An altermagnet is a recently identified class of magnets that exhibit a zero net magnetic moment but break symmetry under the combined operations of parity and time reversal. It typically consists of two magnetic sites of opposite spins related by rotation within the unit cell. Here, we use circular dichroism (CD) in resonant inelastic X-ray scattering (RIXS) to identify a new form of altermagnetism, namely bi-altermagnetism, in the correlated insulator Fe2Mo3O8, which comprises two altermagnetic sublattices: one with alternating quasi-octahedral Fe environments and the other with alternating tetrahedral Fe environments. We experimentally revealed the emergence of CD in an achiral, zero-magnetization system, thereby probing mirror-symmetry breaking associated with altermagnetic order. Notably, the CD appeared at sublattice-specific excitations of the octahedral and tetrahedral sites, indicating symmetry breaking in both altermagnetic sublattices. Calculations based on a model with the bi-altermagnetic order along the c axis successfully reproduce the observed CD. Our findings provide compelling evidence for bi-altermagnetism in Fe2Mo3O8, and showcase the use of RIXS-CD as a probe of magnetic sublattices in systems with zero net magnetization.

Large Language Models (LLMs) are increasingly utilised in software engineering, yet their ability to generate structured artefacts such as UML diagrams remains underexplored. In this work we present NOMAD, a cognitively inspired, modular multi-agent framework that decomposes UML generation into a series of role-specialised subtasks. Each agent handles a distinct modelling activity, such as entity extraction, relationship classification, and diagram synthesis, mirroring the goal-directed reasoning processes of an engineer. This decomposition improves interpretability and allows for targeted verification strategies. We evaluate NOMAD through a mixed design: a large case study (Northwind) for in-depth probing and error analysis, and human-authored UML exercises for breadth and realism. NOMAD outperforms all selected baselines, while revealing persistent challenges in fine-grained attribute extraction. Building on these observations, we introduce the first systematic taxonomy of errors in LLM-generated UML diagrams, categorising structural, relationship, and semantic/logical. Finally, we examine verification as a design probe, showing its mixed effects and outlining adaptive strategies as promising directions. Together, these contributions position NOMAD as both an effective framework for UML class diagram generation and a lens onto the broader research challenges of reliable language-to-model workflows.

Electron-on-neon (eNe) charge states coupled to superconducting circuits are a promising platform for quantum computing. Control over the formation of these charge states requires techniques to track and control the growth of solid Ne films on the circuit surface. We demonstrate a real-time Ne film-growth monitor using high-transition-temperature (high-$T_c$) YBCO microwave resonators. The high $T_c$ enables tracking of the film thickness near Ne's triple temperature and below. Across more than 300 solidification experiments, we find that the final Ne thickness varies stochastically from a few nm to a few $μ$m for films solidified from the liquid phase. By increasing the driving power in the resonator, we consistently reduce the final thickness to below 100 nm. These results represent an important step toward controlled formation of Ne films for eNe qubits and highlight the broader utility of high-$T_c$ resonators for hybrid quantum systems.

High overtone bulk acoustic resonators are essential components in microwave signal processing and emerging quantum technologies; however, conventional designs suffer from limited impedance matching, spurious mode interference, and restricted scalability. Here we introduce a laterally excited high overtone thickness shear bulk acoustic resonator, abbreviated as X HTBAR, that overcomes these limitations through a fully planar excitation scheme. The X HTBAR employs a 3 micron thick 128 degree Y cut LiNbO3 piezoelectric film on a 500 micron high resistivity silicon substrate, enabling efficient excitation of thickness shear modes through lateral electrodes without the need for bottom electrodes and confining the acoustic field between the top electrodes. This configuration removes parasitic loss channels, increases energy transfer efficiency to greater than ninety nine percent, and provides a stable free spectral range of about 5.75 MHz with very small fluctuations. Experimental measurements show comb like phonon spectra spanning 0.1 to 1.8 GHz, high quality factors in the range of ten to the power of three to ten to the power of five, frequency quality products larger than ten to the power of thirteen at room temperature, and a low temperature coefficient of frequency. In addition, a gridded electrode design together with the intrinsic properties of 128 degree Y cut LiNbO3, including insensitivity to electrode spacing and a large electromechanical coupling coefficient, suppresses spurious modes and allows tunable mode volumes from 0.008 to 0.064 cubic millimeters. These combined features give X HTBAR devices excellent integration compatibility and strong immunity to electrode related perturbations, making them promising multimode phonon sources for large scale quantum interconnects and microwave photonic integrated circuits.

