A problem originating with Erdős and Silverman in the 1970s asks for the minimum integer $r(k)$ such that any set of $n \ge r(k)$ points in the plane has some $k$-subset with no right angles. The case $k=4$ has an interesting gap between the known bounds, namely $8 \le r(4) \le 10$. Here, we consider a relaxation that quantifies the deviation from right angles. Specifically, we study $Γ_k(n)$, the supremum of angles $γ$ such that every $n$-set of points in $\mathbb{R}^2$ has a $k$-subset with all angles outside of the interval $90^\circ \pm γ$. We show that $4^\circ \le Γ_4(10) \le 9.292^\circ$. For large $n$, the quantity $Γ_3(n)$ is closely related to a classical minimax angle problem pioneered by Blumenthal, Erdős and Szekeres. We give bounds on $Γ_k(n)$ for a general $k$ and large $n$.

A non-self OU sequence is a cyclic sequence of crossing information of non-self crossings that is obtained by traversing a knot component of an oriented link diagram. In this paper, we investigate what information can be derived from non-self OU sequences, and we completely characterize pairs of non-self OU sequences of diagrams of two-component links. We also characterize the pairs for specific prime links with crossing number up to five.

We propose a new class of short matrix recurrences for the solution of nonsymmetric linear equations of the type $\mathbf{A}_1\mathbf{X}\mathbf{B}_1+\ldots+\mathbf{A}_p\mathbf{X}\mathbf{B}_p=CD^T$. These iterative methods combine local subspace projection to speed up convergence with rank truncation strategies and randomization procedures to limit memory consumption. Computational experiments on a benchmark problem as well as a challenging discretized mixed formulation of a diffusion equation with random inputs illustrate the potential of the proposed methodology.

We use the Unified Transform Method (UTM) for the vector case to resolve an interface problem for the Dirac equation on two semi-infinite domains and two finite domains in the massless and massive cases, respectively. The UTM for the vector case is a variation of the UTM for the scalar case. The solutions obtained for an interface problem on two semi-infinite domains and two finite domains, respectively, in the massive case are convergent explicit integral representations.

We show that the MXene Ta$_2$CS$_2$ provides an excellent platform for hosting multiple coupled degrees of freedom, viz., valley, spin, orbital, and layer. The interplay among these degrees of freedom gives rise to a range of intriguing properties in reciprocal space, including valley-orbital and orbital-layer coupling. In the presence of spin-orbit interaction, these couplings lead to valley-dependent and layer-dependent spin splitting of the electronic bands. We further show that the intrinsic electric polarization in Ta$_2$CS$_2$ introduces an additional tuning parameter, enabling control over these coupled degrees of freedom and resulting in switchable valley-dependent orbital moments and Zeeman-like spin splitting. We demonstrate that these nontrivial orbital and spin textures manifest in the orbital and spin Hall effects, respectively. Our results establish noncentrosymmetric MXenes as a promising platform for exploring the interplay among multiple degrees of freedom, their tunability, and the resulting orbital and spin transport phenomena in these two-dimensional materials, thereby paving the way for next-generation spin-orbitronic devices.

Let $\mathcal{D}$ be a family of digraphs. A digraph $D$ is \emph{$\mathcal{D}$-saturated} if it contains no member of $\mathcal{D}$ as a subdigraph, but for any arc $e$ in the complement of $D$, the digraph $D + e$ contains some member of $\mathcal{D}$ as a subdigraph. The \emph{saturation number} $\mathrm{sat}(n,\mathcal{D})$ and the \emph{extremal number} $\mathrm{ex}(n,\mathcal{D})$ are the minimum number and the maximum number of arcs among all $n$-vertex $\mathcal{D}$-saturated digraphs. For a positive integer $k$, let $\mathcal{D}_k$ denote the family of \emph{$k$-strongly connected digraphs}. In this paper, firstly, we prove that $$\mathrm{sat}(n,\mathcal{D}_k)=(k-1)(2n-k)+\binom{n-k+1}{2}.$$ Then for $n\geq 3(k-1)$, we prove that $$\mathrm{ex}(n,\mathcal{D}_k)\leq \binom{n-k+1}{2}+\frac{17}{6}(k-1)(n-k+1).$$ In addition, we conjecture that for sufficiently large $n$, $$\mathrm{ex}(n,\mathcal{D}_k)=\binom{n}{2}+\frac{3}{2}(k-\frac{4}{3})(n-k+1).$$

