Due to the directive property of each antenna element, the received signal power can be severely attenuated when the emitter deviates from the array boresight, which will lead to a severe degradation in sensing performance along the corresponding direction. Although existing rotatable array sensing methods such as recursive rotation (RR-Root-MUSIC) can mitigate this issue by iteratively rotating and sensing, several mechanical rotations and repeated eigendecomposition operations are required to yield a high computational complexity and low time-efficiency. To address this problem, a pre-rotation initialization with recieve power as a rule is proposed to signifcantly reduce the computational complexity and improve the time-efficiency. Using this idea, a low-complexity enhanced direction-sensing framework with pre-rotation initialization and iterative greedy spatial-spectrum search (PRI-IGSS) is develped with three stages: (1) the normal vector of array is rotated to a set of candidates to find the opimal direction with the maximum sensing energy with the corresponding DOA value computed by the Root-MUSIC algorithm; (2) the array is mechanically rotated to the initial estimated direction and kept fixed; (3) an iterative greedy spatial-spectrum search or recieving beamforming method, moviated by reinforcement learning, is designed with a reduced search range and making a summation of all previous sampling variance matrices and the current one is adopted to provide an increasiong performance gain as the iteration process continues. To assess the performance of the proposed method, the corresponding CRLB is derived with a simplified rotation model. Simulation results demonstrate that the proposed PRI-IGSS method performs much better than RR-Root-MUSIC and achieves the CRLB in term of mean squared error due to the fact there is no sample accumulation for the latter.

We prove the conjecture that higher Verlinde categories are geometrically reductive. This is one of the two properties required in order for recent results on algebraic geometry in tensor categories to apply to these categories. We also reduce two further conjectures concerning geometric reductivity for tensor categories to other conjectures appearing in the literature.

We show how the Husain-Kuchař model can be understood as a Carrollian limit of the Holst term in the context of background-independent field theories described in terms of coframes and spin connections. We also discuss the footprint of the Carrollian symmetry in the Hamiltonian formulation of the Husain-Kuchař action.

This paper deals with the longstanding quest of the possible existence of finite-time singularities in the equations governing the dynamics of inviscid fluids, namely, Euler equations. Here, two contributions are brought for the case of perfect fluids with finite initial energy. First, a self-similar velocity field inspired by Leray Ansatz is proposed which allows for a separation of variables that transforms the original partial differential Euler equations to a nonlinear system of ordinary differential equations. This system can be solved semi-analytically and allows a continuum set of solutions parametrised by a self-similar exponent, $ν$. Second, we use the conservation laws of Euler equations to select the possible finite-time singular solutions and the related self-similar exponents. We find that the helicity is the driving mechanism of the blow-up through a self-focusing mechanism. The flow near the singularity separates into two phases. A first phase is within a tubular region that shrinks as a power-law $(t_c-t)^ν$, with $t_c$ the blow-up time, where the helicity is focused. This region is separated by a sharp interface from an outer region where the vorticity, and thus helicity, is identically zero. We found that the finite-time singularity may be either point-like or line-like depending on the dynamics of the tubular region along its axis of symmetry. Incidentally for a point-like singularity we recover the Leray scaling $ν=1/2$ paving the way to a generalisation of this approach for the Navier-Stokes equations. Finally, we conjecture that if the helicity vanishes initially, no finite-time singularity would be possible, since in this case the singularity occurs at infinite time from the initial condition.

For decades it is known that Quantum Computers might serve as a tool to solve a very specific kind of problems that have long thought to be incalculable. Some of those problems are of a combinatorial nature, with the quantum advantage arising from the exploding size of a huge decision tree. Although this is of high interest as well, there are more opportunities to make use of the quantum advantage among non-perfect information games with a limited amount of steps within the game. Even though it is not possible to answer the question for the winning move in a specific situation, people are rather interested in what choice gives the best outcome in the long run. This leads us to the search for the highest number of paths within the game's decision tree despite the lack of information and, thus, to a maximum of the payoff-function. We want to illustrate on how Quantum Computers can play a significant role in solving these kind of games, using an example of the most popular German card game Skat. Therefore we use quantum registers to encode the game's information properly and construct the corresponding quantum gates in order to model the game progress and obey the rules. Finally, we use a score operator to project the quantum state onto the winning subspace and therefore evaluate the winning probability for each alternative decision by the player to be made by using quantum algorithms, such as quantum counting of the winning paths to gain a possible advantage in computation speed over classical approaches. Thus, we get a reasonable recommendation of how to act at the table due to the payoff-function maximization. This approach is clearly not doable on a classical computer due to the huge tree-search problem and we discuss peculiarities of the problem that may lead to a quantum advantage when exceeding a certain problem size.