A search for new physics in events featuring a single photon and missing transverse momentum is presented, using proton-proton $\sqrt{s}$ = 13 TeV collision data corresponding to an integrated luminosity of 101 fb$^{-1}$ collected by the CMS experiment at the CERN LHC between 2017 and 2018. This analysis, combined with a previous study of 36 fb$^{-1}$ of 2016 data (totaling 137 fb$^{-1}$), reveals no significant deviations from standard model expectations. The results are then used to establish 95% confidence level limits on parameters in theoretical models involving dark matter and large extra dimensions. Compared to the 2016-only analysis, this search achieves up to a 14% improvement in exclusion reach for mediator masses in simplified dark matter models, along with 11% and 10% enhancements in the limits on the effective field theory suppression scale and the fundamental Planck scale, respectively. These results are the most stringent constraints on these parameters to date.

Security-Constrained DC Optimal Power Flow (SC DCOPF) is an important tool for transmission system operators, enabling economically efficient and physically secure dispatch decisions. Although CPU-based commercial solvers (e.g., Gurobi) can efficiently solve SC-DCOPF problems with a reasonable number of security constraints, their performance degrades rapidly as both system size and the number of contingencies grow into thousands. In this paper, we design a computational graph representation of the SC-DCOPF-based market-clearing problem, inspired by the third ARPA-E Grid Optimization Competition. Using a tool from the neural network verification community known as Interval Bound Propagation (IBP), we quickly compute bounds on the optimal objective across the full set of N-1 contingencies. Our results demonstrate that IBP can compute certified bounds with mean optimal solution gaps below 3.98% on small cases, and it can efficiently scale up to 8,316 bus systems with thousands of contingencies.

Preserving spin symmetry in variational quantum algorithms is essential for producing physically meaningful electronic wavefunctions. Implementing spin-adapted transformations on quantum hardware, however, is challenging because the corresponding fermionic generators translate into noncommuting Pauli operators. In this work, we introduce an exact and computationally efficient factorization of spin-adapted unitaries derived from fermionic double excitation and deexcitation rotations. These unitaries are expressed as ordered products of exponentials of Pauli operators. Our method exploits the fact that the elementary operators in these generators form small Lie algebras. By working in the adjoint representation of these algebras, we reformulate the factorization problem as a low-dimensional nonlinear optimization over matrix exponentials. This approach enables precise numerical reparametrization of the unitaries without relying on symbolic manipulations. The proposed factorization provides a practical strategy for constructing symmetry-conserving quantum circuits within variational algorithms. It preserves spin symmetry by design, reduces implementation cost, and ensures the accurate representation of electronic states in quantum simulations of molecular systems.

We introduce the notion of selfless W$^*$-probability space and study its connection with Connes' bicentralizer problem. In particular, we show that if $M$ is a separable type ${\rm III_1}$ factor with trivial bicentralizer, then $(M, φ)$ is selfless for every faithful normal state $φ\in M_\ast$.

