A finite group $G$ is called a Schur group if every Schur ring over $G$ is schurian, i.e. associated in a natural way with a subgroup of the symmetric group $Sym(G)$ that contains all right translations of $G$. The list of all possible abelian Schur groups was obtained by Evdokimov, Kovács, and Ponomarenko in 2016. In two papers, we complete a classification of abelian Schur groups. In the present paper, we study schurity of several groups from the list. First, we prove that a direct product of the elementary abelian group of order 4 and a cyclic group, whose order is an odd prime power or a product of two distinct odd primes, is a Schur group. Second, we establish nonschurity of some other groups from the list.

We introduce the task of out-of-order membership to a formal language L, where the letters of a word w are revealed one by one in an adversarial order. The length |w| is known in advance, but the content of w is streamed as pairs (i, w[i]), received exactly once for each position i, in arbitrary order. We study efficient algorithms for this task when L is regular, seeking tight complexity bounds as a function of |w| for a fixed target language. Most of our results apply to an algebraically defined variant dubbed out-of-order evaluation: this problem is defined for a fixed finite monoid or semigroup S, and our goal is to compute the ordered product of the streamed elements of w. We show that, for any fixed regular language or finite semigroup, both problems can be solved in constant time per streamed symbol and in linear space. However, the precise space complexity strongly depends on the algebraic structure of the target language or evaluation semigroup. Our main contributions are therefore to show (deterministic) space complexity characterizations, which we do for out-of-order evaluation of monoids and semigroups. For monoids, we establish a trichotomy: the space complexity is either Θ(1), Θ(log n), or Θ(n), where n = |w|. More specifically, the problem admits a constant-space solution for commutative monoids, while all non-commutative monoids require Ω(log n) space. We further identify a class of monoids admitting an O(log n)-space algorithm, and show that all remaining monoids require Ω(n) space. For general semigroups, the situation is more intricate. We characterize a class of semigroups admitting constant-space algorithms for out-of-order evaluation, and show that semigroups outside this class require at least Ω(log n) space.

Operating matter-wave interferometers as quantum detectors for fundamental physics or inertial sensors with unprecedented accuracies relies on noise rejection, often implemented by correlating multiple sensors. They can be spatially separated (gradiometry or gravitational-wave detection) or consist of different internal states (magnetometry or quantum clock interferometry), with a signal-amplitude modulation serving as a signature of a differential phase. In this work, we introduce Parameter Estimation from Amplitude Collapse (PEAC) by applying statistical inference techniques for different magnetically sensitive substates of an atom interferometer. We demonstrate that PEAC provides higher trueness, resulting in a substantially reduced bias compared to standard methods for perfectly correlated signals, while achieving competitive precision near, but not at, vanishing amplitudes. This indicates that vanishing signals do not constitute the most favourable working point for high-accuracy sensing, relevant to quantum clock interferometry. PEAC presents a generally applicable complementary evaluation method for correlated interferometers without phase stability, increasing the overall accuracy and enabling applications beyond atom-based interferometry.

In the current Large Language Model (LLM) ecosystem, creators have little agency over how their data is used, and LLM users may find themselves unknowingly plagiarizing existing sources. Attribution of LLM-generated text to LLM input data could help with these challenges, but so far we have more questions than answers: what elements of LLM outputs require attribution, what goals should it serve, how should it be implemented? We contribute a human-centric data attribution framework, which situates the attribution problem within the broader data economy. Specific use cases for attribution, such as creative writing assistance or fact-checking, can be specified via a set of parameters (including stakeholder objectives and implementation criteria). These criteria are up for negotiation by the relevant stakeholder groups: creators, LLM users, and their intermediaries (publishers, platforms, AI companies). The outcome of domain-specific negotiations can be implemented and tested for whether the stakeholder goals are achieved. The proposed approach provides a bridge between methodological NLP work on data attribution, governance work on policy interventions, and economic analysis of creator incentives for a sustainable equilibrium in the data economy.