Existing aging theories describe what changes with age but do not prescribe how to intervene. We propose a control-theoretic framework that is not merely descriptive but prescriptive: it specifies which intervention, at which dose and sequence, under which safety constraints, will restore a measured biological state to a functional region. Aging is defined as the progressive loss of safe controllability; biological age is the minimum safe control cost of functional restoration. Drugs are modeled as vector fields on biological state space whose non-commutativity, quantified by Lie brackets, predicts that intervention order determines outcome. The core differentiation from prior theories is operational: the framework outputs ranked targets, optimal sequences, safety-constrained protocols, and falsifiable predictions directly usable in drug discovery, rather than mechanistic ontologies or correlative biomarkers. We present a five-dimensional ODE model with analytic Lie-bracket derivation, a modality-aware control layer, three translational case studies, an implementation architecture with power analysis, and empirical scoring of aging interventions across five biological epochs. Twenty falsifiable predictions are enumerated. The central claim is that control-value reduction predicts translational success better than Hallmark annotation or biomarker reversal alone. If validated, this provides the missing interventional layer connecting aging biology to rational gerotherapeutic discovery.

First-order phase transitions produce gravitational waves and primordial black holes. They always occur in field theories where symmetries are radiatively broken and masses are correspondingly generated. These theories predict a period of supercooling: phase transitions become effective at temperatures much smaller than the symmetry-breaking scale. This paper reviews a model-independent approach to study phase transitions in this scenario, which can be adopted if supercooling is strong enough. Perturbative methods can be used to determine the effective action and such model-independent approach allows us to obtain ready-to-use formulas that can be applied to any specific model of this sort.

Content moderation is a central mechanism through which platforms attempt to balance user engagement with community governance. Yet existing research has largely treated moderation as a uniform intervention, overlooking how moderator source, violation context, and linguistic style jointly shape user behavior. Drawing on the Human--AI Interaction Theory of Interactive Media Effects (HAII-TIME), this study examines how these three dimensions produce divergent post-moderation behavioral trajectories in a large-scale observational dataset of 11,795,036 moderation events across 9,285,410 users and 61,261 subreddits on Reddit (2021--2025). Using probabilistic behavioral classification, ANOVA, and OLS regression with PCA-derived linguistic features, we find that bot moderation consistently produces higher compliance and lower self-censorship than human or modteam moderation, challenging the assumption that human agency cues are inherently advantageous. Modteam moderation produces the strongest self-censorship effects, suggesting that institutional depersonalization is a meaningful driver of behavioral withdrawal. Violation severity emerges as a critical contingency: linguistic strategies effective in routine contexts -- elaborated explanation, community-scale appeals, direct personal address -- can backfire for serious violations, whereas prosocially framed and emotionally emphatic messages become most effective when stakes are highest. Of 480 linguistic interactions tested, 33 survive FDR correction. These findings extend HAII-TIME by introducing violation salience as a moderator of cue-based processing, and offer empirical grounding for context-adaptive moderation design.

In this paper, we study the Hecke eigenvalues of Ikeda lifts. Using the spherical map for the Hecke algebra of the symplectic group, we obtain an explicit formula for the eigenvalues $λ_F(p^r)$. From this formula, we show that $λ_F(p^r)$ can be written as a polynomial in $p^{\pm 1/2}$ with a positive leading term. Furthermore, we prove that the coefficients of this polynomial are bounded and, as a consequence, the Hecke eigenvalues $λ_F(p^r)$ are positive for all sufficiently large primes $p$.