Geographic constraints have long structured access to high-growth career opportunities, concentrating upward mobility within a limited set of cities and organizations. The expansion of remote work potentially alters this opportunity structure by decoupling job matching from physical proximity, yet its implications for career mobility remain unclear. Using 48 million U.S. job transitions between 2020 and 2024 linked to employer-level measures of remote eligibility, we estimate how entering remote-eligible jobs shapes career outcomes at job transitions. Workers entering remote-eligible jobs experience significantly higher wage growth and higher rates of upward seniority mobility than comparable workers entering fully on-site roles. These transitions are also associated with greater cross-metropolitan job mobility and moves toward smaller, less prestigious employers. Importantly, effects are largest among lower-income workers and those originating from regions with limited high-skill opportunity density. Together, the findings indicate that remote work relaxes geographic constraints in job matching, reshaping the distribution of upward mobility across places and workers.

This work explores the integration of pixel antennas and rate-splitting multiple access (RSMA) to enhance spectral efficiency in multi-user multiple-input single-output (MU-MISO) systems. Pixel antennas offer controllable antenna characteristics via antenna coding from the analog domain, whereas RSMA provides efficient interference management from the digital domain. We propose a novel pixel antenna empowered RSMA transmission framework where each user employs a pixel antenna. Under imperfect channel state information at the transmitter, we formulate a joint precoding and antenna coding design problem to maximize the ergodic sum-rate. An alternating optimization algorithm based on the weighted minimum mean square error (WMMSE) approach and the successive exhaustive Boolean optimization (SEBO) is first developed to solve the problem. We then propose an efficient online antenna coder selection algorithm relying on an offline-designed codebook to reduce computational complexity. Numerical results show that the proposed pixel antenna empowered RSMA significantly improves spectral efficiency compared to both RSMA with fixed antennas and space-division multiple access (SDMA) employing the same pixel antenna configuration. Moreover, compared to SDMA, RSMA maintains the same performance with a simpler pixel antenna configuration or a smaller codebook size.

Grating interferometry is a promising diagnostic technique that enables simultaneous acquisition of three complementary, synergistic X-ray images: transmission, differential phase, and dark-field. Its key advantage over other setups is its ability to use large pixels and, hence, large-area detectors, as well as its compatibility with low-coherence, compact X-ray sources, both of which are key factors for human-scale imaging. It has already demonstrated strong potential for chest imaging applications, including the diagnosis of pulmonary emphysema, fibrosis, and cancer. To retrieve transmission, differential phase, and dark-field images from data, an algorithm is required to separate the distinct mechanisms contributing to measured contrast. Since its realization, this image-retrieval step has remained fundamentally unchanged. In this work, we develop a novel transmission- and dark-field retrieval algorithm for grating-interferometry derived from the X-ray Fokker-Planck equation. To demonstrate and validate our Fokker-Planck algorithm, we apply it to experimental measurements of a test sample and to data from a mouse chest acquired with varying exposure times and added Poisson noise. The retrieved images were qualitatively and quantitatively compared with those retrieved using a conventional sinusoidal-fitting approach. Across both samples, the Fokker--Planck method produced images consistent with conventional retrieval, with a comparable signal-to-noise ratio. Notably, our Fokker-Planck method suppresses artefacts arising in the conventional approach under grating perturbations (e.g., structural defects like scratches) and reduced flux or visibility, yielding smoother and more reproducible images. Additionally, we demonstrate that our Fokker-Planck method has an advantage over the conventional dark-field retrieval method for fast sample imaging with short exposure times and high noise.