We study the problem of maximizing a non-negative monotone submodular objective $f$ subject to the intersection of $k$ arbitrary matroid constraints. The natural greedy algorithm guarantees $(k+1)$-approximation for this problem, and the state-of-the-art algorithm only improves this approximation ratio to $k$. We give a $\frac{2k\ln2}{1+\ln2}+O(\sqrt{k})<0.819k+O(\sqrt{k})$ approximation for this problem. Our result is the first multiplicative improvement over the approximation ratio of the greedy algorithm for general $k$. We further show that our algorithm can be used to obtain roughly the same approximation ratio also for the more general problem in which the objective is not guaranteed to be monotone (the sublinear term in the approximation ratio becomes $O(k^{2/3})$ rather than $O(\sqrt{k})$ in this case). All of our results hold also when the $k$-matroid intersection constraint is replaced with a more general matroid $k$-parity constraint. Furthermore, unlike the case in many of the previous works, our algorithms run in time that is independent of $k$ and polynomial in the size of the ground set. Our algorithms are based on a hybrid greedy local search approach recently introduced by Singer and Thiery (STOC 2025) for the weighted matroid $k$-intersection problem, which is a special case of the problem we consider. Leveraging their approach in the submodular setting requires several non-trivial insights and algorithmic modifications since the marginals of a submodular function $f$, which correspond to the weights in the weighted case, are not independent of the algorithm's internal randomness. In the special weighted case studied by Singer and Thiery, our algorithms reduce to a variant of their algorithm with an improved approximation ratio of $(k+1)\ln2<0.694k+0.694$, compared to an approximation ratio of $\frac{k+1}{2\ln2}\approx0.722k+0.722$ guaranteed by Singer and Thiery.

In 1927, Artin and Schreier showed that a field is real closed if and only if its absolute Galois group has order two. Inspired by this characterisation and drawing on earlier work of Neukirch, Pop conjectured the following $p$-adic analogue: a field is $p$-adically closed if and only if its absolute Galois group is isomorphic to that of $\mathbb{Q}_p$. In 1995, the conjecture was independently solved by Efrat for $p \ne 2$ and by Koenigsmann in full generality. Using novel techniques in the theory of valued fields developed over the last 25 years, we give a new, elementary, and self-contained proof of this theorem, with a Galois characterisation of henselianity at the heart of the proof and without relying on Galois cohomology. We further highlight connections to the recent work of Jahnke-Kartas on perfectoid fields and model-theoretic transfer techniques. We provide a systematic account of all of our methods to encourage further investigations.

The survey experiment is widely used in economics and social sciences to evaluate the effects of treatments or programs. In a standard population-based survey experiment, the experimenter randomly draws experimental units from a target population of interest and then randomly assigns the sampled units to treatment or control conditions to explore the treatment effect of an intervention. Simple random sampling and treatment assignment can balance covariates on average. However, covariate imbalance often exists in finite samples. To address the imbalance issue, we study a stratified approach to balance covariates in a survey experiment. A stratified rejective sampling and rerandomization design is further proposed to enhance the covariate balance. We develop a design-based asymptotic theory for the widely used stratified difference-in-means estimator of the average treatment effect under the proposed design. In particular, we show that it is consistent and asymptotically a convolution of a normal distribution and two truncated normal distributions. This limiting distribution is more concentrated at the true average treatment effect than that under the existing experimental designs. Moreover, we propose a covariate adjustment method in the analysis stage, which can further improve the estimation efficiency. Numerical studies demonstrate the validity and improved efficiency of the proposed method.