We study mutually unbiased bases (MUBs) as structured finite initialization and adaptation families for variational quantum algorithms. The main theoretical result is that, in every dimension admitting a complete set of MUBs, the complete MUB ensemble maximizes isotropic Gaussian random-Hamiltonian width among all unions of d+1 orthonormal bases in C^d. Equivalently, within this basis-union class, it gives the smallest expected best-of-set minimum for random-Hamiltonian minimization. The proof represents each orthonormal basis as a regular-simplex Gaussian block and uses a centered-convex Gaussian correlation inequality to show that the independent-block case, realized by complete MUBs, is stochastically extremal. We also record a radial extension for Hamiltonians H=RG with R nonnegative and independent, and the unrestricted qubit case, where complete qubit MUBs are globally optimal among arbitrary six-state ensembles by a Bloch-sphere/octahedron mean-width argument. We then separate this coverage theorem from variational training dynamics. For diagonal QUBO costs, the MUB-family dependence of a fully matched construction collapses; for the canonical b=0 label it reduces to ordinary X-mixer QAOA. The empirical method is therefore adaptive MUB-XRot warm-start QAOA rather than canonical matched-mixer MUB-QAOA. In a cross-problem benchmark over MaxCut, weighted MaxCut, MIS, weighted MIS, and knapsack, adaptive MUB-XRot is non-worse than standard QAOA in 80.0% of 1500 paired cases, with win/tie/loss 829/371/300 and mean decoded-ratio improvement +0.1616. A separate QRAO MaxCut study shows that bit-flip MUB-family search reaches mean relaxed ratio 0.921 and improves over the X-variational baseline by +0.0608. The evidence is quality-oriented and incurs substantial runtime overhead; no quantum-advantage claim is made.

We study \textsc{OCO-S$^2$}, an online convex optimization setting in which decisions drive a stable dynamical state, losses are incurred along the induced state trajectory, and first-order feedback is available only through sparse block communication with partial participation. This coupling creates a dynamic-regret problem beyond pointwise OCO: the learner updates and holds decisions at the block scale, whereas the hindsight comparator may vary at the per-round scale. We propose \textsc{OCO-S$^2$-OGD}, a projected block online gradient method that updates deployed decisions using sparse block-level distributed feedback. We prove dynamic-regret bounds for the incurred trajectory cost, quantifying the tradeoff among block communication, comparator variation, state-memory truncation, and partial participation. We further introduce a prediction-augmented variant, \textsc{OCO-S$^2$-OGD-P}, and show that accurate block-level predictions improve the optimization term in the regret bound through their realized gradient-mismatch error. Overall, this work provides a regret-theoretic foundation for communication-efficient online decision-making in systems where algorithmic updates and physical state trajectories are intrinsically coupled.

Entanglement in continuous-variable Gaussian systems is a key resource, and common reservoirs can both suppress and generate correlations. Existing work focused on pre-entangled states or Markovian baths, leaving open whether separable squeezed inputs entangle in structured environments or under modulation. We study two bosonic modes coupled to a common reservoir, each initialized in a separable squeezed vacuum. Dynamics are analyzed utilizing Gaussian covariance methods, evolved under approximate Non-Markovian quantum state diffusion (QSD), finite-temperature pseudomode embeddings, and Bures-based non-Markovian diagnostics. We identify three mechanisms absent in Markovian dynamics: (1) A detuning condition that freezes entanglement trajectories across reservoir correlation times; (2) birth, death, and revival of entanglement from orthogonal inputs; and (3) integer-locked beating with square-wave oscillations produced by periodic detuning. All mechanisms persist at finite temperature, with deviations bounded within 5% in cryogenic regimes and 20% at moderate occupations. These deviation bounds align with cryogenic cavity, phononic, and optomechanical platforms, where structured spectral densities and detuning modulation are already accessible. Structured reservoirs are shown to emerge as tunable entanglement resources for continuous-variable quantum technologies.

We explore some connections between vectors of integers and integer partitions seen as bi-infinite words. This methodology enables us on the one hand to obtain enumerations connecting products of hook lengths and vectors of integers. This yields on the other hand a combinatorial interpretation of the Macdonald identities for affine root systems of the $7$ infinite families in terms of Schur functions, symplectic and special orthogonal Schur functions. From these results, we are able to derive $q$-Nekrasov--Okounkov formulas associated to each type. The latter for limit cases of $q$ yield Nekrasov--Okounkov type formulas corresponding to all the specializations given by Macdonald.

