Papers

We understand little about how capabilities acquired in one language carry over to another, or what governs this transfer: evaluations rely on incomparable, saturation-prone datasets and rarely examine its determinants jointly. Identifying what predicts transfer would let us avoid exhaustive evaluation across all language pairs and let developers target the factors that limit performance in low-resource languages. To evaluate cross-lingual capability transfer, we introduce Multilingual GSM-Symbolic, an extensible multilingual mathematical dataset covering 30,000 item-matched question-answer pairs and spanning 15 languages. It utilises symbolic templates to prevent overfitting and ensure generalisation by allowing generation of millions of high-quality variations from a single sample. Using Multilingual GSM-Symbolic, we quantify the largest determinants of capability as model size ($\beta = 1.77$), language resource level ($\beta = 0.77$), reasoning ($\beta = 0.67$) and typological distance ($\beta = -0.25$). This joint estimation allows these determinants to be expressed in terms of one another: a 32B model evaluated in Marathi performs like a 10B model in English. Our findings have important implications for model developers, showing that model size and reasoning narrow the performance gap between low- and high-resource languages ($\beta = -0.27$ and $\beta = -0.20$, respectively), while similar levers have little or no effect on typologically distant languages. Overall, our analysis framework explains 92% of between-language variation, but only 23% of the model-by-language variation, and predicts a model's performance on an unseen language within 6.0pp (r=.96). Incorporating measurements from just 10 templates in the target language reduces this to 4.19pp, enabling reasonable estimates of performance with little or no downstream dataset.

We investigate the performance characteristics of an active magneto gyrator that consists of an inertial charged active particle confined in a two-dimensional asymmetric parabolic potential coupled to two thermal baths maintained at two different temperatures and in the presence of a magnetic field applied perpendicular to the plane of motion. In contrast to the passive Brownian gyrator, where the power-efficiency trade-off imposes strict operational limits, the active magneto gyrator exhibits striking violations of this rule, allowing regimes in which both output power and efficiency increase simultaneously with load strength. Moreover, while the Thermodynamic Uncertainty Relation (TUR) predicts that highly efficient engines necessarily produce strongly fluctuating power, rendering the Brownian gyrator unusable as the efficiency approaches the Carnot bound, the active magneto gyrator circumvents this constraint. Specifically, it achieves high efficiency with minimal power fluctuations, thus defying the TUR. Remarkably, efficiency can even surpass the Carnot limit and approach 100%, without compromising stability. This condition cannot be achieved in the absence of either activity or a magnetic field. These results highlight the active magneto gyrator as a promising setup for designing stochastic heat engines that can transcend Carnot efficiency.

Renormalization group (RG) flows for systems subject to an external field can be derived either by fixing the field or by fixing the conjugate order parameter. We show how to implement these boundary conditions within the functional renormalization group approach. We derive and compare the corresponding flow equations for $\phi^4$ theory and show that some scaling variables and scaling exponents associated with the linearized flow of the relevant three-point vertex in the vicinity of the Ising fixed point depend on the boundary conditions. We also discuss the effect of elasticity on Ising criticality. In this case two of the fixed points (namely the renormalized Ising fixed point and the spherical fixed point) obtained for constant strain are shifted to physically inaccessible regimes of parameter space when we perform the RG at constant stress.

A well-known theorem states that the Clifford+T gate set is universal for quantum computing. The theorem combines approximation using a distance measure on unitary matrices with equality up to global phase. Previous proofs combine these two notions for specific distance measures, but do not identify the properties that govern how they work together. Which properties are sufficient to state and prove the theorem? We answer this question by defining projective distance measures using four axioms. We prove that the universality theorem holds for every distance measure satisfying these axioms. Thus, our formulation of the theorem is independent of any particular choice of distance measure. We show that the Hilbert-Schmidt distance is already a projective distance measure. We also develop a general construction that transforms a large class of distance measures into projective distance measures and apply it to obtain projective versions of the operator-norm distance, the Frobenius distance, and the trace distance. Finally, we formalize the proof of the universality theorem in Lean.

