The impact of external forcing is well studied in the Kuramoto model without inertia, but remains unclear for inertial Kuramoto oscillators (KMI) with bimodal intrinsic frequency distributions. This article fills that gap, showing that competition between external forcing and intrinsic bimodality can suppress the intermediate standing wave states of bimodal KMI by entraining oscillators to the external forcing. Using a self-consistent analytical framework, we show that, for a bimodal distribution, forcing makes the backward transition discontinuous, unlike the continuous transition in the unimodal case. Further, for a bi-delta distribution, we derive a closed form expression for the backward solution branch. These results clarify how intrinsic frequency structure shapes the effect of external forcing, with implications for biological systems (e.g., photoreceptor and pacemaker cells) and for pinning-control strategies in multi-agent networks.

This paper studies expected performance and practical feasibility of the most commonly used classes of source-level likelihood-ratio (LR) systems when applied to a trace-reference comparison problem. The paper compares performance of these classes of LR systems (used to update prior odds) to each other and to the use of prior odds only, using strictly proper scoring rules as performance measures. It also explores practical feasibility of the classes of LR systems. The present analysis allows for a ranking of these classes of LR systems: from specific-source feature-based to common-source anchored or non-anchored score-based. A trade-off between performance and practical feasibility is observed, meaning that the best performing class of LR systems is the hardest to realise in practice, while the least performing class is the easiest to realise in practice. The other classes of LR systems are in between the two extremes. The one positive exception is a common-source feature-based LR system, with good performance and relatively low experimental demands. The paper also argues against the claim that some classes of LR systems should not be used, by showing that all systems have merit (when updating prior odds) over just using the prior odds (i.e. not using the LR system).

High-level synthesis (HLS) transforms an algorithmic description of hardware from a higher abstraction (e.g., C/C++) into a register-transfer level (RTL) design, offering reduced development time and greater flexibility in design space exploration. However, such machine-generated RTL designs may contain major functional bugs or security vulnerabilities due to limitations or errors in the HLS tools. One of the most reliable methods to identify these vulnerabilities is formal verification, particularly model checking. Nevertheless, the large size of the generated RTL often causes model checking to struggle to conclude within reasonable time or resource limits. In this study, we propose utilizing the high-level design features from the HLS flow to construct a set of helper assertions aimed at guiding the model checker and accelerating the verification process. To identify the most effective set of helpers to assist the model checker, we develop a proving mechanism that iteratively reuses proving information to select the potentially most useful set of helpers. We evaluate the proposed framework on a set of HLS design benchmarks. Experimental results demonstrate that, when compared to vanilla model checking, our approach achieves a speedup of up to 6.05x, and 2.23x on average.

We introduce and study the finite-approximate solvability of operator equations \(Lu = h\) in a Hilbert space setting, where a bounded operator \(L \colon U \to H\) is paired with a finite-dimensional constraint operator \(π\colon H \to H_0\). The objective is to match exactly the prescribed component \(πh\) while approximating the remainder. We prove that the problem of finding \(u\) such that \(\|Lu - h\| < \varepsilon\) and \(π(Lu) = πh\) is solvable for all \(\varepsilon > 0\) if and only if \(αT_α^{-1}h \to 0\) as \(α\to 0^+\). We further show that dropping any of the structural assumptions on \(L\), \(Γ\), or \(π\) leads to a failure of the equivalence. When \(π\colon H \to H_0\) has an infinite-dimensional range that is compactly embedded in \(H\), the operator \(T_α\) may no longer be invertible. However, a Galerkin scheme \(π_n \to π\) recovers approximate solvability through the resolvents \((α(I - π_n) + Γ)^{-1}\).

Recent anomalies in nuclear transitions observed by the ATOMKI collaboration suggest the existence of a new boson with a mass of $\sim 17$ MeV. A theoretically consistent interpretation requires a framework that not only matches the kinematics but also reproduces the observed decay rates while satisfying stringent experimental constraints. Among various possibilities, an axial-vector or mixed vector-axial-vector mediator $Z'$ emerges as the most viable candidate. However, getting such couplings for a light $Z'$ gauge boson is highly non trivial task. In this work, we construct a gauged chiral, flavor specific $U(1)_X$ extensions of the Standard Model where the associated $Z'$ boson acts as the $17$ MeV particle. By employing a two Higgs doublet framework, we generate the necessary non-vanishing axial-vector couplings while ensuring gauge anomaly cancellation and consistent fermion mass generation. Focusing on the $^8\mathrm{Be}$ and $^4\mathrm{He}$ signals, we show that in this model the viable parameter space to resolve the ATOMKI anomalies is also consistent with a diverse set of experimental constraints, including atomic parity violation, beam dump experiments, meson decays, and neutrino nucleus and neutrino electron scatterings. Our results demonstrate that this framework offers a theoretically sound and phenomenologically robust solution to the ATOMKI anomaly.