This study provides an analytical foundation for adversarial synchronization control in Kuramoto oscillator networks, where small gradient-based perturbations applied repeatedly to oscillator phases can dramatically enhance or suppress collective synchronization. Using the Ott--Antonsen reduction, we derive an exact closed-form expression for the effect of a single adversarial perturbation (kick) on the order parameter. A key finding is that each kick produces a finite, coupling-independent increment in the order parameter even when synchronization is arbitrarily weak, which combined with slow relaxation near the critical coupling and mean-field feedback explains the disproportionate amplification previously observed in numerical simulations. Fixed-point analysis further reveals a fundamental asymmetry between enhancement and suppression, with the latter governed by noise-induced escape in finite systems. Extending the framework to networks via the annealed network approximation, we show that the theory captures the synchronization behavior of representative model networks and identify a decoupling between kick sensitivity and mean-field dominance in scale-free networks. These results offer a tractable theoretical basis for understanding and designing kick-based synchronization control in oscillator networks.

We develop the discrete set of Dyson-Schwinger equations for scalar fields and solve them for some cases. We show that their solutions are Gaussian in the continuum limit as expected from the theorems of Aizenman and of Aizenman and Duminil-Copin for $d\ge 4$. Extension to lower dimensionality fails, as it should, by observing that the triviality theorems used in our proof are not applicable in such cases.

RuO$_2$ has been regarded as a prototypical candidate for metallic altermagnet, offering a potential platform for high-speed and high-efficiency spintronics. However, the magnetic ground state of RuO$_2$ remains a topic of active debate due to conflicting experimental reports. In this work, we investigate the effect of electron correlations in RuO$_2$ using density functional theory combined with dynamical mean-field theory (DFT+DMFT). In contrast to previous DFT-based studies, DFT+DMFT captures essential dynamical correlation effects, yielding spectral functions and optical conductivities in excellent quantitative agreement with experiments, and further reveals that RuO$_2$ resides in the close vicinity of both the paramagnetic-altermagnetic phase boundary and the itinerant-localized crossover, rendering the magnetic ground state highly susceptible to external perturbations. Indeed, even a minimal compressive strain of $\sim$0.5% is sufficient to drive the system into an altermagnetic phase. These findings elucidate the origin of the conflicting experimental observations and reveal that dynamical correlation effects are the key driving force behind the highly tunable magnetic ground state of RuO$_2$.

The Möbius energy of a curve is a topic of interest to physical knot theorists, harmonic analysts, and geometric analysts. In particular, there are many open questions regarding the gradient flow and critical points. The Gateaux derivative indicates the variation is dependent on curvature and torsion, and so to better understand the gradient, we investigate the family of helix curves, where the ratio of torsion to curvature is a constant proportional to the pitch. We fix the radius of the helix, and study the coiling in both directions: as the helix unravels to a straight line, and as it coils infinitely tight. Specifically, we study the arclength-rescaled Möbius energy density, which is a naturally tractable quantity under the Möbius energy's chord-arc comparison of inverse-square laws. The asymptotics of the uncoiling helix, corresponding to an energy decay, can be proven with a short chain of estimates. However, the asymptotics of the helix as it coils infinitely tight, blowing up the energy, is a much more involved calculation. Our strategy for calculating the asymptotics, initially reminiscent of the work by Kim-Kusner, begins with a meromorphic extension of the integrand. However, proving the asymptotic equivalence requires a fundamentally distinct strategy because our integrand has infinitely many poles. keywords: Möbius energy, helix, complex asymptotics, knot energies, physical knot theory, coiling, curves

Majorization inequalities for symmetric polynomials have interested mathematicians for centuries, from the AM-GM inequality for two variables going back at least to Baudhāyana's Śulbasūtra and Euclid's Elements in the first millenium BCE, through classical results of Newton, Muirhead and Gantmacher, to more recent extensions to Schur polynomials and zonal spherical functions. These have been established case by case, with no unified approach. Although it is known that majorization inequalities follow from symmetry and convexity in the indexing partition, the difficulty of proving convexity in specific cases has left a number of outstanding conjectures inaccessible until now. The key insight of this paper is that log-convexity provides a more versatile tool and a unifying principle. It implies convexity and hence majorization, and it is preserved under multiplication and weighted averaging, making it well suited to inductive arguments in a wide range of settings. Using this idea, we prove new majorization inequalities for Macdonald polynomials, Jack polynomials and Heckman-Opdam hypergeometric functions, unifying existing results and resolving several open conjectures.

