Organic Electrochemical Transistors (OECTs) stand out for their interplay between ionic and electronic conduction, making them ideal analogues to biological synapses for neuromorphic computing and biosensing applications. Furthermore, they can be printed into integrated circuits on flexible substrates, enabling low-cost and high-throughput fabrication of complete electronic systems. However, most OECT electrolytes for integrated circuits still lack biocompatibility and suffer from rheology-related printing challenges. This paper presents a novel material basis that can be combined with an ionic liquid to fabricate an electrolyte for OECTs that only contains biocompatible materials. It allows rheological adjustments to enable the use of electrolyte in both inkjet and screen printing. Furthermore, the electrolyte is UV-curable, enabling it to transition into solid-state structures after printing. Extended ink and device lifetimes for screen-printed structures enable the fabrication of advanced OECTs that can operate in ambient air for over 30 days after fabrication. Ultimately, a fully screen-printed transistor using only biocompatible materials on a leaf substrate is shown

The planar Turá number of a graph $F$ is the maximum number of edges an $n$-vertex $F$-free planar graph can have. We study the case where $F$ is forbidden as an induced subgraph, thereby introducing the induced planar Turá numbers. We will determine a sharp upper bound when $F$ is $Θ_4$, a $4$-cycle with a diagonal edge, and obtain exact extremal values in case $F$ is a path $P_k$ on $k$ vertices, for $k=3,4$ and $5$.

The dispersion of fast radio bursts (FRBs) measures the column density of free electrons, tracing the diffuse ionized gas that contains more than $90\%$ of all baryons. On linear scales the FRB dispersion field is an approximately unbiased tracer of the matter distribution, an idea long assumed in the FRB large-scale structure literature and recently formalized by Zhou and Zhang [arXiv:2510.11022]. This follows from baryon-mass conservation, which forces the total baryon field to have unit linear bias, with dispersion inheriting this bias up to small corrections from the stellar and neutral-gas components. We show these corrections can be bounded at the percent level using existing galaxy and 21 cm surveys, and confirm with the FLAMINGO hydrodynamical simulations that the electron bias varies at the percent level across a wide range of feedback prescriptions. The dispersion-galaxy cross-power spectrum at linear scales directly constrains $B_8 \equiv σ_8(Ω_b/0.05)^{1/2}$, a baryonic analog of $S_8$, independently of feedback physics. Because most of the per-object variance in dispersion is cosmological signal rather than noise, $\sim\!10^5$ localized FRBs can match the statistical power of $\sim\!10^8$ weak-lensing galaxy shape measurements. FRB dispersion thus joins weak lensing and redshift-space distortions as a new unbiased tracer of matter on large scales.

Partial differential equations (PDEs) are fundamental across numerous scientific fields. As these problems scale to high dimensions, classical numerical schemes introduce severe computational bottlenecks, known as the curse of dimensionality. Attempts to solve this problem typically rely on either classical sparsity and low-rank decompositions, or neural network surrogate models. On the other hand, Quantum Computing offers a promising alternative, as it allows us to operate in significantly larger spaces while demanding far fewer resources. In this work, we present a quantum subroutine to solve second-order linear PDEs by exploiting the structural properties of the filter in Fourier space using Quantum Block Encoding (QBE) with quantum reversible arithmetic. This approach serves as a specialized alternative to standard quantum matrix inversion, which typically relies solely on Quantum Singular Value Transformation (QSVT) without exploiting the inherent structural properties of the matrix. We validate the proposed methodology against its classical counterpart to prove its correctness. This framework provides a foundation for extending these methods toward quantum group Fourier transforms, wavelet-based analysis, and equivariant quantum neural networks (EQNNs), offering a promising path toward solving broader classes of problems, including nonlinear PDEs.