The dipole anisotropy in galaxy and QSO number counts induced by the motion of the observer (the kinematic dipole) provides an important test of cosmological isotropy and a comparison with the Cosmic Microwave Background (CMB) dipole. Traditionally, the Ellis \& Baldwin expression,$\mathcal{A}=2+x(1+α)$, has been widely adopted, assuming power-law number counts and a single power-law spectral energy distribution (SED). Realistic surveys, however, involve a range of non-ideal effects, including diverse SEDs, finite instrumental bandpasses, non-power-law number counts, multi-band photometry and photo-$z$ selections, and direction-dependent or stochastic detection limits. In this paper, we incorporate these effects explicitly at the theoretical level and present a unified formulation of the kinematic dipole for a general parent population and a general multi-dimensional selection function. We show that the dipole amplitude is not described by a single index, but is instead given by a functional, $\mathcal{A}[\mathcal{W},f]$, defined as the Doppler response of the selection function acting on the underlying population. We demonstrate that the classical Ellis--Baldwin result is recovered as a special limiting case of this formalism, and clarify the relation between the theoretical coefficient $\mathcal{A}$ and the dipole vector estimated from finite catalogs, separating theoretical response from statistical uncertainty. This framework provides a basis for reinterpreting reported discrepancies in kinematic dipole measurements across surveys and is directly applicable to future wide-area, multi-band observations.

We perform a Bayesian inference of the dense-matter equation of state (EOS) within a unified framework that incorporates hadronic matter, quark matter, and a smooth hadron-to-quark crossover. The EOS is constrained using physical consistency conditions, gravitational wave data from GW170817, NICER mass versus radius measurements, and hypothetical future high-precision radius observations. In contrast to most previous studies that assume a sharp first-order phase transition or fix part of the EOS, we simultaneously infer hadronic, quark, and crossover parameters within a single statistical framework. We find that current observations strongly constrain the density dependence of the nuclear symmetry energy, particularly its slope and curvature. In contrast, the highest density hadronic parameters and quark-matter properties remain only weakly constrained. We further show that the trace anomaly exhibits a remarkably universal behavior across the accepted EOS ensemble and remains largely insensitive to current observational constraints. This indicates that the present data primarily probe the low to intermediate density EOS. At the same time, robust inference of quark matter and genuinely high-density physics will require next-generation precision radius measurements or complementary observables.

Photonic quantum technologies require efficient sources of pure single photons. We present a heralded single-photon source based on spontaneous parametric down-conversion in a monolithic cavity optimized for high spectral and spatial purity. The source heralds single photons at a wavelength of 1540 nm and a spectral bandwidth of 168 MHz, with a maximum heralding efficiency of 70% including all transmission and detection losses, while keeping the multi-photon contamination below 3%. The cavity enhancement predominantly generates photons into the central cavity mode, with a theoretical upper bound on the spectral purity of 79.4% arising from nonzero overlap with adjacent cavity modes. Spectral isolation of the central cavity mode with an etalon yields an increased measured spectral purity of (96.2 $\pm$ 2.7)%.

We study the stability of the exterior of Type I and Type II singularity formation for the wave maps equation in $\mathbb{R}^{d+1}$ with $d\geq2$ and the power nonlinear wave equation in $\mathbb{R}^{d+1}$ with $d\geq3$:Given characteristic initial data on the backwards lightcone of the singularity $\mathcal{C}=\{t+r=0\}$ converging to the singular background solution along with suitable data on an outgoing cone, we establish existence in a region $\{t+r\in(0,v_1),t-r\in(-1,0)\}$ for some suitably small $v_1$, i.e. all the way to the Cauchy horizon. Our result hinges on a particular set of assumptions on the regularity properties of these initial data, which conjecturally can be recovered by a more detailed stability analysis of the behaviour inside the past light cone; indeed, in certain settings, this was achieved in [BDS21,KAD26], and we strongly expect they can be proved in many other settings as well. The proof goes via a suitable change of coordinates and an application of the scattering result of [KK25], which, in particular, also applies to scaling-critical potentials. While no symmetry assumption is made for the power nonlinear wave equation, we only provide the proof in the corotational symmetry class for the wave maps equation, but we also sketch how to lift this restriction.