Neural surrogate models for Partial Differential Equations (PDEs) on unstructured 3D geometries are often limited by poor generalization and the high cost of generating large-scale training datasets. Consequently, pre-training on massive datasets of related PDE dynamics has emerged as a critical alternative to enhance the robustness and scalability of these models. However, this strategy is neither compute- nor data-efficient, as it relies on massive pre-computed data that is very costly to generate. In this work, we introduce a disk-data-free pre-training framework tailored to both steady-state and transient regimes. For steady-state problems, we propose a geometry-driven strategy that leverages intrinsic shape descriptors to learn representations of complex 3D domains. For transient problems, we introduce a physics-driven approach based on online generation of synthetic PDE data, enabling scalable pre-training without reliance on expensive datasets. Across multiple experiments, our approach achieves faster convergence, greater data efficiency, and higher accuracy during fine-tuning, particularly under realistic low-data regimes. This methodology provides a practical pathway toward data-efficient neural emulators for large-scale simulations. Code and models are available at https://github.com/tum-pbs/GMP.

For the coupled three-dimensional double well $H=\tfrac12|p|^2+2\sum_i(q_i^2-1)^2-\sum_{i<j}q_i^2q_j^2$ we exhibit, at the first excited energy level (and also at the ground state), a linear functional on polynomials of degree $\le 6$ that satisfies every constraint of the standard level-3 eigenstate bootstrap, has a strictly positive definite moment matrix, and nevertheless assigns a negative value to a nonnegative polynomial. It is therefore an interior point of the level-3 relaxation that is realized by no quantum state. The construction reflects a fact that holds at every level: the eigenstate rows never reach the top-degree momentum moments. At level 3, where strictly feasible points exist, this means that the corresponding block of the moment matrix carries no information about which energies admit one. Every algebraic ingredient is an exact rational certificate, and the only numerical ingredients (spectral enclosures of an eigenfunction) are carried out in rigorous ball arithmetic.

Critic-free reinforcement fine-tuning (RFT) for agentic large language models is often done through GRPO-style methods, which compute a group baseline over repeated rollouts to reduce target variance. However, this setup is ill-suited to agents acting in stateful environments such as live services or security sandboxes, where repeated rollouts are impractical to obtain and aggressive updates entrench the noise of long, sparsely verified trajectories. We propose Follow the Winners (FTW), a critic-free policy-learning algorithm that adapts the cross-entropy method to RFT, replacing group rollouts with an ordinal filter on replay-buffer samples that yields polynomial concentration in the order statistic of returns. We derive FTW through a control-as-inference lens, which also recovers GRPO and DPO as specific modelling choices, identifying GRPO as risk-neutral while DPO and FTW share a bounded risk-seeking offset that FTW controls. We identify this offset as an inherent trade-off of variance reduction through ordinal filters on samples, whereas a critic model induces a different trade-off between bias and variance. Scaled to agentic LLM post-training, FTW matches GRPO and PPO on Sokoban and Search-R1 baselines, showing a viable trade-off from a value model or group rollouts to CPU memory.

Quantum computing has developed rapidly in recent years and has shown potential advantages over classical computing in various domains. In this paper, we study whether quantum computing can accelerate the convergence rate of discrete simulation optimization in the fixed-budget setting. We first formulate the quantum discrete simulation optimization problem by defining the quantum simulation oracle, the algorithmic performance measure, and the corresponding optimality guarantee. Based on this formulation, we establish a minimax lower bound on the expected optimality gap for any quantum algorithm. The lower bound analysis reduces the discrete simulation optimization problem to a sequential quantum phase-testing problem, and the resulting lower-bound argument may be of independent interest. By comparing the quantum lower bound with its classical counterpart, we show that the optimal convergence rate in the quantum setting exhibits a quadratic improvement in its dependence on the simulation budget, at the cost of a worse dependence on the number of decisions. We then propose the first fixed-budget quantum algorithm, called QUEST, for discrete simulation optimization. The algorithm combines a quantum Monte Carlo subroutine with a sequential elimination framework and uses a slow-measurement mechanism to help preserve quantum superposition during the optimization process. We prove that QUEST achieves the optimal convergence rate up to logarithmic factors. Numerical experiments further show that QUEST outperforms its classical counterpart, which provides empirical evidence for the quantum advantage in improving the convergence rate of discrete simulation optimization algorithms.

