This paper presents a random approach to the multibonacci sequence. We generalise the model introduced by Benjamin, Levin, Mahlburg, and Quinn, which is based on a random tiling method using dominoes and squares that leads to the Fibonacci sequence, and which was extended to the tribonacci case in a previous work by the authors. Our approach employs tiling with linear $k$-ominoes, $k=1,\ldots,s$, combined with specific colouring, to generate a weighted multibonacci sequence. For a natural random variable~$X$ defined by this model, we establish the distribution of $X$ in terms of multibonacci numbers and compute $\mathbb{E}[X] = 2^{s+1}-3$.

Integrated Sensing and Communication (ISAC) enables sensing capabilities by reusing communication signals, making it particularly attractive for large-scale deployments through signals of opportunity. While most existing ISAC research targets wideband systems, Low Power Wide Area Network (LPWAN) technologies such as LoRa remain largely unexplored from a radar-like sensing perspective. Existing LoRa-based approaches mainly focus on motion detection or require modifications of the communication waveform, limiting their applicability in deployed networks. This paper investigates the feasibility of radar-like sensing using unmodified LoRa communication signals as signals of opportunity in a purely passive bistatic ISAC configuration. The proposed approach focuses on Doppler-based sensing to enable target separation and super-resolved target estimation without interfering with existing LoRa network operation. The analytically derived sensing capabilities are compared against simulation results and validated through bistatic measurements using two USRP B210 software-defined radios, confirming the feasibility of Doppler-based LoRa sensing under practical conditions and revealing relevant implementation challenges. The results demonstrate that LoRa-based ISAC enables highly scalable, large-area, low-resolution sensing by leveraging existing infrastructure, providing a complementary sensing capability to area-limited high-resolution 6G ISAC systems, and a foundation for future multi-node and data fusion extensions.

While deep learning-based transient stability assessment (TSA) approaches have exhibited great potential in power system stability monitoring, they are prone to undergo performance degradation in practical contexts with frequent variations of operating conditions. To address this issue, this work develops an adaptive TSA framework via domain adaptation-enabled deep transfer learning. First, for the sake of capturing the primary transient stability characteristics, a robust metric, i.e., heterogeneous hybrid distribution metric (HHDM), is designed through mathematical means to effectively handle multi-scale Gaussian and long-tail distributions of transient responsive data and to precisely quantify the intrinsic distributional discrepancies between the source and target domains corresponding to different operating scenarios. With the help of the HHDM, a Bayesian theory-based dual-distribution domain adaptation method is constructed, aligning not only marginal probability distributions between domains but also the distributions of sub-domain categories. Such alignments enable fine-grained transient stability feature transfer, helping significantly improve the adaptability of a well-trained TSA model to target domains. Furthermore, a multilayer sparse regularization algorithm is introduced to mitigate feature volatility caused by variations in operating scenarios, thereby enhancing the model's generalization in the presence of unforeseen scenarios. Numerical tests on three test systems illustrate that, compared with conventional methods, the proposed framework improves online TSA accuracy by 0.5% to 5% in a cost-effective manner, with the learning cost for TSA model update largely reduced.

A general solution of the Balitsky Kovchegov (BK) equation well describes the partonic behavior within the saturation regime and beyond this limit. This solution can potentially define the unpolarized color dipole gluon transverse momentum dependent (TMD) distribution in the small x regime for full k perp range. In this work, we Fourier-Bessel transform this general S matrix of the BK equation and, within the leading logarithmic approximation, obtain a closed form expression of unpolarised Gluon TMD. The distribution exhibits a smooth and well behaved k perp dependence from low to high transverse momenta. Numerical evaluation for different values of x accessible at the Electron Ion Collider (EIC), shows a characteristic inversion of the x ordering at the saturation scale. The result is in close agreement with the behavior observed in the unintegrated color dipole gluon distribution computed within the Bartels Golec Biernat Kowalski (BGK) model, suggesting that this feature is a model independent signature of gluon saturation.