The Damas-Hindley-Milner (ML) type system owes its success to principality, the property that every well-typed expression has a unique most general type. This makes inference predictable and efficient. Unfortunately, many extensions of ML (GADTs, higher-rank polymorphism, and static overloading) endanger princpality by introducing _fragile_ constructs that resist principal inference. Existing approaches recover principality through directional inference algorithms, which propagate _known_ type information in a fixed (or static) order (e.g. as in bidirectional typing) to disambiguate such constructs. However, the rigidity of a static inference order often causes otherwise well-typed programs to be rejected. We propose _omnidirectional_ type inference, where type information flows in a dynamic order. Typing constraints may be solved in any order, suspending when progress requires known type information and resuming once it becomes available, using _suspended match constraints_. This approach is straightforward for simply typed systems, but extending it to ML is challenging due to let-generalization. Existing ML inference algorithms type let-bindings (let x = e1 in e2) in a fixed order: type e1, generalize its type, and then type e2. To overcome this, we introduce _incremental instantiation_, allowing partially solved type schemes containing suspended constraints to be instantiated, with a mechanism to incrementally update instances as the scheme is refined. Omnidirectionality provides a general framework for restoring principality in the presence of fragile features. We demonstrate its versatility on two fundamentally different features of OCaml: static overloading of record labels and datatype constructors and semi-explicit first-class polymorphism. In both cases, we obtain a principal type inference algorithm that is more expressive than OCaml's current typechecker.

Smart radio environments (SREs) enhance wireless communications by allowing control over the channel. They have been enabled through surfaces with reconfigurable electromagnetic (EM) properties, known as reconfigurable intelligent surfaces (RISs), and through flexible antennas, which can be viewed as realizations of SREs in the EM domain and space domain, respectively. However, these technologies rely on electronically reconfigurable or movable components, introducing implementation challenges that could hinder commercialization. To overcome these challenges, we propose a new domain to enable SREs, the frequency domain, through the concept of movable signals, where the signal spectrum can be dynamically moved along the frequency axis. We first analyze movable signals in multiple-input single-output (MISO) systems under line-of-sight (LoS) conditions, showing that they can achieve higher average received power than quantized equal gain transmission (EGT). We then study movable signals under non-line-of-sight (NLoS) conditions, showing that they remain effective by leveraging reflections from surfaces made of uniformly spaced elements with fixed EM properties, denoted as fixed intelligent surfaces (FISs). Analytical results reveal that a FIS-aided system using movable signals can achieve up to four times the received power of a RIS-aided system using fixed-frequency signals.

One pathway to producing high brightness electron beams is to use a radio-frequency (rf) driven high field photogun to rapidly accelerate photoemitted electrons to the relativistic regime and preserve the brightness. However, the highest attainable field is limited by rf breakdowns of materials used in a photogun. Shortening rf pulse duration feeding into a photogun provides a viable pathway to achieve high field and prevent rf breakdowns. Here we propose and investigate Compressed Ultrashort Pulse Injector Demonstrator (CUPID), a nanosecond rf pulses driven photogun powered by a klystron and rf pulse compression system capable of achieving 300 MW at 20 ns duration, to produce bright electron beams with high electric field. We first introduce the design of the CUPID photogun and its expected rf performance at 500 MV/m driven by high power nanosecond rf pulses, followed by beam dynamics studies showing its capability for producing bright electron beams with 60 nm emittance when forming a photoinjector with a superconducting solenoid and downstream accelerating structures. Finally, we show a proof-of-concept start-to-end simulation of the CUPID photoinjector paired with the existing Linac Coherent Light Source (LCLS) copper accelerator free-electron laser (FEL) to demonstrate achievable mJ pulse energy very hard x-ray photons at 40 keV or higher.

Forces transmitted by bones are routinely studied in human biomechanics, but it is challenging to measure them non-invasively, especially outside of laboratory settings. We introduce a technique for non-invasive, in vivo measurement of tibial compressive force using flexural waves propagating in the tibia. Modelling the tibia as an axially compressed Euler-Bernoulli beam, we show that tibial flexural waves have load-dependent frequency spectra. Specifically, under physiological conditions, peak locations in the wave acceleration spectra vary linearly with the compressive force on the tibia and may be used as proxies for the compressive force. We test the validity of this technique using a proof-of-concept wearable system that generates flexural waves via a skin-mounted mechanical transducer and measures the spectra of these waves using a skin-mounted accelerometer. In agreement with beam theory, data from 9 participants demonstrate linear relationships between tibial compressive force and spectral peak location, with Pearson correlation coefficients $r=0.82 - 0.99$ (mean $r=0.93$) for medial-lateral swaying and $r=0.81 - 0.98$ (mean $r=0.93$) for walking trials. This flexural wave-based technique could give rise to a new class of wearable sensors for non-invasive physiological bone load monitoring and measurement, impacting research in human locomotion and sports medicine.