Sensing privacy and communication confidentiality play fundamentally different but interconnected roles in adversarial wireless environments. Capturing this interplay within a single physical-layer framework is particularly challenging in integrated sensing and communication (ISAC) systems, where the same waveform simultaneously serves dual purposes. We study a secure ISAC system in which a monostatic transmitter simultaneously sends a confidential message to a legitimate receiver and senses an environmental state, while a passive adversary attempts both message decoding and state estimation. We partially characterize the fundamental trade-offs among three performance measures: the transmitter's secrecy rate, its detection exponent, and the adversary's detection exponent. Beyond the joint input distribution that governs overall performance, the trade-offs are further shaped by the transmitter's ability to extract keys via feedback and hide both the content and structure of the codewords via wiretap and resolvability codes. We derive an achievable region, and illustrate the resulting design trade-offs through a numerical example.

Methyl cyanide, CH$_3$CN, is present in diverse regions in space, in particular in the warm parts of star-forming regions where it is a common molecule. Rotational transitions of $^{13}$CH$_3$CN and CH$_3$$^{13}$CN in their $v_8 = 1$ lowest excited vibrational states ($E_{\rm vib} \approx 520$ K) are quite prominent in Sagittarius B2(N). In order to be able to search for transitions of the next higher vibrational state $v_8 = 2$, we recorded spectra of samples enriched in $^{13}$CH$_3$CN and CH$_3$$^{13}$CN up to $v_8 = 2$ in the 35 to 1091~GHz region and reinvestigated existing spectra of CH$_3$CN in its natural isotopic composition between 1085 and 1200 GHz. Perturbations caused by near-degeneracies in $K = 4$ of $v_8 = 2^0$ and $K = 2$ of $v_8 = 2^{-2}$ yielded accurate information on the energy spacing of 22.93 and 21.79 cm$^{-1}$ between the $l$-components of $^{13}$CH$_3$CN and CH$_3$$^{13}$CN, respectively. Fermi-type interaction between $K = 13$ and 14 of $v_8 = 1^{-1}$ and $v_8 = 2^{+2}$ probe the energy differences between the two states of both isotopomers. In addition, a $ΔK \pm2$, $Δl \mp1$ interaction between the ground vibrational state of $^{13}$CH$_3$CN and $v_8 = 1^{+1}$ provides information on their energy spacing. Furthermore, we obtained improved or extended ground state rotational transition frequencies of $^{13}$CH$_3$$^{13}$CN and extensive data for $^{13}$CH$_3$C$^{15}$N and CH$_3$$^{13}$C$^{15}$N. Finally, we report the results of our search for transitions of $^{13}$CH$_3$CN and CH$_3$$^{13}$CN in their $v_8 = 2$ states toward Sagittarius B2(N).

The interaction between spin and gravitational waves causes spinning bodies to deviate from their geodesics. In this work, we obtain the analytic solution of the Mathisson--Papapetrou--Dixon equations at linear order in the spin for plane gravitational wave spacetimes. Our approach combines a parallel-transported tetrad with the translational Killing symmetries of plane wave spacetimes, yielding six conserved quantities that fully determine the momentum, spin evolution, and worldline. The resulting transverse and longitudinal motions are expressed in closed form as single integrals of the retarded time, providing a unified and model-independent framework for computing spin--curvature-induced deviations. This analytic solution offers a versatile tool for studying spin-dependent effects in gravitational memory, Penrose-limit geometries, and high-energy scattering regimes.

The efficient user scheduling policy in the massive Multiple Input Multiple Output (mMIMO) system remains a significant challenge in the field of 5G and Beyond 5G (B5G) due to its high computational complexity, scalability, and Channel State Information (CSI) overhead. This paper proposes a novel Grover's search-inspired Quantum Reinforcement Learning (QRL) framework for mMIMO user scheduling. The QRL agent can explore the exponentially large scheduling space effectively by applying Grover's search to the reinforcement learning process. The model is implemented using our designed quantum-gate-based circuit, which imitates the layered architecture of reinforcement learning, where quantum operations act as policy updates and decision-making units. Moreover, the simulation results demonstrate that the proposed method achieves proper convergence and significantly outperforms classical Convolutional Neural Networks (CNN) and Quantum Deep Learning (QDL) benchmarks.