This work investigates how restitution modeling affects the dynamics of rocking blocks subjected to harmonic excitation. While several studies have reported discrepancies between experimentally observed impact behavior and the predictions obtained using the classical Housner restitution coefficient, the implications of adopting alternative restitution formulations on the global dynamics of rocking systems remain largely unexplored. The system is formulated as a hybrid non-smooth dynamical model and analyzed through bifurcation diagrams, Lyapunov exponents, and basins of attraction for different slenderness ratios. By comparing the classical restitution model proposed by Housner with the alternative formulation of Mao et al., we show that the choice of restitution model strongly influences the predicted system response. The alternative formulation leads to an earlier onset and greater prevalence of complex oscillations, as well as changes in the type, stability, and accessibility of attractors compared to the classical model. However, as the slenderness ratio increases, the dynamical features produced by both formulations progressively converge, indicating a reduced sensitivity to the restitution model for taller blocks. These results provide a dynamical perspective on why alternative restitution formulations, which predict impact responses closer to experimental observations, can produce markedly different behaviors from those obtained using the classical Housner model.

Diffuse-interface (phase-field) models are a widely used framework for interfacial dynamics in complex fluids, in which sharp interfaces are replaced by smooth transition layers and interfacial forces follow from a free-energy functional. In these models, surface tensions and diffuse thicknesses are not prescribed directly but are encoded implicitly by the bulk multiwell potential and the gradient-energy term through one-dimensional equilibrium profiles. While this link is classical in the binary Cahn--Hilliard setting, calibrating multiphase models is substantially more delicate because multiple pairwise surface tensions must be matched simultaneously and the relevant equilibrium paths are constrained by the Gibbs simplex. The practical problem is therefore: given a chosen bulk potential and a set of target pairwise surface tensions, determine gradient-energy coefficients that reproduce these targets in the full multiphase model. Here we present a thermodynamically consistent calibration procedure for N-phase diffuse-interface free energies of Cahn--Hilliard type. The method determines a symmetric capillary matrix that matches prescribed pairwise surface tensions through the model's equilibrium profiles. We further introduce a rescaling strategy that adjusts diffuse interface widths to mesh-resolvable values while preserving the calibrated surface tensions. The resulting calibrated free-energy closure can be incorporated directly into N-phase mixture simulations, and we demonstrate this by applying it to N-phase Navier--Stokes--Cahn--Hilliard flows.

HVDC protection will be required in future multiterminal HVDC grids to prevent large outages caused by DC faults. Therefore, system-level protection design is essential for the development of HVDC switching stations that connect several converter stations and lines within these grids. This paper presents an optimization method for the design of HVDC circuit breaker (DCCB) configurations in HVDC switching stations and electrical energy hubs. This approach builds on the current practice of using selected configurations based on pre-defined protection strategies. In contrast to these existing methods, the DC switching station design in the proposed method offers significantly more flexibility and allows the consideration of large numbers of relevant operating conditions, leading to more effective, optimal design outcomes. A mixed-integer linear optimization problem is formulated to design the DC protection and minimize the risk of high impact DC faults. An example case study demonstrates that the optimization method allows the calculation of the optimal number of DCCBs for a given DC switching station, based on the failure rates of DC grid components and the DCCB cost relative to the fault impact. With these results, the marginal benefit to risk reduction of each additional DCCB included in a DC switching station is calculated. Moreover, the result of the optimization problem provides the optimal breaker configuration for the required number of DCCBs and can consequently be used as a topological design tool for DC switching stations.

We develop a thermodynamic framework for non-equilibrium affinities based on generalized entropies. In particular, we extend the classical concept of De Donder by introducing $q$-affinities associated with Rényi and Tsallis entropies. This in turn allows us to generalize thermodynamic driving forces to systems with long-range interactions and/or strong correlations. For Rényi entropy, we build on a thermodynamic interpretation due to Baez, where the entropy is expressed through finite differences of the Helmholtz free energy at two temperatures. This leads to a generalized thermodynamic potential whose derivative with respect to a reaction coordinate defines the Rényi $q$-affinity. The resulting expression admits a representation in terms of exponential work averages, establishing a connection to Jarzynski-type fluctuation relations. For Tsallis entropy, we consider Markov jump processes using a master-equation-based approach. We derive a $q$-deformed entropy balance law and obtain an explicit expression for the Tsallis entropy production rate, proving its non-negativity and thus recovering a generalized second-law structure. This allows to identify a local stochastic $q$-affinity with the generalized thermodynamic force entering the entropy production rate.