For a closed orientable surface of genus at least 2, we study the large-scale geometry of the (symmetrized) Lipschitz metric on its space of projective filling geodesic currents. We show that the rank and, hence, asymptotic dimension of the space of filling geodesic currents is infinite. This gives the first example of a natural proper space associated to a closed surface, with a metrically proper isometric action of the mapping class group, that has infinite asymptotic dimension. In contrast, we show that any finite simplex of geodesic currents has rank uniformly bounded above by $8g-9$. We then show a sufficient criterion for its rank and asymptotic dimension to be equal to $8g-9$ and construct examples satisfying it, thus showing the bound is sharp. We further prove that Teichmüller space equipped with the Lipschitz metric has rank equal to $3g-3$. In particular, the space of projective filling geodesic currents and the Teichmüller space are not quasi-isometric.

The canonical Ramsey theorem establishes that for every positive integer $t$, there is a sufficiently large $n$ such that every edge-colouring of a complete graph $K_n$ contains a copy of $K_t$ that is canonically coloured, i.e. monochromatic, rainbow, or lexicographic. In this paper we investigate two variations of this theorem. First, we study canonical Ramsey numbers in the multipartite hypergraph setting. We prove that in every edge-colouring of the 3-uniform complete hypergraph on at least $t^{151t^2}$ vertices, there always exists a canonically coloured copy of $K_{t, t, t}^{(3)}$. This estimate is sharp up to the constant in the exponent. Second, we explore off-diagonal canonical Ramsey numbers. Let $ER(a, b, c)$ denote the minimum number of vertices $n$ required to guarantee a monochromatic $K_a$, a lexicographic $K_b$, or a rainbow $K_c$ in every edge-colouring of the complete graph $K_n$. We establish sharp bounds for these numbers across different parameter regimes. Specifically, we prove that $ER(a, b, c)\geq c^{\Omega(ab)}$ when $c$ is sufficiently large relative to $a$, and that $ER(a, b, c)\leq 2^{O_b(a)}$ when $b\ge 4$ is a fixed constant and $c\le a$. Finally, we analyse the behaviour of the function when avoiding lexicographic triangles (i.e. $b=3$), showing that $ER(a, 3, c)\le (a-1)(c-2)+O(c^6)$.

Describing fermionic systems with attractive interactions, such as superconductors and atomic nuclei, beyond the mean-field level remains a central challenge. In this work, we investigate the performance of Bogoliubov fully self-consistent $GW$ (Bog.~sc$GW$) and second-order Green's function (Bog.~scGF2) methods, implemented within a unified imaginary-time and imaginary-frequency framework. Using the attractive Hubbard model as a benchmark against full configuration interaction (FCI), we find that Bog. scGF2 provides a more accurate description than Bog.~sc$GW$. In particular, Bog.~sc$GW$ systematically overestimates the correlation energy, with errors increasing rapidly as the attractive interaction strength grows. These results highlight the importance of exchange contributions in strongly correlated fermionic systems, even when exchange effects are included only at low order in perturbation theory.