Standard Ornstein-Uhlenbeck (OU) models often yield biased parameter estimates when measurement error is ignored. While the Ornstein-Uhlenbeck State Space Model (OUSSM) addresses this in univariate settings, multidimensional extensions remain limited. This paper introduces the factor OUSSM to model multi-dimensional, mean-reverting systems with observational noise. We resolve critical identifiability challenges in parameter estimation by establishing necessary constraints and validating the method through extensive simulations. We demonstrate the model's versatility by analyzing human gut microbiome dynamics and North Atlantic Sea Surface Temperature (SST) data. The results reveal distinct latent temporal structures in both biological and environmental systems, establishing the factor OUSSM as a robust framework for multivariate time series analysis.

Liquid-liquid phase separation underlies phenomena ranging from protein condensate formation to the phase coexistence of synthetic polymers. Although the random phase approximation (RPA) is widely used to predict such phase behavior, its quantitative accuracy for binodals of polymer solutions, particularly outside the high-density regime, remains incompletely characterized. Here, we develop a field theoretic loop expansion in homopolymer systems by identifying the inverse polymer density $ρ^{-1}$ as the Planck constant $\hbar$ in quantum field theory. We calculate the leading-order and next-to-leading-order corrections to the RPA free energy, denoted as RPA+ and RPA++, respectively. Testing the binodal predicted by the RPA+ against molecular dynamics simulations of bead-spring chains with Gaussian pair interactions, we find that the RPA+ qualitatively improves the dilute-phase coexistence density over the RPA, while the critical point error remains comparable to that of the RPA. Our results establish the loop expansion as a systematic route for refining the RPA-based binodal predictions for polymer phase separation.

Large-scale search engines face a fundamental tension: the index must be updated frequently to maintain freshness, yet updates create resource contention that inflates query latency. In the dominant Lucene-based architecture, segment merges triggered by writes compete with concurrent queries for CPU cycles, disk I/O bandwidth, and operating-system page cache -- a problem we term \emph{write-read contention}. This survey systematically examines the architectural solutions that industry and academia have developed to decouple write pressure from read latency. We identify five principal patterns: (i)~node-level read-write separation; (ii)~compute-storage separation; (iii)~full in-memory indexing; (iv)~log-structured write paths; and (v)~in-place partial updates. We survey representative systems including Elasticsearch, LinkedIn Galene, Uber Sia, Quickwit, Alibaba Havenask, Algolia, Milvus, and Vespa, and discuss an emerging synthesis -- the ScaleSearch architecture -- that combines compute-storage separation with full in-memory indexing and dedicated write nodes. A key contribution of ScaleSearch is \emph{per-field update routing}: each field is assigned its own Kafka topic and update path, allowing scalar fields (price, stock, tags) to be updated in-place in $O(1)$ RAM with immediate visibility while full-text fields follow the segment-based compute-storage path. We conclude with open challenges in hybrid vector-and-full-text retrieval, serverless deployments, and AI-integrated search.

The Domination game is an impartial game on graphs, introduced in 2010, and proved PSPACE-complete in the normal variant in 2026. In this game, Alice and Bob alternately select playable vertices, where a vertex is playable if it dominates at least one vertex not dominated by the vertices selected before in the game. The game ends when the selected vertices form a dominating set. In the normal variant, the player unable to move loses. In contrast to the impartial game, the partizan game has the vertices already colored with $A$, $B$, or $C$, in such a way that Alice (resp. Bob) can only select vertices colored with $A$ (resp. $B$) or $C$. The partizan game was proved PSPACE-hard in 2026. In this paper, we determine the winner of the Normal Partizan Domination game in graphs whose components are complete split graphs, including star forests, for any initial coloring of its vertices. We also obtain partial results for complete bipartite graphs.