As multi-agent AI systems become more common, users increasingly encounter not a single AI voice but a collective one. This shift introduces social dynamics, such as consensus, dissent, and gradual convergence, that can trigger cognitive biases and distort human judgment. We present findings from a controlled experiment (N = 127) comparing three multi-agent configurations: Majority, Minority, and Diffusion. Quantitative results show that majority consensus accelerates opinion change and inflates confidence, consistent with social proof and bandwagon heuristics. Minority dissent slows this process and promotes more deliberative engagement. Qualitative analysis identifies three interpretive trajectories: reinforcing, aligning, and oscillating, shaped by how users interpret agent independence and group dynamics over time. These findings suggest that agent agreement structure, independent of content, functions as a bias-relevant signal in LLM interactions. We hope this work contributes to the Bias4Trust agenda by grounding multi-agent social influence as a concrete and designable source of bias in human-AI interaction.

Early diagnosis and assessment of repetitive subconcussive (rSC) brain injuries are crucial for early clinical intervention. Conventional methods, largely relying on slow fMRI, fail to capture millisecond-level early cortical dynamics, particularly spatiotemporal features associated with pre-configuration dynamics. This study introduces a novel approach integrating dynamic hierarchical spatial features and cortical early behavioral time-domain sensitivity, utilizing EEG and visual attention tasks. We analyzed cortical early behaviors in 24 healthy controls (HC), 21 rSC patients,and a validation cohort of 25 cTBI patients from public datasets. Results reveal distinct temporal patterns in HC: elevated integration at 0-100 ms, rebound dynamics at 100-200ms, and visual perception integration peaks at 200-600 ms. In contrast, rSC patients exhibited significantly impaired dynamic features, with reduced integration levels indicating a decline in pre-configuration dynamics. Signed center distance (SCD) analysis of separation-integration trajectories showed significantly lower early SCD values in rSC patients compared to HC, while cTBI patients displayed negative SCD values, reflecting irreversible damage. Machine learning classification achieved optimal performance in distinguishing between HC, rSC, and cTBI groups using early cortical features, highlighting the critical role of millisecond-level cortical dynamics in rSC diagnosis.

Let $f$ be the Hecke eigenform for the modular group $SL_2(\mathbb{Z})$, and $L(s, \text{sym}^2 f)$ be the symmetric square $L$-function associated with $f$. For $\frac{1}{2}<σ<1$, define $m(σ)$ as the supremum of all numbers $m$ such that \[ \int_{1}^T|L(σ+it, \text{sym}^2 f)|^m \text{d}t\ll_f T^{1+\varepsilon}, \] where $ε>0$ is an arbitrarily small number. In this paper, we established the bound \begin{align*} m(σ)\geq \frac{17}{26-28σ}, \text{ for }\frac{5}{8}\leqσ\leq\frac{52}{73}, \end{align*} which improved our previous result.

Lensless optical imaging eliminates the need for refractive optics, enabling compact and low-cost cameras with a large field-of-view, supporting point-of-care diagnostics and industrial monitoring. Practical deployments, however, remain constrained by ill-posed image reconstruction pipelines that require multiple measurements, careful calibration or object-specific training, thus limiting robustness and scalability. In this work, we introduce a single-shot lensless imaging framework that reconstructs complex objects from only a single recorded intensity pattern using a genetically programmed iterative algorithm. Our method couples a wave-propagation model with an adaptive meta-optimisation strategy to jointly estimate the object amplitude, object phase, and effective object-detector distance. Experiments demonstrate high-fidelity recovery of amplitude objects, including a USAF target and 2~$μ$m silicon beads on a glass slide, as well as a phase-dominant biological sample consisting of U2OS cells on a glass slide. Across multiple object types, wavelengths, and propagation distances, the same learned policy maintains high reconstruction quality with minimal retuning, indicating strong out-of-distribution generalisation. As a practical demonstration, the framework is integrated with a $β$-amyloid-based optical digital bead assay under wide field-of-view acquisition. The resulting platform combines single-shot capture, compact hardware, and accurate reconstruction of complex fields, enabling rapid, portable assays in which throughput, alignment tolerance, and cost are critical.