Large Language Model (LLM) agents are increasingly deployed in high-stakes settings such as industrial maintenance and equipment fault troubleshooting, where workers occupy a variety of roles. A capable agent must therefore act in a way that is calibrated to user's role: taking actions and providing information that respect the role's knowledge and capability boundaries. Unlike coding, where mistakes are usually recoverable, agent responses in these settings are enacted on physical equipment, and can therefore cause irreversible equipment damage, production loss, or personnel harm. Existing benchmarks, however, largely overlook the need for agents to infer what a role intends and acting only through tools that role may legitimately use, a capability which we term Perspective Awareness. To this end, we introduce ReFract, a benchmark of 150 expert-validated entries in which an agent must act differently in response to the same query depending on user's role. Entries of ReFract are grounded in anonymized queries from domain support conversations, against which we construct Text World Models that simulate the agent's operating environments and assemble perspective-aware action trajectories. State-of-the-art LLMs solve at most 69% of the tasks with more than 50% of their trajectories contain attempts of taking perspective-violating actions. ReFract exposes perspective awareness as a distinct, largely unsolved axis of agent evaluation and motivates agents that calibrate not just how to act, but for whom.

Climate oscillations are intrinsically out-of-equilibrium phenomena, yet the connection between their predictability and nonequilibrium thermodynamic properties remains unexplored. We develop a coarse-grained stochastic thermodynamic framework for Ornstein-Uhlenbeck (OU) processes and apply this framework to climate data via linear inverse models (LIMs), linking predictability, entropy production, dynamical activity, and path action. Climate oscillations are often studied in a 2d phase space of climate indices, which are even under time-reversal, motivating our focus on 2d OU dynamics with even variables. We find that coordinate-invariant properties of 2d OU processes can be reduced to a minimal three-parameter description: two diffusivities and a phase-space rotation. We show that these quantities fundamentally characterize distinct aspects of the dynamics. We find that higher irreversibility and dynamical activity do not necessarily imply reduced predictability. Rather, it is the path action which is most closely connected to a commonly used measure of predictability, the anomaly correlation coefficient (ACC). As an illustrative example, we apply this framework to the Madden-Julian Oscillation (MJO) over the twentieth century. We find that the MJO has become simultaneously more predictable, as seen previously, while at the same time becoming more irreversible and more active. Predictability is driven predominantly by the reduced mean diffusion. Entropy production reflects the combined evolution of all three parameters. These results suggest that stochastic thermodynamics provides a powerful lens for studying nonequilibrium climate phenomena.

Dynkin classified the maximal subalgebras of the simple finite-dimensional Lie algebras. The super version of his problem is solved, for the matrix Lie superalgebras, by Shchepochkina, and, for the simple vectorial ones with polynomial coefficients taken with their Weisfeiler gradings, in the companion paper by Leites and Shchepochkina — with three exceptions left open: the three simple finite-dimensional Lie superalgebras $\mathfrak{osp}_a(4|2)$, $\mathfrak{ag}(2)$ and $\mathfrak{ab}(3)$, which are vectorial in more than one way and are not covered by the general argument. Here we settle these three cases for graded subalgebras. For each of the three Lie superalgebras, we list all the $\mathbb{Z}$-gradings to which the method of that paper applies — two for $\mathfrak{osp}_a(4|2)$, five for $\mathfrak{ag}(2)$, eight for $\mathfrak{ab}(3)$ — and describe, for every one of them, all the maximal graded subalgebras, the semi-simple ones explicitly. A simple criterion upgrades most of the answers from “maximal graded\rq\rq\ to “maximal\rq\rq. Every answer is computed over $\mathbb{Q}$. Two by-products: the classical list of five cases into which the graded subalgebras of a vectorial Lie superalgebra split is incomplete for ambients of depth $>1$ — a sixth case has to be added, and it is non-empty precisely here; and the parameter $a$ of the copies of $\mathfrak{osp}_a(4|2)$ sitting inside $\mathfrak{ag}(2)$, resp. $\mathfrak{ab}(3)$, is computed intrinsically.