Neural networks offer highly expressive turbulence closures, yet their complexity obscures the physical mechanisms they aim to model, and their computational cost can limit their tractability. To address these limitations, we introduce a sparsity-promoting subgrid-scale (SGS) stress closure modeling framework that identifies explicit polynomial model forms using sparse regression. Candidate models are constructed through scaling a minimal tensor basis by a truncated polynomial expansion of invariant scalars, thereby enforcing fundamental invariance properties while regulating the highest order of admissible terms. Arbitrary filter anisotropy is incorporated to enable consistent representation of turbulent structures across computational grids with anisotropic scales and resolutions. We also explicitly constrain SGS energy dissipation during training to improve functional performance and promote numerical stability. The framework is trained on a small dataset of idealized turbulence and evaluated through a series of a priori and a posteriori tests. Sensitivity studies examine the effects of variations in model order and optimization penalties for regularization and dissipation across a range of canonical flow configurations. We also evaluate on a separated flow benchmark to assess generalizability to a more complex turbulent regime. In many cases, the sparse regression closures achieve predictive accuracy comparable to an invariance-preserving neural network while retaining markedly simpler parametric forms. Moreover, we demonstrate that the sparse closures can be trained and evaluated at a fraction of the cost of the neural network model.

Guiding relativistically intense laser pulses in low-density plasmas enables extended acceleration lengths in laser-plasma accelerators (LPAs), allowing for the production of multi-GeV electron beams. Quantitative interpretation of such experiments is often limited by substantial uncertainties in key plasma parameters, particularly the transverse density profile of hydrodynamic optically field-ionized channels. Distinct plasma density distributions can produce similar terminal beam energies, complicating efforts to infer the underlying interaction physics from measurements at the accelerator exit alone. By combining longitudinally resolved electron beam diagnostics with independent measurements of laser spectral evolution in a 10 GeV LPA, we establish a multi-observable constraint on plasma density profiles. Once plasma downramps are taken into account, excellent agreement is observed with simulation over the entire accelerator length for two plasma channel sizes. The validated simulations indicate that extending the accelerator length to 65 cm would increase the electron beam energy to 15 GeV. They also point the way to achieving $\sim$20 GeV electron beams in $\sim$70 cm via linear matching using the same 24 J laser energy.

In this note we prove an upper bound on the $\mathbb F_p$-rank of the incidence matrix of points and hyperplanes in $(\mathbb Z/p^k \mathbb Z)^n$, improving a recent bound of Laba and Trainer when $k$ is large.

We propose that the symmetry category associated to a 2D quantum field theory with 0-form $G$-symmetry with 't Hooft anomaly $k\in H^4(BG,\mathbb{Z})$ for a large class of Lie groups $G$ is the category of twisted measurable fields of Hilbert spaces over $G$ denoted by $\mathrm{Hilb}^k(G)$, which is equivalent to the category of unitary representations of $C_0(G)$ with convolution product twisted by a multiplicative bundle gerbe labeled by $k$ denoted by $\textbf{Rep}^k(C_0(G))$. We find that the Drinfeld center of the symmetry category $\mathcal{Z}(\mathrm{Hilb}^{k}(G))$ equivalent to the category of unitary representations of the groupoid $C^*$-algebra of the Fell line bundle $Σ_k$ over the conjugation action groupoid $G//_{\rm Ad} G$, denoted by $\textbf{Rep}(C^*(G//_{\rm Ad}G,Σ_k))$, where the twist is characterized by the transgression $τ(k)\in H^2(G//_{\rm Ad}G,U(1))$. To the full generality, our framework applies to a Lie group $G$ that is a direct product of a compact connected Lie group and a number of $\mathbb{R}$ or $GL(1,\mathbb{C})$ factors. We compute the braiding of anyon lines in the bulk 3D SymTFT from this formalism. Finally we provide physical examples for abelian and non-abelian $G$, and discuss the physical consequences of flat gauging continuous global symmetries.

Different gaugings of the global symmetry of a quantum field theory are closely related to its various phases. In this work, we study candidate gaugeable symmetries by analyzing candidate Lagrangian algebra data in the Drinfeld center of a symmetry category $\mathscr{C}^k(G)$ associated to a QFT with continuous global $G$-symmetry and possible 't Hooft anomaly labeled by an integer $k$. We use the combination of the $BF$ theory and the level-$k$ Chern-Simons theory with gauge group $G$ as a semiclassical kernel-theoretic model for the corresponding SymTFT. Under two explicit assumptions, namely that this $BF{+}k$CS theory provides the relevant SymTFT model and that the common $+1$ eigenspaces of the resulting modular kernels detect candidate Lagrangian algebra data in the continuous setting, we derive candidate modular $S$- and $T$-kernels from Hopf-link and framing correlators in $S^3$ semi-classically. We then use these kernels to obtain candidate modular invariants and candidate gaugings. The resulting formulas recover the established cases and suggest a possible extension of this kernel-theoretic picture to compact Lie groups.