Solar flares with signatures in the optical continuum (white light, WL) pose a challenge to the standard flare model and to solar flare simulations. In particular, simulations are so far not able to convincingly reproduce observed WL enhancements. We investigate the effect of different electron beams on an umbral atmosphere and what the differences and similarities to the quiet-Sun response are. We characterized WL emission in one-dimensional simulations of solar flares using the radiation hydrodynamics code RADYN. We used a similar setup as the F-CHROMA grid, but with a starting atmosphere describing umbral conditions. We investigated the influence of different temporal profiles of an electron beam on this umbral atmosphere. Our simulations show maximum WL increases between 40 and 335%, which is comparable to observed values. The reduced umbral background is the main reason for these large increases. We identify hydrogen recombination in an optically thin chromosphere as the dominant process responsible for the increases, with the radiation from the heated photosphere becoming substantial in the later stages due to the longer timescale of the cooling of the photosphere compared to hydrogen recombination in the chromosphere. Shorter, more intense beams (i.e., beams with a higher maximum energy flux) lead to a faster and more dramatic atmospheric evolution. Such beams also cause larger WL enhancements due to a higher electron density in the relevant layers. Both the Balmer ratio and the Paschen ratio are substantially higher in our simulations compared to simulations with a quiet-Sun atmosphere. The detectability and amplitude of WL enhancements depends on the spectral and temporal structure of the electron beam as well as the underlying background radiation. The combination of a short, intense beam and an umbral atmosphere provides an excellent seed for substantial WL enhancements.

Bayesian confirmation faces a classic problem: where do initial priors come from? In cases with abundant data and repeated updating, different priors tend to converge to the same posterior. However, in frontier research this convergence often fails, and confirmation remains sensitive to priors. We examine how physics practice in the case of gravitational wave research deals with such cases and, normatively, when prior sensitivity should be regarded as epistemically problematic. We offer a practice-based account of the prior problem, so far absent from the philosophical literature on Bayesianism. One upshot is a clearer diagnosis of so-called 'analogue confirmation'.

Tunable, microscopic, and energy-efficient solutions for radio-frequency (RF) signal manipulation in the GHz regime are a key technology for efficient communication and sensing applications. Spin waves offer micrometer wavelengths at GHz frequencies, combined with strong magnetic-field tunability, making them inherently well-suited for tunable analog signal processing. Here, we demonstrate a novel concept: a micron-scale tunable RF phase shifter based on the wavelength shift of propagating spin waves. High energy efficiency is achieved by using the stray field of a micromagnet on a piezoelectrically actuated MEMS cantilever to locally induce this shift. The device shows a phase shift of more than 360° at a center frequency of 6.1 GHz using a phase-shifting area of less than 0.02mm$^2$. By changing the magnetic bias field, its functionality is experimentally confirmed over a range of center frequencies from 3 GHz to 8.2 GHz, and simulations show its applicability up to 14 GHz. A system-level characterization of an embedded device version demonstrates the qualification of magnonic phase shifters for highly integrated RF systems.

Consider the Chevalley map $$ p:\mathfrak{gl} _n(F)\to (\mathfrak{gl}_n//\mathrm{GL}_n)(F), $$ where $F=\mathbb{F}_\ell((t))$. We show that the push forward via $p$ of every smooth compactly supported measure on $\mathfrak{gl}_n(F)$ is a measure whose density belongs to $L^q$ for every finite $q$. As a consequence, using the main result of [AGKSc], we obtain local integrability for Harish--Chandra's characters of irreducible cuspidal representations of $\mathrm{GL}_n(F)$.

We study the ways that one tiling space can be a finite regular cover of another. We classify all of the finite regular covers of a tiling space via its structure as an inverse limit space. If the tiling space $\Omega$ can be written as an inverse limit $\varprojlim \Gamma_n$, then the étale fundamental group of $\Omega$, which is defined via a limit of covers, is isomorphic to the inverse limit $\hat \pi_1(\Omega):= \varprojlim \hat \pi_1(\Gamma_n)$ of the profinite completions of the fundamental groups $\pi_1(\Gamma_n)$. This isomorphism allows us to construct all covers of tiling spaces and to use those covers to distinguish spaces that have identical cohomology groups.