We study a constrained basis-selection problem for an ordered block matrix $B=[ B_1\mid\cdots\mid B_n ].$ The successive tail matrices determine a nested family of column spaces, and we consider bases of representatives which are compatible with this induced flag. Our main linear-algebraic result shows that, among bases of representatives, compatibility with the entire flag is characterized by the intrinsic block quotas $r_k=w_k-w_{k+1}$, where $w_k$ is the rank of the $k$-th tail matrix. We then show that the same structure arises naturally in finite-horizon linear control. For the reachability matrix $[A^{N-1}G\mid \cdots\mid G]$, requiring every actuator to be used exactly once turns an actuator schedule into a representative system. Preservation of the complete reachability profile is then equivalent to compatibility with the tail-space flag. This correspondence leads to an exact depth-first search with a future-rank pruning criterion. For an explicit structured family and a fixed search ordering, the baseline search visits $3\cdot2^m+m-2$ nodes before the first solution, whereas future-rank pruning reduces this number to $3m+1$. Exact-arithmetic experiments reproduce these formulas for all tested instances.

Automatic dysarthric speech detection approaches can support traditional clinical diagnosis, which relies on costly and time-consuming evaluation by a speech and language pathologist. Existing automatic approaches predominantly rely on deep learning (DL). More recently, Large Audio Language Models (LALMs) have emerged as a promising alternative given their strong performance across various tasks, but their application to dysarthric speech detection has not yet been established. We propose a framework that fine-tunes LALMs for dysarthric speech detection on speech recordings combined with textual information comprising low-level acoustic features and speaker demographics. Across two LALMs, our framework outperforms DL-based baselines, with Qwen2-Audio-Instruct achieving state-of-the-art performance. An ablation study shows that incorporating acoustic features and speaker demographics during fine-tuning improves LALM performance, while LALMs alone exhibit only chance-level zero-shot performance. These findings establish an effective approach for adapting LALMs to dysarthric speech detection.

Quantum key distribution (QKD) is a fundamental functionality of quantum networks. Extending its range requires quantum repeaters, a technology still under development and not yet demonstrated in combination with quantum cryptographic protocols. Here, we address the elementary operation of a viable quantum repeater scheme by evaluating whether correlated photons distributed via entanglement swapping can support secret key distribution. We employ a state-of-the-art deterministic photon source based on a strain-tuned GaAs quantum dot embedded in a photonic cavity and implement a source-independent QKD protocol between two nodes using entanglement-swapped photons. We benchmark the system and present how high-resolution temporal post-selection can enable secure key exchange, with further rate improvements expected through realistic device and protocol optimizations. Due to its compatibility with a wide range of quantum memory platforms, our approach represents a significant step towards long-distance quantum-safe communication.

Inspired by work of Gaster, Greene, and Vlamis on the chromatic number of curve graphs, we prove that every endomorphism of the total Kneser graph is an automorphism. We also show that the automorphism group of the total Kneser graph is the product of a pair of permutation groups.

We consider the interaction-round-a-face version of the nineteen-vertex model and derive a new quantum spin-$1$ chain. In the isotropic limit, the associated spin chain can be seen as three coupled Babujian-Taktahjan spin chains with different boundary twists. We compute the ground state short-distance correlation functions of the isotropic model in the thermodynamic limit by exploiting the shared integrable structure between the models.

An algebra with zero is an algebra that contains an element 0, called zero, such that all fundamental operations have the property that the result is zero whenever at least one of the arguments takes the value 0. We introduce the notion of the higher commutator of ideals and Rees congruences for such algebras. It is shown that the commutator of Rees congruences is equal to the Rees congruence of the commutator of the corresponding ideals. We apply this result to provide characterisations of n-supernilpotency and n-nilpotency in algebras with zero, as well as n-solvability in groupoids with zero.