We show that the gap in the compactness between black holes and neutron stars witnessed in general relativity may be vanishing in Hořava-Lifshitz (HL) gravity. Assuming a fermion equation-of-state for simplicity, and solving the Tolman-Oppenheimer-Volkoff equation within the HL gravity framework, we see that there exists a minimum fermion mass $m_f^\text{(min)}(q,y)$, above which the gap of the compactness between black hole and fermionic compact object vanishes, for a given deformation parameter $q$ of HL and interaction strength $y$ between fermions. Thus, in HL gravity, the mass and radius of an object found in the lower mass gap by LIGO-Virgo-KAGRA observations might not be able to classify it as a black hole or a neutron star. It is interesting to note that a fermion of mass $\sim 40\ \text{GeV}$ can form a highly compact object of mass $\sim 10^{-4}\ \msun$ and radius $\sim 1\ \text{m}$ that may play the role of the cold dark matter. In addition, we find the possible existence of another class of compact objects whose compactness is comparable to that of a black hole.

In the paper, the physical-layer security for reconfigurable intelligent surface (RIS) aided integrated sensing and communication (ISAC) system is studied. There is an active eavesdropper (AE) as well as a passive eavesdropper (PE), and they cooperate each other. By joint base station beamforming and RIS reflection design, we aim to achieve the best secure data communications with guaranteed sensing performance. Mathematically, taking the constraints on sensing performance and transmission power in consideration, the system secrecy rate maximization problem is formulated with respect to transmit beamforming, RIS reflection, and receive beamforming. The formulated problem is non-convex and is decomposed to three subproblems by applying the alternating optimization (AO). For the decomposed subproblem, we utilize the quadratic penalty method and successive convex approximation (SCA) for the solution derivation. Thereafter, an iterative numerical algorithm, referred to as the joint beamforming and reflection design (JBRD) algorithm, is proposed. Finally, numerical results demonstrate the effectiveness and superiority of the proposed algorithm.

We present a method of constructing statistical intervals that obtain a natural middle ground between Bayesian and frequentist statistical intervals, previously unexplored in literature: To a p% Bayesian credible interval we should assign a p% belief after observing both the dataset and the interval, to p% frequentist intervals we can generally only assign a p% belief before observing either the data or the interval, while to the intervals proposed here we can assign a p% belief after observing the interval, but not necessarily after inspecting the full dataset ourselves. Even in fully non-parametric problems this only requires a prior over the parameter(s) of interest, not a high-dimensional prior over the full distribution, while maintaining many of the practical and philosophical advantages of Bayesian methods. We belief these methods may therefore provide significant advances in statistical methodology to a number of fields. This work is meant as a proof of principle: We concretely implement such intervals for two different problems and study the properties of resulting intervals. We discuss promising directions where the proposed type of interval may provide significant advantages.

We consider the spherically reduced Einstein-Hilbert action, Einstein field equations and Schwarzschild spacetime modified by a renormalization-group (RG) scale-dependent gravitational Newton coupling, and present a systematic and operational approach to such an RG-improvement. The master field equations for spherically symmetric gravitational fields, recently constructed from two-dimensional Horndeski theory, allow us to retain partial contributions from higher-curvature truncations of the effective action, while preserving the second-order nature of the resulting field equations. Static RG-improved black-hole spacetimes with an effective gravitational coupling depending on the areal radius and the Misner-Sharp mass are derived as vacuum solutions to these master field equations, and are thereby identified as solutions to generally covariant two-dimensional Horndeski theories. We discuss explicitly the embedding of previous key works on RG-improvement into the newly developed formalism to illustrate its broad range of applicability. This formalism moreover allows us to establish explicitly the discrepancies in the outcomes of RG-improvement when implemented at the level of the action, in the field equations, or in the Schwarzschild solution.