The OH$^+$ ($X ^3Σ^-$) radical cation has been investigated by combining a 4 K 22-pole ion trap apparatus with high-resolution IR and THz radiation sources. Applying different types of action spectroscopic methods, the fundamental vibrational band in the 3 $μ$m range and the spin manifold of the $N=1 \leftarrow 0$ rotational transition around 1 THz have been extended and refined. Additionally, the spin manifold of the $N=2 \leftarrow 1$ rotational transition, scattered around 2 THz, has been measured for the first time with microwave accuracy. Although all hyperfine components of the pure rotational transitions are affected by considerable Zeeman splittings, a simulation of their contours allowed us to extract the field-free center frequencies with high accuracy. A global fit combining rovibrational and pure rotational transitions from the literature with those newly obtained in this work was performed, leading to improvements in the spectroscopic constants of OH$^+$, particularly those in the ground vibrational state.

Byzantine Reliable Broadcast (BRB) is a fundamental primitive in distributed computing and cryptographic systems; reducing the communication cost of BRB thus remains an important research direction. However, most existing works either focus strictly on the synchronous network model or utilize computationally impractical erasure codes. Therefore, to achieve a practical yet network-robust algorithm, one must turn toward committee sampling techniques. However, Committee sampling techniques often forgo optimal resilience ($f < \lfloor\frac{n}{3} \rfloor$) in the face of asynchrony. This work produces two interesting results: Firstly, we propose a \textit{randomly asynchronous} BRB protocol that can achieve both optimal resilience and asymptotically optimal communication complexity ($O(n|m|)$) through an underutilized technique: \textit{amortization}; and does not utilize computationally expensive \textit{erasure codes}. Next, we show that an optimally resilient BRB protocol utilizing sampled committees cannot exist in a \textit{fully asynchronous} network.

Magnetic MAX phases are nanolaminated metals that combine ceramic-like thermal and mechanical stability with peculiar magnetic ordering, making them attractive for thin-film optoelectronics and spintronics. However, laser-induced magnetization dynamics in MAX phases remains largely unexplored. Here, we investigate laser-induced ultrafast demagnetization in a 40-nm-thick epitaxial film of the magnetic MAX phase (Cr0.5Mn0.5)2GaC, which magnetically orders below ~220 K, using time-resolved magneto-optical Kerr effect spectroscopy. We reveal, that the demagnetization transients exhibit a two-step type-II demagnetization, common for two-dimensional magnetic systems. The second stage dominates the process and has a characteristic time of approximately 100 ps. Applying the three-temperature model, we extract the electron-lattice, spin-lattice, and electron-spin coupling constants. The reconstructed spin heat capacity exhibits a weak temperature dependence, accounting for only a subtle slowing down of demagnetization at elevated temperatures and fluences.

Both for quark flavor asymmetry and valence, we consider the anomalous dimension of the non-singlet twist-two quark operator of arbitrary Lorentz spin N at four loops in SU(nc) color gauge theory and present its term proportional to zeta(3) in closed form. These results have been extracted from published Mellin moments, for N=1,...,16 and N=3,...,15, respectively, by analytic reconstruction using advanced methods of number theory. Via Mellin transformation, we obtain the exact functional forms in x of the respective pieces of Dokshitzer-Gribov-Lipatov-Altarelli-Parisi splitting functions. This allows us to reduce the theoretical uncertainties in the approximations of these splitting functions otherwise amenable from the first few low-N values.

We study the problem of estimating the intensity function of a covariate-driven point process based on observations of the points and covariates over a large window. We consider the nonparametric Bayesian approach, and show that a wide class of Gaussian priors, combined with flexible link functions, achieves minimax-optimal posterior contraction rates in the increasing domain asymptotics and under the assumption that the covariates be ergodic. We also employ Besov-Laplace priors, which are popular in imaging and inverse problems due to their edge-preserving and sparsity-promoting properties. We prove that these yield optimal estimation of spatially inhomogeneous intensities belonging to Besov spaces with low integrability index. These results are based on a general concentration theorem that extends recent findings from the literature. To corroborate the theory, we provide extensive numerical simulations, implementing the considered procedures via suitable posterior sampling schemes. Further, we present two real data analyses motivated by applications in forestry and the environmental sciences.

