Extending interactions beyond nearest neighbors, through nonlocality, substantially enriches the design space of band diagrams, enabling phenomena such as negative or zero group velocities, roton-like extrema, and band-gap localization. However, existing approaches to dispersion tailoring often rely on analytical formulations or Fourier-based identifications, which become impractical for complex coupling mechanisms and offer limited control over physical constraints such as stiffness positivity. This work introduces a general interpolation-based framework for customizing dispersion relations in uniform nonlocal lattices. Rather than reconstructing full dispersion curves, the method enforces prescribed frequency-wavenumber points as interpolation constraints, enabling localized and tunable control of wave behavior. The formulation is applied to both spring- and beam-interaction lattices, and demonstrated on an Euler-Bernoulli beam model with adjustable nonlocal couplings. Through systematic parameter tuning, the framework enables the creation of rotons, the adjustment of group-velocity dispersion, and the design of evanescent waves with controlled exponential decay within band gaps, all while ensuring real, positive-only stiffness parameters and passive mechanical behavior. Altogether, this parametric interpolation strategy provides a physically consistent and computationally efficient route for engineering advanced phononic functionalities in periodic nonlocal systems.

Cosmological phase transitions are a frequent phenomenon in particle physics models beyond the Standard Model, and the corresponding gravitational wave signal offers a key probe of new physics in the early Universe. Depending on the underlying microphysics, the transition can exhibit either direct or inverse hydrodynamics, leading to a different phenomenology. Most studies to date have focused on direct transitions, where the cosmic fluid is pushed or dragged by the expanding vacuum bubbles. In contrast, inverse phase transitions are characterized by fluid profiles where the plasma is sucked in by the expanding bubbles. Using the sound shell model, we derive and compare the gravitational wave spectra from sound waves for direct and inverse phase transitions, providing new insights into the potential observable features and the possibility of discriminating among the various fluid solutions in gravitational wave experiments.

Recent experimental hints from the Large Hadron Collider (LHC) in di-photon and partially in the $τ^+τ^-$ final states suggest the possible existence of an additional Higgs boson with a mass around 95 GeV. Interestingly, these observations are consistent with earlier results from the Large Electron-Positron (LEP) collider, which pointed to an excess in $b\bar b$ final states within a similar mass range. Additionally, CMS has observed an excess in the $γγb\bar{b}$ final state, indicating a possible resonance near 650 GeV decaying into a pair of SM-like Higgs bosons or into a SM-like Higgs boson accompanied by a lighter scalar with mass near 95 GeV. In this work, we investigate whether these anomalies can be simultaneously explained within the Next-to-2-Higgs-Doublet Model (N2HDM), an extension of the Standard Model (SM) scalar sector featuring two complex Higgs doublets and an additional real singlet. Assuming the existence of a CP-even Higgs state compatible with the 95 GeV excesses (restricted to the $γγ$ and $b\bar b$ channels). Our results show that a heavy CP-even Higgs resonance around 650 GeV, produced predominantly via gluon-gluon fusion and subsequently decaying into a 125 GeV Higgs boson together with another scalar at approximately 95 GeV, can be simultaneously accommodated within both the N2HDM Type-II and Type-Y frameworks in parameter regions that remain consistent with the relevant experimental $2σ$ intervals for the reported excesses, once all theoretical and experimental constraints are imposed. This interpretation leads to distinctive and testable predictions for the ongoing LHC Run~3 and the forthcoming High-Luminosity LHC (HL-LHC) phase, in particular through correlated rates in the $γγb\bar b$, $τ^+τ^- b\bar b$, $b\bar b\,γγ$, and $γγτ^+τ^-$ final states.

To understand the physical mechanisms underlying the prompt emission of gamma-ray bursts (GRB), single FRED (Fast-Rise-Exponential-Decay) profile GRBs serve as an ideal sample, as they origin from single epoch central engine activity. These GRBs have been found to exhibit a peculiar morphology-including the elegant cross-energy-similarity across energy bands and the recently discovered composite nature-challenging nearly all existing radiation mechanisms, sparking widespread curiosity about their origins. Here we propose a physical model which includes radiation locations sequentially triggered by propagating magnetic perturbations. It naturally explains all observed properties of these GRBs, including the self-similar FRED profile, multi-band aligned subpulses, hard-to-soft spectral evolution, local intensity tracking, and increasing subpulse durations. Furthermore, our results demonstrate that the duration of these GRBs is not reflecting the activity timescale of the central engine, reconciling recent challenges to the traditional merger-short/collapsar-long dichotomy of GRBs.