Mount Washington is home to extreme, and extremely volatile, weather conditions. Consulting a weather forecast of conditions at the summit is vital for making one's visit as safe as possible. Using the discussion and suggestions arising from a participatory workshop as input, we test a design intervention employing color-coded hazard icons to function as visual summaries of Mount Washington Observatory's current text-heavy forecast through a crowd-sourced study. We find that the use of icons increases the perceived risk of activities involving visiting the mountain. However, we highlight remaining questions around visualization design and design ethics that warrant further study in the domain of how best to communicate cold weather hazards in ways that are mindful of the diversity of literacies and experiences of visitors.

The streaming instability and pebble accretion are two physical mechanisms with demonstrated potentials to drive, respectively, the formation of planetesimals and the growth of planetary systems containing a diverse range of planetary types. Here we explore the protoplanetary disc conditions in terms of turbulence strength, Stokes number and initial disc size that are needed to (i) form planetesimals by the streaming instability, (ii) form gas giant planets in cold orbits, (iii) form super-Earths and sub-Neptunes close to the star and (iv) form rocky planet embryos in temperate orbits. We identify an optimum Stokes number range between St= 0.01 and St= 0.03 where all three planetary classes form and where the streaming instability is triggered for a slightly elevated pebble metallicity. Cold gas giants require a turbulence strength of at most $δ=10^{-4}$ and furthermore need large initial disc sizes to benefit from a prolonged pebble flux; super-Earths and rocky planet embryos tolerate higher turbulence strengths similar to those measured for the vertical shear instability. A higher Stokes number of St=0.1 is detrimental to the formation of cold gas giants due to the short-lived pebble flux. For Stokes numbers below St= 0.003, extremely low values of turbulence ($δ<10^{-5}$) are required to form cold gas giants. We highlight how loss of gas to disc winds, reduction in the migration speed by thermal or dynamical torques or the presence of pressure bumps in the outer disc could increase the parameter space for the formation of cold gas giants. We derive analytically that the mass of the largest planetesimals formed by the streaming instability is of similar magnitude to the threshold mass beyond which pebble accretion becomes efficient, if planetesimals form in the earliest phases of protoplanetary disc evolution.

We consider the one-dimensional quasilinear heat equation with state-dependent heat capacity and thermal conductivity, and design a boundary-output observer based on the backstepping design for a linear heat equation with constant coefficients. Viewing the quasilinear system as a perturbation of the linear one, we establish exponential stability of the origin for the observation error dynamics in $H^1$, with an explicit region of attraction depending on the system parameters, observer gains, and the mismatch between the nonlinear diffusivity and the constant design diffusivity. Importantly, the observation error converges to zero rather than merely to a neighborhood scaling with this mismatch, even though, in contrast to backstepping-based stabilization of nonlinear PDEs, the mismatch need not decay along trajectories and may remain bounded away from zero, acting as a persistent state-dependent multiplicative perturbation. A technical challenge was to perform a sufficiently-fine Lyapunov analysis that does not yield overly conservative results such as mere boundedness of the observation error. Interestingly, while in the linear case the relationship between one of the backstepping observer gains and the convergence rate is monotonic, we show that in the nonlinear setting this is no longer the case: there may exist an optimal value of that gain, beyond which further increases deteriorate the system's performance. Such behavior cannot be predicted without our analysis: one might expect a priori the decay rate to be freely tunable at the expense of a region of attraction that shrinks to zero as the prescribed rate tends to infinity. However, our Lyapunov analysis (supported by numerical experiments) reveals that this intuition is incorrect.