Type Ia supernovae are a cornerstone of modern cosmology, providing first evidence for cosmic acceleration and new tests of dark energy. Son et al. 2025 (S25) claim a strong redshift evolution in standardized supernova luminosities driven by supernova progenitor age, with dramatic cosmological implications: rapidly evolving dark energy, decelerating expansion, and a $9σ$ tension with $Λ$CDM. We show that the underpinning evidence required for this conclusion -- the supernova progenitor-age dependence, the redshift-dependent age difference, and their combined impact -- is either negligible or relies on effects already corrected for in modern supernova analyses. First, the S25 analysis omits the standard host-galaxy stellar mass correction that captures known environmental dependencies that also correlate with stellar age. Applying this correction to the S25 sample, we find no dependence of standardized supernova brightness on host age. Independent data also show no significant difference at low-redshift in standardized brightness between star-forming galaxies and several Gyr older quiescent galaxies of the same stellar mass. Second, the S25 scenario predicts strong redshift evolution of the host-mass effect. Data from the Dark Energy Survey supernova survey measure evolution of $-0.028 \pm 0.034~\mathrm{mag}\,z^{-1}$, consistent with zero and altering the dark-energy equation-of-state measurement ($w$) by $<$0.01 if included. Third, we demonstrate that the claimed $\sim5$~Gyr progenitor age difference between nearby and distant supernovae is overstated by factors of three to five largely due to a conflation of host galaxy age with supernova progenitor age. We conclude that type~Ia supernova cosmology remains robust for current measurements of dark energy.

We revisit the holographic description of the thermal first order phase transition of N=4 SYM compactified on a spatial circle. At the transition, the dominant bulk saddle exchanges between a geometry with a compact spatial circle and one with a compact Euclidean time circle. We construct a one-parameter family of Euclidean geometries that describes the unstable branch of the transition, completing the swallow-tail structure of the free energy. Although these configurations are thermodynamically unstable, they provide a continuous interpolation between the confining soliton and the deconfined black hole phases. Using probe fundamental strings, we show that the theory remains confining along the unstable branch, with a string tension that decreases smoothly and vanishes only in the black hole limit. Introducing fundamental matter via probe D5-branes, we find that chiral symmetry breaking follows the same pattern: the condensate decreases continuously and switches off precisely where confinement disappears. We discuss the implications for the confinement and chiral symmetry breaking mechanisms at large Nc.

Bridging the spatiotemporal scales of magnetic seed field generation and subsequent dynamo amplification in the weakly collisional intracluster medium presents an extreme numerical challenge. We perform collisionless turbulence simulations with initially unmagnetized electrons that capture both magnetic seed generation via the electron Weibel instability and the ensuing dynamo amplification. Going beyond existing pair-plasma studies, we use an ion-to-electron mass ratio of 100 for which we find electron and ion dynamics are sufficiently decoupled. These simulations are enabled by the 10-moment collisionless fluid solver of Gkeyll, which evolves the full pressure tensor for all species. The electron heat-flux closure regulates pressure isotropization and effectively sets the magnetic Reynolds number. We investigate how the strength of the closure influences the transition between a regime reminiscent of previous kinetic pair-plasma simulations and a regime exhibiting dynamo behavior qualitatively similar to magnetohydrodynamics.

We present a distributed framework of the Primal-Dual Hybrid Gradient (PDHG) algorithm for solving massive-scale linear programming (LP) problems. Although PDHG-based solvers demonstrate strong performance on single-node GPU architectures, their applicability to industrial-scale instances is often limited by single-GPU computational throughput. To overcome these challenges, we propose D-PDLP, the first Distributed PDLP framework, which extends PDHG to a multi-GPU setting via a practical two-dimensional grid partitioning of the constraint matrix. To improve load balance and computational efficiency, we introduce a block-wise random permutation strategy combined with nonzero-aware matrix partitioning. By distributing the intensive computation required in PDHG iterations, the proposed framework harnesses multi-GPU parallelism to achieve substantial speedups with relatively low communication overhead. Extensive experiments on standard LP benchmarks (including MIPLIB and Mittelmann instances) as well as huge-scale real-world datasets show that our distributed implementation, built upon cuPDLPx, achieves strong scalability and high performance while preserving full FP64 numerical accuracy.