We investigate the influence of ideal Fermi gas dark matter on the observable properties of neutron stars (NSs). Our analysis considers dark matter (DM) particle masses ($μ$) ranging from $0.2$ GeV to $1$ GeV and various DM mass fractions ($f$). By examining the coexistence of DM and baryonic matter (BM), we explore the formation of either a dense DM core or an extended dark halo within NSs. Our findings indicate that the resulting DM distribution depends critically on both $μ$ and $f$. We systematically explore the parameter space of the fermionic DM model using two representative BM equations of state (EoSs) by applying constraints from NS radius measurements by the Neutron Star Interior Composition Explorer (NICER), observations of $2M_{\odot}$ NSs, and tidal deformability limits from the LIGO/Virgo Collaboration. This comprehensive analysis enables us to exclude specific ranges of $μ$ and $f$, demonstrating that the amount of accumulated DM must be relatively small to satisfy current astrophysical constraints.

Wideband timing of the North American Nanohertz Observatory for Gravitational Waves (NANOGrav) datasets, where a single time-of-arrival (TOA) and a single dispersion measure (DM) are measured using the entire bandwidth of each observation, was first done for the 12.5-year dataset, and proved to be invaluable for characterizing the time-varying dispersion measure, reducing the data volume, and for improving the overall timing precision. The Canadian Hydrogen Intensity Mapping Experiment (CHIME) Telescope has been observing most NANOGrav millisecond pulsars (MSPs) at nearly daily cadence (compared to roughly monthly cadence for other NANOGrav observations) since 2019 with the objective of integration into future pulsar timing array (PTA) datasets. In this paper, we show the results of integration of high-cadence, low-observing-frequency CHIME data with data from the NANOGrav experiment for an isolated MSP PSR J0645$+$5158 and three binary MSPs PSR J1012$+$5307, PSR J2145$-$0750, and PSR J2302$+$4442. Using a wideband timing pipeline which we also describe, we present updated timing results for all four sources, including improvements in measurements of relativistic post-Keplerian parameters for the three binary pulsars in this analysis. For PSR J2302$+$4442, we report an updated strong detection of Shapiro delay from which we measured a companion mass of $0.35^{+0.05}_{-0.04}\ M_{\odot}$, a pulsar mass of $1.8^{+0.3}_{-0.3}\ M_{\odot}$, and an orbital inclination of ${80^{\circ}}^{+1}_{-2}$. We also report updated constraints on the reflex motion for PSR J2145$-$0750 using a combination of Very Long Baseline Array astrometry and our updated measurement of the time derivative of the projected semi-major axis of the pulsar orbit as a prior.

We develop observer design over hypercomplex quaternions in a characteristic-polynomial-free framework. Using the standard right-module convention, we derive a right observable companion form and companion polynomial that encode error dynamics through right-eigenvalue similarity classes. We also give an Ackermann-type formula for real-coefficient target polynomials, where polynomial evaluation is similarity-equivariant. The resulting recipes place observer poles directly over quaternions and clarify when companion-coordinate updates and one-shot Ackermann formulas remain valid.

We study New Massive Gravity (NMG) with Chern-Simons (CS), cubic, and quartic terms under the Compère-Song-Strominger (CSS) boundary conditions. By employing a semi-product of a Virasoro and a $U(1)$ Kac-Moody current algebra as the asymptotic symmetry algebra, we calculate the entropy of BTZ black holes via the degeneracy of states belonging to a Warped-CFT. Then, we compute the linearized energy excitations using the representations of the algebra $U(1)\times SL(2, R)_{R}$ and demonstrate that the energies of excitations are non-negative at two chiral points in the parameter space.

Smooth structures on high dimensional manifolds are classified by maps to the infinite loop space $TOP/O$. The homotopy groups of this space are known to be finite. Given a compact Lie group $G$, this space can be regarded as an equivariant infinite loop space and equivariant maps from a locally linear, high dimensional $G$-manifold to $TOP/O$ classify stable $G$-smoothings. We compute the equivariant homotopy groups $π_V^{C_p}TOP/O\otimes\mathbb{Q}$ where $C_p$ denotes the cyclic group of order $p$. By applying our methods to the group $C_4$, we prove a Chern class analogue of Novikov's theorem on rational Pontryagin classes.