Diffusion-weighted magnetic resonance imaging allows for reconstruction of models for structural connectivity in the brain, such as fiber orientation distribution functions (ODFs) that describe the distribution, direction, and volume of white matter fiber bundles in a voxel. Crossing white matter fibers in voxels complicate analysis and can lead to errors in downstream tasks like tractography. We introduce one option for separating fiber ODFs by performing a nonlinear optimization to fit ODFs to the given data and penalizing terms that are not symmetric about the axis of the fiber. However, this optimization is non-convex and computationally infeasible across an entire image (approximately 1.01 x 106 ms per voxel). We introduce DeepFixel, a spherical convolutional neural network approximation for this nonlinear optimization. We model the probability distribution of fibers as a spherical mesh with higher angular resolution than a truncated spherical harmonic representation. To validate DeepFixel, we compare to the nonlinear optimization and a fixel-based separation algorithm of two-fiber and three-fiber ODFs. The median angular correlation coefficient is 1 (interquartile range of 0.00) using the nonlinear optimization algorithm, 0.988 (0.317) using a fiber bundle elements or "fixel"-based separation algorithm, and 0.973 (0.004) using DeepFixel. DeepFixel is more computationally efficient than the non-convex optimization (0.32 ms per voxel). DeepFixel's spherical mesh representation is successful at disentangling at smaller angular separations and smaller volume fractions than the fixel-based separation algorithm.

Traumatic brain injury (TBI) is intrinsically heterogeneous, and typical clinical outcome measures like the Glasgow Coma Scale complicate this diversity. The large variability in severity and patient outcomes render it difficult to link structural damage to functional deficits. The Federal Interagency Traumatic Brain Injury Research (FITBIR) repository contains large-scale multi-site magnetic resonance imaging data of varying resolutions and acquisition parameters (25 shared studies with 7,693 sessions that have age, sex and TBI status defined - 5,811 TBI and 1,882 controls). To reveal shared pathways of injury of TBI through imaging, we analyzed T1-weighted images from these sessions by first harmonizing to a local dataset and segmenting 132 regions of interest (ROIs) in the brain. After running quality assurance, calculating the volumes of the ROIs, and removing outliers, we calculated the z-scores of volumes for all participants relative to the mean and standard deviation of the controls. We regressed out sex, age, and total brain volume with a multivariate linear regression, and we found significant differences in 37 ROIs between subjects with TBI and controls (p < 0.05 with independent t-tests with false discovery rate correction). We found that differences originated in 1) the brainstem, occipital pole and structures posterior to the orbit, 2) subcortical gray matter and insular cortex, and 3) cerebral and cerebellar white matter using independent component analysis and clustering the component loadings of those with TBI.

Utilizing ultracold spinor gases as large-scale, many-body quantum simulation platforms, we establish a toolbox for the precise control, characterization, and detection of nonequilibrium dynamics via internal spinor phases. We develop a method to extract the phase evolution from the observed spin population dynamics, allowing us to define an order parameter that sharply identifies dynamical phase transitions over a wide range of conditions. This work also demonstrates a technique for inferring spin-dependent interactions from a single experimental time trace, in contrast to the standard approach that requires mapping a cross section of the phase diagram, with immediate applications to systems experiencing complex time-dependent interactions. Additionally, we demonstrate experimental access to and control over non-ergodic relaxation dynamics, where states of similar energy in the (nominally) thermal region of the energy spectrum retain a dependence on the initial state, via the manipulation of spinor phases, enabling the study of non-ergodic thermalization dynamics connected to quantum scarring.

In this paper, we examine identification in dynamic panel logit models with state dependence, a first-order Markov feedback process, and individual unobserved heterogeneity by introducing sufficient statistics for the feedback process and the unobserved heterogeneity. If a sequentially exogenous discrete covariate follows a first-order Markov process, identification via conditional likelihood is infeasible regardless of the time period. We also establish the failure of point identification beyond the conditional likelihood framework, which necessitates additional restrictions for identification. We present two assumptions for identification via conditional likelihood, imposed on the feedback process and the initial condition, respectively.