The distribution of ions and their impact on the structure of electrolyte interfaces plays an important role in many applications. Interestingly, recent experimental studies have suggested the preferential accumulation of $SO_4^{2-}$ ions at the $Na_2SO_{4,aq}$-graphene interface in disagreement with the generally known tendency of cations to accumulate at graphene-electrolyte interfaces. Herein, we resolve the atomistic structure of the $Na_2SO_{4,aq}$-graphene interfaces in the 0.1-2.0 M concentration range using machine learning interatomic potential-based simulations and simulated sum frequency generation (SFG) spectra to reveal the molecular origins of the conundrum. Our results show that Na+ ions accumulate between the outermost and second water layers whereas $SO_4^{2-}$ ions accumulate within the second interfacial water layer indicating cation dominated interfaces. We find that the interfacial region (within ~10 $Å$ of the graphene sheet) is negatively charged due to sub-stoichiometric $Na^+$/$SO_4^{2-}$ ratio at the interface. Our simulated SFG spectra show enhancement and a red-shift of the spectra in the hydrogen bonded region as a function of $Na_2SO_4$ concentration similar to measurements due to $SO_4^{2-}$-induced changes in the orientational order of water molecules in the second interfacial layer. Our study demonstrates that ion stratification and ion-induced water reorganization are key elements of understanding the electrolyte-graphene interface.

Strain and domain engineering offer powerful routes to control phase and domain stability in ferroelectric thin films. While most studies have focused on (100)-oriented growth, the impact of lower-symmetry orientations remains underexplored. We address this gap in knowledge with first-principles based molecular dynamics simulation for the example of prototypical ferroelectric perovskites under (110) strain. Epitaxial (110) strains may indeed outperform the widely studied (100) orientation, as even modest strain values stabilize a diverse set of metastable nanoscale states with potential high functional tunability. In this regime, the films exhibit multidomain configurations with domain wall normal oriented along the clamped in-plane or the relaxed out-of-plane directions and heterophases in BaTiO$_3$ and KNbO$_3$. Besides, complex superdomain patterns and antiferroelectric-like domains are observed in PbTiO$_3$. These metastable nanoscale configurations may allow for large reversible responses.

X-ray absorption spectroscopy and X-ray magnetic circular dichroism have long served as indispensable tools for probing the electronic and magnetic properties of transition-metal compounds with elemental selectivity. In recent years, the emergence of femtosecond lasers has opened a new avenue for studying nonequilibrium dynamics in condensed matter. However, conventional optical techniques lack elemental and orbital specificity, making it difficult to disentangle the coupled charge, spin, and lattice responses in complex materials. The development of X-ray free-electron lasers (XFEL) and laboratory high-harmonic generation (HHG) sources has enabled the extension of X-ray absorption and scattering techniques into the femtosecond time domain. Time-resolved X-ray absorption spectroscopy, X-ray magnetic circular dichroism, and resonant soft X-ray scattering now provide direct, complementary access to element- and momentum-resolved ultrafast dynamics. This review summarizes recent progress in these techniques, focusing on pump-probe measurements of laser-induced demagnetization, spin-state transitions, and valence and structural changes in transition-metal compounds. We also discuss advances in tabletop HHG-based X-ray spectroscopy and its integration with large-scale XFEL facilities. These developments provide powerful routes for visualizing the nonequilibrium evolution of charge, spin, orbital, and lattice degrees of freedom, offering new insights into the ultrafast control of quantum materials.

Skipper Charge-Coupled Devices (skipper-CCDs) are pixelated silicon detectors with deep sub-electron resolution. Their radiation hardness and capability to reconstruct energy deposits with unprecedented precision make them a promising technology for space-based X-ray astronomy. In this scenario, optical and near-infrared photons may saturate the sensor, distorting the reconstructed signal. We present a light-tight shield for skipper-CCDs to suppress optical backgrounds while preserving X-ray detection efficiency. We deposited thin aluminum layers on the CCD surface using an e-beam evaporator and evaluated their blinding performance across wavelengths from 650 to 1000 nm using a monochromator, as well as the X-ray transmission using an $^{55}$Fe source. We find that 50 and 100 nm layers provide >99.6% light suppression, with no efficiency loss for 5.9 and 6.4 keV X-rays. In addition, we used Geant4 simulations to extend these results to a broader energy range and quantify the efficiency loss for different aluminum thicknesses. Results show that thin aluminum coatings are an effective, low-cost solution for optical suppression in skipper-CCDs intended for X-ray detection and space instrumentation.