Let $\Palt=(\C,\T)$ be a $k$-palette. For $0\le t\le k-1$, its $t$th coordinate-extension degree is the minimum, over every choice of $t$ coordinates and every assignment of colors to them, of the proportion of assignments to the remaining $k-t$ coordinates that complete the fixed colors to an admissible $k$-tuple. For a $k$-graph $F$, we define $\pi_t^{\ext}(F)$ as the supremum of this degree over all palettes not admitted by $F$. We prove that \[ \pi_t^{\ext}(F)=0 \quad\text{if and only if}\quad F\text{ is }t\text{-layered}. \] We also relate $t$-layeredness to vanishing orders, min-layeredness, max-layeredness, and layeredness. These results recover and extend previous characterizations of Reiher, Rödl, and Schacht and of Lamaison, and answer a question of Lamaison for $3$-graphs. At $t=0$, the parameter $\pi_0^{\ext}(F)$ is the $(k-2)$-uniform Turán density $\pi_{k-2}(F)$. For every $k\ge3$ and $r\ge2$, we construct a finite $k$-graph $F_{k,r}$ with \( \pi_{k-2}(F_{k,r})=2(r-1)/rk^k. \) Thus $2/k^k$ is an accumulation point for single forbidden $k$-graphs. We also show that the least density of a $k$-graph that fails condition $\Sp$ of Lin, Wang and Zhou is $4/(3k^k)$. Finally, for every admissible matching of size $m$, we construct a $k$-graph that satisfies $\Sp$ for every coordinate pair, has no vanishing order, and has density $2^m/k^k$. This disproves a conjecture of Lin, Wang and Zhou for every $k\ge3$.

Major mergers are transformative events in galaxy evolution, dynamically reshaping the stellar and gas makeup of the hosts, as well as the galaxy-scale magnetic fields (B-fields) that permeate their interstellar medium (ISM), altering both B-field strength and configuration. In this work, we study in detail the link between the co-evolving gas and B-fields in the cold ISM phase of the nearby Antennae galaxy merger (NGC 4038/4039), using CO(3-2) data from the LAsMA receiver at the APEX telescope and ALMA, together with archival 154 $\mu$m dust polarization data from the SOFIA/HAWC+. We characterize trends between measurements of molecular gas intensity and velocity dispersion with polarization measurements at kpc-scales with the APEX and SOFIA data. We find anti-correlations with CO intensity ($\rho\lesssim-0.6$) and CO velocity dispersion ($\rho\lesssim-0.4$), which are signposts of geometric depolarization. Since dust polarization measurements are a density-weighted line-of-sight integrated average of B-field vectors below the beam size, the ALMA data can serve as a proxy of density structures below the SOFIA beam on a channel-by-channel basis. Through a geometric analysis of structures in the ALMA channels, we identify salient kinematic features in the overlap region strongly aligned with the SOFIA-inferred B-field orientation. This indicates that these kinematic features might dominantly lend their orientation to the measured field direction, assuming a correspondence between molecular gas structures and galactic B-fields, owing to their density or high polarization fraction. We also identify a modest trend ($\rho\sim0.5$) between the coherence of the molecular gas, a proxy of the line-of-sight angular dispersion, at small scales, and the SOFIA polarization fraction, showing that the polarization fraction measured at $\sim2$ kpc scales is sensitive to structures at $\sim50$ pc scales.

Constrained Horn clauses (CHCs) are a fragment of first-order logic widely used as an intermediate language for verification. We study constrained resolution as a calculus for reasoning about the satisfiability of sets of CHCs. Constrained resolution forms a simple alternative to model checking algorithms such as CEGAR and IC3 and is here shown to exhibit complementary features. We show that, when CHCs encode programs, forward symbolic execution corresponds to positive unit hyper-resolution, and backward symbolic execution to SLD resolution, which are special cases of constrained resolution. We formalize forward and backward reasoning for linear and non-linear CHCs and transition systems, prove refutational completeness under fair strategies, and develop subsumption criteria for pruning redundant derivations. We moreover show that backward resolution with subsumption generalizes $k$-induction to non-linear CHCs, and that forward constrained resolution is related to the problem of constructing proofs in incorrectness logic. Lastly, we provide an experimental evaluation in the Eldarica CHC solver on benchmarks from CHC-COMP.