We provide sign information for the top Lyapunov exponent for a stochastic differential equation driven by fractional Brownian motion. To this aim we analyze the stochastic dynamical system generated by such an equation, obtain a random dynamical system and construct an appropriate invariant measure. Suitable estimates for its density together with Birkhoff's ergodic theorem imply the negativity of the top Lyapunov exponent by increasing the noise intensity.

Let $G$ be a graph. We denote by $e(G)$ and $ρ(G)$ the size and the spectral radius of $G$. A spanning subgraph $F$ of $G$ is called an even factor of $G$ if $d_F(v)\in\{2,4,6,\ldots\}$ for every $v\in V(G)$. Yan and Kano provided a sufficient condition using the number of odd components in $G-S$ for a graph $G$ of even order to contain an even factor, where $S$ is a vertex subset of $G$ [Z. Yan, M. Kano, Strong Tutte type conditions and factors of graphs, Discuss. Math. Graph Theory 40 (2020) 1057--1065]. In this paper, motivated by Yan and Kano's above result, we present some tight sufficient conditions to guarantee that a connected graph $G$ with the minimum degree $δ$ contains an even factor with respect to its size and spectral radius.

Tomographic techniques are vital in modern medicine, allowing doctors to observe patients' interior features. Individual steps in the measurement process are modeled by `single projection operators' $p$. These are line integral operators over a collection of curves that covers the regions of interest. Then, the entire measurement process can be understood as a finite collection of such single projections, and thus be modeled by an $N$-projections operator $P=(p_1,\dots,p_N)$. The most well-known example of an $N$-projections operator is the restriction of the Radon transform to finitely many projection angles. Characterizations of the range of $N$-projections operators are of intrinsic mathematical interest and can also help in practical applications such as geometric calibration, motion detection, or model parameter identification. In this work, we investigate the range of projection pair operators $\mathcal{P}$ in the plane, i.e., operators formed by two projections ($N=2$) applied to functions in $\mathbb{R}^2$. We find that the set of annihilators to $\mathrm{rg}(\mathcal{P})$ that are regular distributions contains at most one dimension and a range condition can be explicitly determined by what we refer to as `kernel conditions'. With this tool, we examine the exponential fanbeam transform for which no range conditions were known, finding that no (regular) range condition exists, and therefore, arbitrary data can be approximated in an $L^2$ sense by projections of smooth functions. We also illustrate the use of this theory on a mixed parallel-fanbeam projection pair operator.

In our recent work [Van de Moortel, The coexistence of null and spacelike singularities inside spherically symmetric black holes], we analyzed the transition between null and spacelike singularities in spherically symmetric dynamical black holes and demonstrated that the spacelike portion is described by a Kasner metric with positive varying exponents that degenerate to $(1,0,0)$ near the null-spacelike transition. In the present paper, we provide examples of global spacetimes satisfying the assumptions of this previous result and apply its analysis to obtain a large class of asymptotically flat (spherically symmetric) black hole spacetimes that exhibit coexisting null and spacelike singularities. Our main results include: _The construction of one-ended asymptotically flat black hole spacetimes solving the Einstein-Maxwell-charged-scalar-field equations. The proof relies on a new spacelike-characteristic gluing method between any uncharged spherically symmetric solution and the event horizon of a charged dynamical black hole. _The construction of a large class of two-ended asymptotically flat black hole spacetimes solving the Einstein-Maxwell-(uncharged)-scalar-field equations. In both cases, we show that the terminal boundary in the black hole interior only has two distinct components: a weakly singular (null) Cauchy horizon $\mathcal{CH}_{i^+}$ where curvature blows up and a strong singularity $\mathcal{S}=\{r=0\}$. Our construction provides the first examples of black holes with coexisting null and spacelike singularities. These examples hold particular significance in the one-ended case as a model of gravitational collapse, where this phenomenon is conjecturally generic for the Einstein-scalar-field model, even beyond spherical symmetry.