Anthropomorphic language describing artificial intelligence (AI) is widespread in media, policy, and everyday discourse; so too are discussions of AI bad behavior, from hallucinations to inappropriate comments. How does humanizing language about AI shape moral judgments when AI behaves badly? Across four experiments (total N = 1,020), we tested whether lexical anthropomorphism (LA) primes shape judgments of AI moral character, behavior morality, and behavioral responsibility. Studies 1-3 tested interactions between anthropomorphic language and humanizing design cues (icons, names, self-referencing) in the context of amoral errors. Study 4 extended this to genuinely immoral AI behavior across seven moral-violation types. Results indicate humanizing language and design cues have little influence on moral judgments of misbehaving AI. Where effects emerged, high-anthropomorphic primes elevated perceptions of an AI's capacity for dishonesty. The type of moral violation observed was the strongest predictor of moral judgments, with harm and degradation violations producing the broadest negative character assessments. Prime drift, horn effects, and egoistic value orientations emerged as potentially important predictors of AI moral judgments.

Parallel and Distributed Computing (PDC) is a critical yet conceptually challenging area of the undergraduate computer science curriculum. While students often encounter these concepts in theory, few gain exposure to experience in real high-performance computing (HPC) environments. Research shows that when students are engaged in project-based learning they retain knowledge more effectively. They also develop a deeper understanding of concepts taught in the classroom. This paper presents a practical assignment in which students engage directly with the University of Florida's HiPerGator supercomputer to implement and benchmark matrix multiplication using Python and C (via POSIX threads and OpenMP). Students navigate batch scheduling, core allocation, and performance tuning, experiences that are rarely accessible at the undergraduate level. We describe the assignment in detail and provide a three-year evaluation across multiple course offerings, highlighting how structured access to real HPC infrastructure can deepen student understanding of parallelism and multithreading.

Defant and Kravitz introduced generalizations of West's stack-sorting map $s$ from permutations to finite words. This raises questions as to how such generalizations could be applied in the field of combinatorics on words. The Defant-Kravitz generalizations of $s$ depend on how repeated occurrences of the same character within a word may be repositioned, according to their $\textsf{tortoise}$ and $\textsf{hare}$ operations. As demonstrated in this paper, these operations provide a natural way of extending abelian complexity functions for infinite sequences, in a way that gives light to structural properties associated with infinite words. We apply these new ideas to two famous infinite words: the paperfolding word and the Thue-Morse word. In the case of the Thue-Morse word, we discover an interesting connection to the previous work of several authors, such as de Luca and Varricchio, on the ``special'' factors of the Thue-Morse word. This may be seen as providing a basis for a new and interdisciplinary area linking the combinatorics about the stack-sorting of permutations with the field of combinatorics on words.

While Earth locks much of its carbon in its crust as carbonates, Venus retains a comparable carbon inventory almost entirely in its atmosphere as CO$_2$. On Earth, the geological carbon cycle that has produced this vast crustal carbonate inventory is regulated by biology, liquid water, and plate tectonics, which together have stabilised climate over geological timescales. Venus presently lacks all these processes. We test whether Venus's massive CO$_2$ atmosphere is diagnostic of a specific evolutionary pathway by quantifying three routes: primary magma-ocean outgassing, secondary volcanic degassing in a stagnant-lid regime, and remobilisation of crustal carbonates after climate destabilisation. Using a coupled climate--weathering framework, we find that a past habitable Venus could have stored $\sim$20 bar of CO$_2$ as crustal carbonates. Following transition to runaway conditions, crustal heating releases this reservoir over tens of Myr. In stagnant-lid secondary-degassing models with a MORB-like mantle, outgassing reaches only $\sim$25 bar CO$_2$, limited by progressive mantle volatile depletion. However, Venus-like inventories can be achieved through: (i) magmatic carbon enrichment, (ii) increased magmatic delivery to the surface (high extrusion or melt production), and (iii) the recycling of undegassed carbon back into the planet's interior. Primary magma-ocean outgassing can generate $>10^2$ bar CO$_2$, but the retained fraction after early escape remains uncertain. Ultimately, a Venus-like massive CO$_2$ atmosphere is an equifinal outcome and does not uniquely diagnose a temperate past.