LLM-curated hierarchical knowledge bases, namely a tree-structured wiki whose nodes summarize an underlying corpus, have become a dominant substrate for retrieval-augmented applications, yet their storage layer is still treated as an implementation detail. This workload is hierarchical, query-intensive, and continuously evolving, and no existing storage model natively captures all three properties at once. We present WikiKV, a path-indexed key-value storage model purpose-built for this workload, comprising three components: (i) a data-driven schema that bootstraps the hierarchy via Intent-Anchored Schema Induction and refines it through Continuous Evolution Operators; (ii) a consistency protocol for the path-indexed storage model that precludes partial-read observations under concurrent offline rewrites without read-path locking; and (iii) a budgeted navigation operator whose search-accelerated routing reduces the expected number of LLM-assisted descent steps from d to O(1) while preserving anytime semantics with progressively refined answers. We evaluate WikiKV through real-world deployment for the WeChat Official Account AI Assistant and benchmark it against diverse baselines on the AuthTrace dataset, where it achieves balanced low per-operator latency across four query operators against relational, graph, and FS backends, and reaches 63.2% end-to-end answer correctness, exceeding multiple RAG baselines, with the gap widening on low- and high-fan-in multi-document questions. Ablation study further confirms the effectiveness of WikiKV's components.

Let $E$ be a non-isotrivial elliptic curve over a global function field $\mathbb{F}_q(t)$ of characteristic coprime to $2$ and $3$. Under some explicit conditions, we determine the secondary terms for the first moments of prime Selmer groups of cyclic prime twist families of $E$ over $\mathbb{F}_q(t)$.

In this paper, we construct nonconforming finite element spaces $\boldsymbol{V}^{\mathbf{d}\cap\mathring{\boldsymbol{\delta}}}_h\Lambda^k$ for the approximation of $H\Lambda^k\cap H^*_0\Lambda^k$ on simplicial meshes, for $n\ge 2$ and $1\le k\le n-1$, by enforcing adjoint continuity against piecewise Whitney spaces rather than trace matching. It holds, with $\mathbf{d}^k_h$ and $\boldsymbol{\delta}_{k,h}$ denoting respectively the piecewise action of differential and codifferential operators, and $\boldsymbol{\mathfrak{H}}_h\Lambda^k$ being the discrete harmonic forms in the FEEC sense, that $\boldsymbol{\mathfrak{H}}_h\Lambda^k=\{\boldsymbol{\mu}_h\in \boldsymbol{V}^{\mathbf{d}\cap\mathring{\boldsymbol{\delta}}}_h\Lambda^k:\mathbf{d}^k_h\boldsymbol{\mu}_h=0,\ \boldsymbol{\delta}_{k,h}\boldsymbol{\mu}_h=0\}$, which mirrors the continuous Hodge--Laplace kernel on domains with nontrivial topology. The space is not a classical Ciarlet-type finite element space; though, a uniform discrete Poincare inequality and locally supported basis functions (supported on at most two cells) are guaranteed. The resulting primal scheme yields an $O(h)$ error bound for smooth data and $O(h^s)$ on $s$-regular domains ($0<s\le 1$), nontrivial topology admitted. Two- and three-dimensional eigenvalue tests agree with the mixed method on perforated domains, which are given to verify the validity of the scheme.

We report an unconventional anomalous Hall regime in the van der Waals ferromagnet Cr1.2Te2, in which the anomalous Hall effect (AHE) is present for in-plane magnetization but absent for out-of-plane magnetization. In this purely in-plane regime, the anomalous Hall signal exhibits a threefold angular dependence during both in-plane and out-of-plane rotations of the magnetization, which cannot be accounted for by the conventional dipolar contribution but instead requires an octupolar contribution. Although the octupolar term qualitatively captures the observed behavior, the experimentally extracted octupole differs quantitatively from first-principles calculations based solely on the intrinsic Berry-curvature mechanism, indicating an essential role for extrinsic scattering processes.