Quantum autoencoders (QAEs) are learning architectures that compress quantum data into a low-dimensional latent state while preserving the information needed for reconstruction. We study blind single-copy compression of quantum states through a $k$-qubit bottleneck and investigate the minimal circuit width required to attain the information-theoretic optimum under average infidelity. Between the conventional architecture, which is narrow but nonuniversal, and fully general \emph{completely positive and trace preserving} (CPTP) realizations, which are universal but overparameterized, we identify a \emph{Goldilocks} regime. We prove that for every distribution of pure $n$-qubit states, there exists a QAE with exactly $k$ encoder ancillas and $n$ decoder ancillas that achieves the optimal fidelity over all CPTP encoder--decoder pairs. The encoder-side statement is sharp in that we construct source families for which every optimal scheme necessarily uses at least $k$ encoder ancillas, thereby determining the universal encoder threshold exactly. On the decoder side, we show that isometric decoders are exactly optimal for several analytically tractable source families, but we also exhibit an explicit counterexample demonstrating that decoder isometry is not universally sufficient. Nevertheless, numerical experiments indicate that the performance gap is practically negligible.

We study hidden boundary trace regularity for two-dimensional hyperbolic equations with boundary degeneracy governed by $\mcA\vp=-\Div(A\nabla \vp)$, where $A=\diag(1,r^\al)$ and $\al\in(0,1)$. We establish well-posedness in weighted Sobolev spaces and prove an $L^2$ trace estimate for the normal derivative on the nondegenerate side $r=1$. Using truncated geometries and Carleman weights adapted to the anisotropic degeneracy, we derive a large-time observability estimate with a lower-order interior remainder. We also identify a framework-level obstruction at the critical threshold $\al=1$: the weighted Dirichlet coercivity underlying the subcritical analysis loses uniformity and exhibits a logarithmic loss on truncated domains.

Reservoir computing is a framework which is primarily used for temporal information processing, using the intrinsic dynamics of an underlying physical system. The framework, in a quantum setup, is implemented using ergodic dynamics associated with Hamiltonian models. The computational power of the reservoir is closely tied to this underlying dynamical nature, and to probe this further, we study the effectiveness of a reservoir that is made using structured brickwall circuits built from two-qubit gates. Here, the global ergodic nature of the circuit model results from the said arrangement, which has an important role in extracting useful performance with a minimal setup that is independent of an associated Hamiltonian. We focus on the nature of the gates used in this setup and evaluate the resulting reservoir performance, correlating the same with known results on the dynamical nature of the circuit in question. As a baseline, we analyse brickwall circuits composed of Haar-random two-qubit gates, before moving on to dual-unitaries, where tunable ergodic properties allow us to systematically investigate its relationship with reservoir performance. We further consider a class of non-random two-qubit gates obeying a specific solvability condition, wherein the associated dynamics surpasses the equivalent circuit made up of two qubit Haar random unitaries in terms of randomness. Finally, we consider examples of Krylov space analytics, which allow for a reliable prediction of effective circuit reservoirs for sufficient task performance. Using the introduced metrics we validate the reservoir for time-series prediction using standard synthetic data sets to evaluate the fading memory capacity and accuracy for prediction tasks. Our results indicate that structured quantum circuits would serve as effective models that yield better and efficient task performance in reservoir computing applications.

We study the left $K$-invariant $L^r$-Schwartz space and its Fourier transform on split rank one semisimple symmetric spaces $G/H$ for $0<r\leq 2$. We explicitly determine the kernel of the Fourier transform and show that it is spanned by eigenfunctions associated with the discrete spectrum of the Laplace--Beltrami operator on $G/H$.

We require decomposition methods for the ABCD-matrix formulation in rotationally symmetric paraxial geometric optics when designing a multi-component optical system from a given single paraxial specification (represented by an ABCD matrix) to optimize non-paraxial specifications (e.g., optical aberrations). In this study, we propose two kinds of three-matrix decomposition of ABCD matrices by focusing on the fact that the ABCD matrices have three real-number degrees of freedom. In addition, we formulate a transformation between the two kinds of decomposition for a single matrix, which can increase or decrease the number of refraction surfaces in the optical configuration while keeping the paraxial specifications fixed. This nature is useful for the optical design of multi-component systems with optimized non-paraxial characteristics.