Using quasi-simultaneous synchrotron X-ray diffraction and tomography techniques, we have studied in-situ and in real-time the nucleation and co-growth dynamics of the peritectic structures in an Al-Mn alloy during solidification. We collected ~30 TB 4D datasets which allow us to elucidate the phases' co-growth dynamics and their spatial, crystallographic and compositional relationship. The primary Al4Mn hexagonal prisms nucleate and grow with high kinetic anisotropy -70 times faster in the axial direction than the radial direction. In all cases, a ~5 um Mn-rich diffusion layer forms at the liquid-solid interface, creating a sharp local solute gradient that governs subsequent phase transformation. The peritectic Al6Mn phases nucleate epitaxially within this diffusion zone, initially forming a thin shell surrounding the Al4Mn with an orientation relationship of {10-10}HCP // {110}O, [0001]HCP // [001]O. Such ~5 um Mn-rich diffusion layers also cause solute depletion at the liquid side of the liquid-solid interface, limiting further epitaxial phase growth, but prompting phase re-nucleation and branching at crystal edges, resulting tetragonal prism structures that no longer follow the initial orientation relationship. The anisotropic diffusion also led to the formation of core defects at the centre of both phases. Furthermore, increasing cooling rate from 0.17 to 20 °C/s can disrupt the stability of the solute diffusion zone, effectively suppressing the formation of the core defects and forcing a transition from faceted to non-faceted morphologies. Our work establishes a new theoretical framework for how to tailor and control the peritectic structures in metallic alloys through solidification processes.

Motivated by the constructions of binary sequences by utilizing the cyclic elliptic function fields over the finite field $\mathbb{F}_{2^{n}}$ by Jin \textit{et al.} in [IEEE Trans. Inf. Theory 71(8), 2025], we extend the construction to the cyclic elliptic function fields with odd characteristic by using the quadratic residue map $η$ instead of the trace map used therein. For any cyclic elliptic function field with $q+1+t$ rational points and any positive integer $d$ with $\gcd(d, q+1+t)=1$, we construct a new family of binary sequences of length $q+1+t$, size $q^{d-1}-1$, balance upper bounded by $(d+1)\cdot\lfloor2\sqrt{q}\rfloor+|t|+d,$ the correlation upper bounded by $(2d+1)\cdot\lfloor2\sqrt{q}\rfloor+|t|+2d$ and the linear complexity lower bounded by $\frac{q+1+2t-d-(d+1)\cdot\lfloor2\sqrt{q}\rfloor}{d+d\cdot\lfloor2\sqrt{q}\rfloor}$ where $\lfloor x\rfloor$ stands for the integer part of $x\in\mathbb{R}$.

Identifying codes were introduced by Karpovsky et al. as dominating sets $S\subseteq V(G)$ satisfying $N[u]\cap S \neq N[v]\cap S$ for any distinct vertices $u,v$. Later, Junnila et al. introduced the concept of \emph{self-identifying codes} (previously called $(1,\leq1)^+$-identifying codes in earlier work), a dominating set $S\subseteq V(G)$ such that $\bigcap_{c\in N[u]\cap S} N[c] = \{u\}$ for every vertex $u$. In this paper, we obtain bounds on the minimum size of a self-identifying code in the direct products $K_m\times P_n$ and $K_m\times C_n$ that are linear in $n$ with coefficients depending on $m$, and these bounds are asymptotically tight. In particular, for $K_m\times P_n$ with $m,n\ge3$, our bounds closely approaches the size of an identifying code in the same graph, as determined by Shinde and Waphare.