Griffiths phases provide a mechanism for sustaining critical dynamics over extended parameter regions without fine-tuning to an isolated transition point. This behavior has been mainly associated with structural heterogeneity in complex networks. Here we show that quenched heterogeneity in local parameters can generate a chaotic Griffiths phase in a network of map-based neurons. We study globally coupled Chialvo maps with quenched disorder in a local neuronal parameter, thereby isolating intrinsic parameter disorder from topological disorder. As the coupling strength is varied, a chaotic Griffiths phase emerges between desynchronized and coherent chaotic dynamics, characterized by intermittent formation and breakup of neuronal clusters and large fluctuations in the fraction of clustered neurons. Within this regime, cluster sizes exhibit power-law distributions with coupling-dependent exponents, providing evidence of critical behavior over a finite parameter interval. The chaotic Griffiths phase is absent in the homogeneous limit and broadens progressively as the degree of parameter heterogeneity increases. We further introduce topological disorder through small-world connectivity and find that its combined action with local parameter heterogeneity substantially extends the chaotic Griffiths phase. In both globally coupled and small-world networks, the number of positive Lyapunov exponents displays anomalous scaling with system size. These results demonstrate that intrinsic dynamical heterogeneity constitutes an independent mechanism for generating chaotic Griffiths phases and that its interplay with structural disorder enhances extended criticality in neuronal networks.

The physical conditions within the innermost few tens of au of high-mass protostars ($M_*>8~M_\odot$) remain largely unexplored. At these scales, ionised emission may trace photoionised gas, accretion disks, or the base of protostellar jets. We search for ionised emission in the form of radio recombination lines (RRLs) in high-mass star-forming regions. We use archival data from the Atacama Millimeter/submillimeter Array (ALMA) interferometer in band 6 ($\sim$1.3 mm) with a resolution of $\theta_\mathrm{beam}\sim53~\mathrm{mas}\times42~\mathrm{mas}$ to examine the high-mass protostar IRAS18162$-$2048, driving source of the Herbig-Haro (HH) objects HH80-81. We detect, for the first time in this protostar, the thermal emission of the RRL H30$\alpha$ ($\mathrm{rest~frequency}=231.90093$ GHz). The ionised emission is spatially unresolved in our observations, but we estimate an emitting region $\lesssim50$ au at the source distance of 1.4 kpc. The H30$\alpha$ line profile is broad and spectrally resolved with a Local Standard of Rest velocity of $\sim-14~\mathrm{km~s^{-1}}$ (i.e., $\sim-26~\mathrm{km~s^{-1}}$ blue-shifted with respect to the systemic velocity of the cloud) and a full width at half maximum of $\sim82~\mathrm{km~s^{-1}}$. These observations suggest that the H30$\alpha$ line is tracing outflowing blue-shifted material in the well-known radio jet from this object. This detection opens the possibility of detailed studies of the kinematics and physical properties of ionised jets.

We establish the local well-posedness of strong solutions for a thermodynamically consistent diffuse interface model describing two-phase flows with surfactants, specifically the so-called Model C introduced by Garcke, Lam, and Stinner. Because of the non-standard, mixed-order strongly coupled structure of Model C, the classical Agmon-Douglis-Nirenberg theory and conventional Lopatinskii-Shapiro boundary conditions are not applicable due to divergent scaling behaviors. To overcome this, we develop a tailored resolvent analysis, adapted to the temporal regularity of the source term, in a suitable Hilbert space, which yields an exact cancellation of the highest-order cross-couplings in the estimates. This crucial decoupling enables the rigorous application of the operator-valued Mikhlin multiplier theorem to obtain resolvent estimates on $\mathbb{R}$. Furthermore, we analyze a structural variant, denoted as Model D, which achieves a crucial structural decoupling by transferring the interfacial surfactant energy entirely from the gradient part to the potential part, and we readily establish local well-posedness for strong solutions.