The theory of dynamical diffraction (DD) in perfect crystals is the backbone of high-precision neutron and X-ray diffraction experiments, enabling accurate determination of crystal structure factors and the realization of perfect crystal interferometers. In practice, however, real crystals exhibit deformations and imperfections, including surface roughness, defects, temperature gradients, angled crystal faces, and curvature, that degrade interferometer performance and are difficult to model using conventional DD theory, particularly in complex geometries. To address these challenges, a quantum information (QI) model for DD has been under development, with demonstrated experimental agreement for both ideal crystals and in the presence of some imperfections such as surface roughness and defects. Here, we present a unified quantum random walk model that is now suitable for reproducing all established DD effects. We demonstrate this by incorporating a broad range of internal crystal effects influencing DD intensity distributions, including linear temperature gradients, the DD Talbot effect, and angled or miscut crystals. These results establish the QI model as a comprehensive and flexible framework for experimental analysis, as well as for the design of next-generation perfect crystal neutron interferometers and neutron optical components, such as condensing monochromators.

Universally robust dynamical decoupling (UR$n$) sequences were proposed to compensate pulse imperfections arising from arbitrary experimental parameters while achieving high-order error suppression with only a linear increase in the number of pulses. Although their performance was supported by analytical arguments, numerical simulations, and experiments, a complete mathematical proof of the claimed order of error compensation has been absent. In this work, we present a rigorous proof for UR$n$ DD sequences with even $n$. Using a series expansion of a quantity whose modulus is the fidelity $F$, we derive necessary and sufficient conditions for the cancellation of its coefficients up to, but not including, order $n$. The UR$n$ phase prescription satisfies these conditions, and therefore $1-F=O(ε^n)$. Our results establish the UR$n$ construction on firm analytical grounds and clarify the structure responsible for its high-order robustness.

At LaAlO$_3$/KTaO$_3$ interfaces, the superconducting $T_c$ exhibits a striking quasi-linear dependence on crystallographic orientation, coexisting with switchable polar nanoregions (PNRs). We propose an effective minimal Eliashberg framework in which overdamped PNR fluctuations provide the pairing glue, while geometric Rashba coupling controls its angular dependence. Within a reduced isotropic helicity-band description, the dynamic Rashba vertex scales as $\sin(θ)$, yielding a pairing strength $λ(θ)=λ_0+C\sin^2(θ)$. Exact Matsubara-Eliashberg numerical solutions show that this non-linear mapping naturally yields the same qualitative quasi-linear $T_c(θ)$ dependence within the reduced model. Because the Rashba-activated polar channel is amplified by the large atomic spin-orbit coupling of Ta $5d$ orbitals, the same framework also rationalizes why KTaO$_3$ interfaces exhibit both a much stronger orientational dependence and a substantially higher $T_c$ scale than their SrTiO$_3$ counterparts.

Microservice-based systems impose significant organizational coordination challenges, yet the role of individual developers in shaping organizational coupling (OC) remains underexplored. Prior work largely focuses on structural architectural aspects, leaving gaps in understanding how developer roles influence coordination dynamics over time. This study investigates how different developer roles contribute to OC in a large-scale microservices system. The analysis focuses on three key roles, namely Jacks, representing broad knowledge holders, Mavens, representing deep specialists, and Connectors, representing organizational bridges. A longitudinal repository mining analysis of GitHub data, including commits and issue and pull request interactions, is conducted to operationalize OC and quantify its evolution over time. The results show that Connectors are consistently associated with higher levels of OC, while the co-occurrence of multiple roles within the same developer further amplifies coupling effects. In contrast, Jacks and Mavens exhibit more localized and role-specific influences. These findings indicate that OC in microservices is primarily a role-driven phenomenon rather than an inevitable structural property, providing a foundation for role-aware organizational design and targeted decoupling strategies.

We give an explicit description (in component fields) of a holomorphic theory associated to a general supersymmetric background of $\mathcal N=1$ supergravity in ten dimensions. Conjecturally, this provides a sought-for holomorphic realisation of the supergravity twist in such backgrounds, generalising the minimal type I BCOV theory for Calabi-Yau manifolds. Our theory unpacks the recently introduced Courant contact model associated to a holomorphic Courant algebroid. We also show that a coisotropic reduction of this model reproduces the recent model of ref [1], which is formulated in terms of constrained fields.