Cell-free massive multiple-input multiple-output (MIMO) is a key technology for next-generation wireless systems. The integration of cell-free massive MIMO within the open radio access network (O-RAN) architecture addresses the growing need for decentralized, scalable, and high-capacity networks that can support different use cases. Precoding is a crucial step in the operation of cell-free massive MIMO, where O-RUs steer their beams towards the intended users while mitigating interference to other users. Current precoding schemes for cell-free massive MIMO are either fully centralized or fully distributed. Centralized schemes are not scalable, whereas distributed schemes may lead to a high inter-O-RU interference. In this paper, we propose a distributed and scalable precoding framework for cell-free massive MIMO that uses limited information exchange among precoding agents to mitigate interference. We formulate an optimization problem for precoding that maximizes the aggregate throughput while guaranteeing the minimum data rate requirements of users. The formulated problem is nonconvex. We propose a multi-timescale framework that combines multi-agent deep reinforcement learning (DRL) with expert insights from an iterative algorithm to determine the precoding matrices efficiently. We conduct simulations and compare the proposed framework with the centralized precoding and distributed precoding methods for different numbers of O-RUs, users, and transmit antennas. The results show that the proposed framework achieves a higher aggregate throughput than the distributed regularized zero-forcing (D-RZF) scheme and the weighted minimum mean square error (WMMSE) algorithm. When compared with the centralized regularized zero-forcing (C-RZF) scheme, the proposed framework achieves similar aggregate throughput performance but with a lower signaling overhead.

The concept of mutual visibility in a graph encodes combinatorial information about vertex subsets with prescribed visibility properties and serves as a useful algebraic invariant. In this paper, we derive algebraic conditions for the mutual-visibility number of $(d,2)$-graphs with non-negative defect. We then determine this parameter for $(d,2,-2)$-graphs for $d=3$ and $4$, and establish an upper bound for $d=5$. In the case $δ=0$, that is, for Moore graphs of diameter $2$, we focus on the Hoffman-Singleton graph. We establish an upper bound of $20$ for its mutual-visibility number and subsequently employ an integer programming approach to show that this bound is tight. As a corollary, we deduce that the maximum size of an induced matching in the Hoffman--Singleton graph is $10$.

Trapped ion (TI) qubits are a leading quantum computing platform. Current TI systems have less than 60 qubits, but a modular architecture known as the Quantum Charge-Coupled Device (QCCD) is a promising path to scale up devices. There is a large gap between the error rates of near-term systems ($10^{-3}$ to $10^{-4}$) and the requirements of practical applications (below $10^{-9}$). To bridge this gap, we require Quantum Error Correction (QEC) to build logical qubits that are composed of multiple physical qubits. While logical qubits have been demonstrated on TI qubits, these demonstrations are restricted to small codes and systems. There is no clarity on how QCCD systems should be designed to implement practical-scale QEC. This paper studies how surface codes, a standard QEC scheme, can be implemented efficiently on QCCD-based systems. To examine how architectural parameters of a QCCD system can be tuned for surface codes, we develop a near-optimal topology-aware compilation method that outperforms existing QCCD compilers by an average of 3.8X in terms of logical clock speed. We use this compiler to examine how hardware trap capacity, connectivity and electrode wiring choices can be optimised for surface code implementation. In particular, we demonstrate that small traps of two ions are surprisingly ideal from both a performance-optimal and hardware-efficiency standpoint. This result runs counter to prior intuition that larger traps (20-30 ions) would be preferable, and has the potential to inform design choices for upcoming systems.