Large-scale molecular dynamics simulations with high accuracy have been increasingly popular for their capability to bridge the gap between atomistic modeling and mesoscale phenomena. Both machine learning potentials and enhanced sampling approaches offer substantial improvements in high-accuracy simulation efficiency, which can be further boosted through GPU acceleration. However, an efficient framework combining these advances for extending simulations to large systems and long timescales remains elusive. In this work, we proposed a full-life-cycle GPU accelerated metadynamics simulations package GPU-MetaD. Benchmarking across molecular, interface, and bulk systems demonstrates that GPU-MetaD efficiently handles diverse atomic systems and delivers an order-of-magnitude performance improvement. Building on this demonstrated capability, it enables ab-initio-level rare-event sampling for systems comprising millions of atoms on a typical single GPU. This capability allows us to reveal a previously unknown size-dependent two-step nucleation mechanism in gallium nitride (GaN), highlighting the potential of GPU-MetaD for uncovering complex rare events in realistic large-scale materials systems.

Axions and axion-like particles (ALPs) have gained immense attention in searches for beyond Standard Model (BSM) physics. Experiments searching for axions leverage their predicted couplings to Standard Model (SM) particles to look for observable signals. Though weak, these couplings allow axions to be produced abundantly in the interiors of stars such as the Sun. Once created, axions can escape the Sun and while passing through the solar atmosphere, oscillate into photons in the magnetic field producing x-rays. For the first time, we used data from the observation of soft x-rays from the quiet Sun during the 2019-20 solar minimum by the solar x-ray monitor (XSM), onboard India's Chandrayaan-2 lunar exploration mission, to constrain the coupling of axions to photons ($g_{a γγ}$). Using the latest models of the solar atmosphere to calculate the magnetic field and plasma frequency, we constrain $g_{a γγ} \lesssim (0.50 - 2.26) \times 10^{-10}$ GeV$^{-1}$ at $95\%$ confidence level for axion masses $m_a \lesssim 5 \times 10^{-4}$eV.

We present a rigorous identification of candidates for dormant black holes (BHs) and neutron stars (NSs) in binaries using summary statistics from Gaia DR3, rather than full orbital solutions. Although Gaia astrometric orbits have already revealed a small sample of compact object binaries, many systems remain undetected due to stringent quality cuts imposed on the published orbits. Using a forward-modelling framework that simulates Gaia observables, in particular the re-normalised unit weight error (ruwe) and radial velocity (RV) scatter, we infer posterior distributions for companion mass and orbital period via MCMC sampling, marginalising over nuisance orbital parameters. We validate our approach by comparing the predicted masses and periods against full orbit solutions from DR3, and by successfully recovering known compact object binaries as promising candidates. The method is best suited for systems with red giant primaries, which have more reliable Gaia RV scatter and a light centroid more likely dominated by one component, compared to main-sequence stars, and they are less likely to be triples with short-period inner binaries, which produce confounding signatures. We applied the method to three million giants and identify 389 systems with best-fit companion masses $\gtrsim 3\,M_\odot$. Recovery simulations suggest our selection method is substantially more sensitive than the DR3 non-single-star catalogue, particularly for binaries with periods below 1 year and above $\sim 6$ years. These candidates represent promising targets for spectroscopic follow-up and Gaia DR4 analysis to confirm the presence of compact objects. Candidate main-sequence stars with massive companions face a larger set of confounding effects. Therefore, we present an analogous catalogue of 279 additional main-sequence candidates only as an appendix.

AI agents are vulnerable to indirect prompt injection attacks, where malicious instructions embedded in external content or tool outputs cause unintended or harmful behavior. Inspired by the well-established concept of firewalls, we show that a simple, modular, and model-agnostic defense operating at the agent--tool interface achieves perfect security with high utility across all four public benchmarks: AgentDojo, Agent Security Bench, InjecAgent and tau-Bench, while achieving a state-of-the-art security--utility tradeoff compared to prior results. Specifically, we employ two firewalls: a Tool-Input Firewall (Minimizer) and a Tool-Output Firewall (Sanitizer). Unlike prior complex approaches, this defense makes minimal assumptions about the agent and can be deployed out of the box. This makes it highly generalizable while maintaining strong performance without compromising utility. Our analysis also reveals critical limitations in these existing benchmarks, including flawed success metrics, implementation bugs, and most importantly, weak attacks, hindering progress. To address this, we present targeted fixes to these issues for AgentDojo and Agent Security Bench, and propose best practices for more robust benchmark design. Moreover, we introduce a three-stage attack strategy that cascades standard prompt injection attacks, second-order attacks, and adaptive attacks to evaluate the robustness beyond existing attacks. Overall, our work shows that existing agentic security benchmarks are easily saturated by a simple approach and highlights the need for stronger benchmarks with carefully chosen evaluation metrics and strong adaptive attacks.