AI browsing agents are an emerging class of AI-powered bots capable of autonomously navigating websites. Unlike traditional web bots, AI browsing agents typically operate using real browsers and perform everyday tasks, making them difficult to detect. Yet little is known about whether existing AI browsing agents can be distinguished from humans and one another based on their browser or behavioral fingerprints. In this paper, we present the first controlled measurement study of seven AI browsing agents and human users. Using an instrumented honey website, we collect browser and behavioral fingerprint features while AI browsing agents and humans perform three tasks: flight booking, online shopping, and forum interaction. We then train FP-Agent, a multi-class classifier, to evaluate the discriminative power of these features. We find that browser fingerprints provide limited discriminative power when shared by multiple AI browsing agents. Behavioral fingerprints, however, are distinctive: differences in typing, scrolling, and mouse behavior separate AI browsing agents from humans and one another. In a case study evaluating Cloudflare's bot detection, FP-Agent detects all seven AI browsing agents, whereas Cloudflare detects only one. Our findings show that behavioral fingerprints are a critical component to reliably detect and control this emerging form of web traffic.

We present an atomistic quantum transport simulation framework based on the Non-Equilibrium Green's Function (NEGF) formalism to model impact ionization in semiconductor avalanche devices, with direct relevance to near-term quantum networking applications. Conventional descriptions of avalanche breakdown rely predominantly on semiclassical simulation methods, such as local ionization coefficients, semiclassical carrier trajectories, or Monte Carlo sampling, all of which implicitly assume weak correlations and mean-field electronic interactions. These assumptions break down in nanoscale, high-field junctions where carrier multiplication emerges from strongly non-equilibrium, energy-resolved scattering processes. Our approach formulates impact ionization as a multi-particle self-energy within NEGF, enabling a non-perturbative, energy- and atomic orbital-resolved description of carrier multiplication directly from the device spectral function. This formulation captures strongly inelastic scattering processes beyond semiclassical approximations and is implemented in a matrix-based real-space representation suitable for nanoscale device modeling. Using a model semiconductor structure under high electric fields, we demonstrate the emergence of carrier multiplication and analyze its dependence on energy-resolved transport and nonequilibrium charge distributions. The framework provides insight into microscopic mechanisms governing avalanche processes and their impact on device performance. Our results establish a transport baseline for self-consistent calculations of the impact-ionization self-energy and carrier multiplication. By resolving the available and occupied states that underlie avalanche onset, this framework provides a route toward predictive modeling of silicon single-photon avalanche detectors and avalanche photodiodes used in quantum-network receivers.

The rapid deployment of Low Earth Orbit (LEO) satellite constellations has enabled the emergence of in-orbit edge computing and data centers-interconnected satellites equipped with onboard computing capabilities and high-speed inter-satellite links (ISLs). This paper investigates whether such architectures, integrated with a deep learning-based computer vision pipeline, can achieve sub-minute information freshness suitable for real-time wildfire detection. To evaluate this hypothesis, we develop a simulation framework that models orbital dynamics, distributed processing, and network routing, using Age of Information (AoI) as the primary performance metric. A total of 720 simulation trials are conducted across 12 real-world constellation configurations, including Starlink, Kuiper, Telesat, and OneWeb. The results demonstrate that constellation design has a significant impact on AoI performance, with average AoI values ranging from 66.5 s to over 6300 s. The best-performing configurations achieve an average AoI below 70 s and a peak AoI under 100 s, indicating that orbital edge computing systems can provide the level of timeliness required for near-instantaneous environmental monitoring.

The increase in space activities has increased the risks of space debris generation, affecting space safety and sustainability. Traditional space situational awareness (SSA) relies on single star trackers and ground-based tracking facilities. There is limited discussion on the use of in-orbit optical sensors on low Earth orbit (LEO) satellite constellations for SSA, despite their importance for efficient space traffic management systems. In this paper, we aim to address this important challenge. We first present a new analytical system model for utilizing LEO satellite constellations for in-orbit SSA. We then develop a method to evaluate and analyze such a system. We also propose a Poisson expected revisit period algorithm and introduce the period of equivalent orbital distributions to reveal the relationship between revisit period and geometric variables, with insightful results based on real-world and custom satellite constellations. Experiments on real-world constellation show that the representative Poisson expected revisit period ranges from 0.4 days to 5.7 days for targets whose apogee altitude ranges from 552 km to 650 km, while requiring a per-case computation time of 0.4 s to 4.8 s. Our work can inform the future design of in-orbit and onboard computing systems for SSA, such as space object detection and space traffic monitoring systems.