We present a comprehensive characterization of resistive PICOSEC Micromegas detector prototypes, tested under identical conditions, constant drift gap, field configurations, and photocathode at the CERN SPS H4 beam line. This work provides a proof of concept for the use of resistive layer technology in gaseous timing detectors, demonstrating that robustness can be improved without compromising the excellent timing performance of PICOSEC Micromegas. Different resistive architectures and values were explored to optimize stability and ensure reliable long-term operation in challenging experimental environments. The prototype with a 10MΩ resistive layer achieved the best overall performance, with a timing resolution of 22.900 {\pm} 0.002 ps and a spatial resolution of 1.190 {\pm} 0.003 mm, while charge sharing across multiple pads enabled combined timing resolutions below 28 ps. A lower-resistivity (200kΩ) configuration exhibited enhanced charge spread, leading to minor systematic offsets in reconstructed pad centers, yet maintained robust timing and spatial performance. Capacitive charge-sharing architectures improved spatial resolution in some regions but suffered from signal attenuation and nonuniform charge distributions, resulting in slightly degraded timing (33.300 {\pm} 0.002 ps) and complex localization patterns. Mechanical precision, particularly readout planarity and photocathode alignment, was identified as critical for uniform detector response. These studies benchmark the potential of resistive layers for gaseous timing detectors and provide a foundation for scalable designs with optimized timing and spatial resolution across diverse experimental applications.

Imitating the highest earners is a common decision-making heuristic, but in finite populations it can generate persistent fluctuations between strategies. This paper studies whether such fluctuations persist as population size grows in heterogeneous two-strategy populations. We show that the Markov chains describing the discrete imitation dynamics form generalized stochastic approximation processes for a good upper semicontinuous differential inclusion, which defines the associated mean dynamics. We prove that these mean dynamics always converge to equilibria. Using stochastic approximation results, we then show that the amplitudes of fluctuations in the population proportions of the two strategies vanish almost surely as population size tends to infinity. Thus, in well-mixed large populations, highest-earning imitation is unlikely to produce large-scale perpetual fluctuations.

The discovery of hidden-charm pentaquarks and open-flavor tetraquarks motivates the search for even more exotic hadron configurations. In this work, we investigate genuinely exotic molecular pentaquark candidates comprising five different flavors, focusing on the $Ξ_b^{(\prime,\,*)} \bar D^{(*)}$ and $Ξ_c^{(\prime,\,*)} B^{(*)}$ systems. Employing the one-boson-exchange model with the $S$-$D$ wave mixing and coupled-channel dynamics, we identify the most promising molecular pentaquark candidates comprising five different flavors. These include the $Ξ_b \bar D$, $Ξ_b^{\prime} \bar D$, $Ξ_c B$, and $Ξ_c^{\prime} B$ states with $I(J^P)=0(1/2^-)$, the $Ξ_b \bar D^{*}$, $Ξ_b^{\prime} \bar D^{*}$, $Ξ_c B^{*}$, and $Ξ_c^{\prime} B^{*}$ states with $I(J^P)=0(1/2^-,\,3/2^-)$, the $Ξ_b^{*} \bar D$ and $Ξ_c^{*} B$ states with $I(J^P)=0(3/2^-)$, as well as the $Ξ_b^{*} \bar D^{*}$ and $Ξ_c^{*} B^{*}$ states with $I(J^P)=0(1/2^-,\,3/2^-,\,5/2^-)$. Importantly, these loosely bound states exhibit pronounced spin splittings across different total angular momentum configurations after incorporating the spin-dependent interactions or the channel couplings. In addition, we identify several possible isovector molecular pentaquark candidates within the $Ξ_b^{(\prime,\,*)} \bar D^{(*)}$ and $Ξ_c^{(\prime,\,*)} B^{(*)}$ systems. Our predictions provide clear targets for experimental searches at facilities such as LHCb and Belle II, where the unique five-flavor quark configuration offers a distinctive experimental signature.