Parity and time-reversal (PT ) symmetry is shown as the natural cause of quasi-integrability of deformed integrable models, crucial to represent real physical systems as they posses various irregularities. The condition for asymptotic conservation of quasi-conserved charges appear as a direct consequence of the PT -symmetric phase of the system, ensuring definite PT -properties of the corresponding Lax pair as well as that of the anomalous contribution, consistent with the Wilson-loop criterion for integrability-like behavior. As a result, the quasi-deformed charge densities always acquire definite PT -properties suitable for the asymptotic conservation, as the Abelianization approach to construct them also preserves the definite PT -behavior of the Lax pair. This PT -symmetry based origin of quasi-conservation is general and has been demonstrated for quasi-deformations of multiple systems such as KdV, NLSE and non-local NLSE.

Scalar-induced gravitational waves (SIGWs) open a unique window into early-universe physics. While their generation from adiabatic perturbations has been extensively studied, the contribution from isocurvature perturbations remains largely unexplored. In this work, we develop a lattice simulation framework to compute the stochastic gravitational wave background from both pure isocurvature and mixed initial conditions. Our numerical results show excellent agreement with semi-analytical predictions in the pure isocurvature case. We further analyze multi-peak structures under general initial conditions and find that they closely match those produced in purely adiabatic scenarios. Additionally, we examine SIGWs in early matter-dominated eras, revealing that the peak amplitude and spectral slope are sensitive to the microphysical properties of the dominant field, such as the primordial black hole mass, abundance, or soliton decay rate. This study establishes lattice simulations as a robust tool for predicting SIGW spectra from complex primordial perturbations, with important implications for interpreting current and future gravitational wave observations.

Single photons in Laguerre-Gaussian (LG) beams, which carry orbital angular momentum (OAM), could enable more robust and efficient photonic quantum communication and information processing, as well as enhanced sensitivity in quantum metrology and imaging. However, as most implementations are indirect or require additional mode-shaping elements, direct generation of single photons with OAM has received growing interest. Colloidal lead halide perovskite quantum dots (QDs) have recently emerged as a versatile material that can produce indistinguishable single photons quasi-deterministically at high rate. Here, we integrate single CsPbBr$_3$ QDs into an open Fabry-Perot microcavity with a nanofabricated Gaussian-shaped deformation, demonstrating Purcell-enhanced single-photon generation into individual cavity modes with up to 18.1 $\pm$ 0.2 times accelerated decay, down to tens of picoseconds. By in-situ tuning of the cavity resonance, we can selectively couple a single QD to different LG modes carrying OAM and observe the spatial patterns of the generated single-photon beams emitted from the cavity. Our findings open the door to high photon rate sources that directly generate single-photon LG beams for advanced quantum photonic applications.

In the light of the recent Particle Data Group (PDG) release, we revisit the running quark and lepton Yukawa couplings, together with the quark mixing parameters, across a range of energy scales. The 2024 PDG determinations of low-energy fermion masses feature significantly smaller uncertainties, resulting from a reduced estimate of systematic errors compared to the more conservative treatment in the 2022 analysis. To assess the impact of these changes, we present running parameters obtained using both the 2022 and 2024 datasets, within the frameworks of the Standard Model (SM) and its minimal supersymmetric extension (MSSM). The evolved values, along with their associated $1σ$ uncertainties, are given within the SM framework at benchmark scales of $M_Z$ and $10^3$, $3\cdot 10^3$, $10^4$, $10^5$, $10^7$, $10^9$, $10^{12}$, and $10^{16}$ GeV. Within the MSSM, we additionally provide GUT-scale results for different choices of $\tanβ$, assuming supersymmetry breaking scales of 3 and 10 TeV, including an approximate way for taking supersymmetric loop threshold corrections into account. We furthermore discuss implications of the updated results for constructing and testing theories beyond the SM.