Quasi-cyclic low-density parity-check (QC-LDPC) codes are widely used in modern communication standards due to their simple structure and efficient encoder and decoder implementations. However, the commutativity of the circulant permutation matrices used in their construction significantly limits their girth and minimum distance, affecting iterative decoding performance. In this paper, we investigate protograph-based codes constructed using permutation polynomials of higher degree, focusing on a closed family of non-commuting binomial permutation polynomials that enables these constructions to exceed both of these girth and minimum distance upper bounds while maintaining a simple representation. Simulation results demonstrate improved decoding performance compared to constructions based on affine permutation polynomials, which include QC-LDPC codes.

S. Lie was the first to try to classify maximal subalgebras of simple vectorial (i.e., consisting of vector fields) Lie algebras with polynomial coefficients. In Appendix it is shown that, as stated, the problem is wild: describing all subalgebras contains the classification of pairs of matrices up to simultaneous conjugation, so there are too many such subalgebras. Several researchers distinguished various classes of maximal subalgebras important in applications. Here, in simple (or in Cartan prolongations close to simple) vectorial Lie superalgebras with polynomial coefficients considered with gradings associated with Weisfeiler filtrations, we describe maximal simple (and close to simple) graded subalgebras — a superization of what Sophus Lie tackled. Together with I. Shchepochkina's description of the maximal subalgebras of matrix Lie superalgebras, see arXiv:hep-th/9702122, this paper solves the super and infinite-dimensional version of Dynkin's problem — the description of the maximal subalgebras of simple finite-dimensional Lie algebras — except for the 3 exceptional ambients considered elsewhere.

Particle physics analysis depends on information retrieved from particle tracks in a detector. Traditionally, this involves collecting individual detector hits, recombining them to form tracks, and fitting them to a model function. Large Language Models (LLMs) have demonstrated remarkable proficiency in comprehending the grammar and semantics of languages. Our exploratory study leverages transformers to conceptualise particle tracking as a language translation problem, wherein the language of detectors is translated into the language of physics. A simple decoder-only architecture with a custom tokenizer was designed for this task, and the behaviour of the model in this atypical setting provided interesting insights. We evaluated the advantages of this formulation in terms of track-parameter accuracy, and the ease of representing multi-track events, and finally tested the model on real cosmic-muon data. On synthetic datasets, the model outperformed a simple regression technique by an order of magnitude in track-parameter accuracy while being on par with the random sample consensus (RANSAC) method. The model also identified multi-track events with an accuracy of 98%. The analysis of real cosmic-muon events showed an excellent agreement of the zenith angle distribution with expectations. Our results suggest that a compact language model shows competitive performance and a natural ability to represent multi-track events. Further studies with complex geometries are required to understand the full potential of this technique.

Distributed Fiber Optical Sensing (DFOS) leverages optical backscattering signals to predict failure events and enable proactive Just-In-Time (JIT) restoration. Modern network infrastructures have optical components and fibers as key enablers of high throughput and low latency. The integration of sensing features in this optical infrastructure adds features such as network diagnosis, spatial positioning and sensing, and opens up opportunities for the implementation of intelligent network control expected for the next-generation networks. In this paper, we study how the quantity and the placement of the DFOS devices in an all-optical network can mitigate failure events. In our evaluation, we consider metropolitan and data center elastic optical networks. This work also evaluates sensing devices with various prediction time capabilities, in order to assess their effectiveness when considering a variable number of deployed devices and different placement heuristics. The evaluation uses key performance metrics, including the bandwidth blocking rate, number of affected circuits by failure events, and the service downtime. Simulation results demonstrate that the Greedy Shortest Path Coverage (GSPC) heuristic substantially reduces the number of circuits affected by failure when DFOS devices cover only 5% of links, while 25% coverage shows a performance gain comparable to the full coverage scenario, which is an opportunity for significant cost reduction. Finally, for the 5% sensing coverage scenarios, our results illustrate that prediction windows of 15 ms and 7.5 ms are sufficient for JIT restoration in metropolitan and data center networks, respectively.