Accurate property characterization is a major bottleneck in materials design. While first-principles methods and task-specific machine-learning models have driven important progress, they remain fundamentally limited in scalability and generalizability across the vast space of structures and properties relevant to real-world materials design. We present MatterSim-MT, a multi-task foundation model for in silico materials simulation and property characterization. The model is pretrained on over 35 million first-principles-labeled structures covering 89 elements, temperatures up to 5000 K and pressures up to 1000 GPa, and is fine-tuned on various properties including Bader charges, magnetic moments, Born effective charges, and dielectric matrices. Out of the box, MatterSim-MT not only serves as a foundation model for predicting material structure, dynamics and thermodynamics, its multi-task architecture also enables a wide range of complex simulations that cannot be captured by potential energy surfaces alone. For example, we demonstrate pressure-dependent LO-TO phonon splitting in SiC with close agreement with experiment, electric hysteresis in ferroelectric BaTiO3, and the cationic-to-anionic redox transition during delithiation of a Li-rich cathode material. Finally, we show that MatterSim-MT scales well with more data and parameters, can be efficiently fine-tuned to higher levels of theory, and can be efficiently extended to new systems via active learning. Overall, we believe this approach provides a scalable route to accurate in silico materials characterization.

We investigate elastic scattering by a compact, horizonless body in curved spacetime, considering a massless scalar wave incident on a static, spherically symmetric, uniform-density star of radius $R$ and mass $M$ with a Schwarzschild exterior. We introduce an exact Debye-series decomposition of the scattering matrix, in the spirit of Debye expansions in Mie scattering. This decomposition separates direct surface reflection from contributions involving transmission into the interior and subsequent propagation, and admits a natural trajectory interpretation. We then determine the associated Regge-Debye pole spectrum in the complex angular-momentum plane. For neutron-star-like tenuities ($R>3M$), the spectrum exhibits two pole families: a surface-wave branch associated with the surface matching condition and a broad-resonance branch associated with the interior regularity condition. For ultracompact objects ($R<3M$), the surface-wave branch persists, while the interior-resonance sector splits into broad- and narrow-resonance branches. We next reconstruct the scattering amplitude from the Debye partial-wave contributions and find excellent agreement with direct partial-wave calculations. Finally, we develop complex angular-momentum representations order by order in the Debye series, making explicit how the pole families and non-pole sectors contribute to each Debye term. In the neutron-star-like regime, we find a genuine competition between Regge-Debye pole sums and branch-cut contributions, and show that, at high frequency, the rainbow-like enhancement already arises from the first interior-transmission contribution and is dominated by the interior-resonance Regge-Debye poles. By contrast, in the ultracompact regime, the Debye amplitudes are overwhelmingly pole dominated.

The Monotone Min-Plus Product problem is a useful primitive that has seen many algorithmic applications over the past decade. In this problem, we are given two $n\times n$ integer matrices $A$ and $B$, where each row of $B$ is a monotone non-decreasing sequence of integers from $\{1,\dots,n\}$, and the goal is to compute their Min-Plus product, defined as the $n\times n$ matrix $C$ with $C_{i,j} = \min_{k}\{A_{i,k} + B_{k,j}\}$. The fastest known algorithm for this task [Chi, Duan, Xie, and Zhang, STOC'22] runs in $n^{(ω+3)/2+o(1)} = O(n^{2.686})$ time, significantly improving over the brute-force cubic algorithm. However, its main disadvantage is that it requires randomization, which is then inherited by all downstream applications. Our main result is a deterministic algorithm for Monotone Min-Plus product with the same time complexity $n^{(ω+3)/2+o(1)} = O(n^{2.686})$ as its randomized counterpart, improving upon the previous deterministic bound $O(n^{2.875})$ [Gu, Polak, Vassilevska Williams, and Xu, ICALP'21]. Our derandomization also applies to previously studied extensions and variants (e.g., [Dürr, IPL'23]), including rectangular matrices, bounded range $[n^μ]$, and column-monotone matrices. As an immediate consequence, we derandomize state-of-the-art algorithms for multiple problems, including Language Edit Distance, RNA Folding, Optimum Stack Generation, unweighted Tree Edit Distance, Batched Range Mode, and Approximate All-Pairs Shortest Paths. Our techniques also yield a deterministic algorithm for the Monotone Min-Plus Convolution problem that runs in $n^{1.5+o(1)}$ time, nearly matching the best known randomized time complexity $\widetilde{O}(n^{1.5})$ [Chi, Duan, Xie, and Zhang, STOC'22]. This algorithm can be used to derandomize state-of-the-art algorithms for Jumbled Indexing for binary strings and several variants of Knapsack.

We obtain special solutions of the $q$-Heun equation which are expressed as finite summations of $q$-hypergeometric functions. These solutions are obtained by considering the $q$-integral transformations of the polynomial-type solutions.