In this research article, we obtain few theta function identities of level ten employing Ramanujan's $_1 ψ_1$ summation formula. Using these identities, we derive a new modular equation of degree five. Further, we establish Eisenstein series identities of level ten using Bailey's very-well poised $_6 ψ_6$ summation formula.

Motivated by Ridgway's proof of the perceptron algorithm, we study a simple subgradient method for convex inequality systems in Hilbert space. Assuming strict feasibility and bounded subgradients, we establish finite termination for several natural step sizes. We also examine what can go wrong without strict feasibility: finite convergence may fail even for one function, and with several functions the method may converge to a point outside the feasible set. The linear setting recovers the classical perceptron algorithm.

Reconfigurable antenna systems (RASs), such as fluid antennas and movable antennas, are poised to play a pivotal role in sixth-generation (6G) systems by dynamically adapting the antenna elements for system performance enhancement. However, unlocking their full potential requires channel models that accurately capture the influence of antenna configurations on the radiation, propagation, and reception of signals. Existing channel models suffer from several limitations, such as neglecting polarization effects, being restricted to specific antenna types, or relying on oversimplified assumptions. In this paper, we propose a general electromagnetic (EM)-based channel model grounded in spherical vector wave expansion (SVWE). The proposed EM-based channel model captures the impact of antenna position and orientation on the channel gain, thereby making it particularly well-suited for RASs. The effectiveness and accuracy are validated through comparisons with commercial simulation software, demonstrating excellent agreement in predicted channel gains. Moreover, it is shown that antenna orientation is a critical factor governing communication performance, and that dynamically adjusting the antenna orientation yields up to 70% improvement in achievable communication rate compared to a fixed-antenna configuration.

The performance of a quadrupole mass filter (QMF) is highly sensitive to deviations from ideal electrode geometry. In this work, we investigate the effect of small inward and outward tilting of cylindrical rods on the resolution and transmission characteristics of a QMF. Such geometric perturbations introduce an axial variation in the radial confinement potential, resulting in Mathieu parameters that vary along the ion trajectory. To examine this effect, the ion stability diagram is computed using a Runge Kutta (RK45) method with axially-varying Mathieu parameters. The modified stability region exhibits shift and contraction depending on the magnitude and nature of rod inclination. The evolution of higher order field components, particularly the dodecapole term, is analyzed along the axial direction. Ion trajectory simulations are performed using SIMION to evaluate the corresponding changes in QMF transmission characteristics in the first stability zone of operation. While simulations at fixed operating conditions indicate a transmission resolution trade off at small tilting angles leading to resolution enhancement, analysis at constant peak transmission reveals that even slight deviations from the parallel configuration lead to a degradation in resolution. These results highlight the critical role of minute geometric imperfections in QMF operation and provide insights into tolerance limits and design optimization for improved mass filter performance.

We propose a structural framework for branching multiplicities in representation theory, emphasizing their behavior under variation of infinitesimal characters. For the orthogonal reductive pairs $(G,G')$ with complexified Lie algebras $(\mathfrak{o}(n+1,\mathbb{C}), \mathfrak{o}(n,\mathbb{C}))$, we show that branching multiplicities are governed by universal systems of linear inequalities on the parameter space of reduced coherent families introduced in this paper. To describe the loci where multiplicities may change, we introduce \emph{fences}: piecewise-linear hypersurfaces that divide the parameter space into convex regions. We prove that the multiplicity function is locally constant on each such region bounded by these fences. The framework applies uniformly to finite-dimensional representations and to admissible smooth Fréchet representations of real reductive groups. It accounts for classical results such as the Weyl branching law and provides a unified explanation for a range of phenomena, including the Gross--Prasad conjecture, sporadic symmetry breaking operators, and fusion rules for Verma modules. These results establish a general paradigm for branching multiplicities in orthogonal Gelfand pairs.

We prove that for any pair of irreducible principal series representations $(π_1,π_2)$ of $\operatorname{GL}_n(\mathbb{R})$ in general position, the notions of exceptional pole of type 1 and type 2 coincide. Using this identification, we express the Rankin--Selberg $L$-function $L(s,π_1\timesπ_2)$ in terms of the exceptional $L$-factors attached to the irreducible constituents of the derivatives of $π_1$ and $π_2$.