We present a first-principles determination of heavy meson light-cone distribution amplitudes (LCDAs) from lattice QCD in the continuum limit, improving substantially on our previous pioneering study. Within the heavy-quark large-momentum effective theory (HQLaMET) framework, supplemented by lattice QCD calculations of the OPE moments, we analyze six ensembles with lattice spacings ranging from $a=0.0519-0.1053$\,fm and pion masses from $m_π=135.5-317.2$\,MeV, thereby enabling controlled continuum, chiral, and infinite-momentum extrapolations to the physical point. Momentum-smeared sources, hypercubic-smeared Wilson lines, and optimized interpolating operators are adopted to significantly improved signals for the nonlocal correlators. Within a unified framework, we determine both QCD LCDAs and HQET LCDAs. Our resulting QCD LCDAs of $D$ meson peak at $y\approx 0.2-0.3$, with total uncertainties below $30\%$ for $0.1<y<0.9$. The leading-twist HQET LCDA is constructed using a peak-and-tail factorization, in which the nonperturbative peak region is obtained from lattice QCD and the perturbative tail is incorporated from HQET, with the two regions combined through a model-independent Laguerre-polynomial parametrization. At $μ=1$\,GeV, we obtain the inverse moment of HQET LCDA $λ_B=0.340(20)$\,GeV and first inverse-logarithmic moment $σ_B^{(1)}=1.685(63)$, consistent with experimental constraints and phenomenological determinations. Direct lattice calculations based on operator product expansion provide a nontrivial cross-check of the LaMET results. Final results and phenomenological impact of these results are presented in a companion paper~\cite{HeavymesonDA_short_paper}. Our results remove the single-lattice-spacing limitation of the previous study, and provide a robust determinations of heavy meson LCDAs in both QCD and HQET for next-generation heavy flavor physics.

We theoretically and experimentally study finite-time optimal control of a colloidal particle steered through a spatially inhomogeneous environment, modeled by a position-dependent energetic cost at the final state. The competition between this state-dependent penalty and path-dependent dissipation gives rise to a sharp transition in the control strategy at a critical control duration. We further show that this transition can be linked to a dynamical phase transition in nonequilibrium relaxation after a quench, where the control cost maps onto the rate function governing rare trajectories.

Localized features such as singularities, sharp gradients, discontinuities, and moving sources require adaptive finite element discretizations. Conventional refinement strategies introduce significant computational overhead through mesh-topology modifications, constraint handling for non-matching interfaces, and repeated remeshing with state transfer. This work presents an unfitted multi-level hp-refinement strategy that enriches a fixed base discretization by independently positioned overlay meshes. The global approximation space is constructed by superposition of the active spaces across all refinement levels, while homogeneous constraints on artificial overlay boundaries ensure global $C^0$ continuity. Coupling between non-matching meshes is assembled over admissible integration regions defined by intersections of element partitions, enabling reuse of standard element-level finite element routines within a lightweight superposition framework. In contrast to fitted multi-level approaches, overlay boundaries are not required to align with underlying mesh interfaces. This reduces inter-level coupling and allows refinement zones to be inserted, translated, and removed without modifying the base discretization. Numerical studies for discontinuous and singular benchmark problems, as well as a moving source, demonstrate the performance of the method. The unfitted approach retains exponential convergence for non-smooth problems and achieves improved error-to-cost ratios compared to fitted multi-level hp-refinement. For representative cases, comparable accuracy is obtained with substantially fewer degrees of freedom, while localized high-order refinement accurately tracks moving features.

The relation between uniformly accelerated laboratories and laboratories supported in a gravitational field lies at the conceptual core of the Equivalence Principle, yet its precise kinematical content beyond strictly local considerations remains subtle. In this work we develop a unified metric description of these configurations using the standard Arnowitt-Deser-Misner (ADM) formulation of General Relativity, which provides an explicit decomposition of spacetime into spatial hypersurfaces and their temporal evolution. In this setting the ADM shift vector is interpreted as a physical quantity encoding the kinematical relation between spatial slices and their temporal embedding associated with a chosen foliation. This interpretation allows uniformly accelerated laboratories and laboratories supported in a gravitational field to be described within a common structural framework, showing that configurations experiencing identical proper acceleration share an equivalent local shift structure. This viewpoint clarifies the apparent asymmetry between the spatial displacement and energetic cost associated with accelerated motion and their apparent absence in phenomenological descriptions of observers supported in a gravitational field. The formulation remains fully equivalent to standard General Relativity at the level of the field equations and constraints while making explicit kinematical features that are usually implicit in its geometric description. Consequences of this interpretation include a relational account of gravitational time dilation and the emergence of observer-dependent horizons.