We determine the dark matter (DM) distribution in galaxies by jointly modelling stellar kinematics from IFU observations and the gaseous kinematics encoded in a single integrated HI spectrum. The stellar kinematics are described by a triaxial orbit-superposition Schwarzschild model, while the HI gas is described by an idealised disc model; both are governed by the same gravitational potential. The potential comprises the stellar mass, a generalised NFW DM halo, and a central black hole. We validate the method on 58 simulated galaxies generated from the TNG50 cosmological simulation. For each galaxy, we create two versions of mock data with azimuthal angles viewed side-on and end-on thus 116 mock observations in total. Our model recovers the total mass, stellar mass, and DM mass profiles within the data range; the median DM mass of the 58 simulated galaxies is recovered with a relative systematic bias smaller than 20% across all radii from 2--20 kpc. The statistical uncertainties on the DM masses within 5 kpc remain similar to those found with the model constrained by IFU data only. In contrast, the relative uncertainty on the DM mass in the outer regions decreases once the HI spectrum is included; at 20 kpc, it drops markedly, from about 85% to roughly 30%. The DM density slope defined explicitly in the gNFW model is systematically underestimated and thus does not yield a reliable quantity from observations using our approach. Instead, we introduce density slopes evaluated between 2 and 20 kpc, which are statistically well recovered for both the total mass and the DM mass. We demonstrate the reliability of this method in uncovering DM distribution and emphasize its promise for application to large samples of observed galaxies.

Scientific discovery in computational physics can often be framed as the optimization of quantitatively evaluable objectives subject to physical constraints. While researchers excel at formulating such problems, they frequently devote substantial effort to iterative refinement of methods and solution strategies. To accelerate this process, we introduce PhyNex, an autonomous agent that systematically explores the solution space of scorable scientific tasks by coupling large language model (LLM)-guided search with domain-specific computational tools that enforce physical consistency. PhyNex operates via progressive local search, accumulates reusable knowledge from both successful and failed attempts, and produces interpretable exploration trajectories that reveal which algorithmic components drive performance improvements. We validate PhyNex on three representative and scientifically important problems: predicting frequency-dependent dielectric spectra of semiconductors from crystal structure, designing probabilistic-circuit heuristics for Max-Cut on graphs, and optimizing charging protocols for Dicke quantum batteries in the chaotic coupling regime. Across the three tasks, PhyNex autonomously identifies solutions that match or exceed state-of-the-art approaches designed by human scientists, yielding search-averaged improvements of up to 3.8\% in spectral similarity, up to 15.0\% in normalized mean cut for Max-Cut, and 5.9\% in ergotropy at the $80\mathrm{k}$ training checkpoint in open exploration. These findings demonstrate that LLM-based agents with structured, feedback-driven exploration can substantially accelerate the path from problem specification to effective implementation, suggesting a practical division of labor in which scientists define objectives and constraints while automated systems navigate the methodological search space.

We address the existence of normal forms for rough ordinary differential equations. We assume suitable smoothness and the hyperbolicity of an equilibrium point. In this context, we establish local formal equivalence of the two solution flows generated by a random nonlinear RDE and its linearized version. This provides the foundation for extending normal form theory to rough differential equations.

We propose a median digital-net algorithm for $L^2$-approximation of non-periodic functions over $[0,1]^s$, inspired by the recently developed median lattice algorithms for the periodic setting. The algorithm requires no smoothness or weight parameters but only a sufficiently large candidate Walsh index set $K$. It proceeds in three stages: generating multiple estimates of the Walsh coefficients in $K$ using independent randomized digital-net samples; taking the respective median of both the estimates and their absolute values; then, based on these median values, identifying the dominant coefficients and constructing a truncated Walsh series as the final approximation. We prove that if the target function has dominating mixed partial derivatives up to order $\alpha$, all having finite Vitali variation of fractional order $\lambda$, then the algorithm achieves an $L^2$-error of $\mathcal{O}(M^{-\alpha-\lambda+\epsilon})$ with high probability, where $M$ is the total number of function evaluations and $\epsilon>0$ is arbitrarily small. Furthermore, the implied constant grows at most polynomially in the dimension $s$ under suitable decay conditions on the ANOVA components of the target function. On the implementation side, we provide both parameter-dependent and -independent constructions of the index set $K$, and employ the fast Walsh--Hadamard transform and Gray code to accelerate the algorithm. Numerical experiments support the theoretical analysis and demonstrate that the proposed algorithm remains effective in high-dimensional settings.