Understanding the emergence of novel collective behaviors in strongly interacting systems lies at the heart of quantum many-body physics. Valuable insight comes from examining how few-body correlations manifest in many-body systems, embodying the ``from few to many'' philosophy. An intriguing example is the set of universal relations in ultracold atomic gases, which connect a wide range of observables to a single quantity known as the contact. In this Letter, we demonstrate that universal relations manifest in a distinct class of quantum many-body systems, long-range quantum spin chains, which belong to a completely new universality class. Using effective field theory and the operator product expansion, we establish connections between the asymptotic behavior of equal-time spin correlation functions, the dynamical structure factor, and the contact density. The theoretical predictions for equal-time correlators are explicitly verified through numerical simulations based on matrix product states. Our results could be readily tested in state-of-the-art trapped-ion systems.

A search is presented for narrow resonances, with a mass between 0.6 and 1.8 TeV, decaying to pairs of jets, in proton-proton collisions at $\sqrt{s}$ = 13 TeV. The search is performed using dijets that are reconstructed, selected, and recorded in a compact form by the high-level trigger in a technique referred to as "data scouting", from data collected in 2016$-$2018 corresponding to an integrated luminosity of 117 fb$^{-1}$. The dijet mass spectra are well described by a smooth parameterization, and no significant evidence for the production of new particles is observed. Model-independent upper limits are presented on the product of the cross section, branching fraction, and acceptance for the individual cases of narrow quark-quark, quark-gluon, and gluon-gluon resonances, and are compared to the predictions from a variety of models of narrow dijet resonance production. The upper limit on the coupling of a dark matter mediator to quarks is presented as a function of the mediator mass. The sensitivity of this search goes beyond what is expected from statistical scaling with the integrated luminosity alone, as a consequence of the use of fewer parameters in the background function within a more robust statistical procedure.

We propose a simplified localization method for Bose gases, based on a Poincare-type inequality, which leads to a new derivation of Bose--Einstein condensation for dilute Bose gases beyond the Gross--Pitaevskii scaling regime.

Using $(2.712\pm0.014)\times10^{9}$ $ψ(3686)$ events collected with the BESIII detector at the BEPCII collider, we report an evidence of $Ξ^{0}$ transverse polarization with a significance of 4.4$σ$, a precise measurement of the branching fraction and the ratios between the $S$-wave and $D$-wave contributions of $ψ(3686)\toΞ^{0}\barΞ^{0}$. The weak decay parameters ($ϕ_{Ξ^0/\barΞ^{0}}$, $α_{Ξ^0/\barΞ^{0}}$) and the angular distribution ($α_ψ$) are also measured with higher precision compared to the previous measurements. Furthermore, two the $CP$ observables are also determined to be $A^{Ξ^0}_{CP} = -0.014 \pm 0.030 \pm 0.010$ and $Δϕ^{Ξ^0}_{CP} = 0.000 \pm 0.028 \pm 0.003$~rad, which are still consistent with $CP$ conservation at 1$σ$ level under the current statistics.

Hastie et al. (2022) found that ridge regularization is essential in high dimensional linear regression $y=β^Tx + ε$ with isotropic co-variates $x\in \mathbb{R}^d$ and $n$ samples at fixed $d/n$. However, Hastie et al. (2022) also notes that when the co-variates are anisotropic and $β$ is aligned with the top eigenvalues of population covariance, the "situation is qualitatively different." In the present article, we make precise this observation for linear regression with highly anisotropic covariances and diverging $d/n$. We find (both theoretically and empirically) that simply scaling up (or inflating) the minimum $\ell_2$ norm interpolator by a constant greater than one can improve the generalization error. This is in sharp contrast to traditional regularization/shrinkage prescriptions. Moreover, we use a data-splitting technique to produce consistent estimators that achieve generalization error comparable to that of the optimally inflated minimum-norm interpolator. Our proof relies on matching upper and lower bounds for expectations of Gaussian random projections for a general class of anisotropic covariance matrices when $d/n\rightarrow \infty$.

We study the role of Carathéodory extremal functions in the Schur-Agler class generated by a collection of test functions. We show that under certain conditions, $\mathbb{D}$ and $\mathbb{D}^2$ are the only domains where finitely many test functions can generate the Schur class. As applications, we give a description of the Carathéodory extremals in the unit ball of the multiplier algebra of the Drury-Arveson space and give operator-theoretic Herglotz representations for any Carathéodory hyperbolic domain.