Microwave-to-optical quantum transducers will enable coherent interconnection between distant superconducting quantum devices. Ongoing explorations with several platforms have shown promising results at single-photon levels. However, in all these demonstrations, elimination of noise due to the concurrence of the weak transduced signal with intense pump pulses remains a challenge, requiring high suppression filtering setups. A memory-assisted transducer, on the other hand, offers a versatile approach that not only mitigates the noise but also enables the on-demand retrieval of the transduced signal. Here, we integrate a quantum memory protocol with transduction in a three-level atomic system to demonstrate on-demand retrieval of transduced signals. Due to the zero-first-order Zeeman transitions at zero magnetic fields, providing long optical and spin coherence times, and GHz range hyperfine splitting, we use a low-doping concentration $^{171}{\rm Yb}^{3+}$:${\rm Y}_2{\rm SiO}_5$ crystal at 30\,mK temperature. We achieve on-demand transduction assisted by memory with $0.4\ (\text{and }0.3)$ noise photons in the detection window at a storage duration of $460\ (\text{and }620) \, μ\textrm{s}$. To demonstrate the coherent nature of the protocol, we show interference patterns resulting from transduced signals due to varying phase or frequency of the input microwave pulses. Further, multimode transduction capacity is demonstrated, utilizing the spin and optical inhomogeneous broadening. The on-demand capability of the protocol allows synchronizing qubits in a quantum repeater protocol, while multimode capacity increases the entanglement generation rate. To the best of our knowledge, this is the first demonstration of an on-demand microwave-to-optical transducer assisted by memory.

Total variation denoising (TVD) is a classical method for denoising and curve fitting, yet an explicit pointwise description of its fitted values has only recently been established in the mean regression setting by arXiv:2410.03041v4. This raises the question of whether a similar representation holds for quantile regression. We answer this question affirmatively by deriving an exact minmax/maxmin representation for the quantile TVD estimator, providing a complete pointwise characterization of its solution set. Given that the quantile TVD estimator is generally non-unique, the existence of such a representation is perhaps surprising. We show that the set of admissible fitted values at any location forms a compact interval, whose endpoints are characterized exactly by minmax/maxmin functionals of local order statistics over nested intervals. We next develop several structural properties of the quantile TVD solution set. First, the solution set is closed under coordinatewise maximum and minimum, guaranteeing the existence of extremal elements -- upper and lower envelope solutions. Second, this reveals that quantile TVD is intrinsically non-crossing across quantile levels when a common tuning parameter is used. We prove this is driven by submodularity of the total variation penalty, and show that any penalized quantile regression estimator with a submodular penalty enjoys this property. From an estimation error perspective, our representation enables a refined pointwise analysis via a transparent local bias-variance decomposition, facilitating new pointwise risk bounds and near-optimal rates for locally Holder smooth functions. Our results hold under heavy-tailed noise (e.g., Cauchy) and substantially extend existing guarantees beyond locally constant signals. Altogether, these results advance the theory of quantile TV regression via exact pointwise min-max representations.

We investigate inverse scattering problems for Dirac equations that arise as continuum models of waveguide arrays. We first establish the well-posedness of the forward models. For the associated inverse problems, we develop the inverse Born series and the reduced inverse Born series, providing analysis of convergence and rigorous error estimates. Numerical experiments are presented to validate the proposed algorithms and demonstrate their effectiveness.