We present the first study of short-baseline neutrino oscillation searches using a tagged neutrino beamline, taking the proposed nuSCOPE facility at CERN as a benchmark. In this Letter we demonstrate that tagged neutrino beams, where the neutrino flavor, energy, and propagation distance are determined with exceptional event-by-event precision, provide a new experimental approach to search for non-standard neutrino oscillations. We evaluate the sensitivity to sterile-neutrino-induced oscillations in the $\nu_\mu$ disappearance, $\nu_\mu \rightarrow \nu_e$ appearance, and $\nu_e$ disappearance channels, demonstrating the ability to probe multiple flavor transitions and both appearance and disappearance modes within a single experiment. Our results show that tagged beams enable sensitivity improvements to mass-squared splittings spanning several orders of magnitude while substantially reducing the dependence on neutrino flux predictions that limits conventional searches. We find that nuSCOPE can probe a broad region of parameter space motivated by existing anomalies and extend coverage into previously unexplored territory, demonstrating the strong potential of tagged neutrino beams for precision oscillation physics.

We construct quantum dynamical Weyl group elements associated with quantum loop groups of arbitrary shuffle type. Using the construction, we define the quantum lattice operator and the algebraic quantum difference equations for each tensor products of semisimple modules $V$ in category $\mathcal{O}$. We prove that algebraic quantum difference operators form a family of commuting operators, and they also commute with the qKZ operators for the tensor products of modules of the above type in $\mathcal{O}$. This recovers the construction in \cite{OS22} and can be viewed as the difference analog of the trigonmetric Casimir connection when the quantum loop group corresponds to the finite type symmetrisable Cartan matrix.

Secure software engineering in practice is a multi-stage workflow involving vulnerability analysis, remediation, and fix verification. However, current LLM-based software security approaches often focus on isolated tasks such as detection or patch generation, with limited attention to agentic architectures reflecting industrial workflow. This creates a gap between existing LLM-based vulnerability-handling methods and real-world practices. In this paper, we study a role-based agentic workflow for vulnerability analysis and mitigation consisting of Planner, Analyzer, Fixer, and Verifier roles. To explore the effect of static analysis tool, the analyzer agent was integrated with the CodeQL in one of the workflows. The models used include nemotron-cascade-2:30b, qwen3-coder-next, and gpt-oss:120b. Our evaluation uses 25 real-world C/C++ vulnerabilities. The study reports 44% vulnerability detection accuracy comparable to GPT 5.5 and 19% fix accuracy. We also list implications from this study in context of software security practitioners.

In this article we propose a novel thermodynamical model which couples the evolution of the thickness of a grounded shallow ice sheet with the evolution of its internal temperature. Both the grounded shallow ice sheet surface elevation and the ice internal temperature are subjected to physical constraints. The equations governing the evolution of the grounded shallow ice sheet thickness are degenerate, and the ice internal temperature evolves in a moving domain. First, we formally model the phenomenon under consideration by adopting strategies akin to those employed in the construction of diffuse-interface models. Second, we establish the existence of solutions for one such formal model by means of the penalty method, and we observe that the low regularity of the problem under consideration prevents us from obtaining a standard concept of solution.

In this article, we present a novel class of degenerate solutions to the massless Dirac equation, corresponding to a wide variety of electromagnetic 4-potentials and fields, including both zero field and circularly polarized electromagnetic waves. An interesting property of these solutions is that the spin of the particles rotates in synchronization with the electric and magnetic fields of the electromagnetic waves. These results could be utilized for the development of optical memories based on materials supporting massless Dirac fermions, such as graphene.