Effective field theories have established themselves as key pillars of modern nuclear physics. They enable a quantitative understanding of the strong nuclear force, provided low-energy constants that parametrize short-distance physics can be determined from experimental data. This, however, often becomes prohibitively expensive due to a significant computational cost of solving the A-body problem. The computational challenge is particularly severe for three-body forces, which are at the frontier of nuclear and atomic physics and play an important role in the equation of state of neutron stars. Here we prove that for a parametric low-rank update of a Hamiltonian, the A-body problem at a fixed energy exactly reduces to a low-dimensional matrix equation regardless of the size of the Hilbert space. As a proof-of-principle, we present exact and computationally cheap snapshot-based emulators for few-body scattering and bound states. Unlike alternatives, our emulators can be used far away from the snapshot region without loss of precision and yield accurate results for parameter values not accessible using conventional solution techniques. Our approach is not restricted by the interaction type, number of particles, and methods for generating snapshots and can be applied to mitigate the computational burden of the A-body problem to a broad class of problems in nuclear, atomic, and molecular physics.

In this study, by utilizing the constructed generalized free energy alongside the Mean First-Passage Time and the Kramers escape rate from stochastic dynamics, we have obtained a comprehensive landscape of the phase transitions for the Bardeen-AdS-class black hole. This black hole model admits two distinct categories of solutions. Type I black holes feature a regular black hole solution, and Type II black holes possess a vacuum state solution. In the phase transition between the small black hole and the large black hole for Type I, the process may pass through a stable, metastable, or unstable regular black hole as an intermediate state. In contrast, for Type II black holes, the phase transition occurs exclusively between the vacuum state and the small black hole, and the transition process does not involve any regular black hole intermediate states.

As emerging quantum architectures evolve into heterogeneous networks combining different physical substrates, such as qubits for logic and higher-dimensional qudits for robust communication, the traditional scalar metrics of quantum error correction become insufficient. To address this, we introduce a mathematical framework based on dimension multisets to characterize quantum error-correcting codes (QECC) and absolutely maximally entangled (AME) states in mixed-dimensional Hilbert spaces. By replacing scalar weights with multisets, we accurately capture the exact physical composition of error supports across these diverse systems. Our central result is the mixed-dimensional quantum MacWilliams identity, which establishes the formal algebraic relationship between Shor-Laflamme enumerators and unitary weight enumerators. From this foundation, we deduce the mixed-dimensional shadow identity and derive rigorous, generalized constraints on code parameters, explicitly formulating the mixed-dimensional quantum Hamming, Singleton and Scott bounds, and developing a linear program to systematically evaluate code viability. For the Singleton bound, a tighter bound that has no homogeneous analogue is derived for pure mixed-dimensional codes. Finally, we deploy this enumerator machinery to thoroughly analyze AME states, utilizing shadow inequalities to constrain their existence and introducing a combinatorial grid method for the explicit construction of mixed-dimensional tripartite AME states.

We prove a criterion for the mildness of a finitely presented pro-$p$ group $G$. It implies as a special case a cohomological mildness criterion via Massey products, generalizing results due to Schmidt and Gärtner. It subsumes Labute's non-singular circuit criterion. We further show connections with the triangle condition for the mildness of pro-$p$ right-angled Artin groups, due to Quadrelli, Snopce and Vannacci.

Generative recommender systems have recently emerged as a promising paradigm by formulating next-item prediction as an auto-regressive semantic IDs generation, such as OneRec series works. However, with the next-item-agnostic prediction paradigm, its could beam out some next potential items via Semantic IDs but hard to estimate which items are better from them, e.g., select the top-10 from beam-256 items, leading to a gap between generation and ranking performance. To fulfill this gap, we propose RecoChain, a unified generative retrieval and ranking framework that integrates candidate generation and ranking within a single Transformer backbone. Specifically, in inference, the model first generates candidate items via hierarchical semantic ID prediction, then performs the SIM-based ranking process to estimate the click possibility of corresponding item candidate continuously. Extensive experiments on large-scale real-world datasets demonstrate that our approach effectively bridges the gap between generative retrieval and ranking, achieving improved Top-K recommendation performance while maintaining strong generative capability.