The suggestion made by C. F. Chyba and K. P. Hand about electric power generation from Earth's rotation through its own magnetic field is intriguing [1, 2]. Due to the importance of the subject, we have re-analyzed the theoretical arguments and derivations leading to their conclusion, by paying special attention to several issues possibly neglected before. The model they consider is a magnetic cylindrical shell moving with velocity $\mathbf{v}$ in the $y$ direction at a right angle to the direction of the Earth's magnetic field $\mathbf{B}_\infty$. First we analyze the electromagnetic boundary conditions when the shell is moving with a constant velocity $\mathbf{v}$, as this point, although of importance, has not been taken care of in [1, 2]. Indeed, this procedure leads us to differences in the values of electromagnetic fields when compared with the expressions given in the cited references. Second and as a result, we find that the mechanical force created by the moving shell becomes different from the one derived in [1, 2]. Obviously, the expression for the amount of electric power generation from Earth's rotation will also be different from the previously obtained one. The latter is important for evaluating the amount of produced power, maximizing it by choosing the parameters of the shell, and for the comparison with experimental findings.

The quantum transduction, or equivalently quantum frequency conversion, is vital for the realization of, e.g., quantum networks, distributed quantum computing, and quantum repeaters. The microwave-to-optical quantum transduction is of particular interest in the field of superconducting quantum computing, since interconnecting dilution refrigerators is considered inevitable for realizing large-scale quantum computers with fault-tolerance. In this review, we overview recent theoretical and experimental studies on the quantum transduction between microwave and optical photons. We describe a generic theory for the quantum transduction employing the input-output formalism, from which the essential quantities characterizing the transduction, i.e., the expressions for the transduction efficiency, the added noise, and the transduction bandwidth are derived. We review the major transduction methods that have been experimentally demonstrated, focusing on the transduction via the optomechanical effect, the electro-optic effect, the magneto-optic effect, and the atomic ensembles. We also briefly review the recent experimental progress on the quantum transduction from superconducting qubit to optical photon, which is an important step toward the quantum state transfer between distant superconducting qubits interconnected over optical fibers.

This study examines the distribution and evolution of lithium in both anode and cathode materials of commercial lithium-ion coin cells subjected to high C-rate cycling, providing insights into the mechanisms of lithium loss, trapping, and plating. Cells were cycled at 1C to 3C rates, and post-mortem analysis was performed using Li nuclear reaction analysis (Li-NRA), x-ray diffraction (XRD), and scanning electron microscopy (SEM) equipped with energy-dispersive x-ray spectroscopy (EDS). Li-NRA, using the resonant nuclear reaction between an incident high-energy proton and lithium, was used to measure the depth distribution of Li in the cathode and anode layers. The Li-NRA analysis revealed a surface lithium peak on the anode, likely associated with SEI formation and lithium plating, while the cathode exhibited a decrease in lithium content by ~19.7%. XRD analysis of the cycled cathode showed an expansion of the c-lattice parameter and peak shifts consistent with lithium depletion and structural deformation, supported by SEM imaging. In contrast, the dead graphite anode shows an enhanced peak at 43.3°, which corresponds to the presence of Li2Co3. 3-C rate cycling also led to capacity fade and an increase in internal resistance, highlighting the impact of lithium plating on cell performance.

The Standard Model of particle physics is standardly formulated in terms of principal fibre bundles and their associated representations -- what may be called a symmetry-first approach. This paper develops an alternative geometry-first formulation in which the fundamental objects are Hermitian vector bundles equipped with compatible covariant derivatives, and symmetry groups arise as automorphism groups rather than being postulated. Working entirely in this framework, I give new derivations of two central mechanisms of the Standard Model. First, the Higgs mechanism: mass acquisition for gauge bosons is identified with the extrinsic curvature of a sub-bundle singled out by the Higgs vacuum, requiring no appeal to symmetry breaking, Goldstone's theorem, or gauge fixing. Second, the Yukawa mechanism: fermion mass terms are constructed as fibrewise contractions determined by the inner-product and orientation structures of the fundamental bundles, eliminating a centraliser ambiguity that arises in the standard representation-theoretic treatment. I also show that charge quantisation follows from the discrete algebraic structure of tensor powers of the fundamental line bundle -- a derivation that applies even when the relevant automorphism group is non-compact. Finally, I identify the structural conditions under which the symmetry-first and geometry-first formulations are genuinely equivalent, showing that the Standard Model satisfies these conditions but that theories based on exceptional Lie groups do not.