Optical interferometry is a cornerstone technique for precise phase measurements across various fields. In many applications, for example, biological imaging, it often necessitates stringent limits on light intensity to prevent adverse effects on light-sensitive samples, a condition known as dose-limited regimes. Maximizing the precision per dose is therefore crucial. In quantum metrology, quantum correlations enable high precision in phase estimation while adhering to dose constraints. Nevertheless, photon loss, including absorption by a sample, substantially diminishes the benefits of quantum enhancement in interferometry. In this work, we experimentally investigate a dose-efficient approach to quantum phase estimation using sequential strategies in the presence of loss. Performance of sequential strategies with and without control is evaluated through quantum Fisher information (QFI) per dose. Experimental results show that both sequential strategies exceed the classical limit and outperform the parallel strategy using unbalanced N00N states. Notably, the control-enhanced sequential strategy attains superior QFI per dose, approaching the quantum limit. These results highlight the promise of sequential strategy for imaging and sensing in resource-constrained scenarios, marking a significant step toward practical and efficient quantum metrology in lossy environments.

In this paper, we employ MP codes whose defining matrices are $\tau$-optimal defining ($\tau$-OD) matrices to construct new quantum codes and quantum $(r,\delta)$-LRCs. Specifically, we report the following results: We establish a unified $\tau$-monomial decomposition theorem for invertible self-adjoint matrices over finite fields of arbitrary characteristic, which generalizes the result in "Quantum codes using the $\tau$-OD MP construction" where the characteristic was required to be odd. Based on this theorem, we prove the existence of $\tau$-OD matrices over $\mathbb{F}_{q^2}$ for any characteristic and demonstrate that there exist several new infinite families of $\tau$-OD matrices over $\mathbb{F}_{q^2}$ of characteristic $2$. As an application of MP codes involving $\tau$-OD matrices, we construct several infinite families of quantum codes with flexible parameters. Within this framework, we present $222$ record-breaking quantum codes that surpass the best-known records maintained in Grassl's database. We propose two effective schemes for constructing optimal pure quantum $(r,\delta)$-LRCs via MP codes. Accordingly, we construct four new infinite families of optimal pure quantum $(r,\delta)$-LRCs with flexible parameters. Notably, we report an interesting phenomenon by exhibiting $30$ optimal pure quantum $(r,\delta)$-LRCs derived from our framework; that is, there exist quantum codes that are not only optimal pure quantum $(r,\delta)$-LRCs but also, according to Grassl's database, best-known, optimal, or record-breaking quantum codes. To the best of our knowledge, the new discovery that quantum codes are simultaneously optimal pure quantum $(r,\delta)$-LRCs and record-breaking quantum codes has not been previously reported in the literature.

We study the time-asymptotic stability of viscous-dispersive shock waves for the outflow problem of the barotropic Navier--Stokes--Korteweg equations, which describe viscous fluids with internal capillarity. Assuming that the far-field state is subsonic or transonic and that the velocity at the boundary is larger than the far-field velocity, we prove that the solution converges to the corresponding viscous-dispersive shock wave as $t \to +\infty$, provided that the shock amplitude and the initial perturbation are sufficiently small. The proof is based on the method of $a$-contraction with shifts (for viscous equations) introduced in \cite{KV17,KV21,KVW23}. A main difficulty comes from controlling the boundary effect of the viscous-dispersive shock wave, as well as the influence of capillarity near the boundary.

Recently discovered altermagnetism in collinear compensated magnets shows even-parity spin texture in momentum space. Beyond the collinear spin ordering, unique odd-parity spin textures emerge in noncollinear compensated magnets. The noncollinear candidates, however, remain unexplored toward a room-temperature metallic altermagnet. Here, we demonstrate that MnAu2 exhibits metallic p-wave magnetism and large spin splitting induced by helical spin ordering. By adapting the band-unfolding scheme based on the translation operators combined with spin rotations, first-principles calculations reveal an unconventional Fermi surface around the $\tilde{M}$-point composed of a single electron pocket with $p$-wave spin texture. Moreover, the spin twist in the helimagnet triggers topologically non-trivial hedgehog Berry curvature, which links to the nonlinear Hall effect and spin Hall effect. Considering the experimental T$_C$ = 335 to 370 K, MnAu$_2$ could establish itself as an ideal candidate for a room-temperature metallic $p$-wave magnet, promising for versatile spintronic applications.