In this paper, we introduce a family of novel sparse array designs called the augmented ULAs (AULAs) for the localization of non-circular signals (NCS). Accurate direction of arrival (DOA) estimation and the ability to resolve multiple targets are critical in modern wireless communication systems. Most existing sparse arrays are optimized solely for the difference co-array, making them less efficient at utilizing the sum co-array resulting from the non-zero pseudo-covariance of NCS. Meanwhile, state-of-the-art designs for joint optimization of the sum and difference co-arrays remain constrained by a three-way performance trade-off. The proposed AULAs configure single sparse and two dense ULAs alongside two separate elements to achieve a perfect splicing of holes and lags in the difference and sum co-array. This results in a larger virtual aperture and increased DOFs for NCS. Building on this structure, other variants of AULAs are developed, each exhibiting distinct characteristics. The shifted AULAs (SAULAs) judiciously displace the AULAs structure to minimize co-array redundancy and further enhance the DOFs. A transformed SAULAs (TSAULAs) design is proposed, which mitigates mutual coupling effects by converting the dense ULAs of SAULAs into sparse ULAs. By reconfiguring the elements of TSAULAs, the complementary TSAULAs (Co-TSAULAs) design inherits the desirable properties of SAULAs and TSAULAs.All these structures belong to a unified design framework, within which one configuration can be adapted into another during the design phase to meet different performance requirements. Meanwhile, they provide in-built physical locations for convenient extension to a larger aperture. Closed-form expressions for precise element placements, DOFs, and weight functions are derived. Simulation results validate the effectiveness of the proposed approach.

Altermagnets host chirally split magnons that promise unique functionalities for information processing. However, their distinctive transport signatures, crucial for experimental identification and manipulation, remain elusive. Here, we predict that a spin accumulation electrically injects a ``vector" or multidirectional magnon spin current into an altermagnet, comprising both longitudinal and sizable transverse components. Notably, this transverse current exhibits a sign reversal away from the source and can be switched on or off by reorienting the Néel vector. While such a transverse current is found to be not forbidden even in conventional antiferromagnets, we demonstrate through quantum-kinetic calculations that in altermagnets, the transverse response is enhanced by two orders of magnitude due to broken parity-time symmetry. This giant enhancement provides a decisive transport fingerprint for detecting magnon spin splitting and Néel-vector orientation, offering a clear criterion to experimentally distinguish altermagnets from conventional antiferromagnets.

We prove that a hereditary graph class $\mathcal{G}$ defined by finitely many excluded induced subgraphs has bounded tree-$α$ if and only if it is "$(\mathrm{tw},ω)$-bounded" (that is, for all $t\in \mathbb N$, the class of all $K_t$-free graphs in $\mathcal{G}$ has bounded treewidth). Equivalently, $\mathcal{G}$ has bounded tree-$α$ if and only if it excludes a complete bipartite graph, a forest whose components each have at most three leaves, and the line graph of such a forest. This resolves two conjectures of Dallard, Krnc, Kwon, Milanič, Munaro, Štorgel, and Wiederrecht: the above, and a weaker one that for all $a,b\in \mathbb N$, every hereditary class that excludes $K_{a,a}$ and the $b$-vertex path has bounded tree-$α$. The latter was already open even for $(a,b)\in \{(2,7),(3,5)\}$, and only recently proved for $(a,b)=(2,6)$.

We give a tug-of-war interpretation of the regularized $p$-Laplacian $\divgg\big((1+|Dv|^2)^{p/2-1}Dv\big)=0$ in a bounded domain $Ω\subset\R^n$, $p\ge 2$. The key is the linear lift $w(x,x_{n+1})=v(x)+x_{n+1}$, which identifies this equation with $Δ_p w=0$ in $\R^{n+1}$. Projecting the standard $(n+1)$-dimensional $p$-harmonious scheme onto $\R^n$ yields a discrete dynamic programming principle for which we prove existence, uniqueness, and Borel measurability of solutions with strip boundary data, identify the unique fixed point with the value of the projected game, and establish convergence to the viscosity solution as $\varepsilon\to 0$.

We compute the gravitational-wave signal generated by the radial infall of a stellar-mass black hole into a thin-shell Schwarzschild traversable wormhole. Modeling the black hole as a test particle, we derive analytic expressions for the emitted waveform, including contributions from the mass quadrupole and higher-order multipoles. The resulting signal exhibits a characteristic pulse-gap structure associated with repeated throat crossings. We further compute the amplitude spectral density and compare it with representative ground-based detector sensitivities, finding that such signals could lie within the sensitivity range for optimally oriented sources at distances of order ~500 Mpc. These results provide a potential observational signature of traversable wormholes in gravitational-wave data.