Recent progress has been made in capturing spectral features of electronic states of double-excitation character in time-dependent density functional theory (TDDFT) through a frequency-dependent kernel. While it might appear that this development is limited to the perturbative regime, we show that when used within response-reformulated TDDFT, it accurately captures strong-field dynamics involving states of double-excitation character. More generally, this demonstrates how RR-TDDFT enables exchange-correlation functional developments in the response regime, which have so far been more successful than those in the non-linear regime, to be exploited for non-perturbative dynamics, thus significantly broadening their range of applications.

Given a finite directed acyclic graph $R$, we construct from it two graphs $E_R$ and $F_R$, one by adding a loop at every vertex of $R$ and one by replacing every arrow of $R$ by countably infinitely many arrows. We show that the graph C*-algebra $C^*(F_R)$ is isomorphic to the AF core of $C^*(E_R)$. Examples include C*-algebras of a quantum flag manifolds and quantum teardrops. We discuss in detail the quantum Grassmannian $Gr_q(2,4)$ and use our description as AF core to study its CW-structure.

The BTZ black hole provides a tractable (2+1)-dimensional example for investigating string dynamics in curved spacetime. However, a systematic and robust analysis of the solution space of strings in the near-horizon region of BTZ black holes remains elusive in the literature. This work aims to fill this gap by employing the string-Carroll expansion. This formalism provides a natural setting for working with the near-horizon region, because near-horizon expansions for non-extremal black holes match string-Carroll expansions. Using this formalism, and expanding the string action and pullback fields in powers of an effective speed of light, we study the dynamics of closed bosonic strings in the near-horizon, non-extremal BTZ spacetime. Our approach classifies the general characteristics and further reveals some novel features of the families of string solutions.

The AC Optimal Power Flow (AC-OPF) problem is a non-convex, NP-hard optimization task essential for secure and economic power system operation. While interior-point methods are widely used due to their computational efficiency, spatial branching techniques offer global optimality guarantees at significantly higher computational cost. In this work, we propose data-boosted variants of both approaches that leverage historical operating data to enhance performance. Specifically, data are used to guide initialization in interior-point methods and to restrict the search region in spatial branching. This unified perspective enables a systematic assessment of how learning can accelerate both local and global optimization strategies. We conduct an extensive empirical study across networks of varying sizes under both standard conditions and modified configurations designed to induce local optima. Our results show that data-boosted strategies consistently improve convergence and reduce computation times for both approaches. However, spatial branching remains computationally demanding even with data-driven enhancements, while interior-point methods exhibit remarkable robustness, often converging to globally optimal solutions, even in challenging instances with multiple local optima. These findings highlight the practical effectiveness of modern interior-point solvers and suggest that global optimization methods for AC-OPF still face significant scalability challenges, even when augmented with data-driven guidance.

In this paper, we study a variant of the classical Wythoff's game. The classical form is played with two piles of stones, from which two players take turns to remove stones from one or both piles. When removing stones from both piles, an equal number must be removed from each. The player who removes the last stone or stones is the winner. Equivalently, we consider a single chess queen placed somewhere on a large grid of squares. Each player can move the queen toward the upper-left corner of the grid, either vertically, horizontally, or diagonally, in any number of steps. The winner is the player who moves the queen into the upper-left corner, the position (0,0) in our coordinate system. We call (0,0) the terminal position of Wythoff's game. In our variant of Wythoff's game, we have a set of positions {(0,0),(1,0),(0,1),(1,1),(2,0),(0,2)} as the terminal set. If a player moves the queen into this terminal set, that player is the winner of the game. The P-positions of this variant are described by the P-positions of Wythoff's game and Hofstadter's G-Sequence. This variant has two remarkable properties. For a position (x,y) with x >= 8 or y >= 8, the Grundy number of the position (x,y) is 1 in this variant if and only if (x,y) is a P-position of Wythoff's game. There is another remarkable property.For a position (x,y) with x >= 8 or y >= 8, (x,y) is a P-position of of the misere version of this variant if and only if (x,y) is a P-position of of Wythoff's game.