We develop a data-driven framework for assessing the resilience of linear time-invariant systems against malicious false-data-injection sensor attacks. Leveraging sparse observability, we propose data-driven resilience metrics and derive necessary and sufficient conditions for two data-availability scenarios. For attack-free data, we show that when a rank condition holds, the resilience level can be computed exactly from the data alone, without prior knowledge of the system parameters. We then extend the analysis to the case where only poisoned data are available and show that the resulting assessment is necessarily conservative. For both scenarios, we provide algorithms for computing the proposed metrics and show that they can be computed in polynomial time under an additional spectral condition. A numerical example illustrates the efficacy and limitations of the proposed framework.

Black holes constitute nature's fastest quantum information scramblers, a phenomenon captured by gravitational analogue systems such as position-dependent XY spin chains. In these models, scrambling dynamics are governed exclusively by the hopping interactions profile, independent of system size. Utilizing such curved spacetime analogues as quantum batteries, we explore how the black hole scrambling affects charging via controlled quenches of preset scrambling parameters. Our analysis reveals that the intentionally engineered difference between post-quench and pre-quench scrambling parameters could significantly enhance both maximum stored energy $E_{\max}$ and peak charging power $P_{\max}$ in the quench charging protocol. Furthermore, the peaks of extractable work and stored energy coincide. This is because the system's evolution under a weak perturbation remains close to the ground state, resulting in a passive state energy nearly identical to the ground state energy. The optimal charging time $τ_*$ exhibits negligible dependence on the preset initial horizon parameter $x_{h0}$, while decreasing monotonically with increasing quench horizon parameter $x_{ht}$. This temporal compression confines high-power operation to regimes with strong post-quench scrambling $x_{ht} > x_{h0}$, demonstrating accelerated charging mediated by spacetime-mimicking scrambling dynamics.

Quantum machine learning (QML) promises significant speedups, particularly when operating on quantum datasets. However, its progress is hindered by the scarcity of suitable training data. Existing synthetic data generation methods fall short in capturing essential entanglement properties, limiting their utility for QML. To address this, we introduce QuFoundry, a low-depth quantum data generation framework that produces entangled, high-quality samples emulating diverse classical and quantum distributions, enabling more effective development and evaluation of QML models in representative-data settings.

Correlators in monomial Hermitian matrix model strongly depend on the choice of eigenvalue integration contours. We express Schur correlator in case of several different integration contours (mixed phase case) as a sum over products of Schur correlators for just one type of contour (pure phase), where expansion coefficients are manifestly made from Littlewood-Richardson and Mugnaghan-Nakayama coefficients. Further, for pure phase Schur correlators we find concise superintegrability formulas that unify both usual and exotic cases, that before looked very different from one another.

Maximum distance separable (MDS) codes are widely used in distributed storage systems as they provide optimal fault tolerance for a given amount of storage overhead. The seminal work of Dimakis~\emph{et al.} first established a lower bound on the repair bandwidth for a single failed node of MDS codes, known as the \emph{cut-set bound}. MDS codes that achieve this bound are called minimum storage regenerating (MSR) codes. Numerous constructions and theoretical analyses of MSR codes reveal that they typically require exponentially large sub-packetization levels, leading to significant disk I/O overhead. To mitigate this issue, many studies explore the trade-offs between the sub-packetization level and repair bandwidth, achieving reduced sub-packetization at the cost of suboptimal repair bandwidth. Despite these advances, the fundamental question of determining the minimum repair bandwidth for a single failure of MDS codes with fixed sub-packetization remains open. In this paper, we address this challenge for the case of two parity nodes ($n-k=2$) and sub-packetization $\ell=2$. Under these parameters, we establish a correspondence between repair schemes and point sets on the projective line $\mathbb{P}^1$, and then derive a lower bound on repair bandwidth utilizing the sharply 3-transitive action of $\text{PGL}_2(\Fq)$. Furthermore, we extend this lower bound to the repair I/O, and construct two classes of explicit MDS array codes that achieve these bounds, offering practical code designs with provable repair efficiency.