One says that the local large deviation principle (LLDP) is satisfied for a family of random vectors $\{ζ_T\}_{T\ge 0}$ in $\mathbb R^d,$ $d\ge 1,$ if there exists a function $D:\mathbb R^d\to [0,\infty],$ $D\not \equiv \infty,$ such that, for any $α\in \mathbb R^d$, \[ \lim_{T\to \infty}T^{-1}\ln \mathbf{P} (|ζ_T -α|<\varepsilon_T)= - D(α)\] for $\varepsilon_T\to 0$ slowly enough. In this paper, we establish necessary and sufficient conditions for the LLDP that are very close to each other. Namely, if the LLDP is satisfied then, for $M_T\to\infty$ slowly enough as $T\to\infty$, there exists the limit \[ A(μ):= \lim_{T\to\infty}T^{-1}\ln \mathbf{E} (e^{T\langle μ, ζ_T\rangle}; |ζ_T|\le M_T)\in (-\infty, \infty],\quad μ\in \mathbb R^d,\] which is equal to the Legendre--Fenchel transform $\mathcal L_D$ of the rate function $D$. Conversely, if the above limit $A(\cdot )$ exists and is an essentially smooth function, then the LLDP is satisfied with the rate function $D$ equal to $\mathcal L_A.$ This "relaxed version" of the Gärtner--Ellis theorem's main condition does not involve the restrictive integrability assumptions from the latter and is most adequate to the nature of the local large deviation problem.

We present a detailed X-ray study of the quiescent and flaring coronae of three active main-sequence K-type stars, V834 Tau, LQ Hya, and BY Dra, using \textit{XMM-Newton} observations. The quiescent coronae are well described by two-temperature thermal plasma models, with cool and hot components at 0.26-0.30 keV and 0.93-1.01 keV, respectively. Despite similar coronal temperatures, X-ray luminosities (10$^{29.18\mbox{--}29.75}$ erg s$^{-1}$) and overall abundances, the relative emission measures of the cool and hot components differ among the stars. High-resolution spectroscopy reveals significant iron depletion by factors of 5-10 relative to photospheric values, and an inverse first-ionisation-potential effect in all three stellar coronae. Six energetic flares are detected, with peak temperatures of 30 -- 133 MK and released energies of $0.6\mbox{--}4.2\times$10$^ {33}$ erg, classifying them as superflares. Most flares exhibit decay times roughly twice their rise times, although one event shows a decay phase nearly twenty times longer than its rise. Time-resolved spectroscopy and loop scaling laws yield flare parameters consistent with previous studies of active stars. LQ Hya displays recurrent superflares at the same rotational phase across observations separated by six months, suggesting a long-lived, complex magnetic field structure. These results provide insights into the magnetic activity and flare energetics in active stars, and their implications for stellar and exoplanetary environments.

This paper presents a high-order accurate Continuous Galerkin Finite Element Method (CGFEM) for solving the initial boundary value problems governed by the Incompressible Navier-Stokes (INS) equations. We discretize the INS equations using the CGFEM approach in Summation-By-Parts (SBP) form. Lagrange polynomials of up to 4th order are employed. The boundary conditions are imposed weakly using the Simultaneous Approximation Term (SAT) technique, which accommodates discontinuous boundary data without special treatment. The resulting SBP-SAT formulation guarantees an energy stable discretization. The efficiency of the proposed framework is demonstrated by solving a series of numerical tests. Initially, the Method of Manufactured Solutions (MMS) is employed to demonstrate 4th order convergence. Subsequently, the 4th order accurate scheme is applied to a classical benchmark problem featuring discontinuous boundary conditions: the lid-driven cavity flow over a wide range of Reynolds numbers. Accurate and oscillation-free solutions are achieved even in the vicinity of the discontinuous top corner boundaries. Lastly, a canonical backward-facing step flow problem is solved, where accuracy and efficiency are demonstrated.

The energy of a graph $G$ is the sum of the absolute values of the eigenvalues of the adjacency matrix of $G$. Some variants of energy can also be found in the literature which are defined on the concepts of Laplacian matrix, Distance matrix, Common neighbourhood matrix and Seidel matrix. The Seidel matrix of the graph $G$ is the square matrix in which $ij^{th}$ entry is $-1$ or $1$, if the vertices $v_i$ and $v_j$ are adjacent or non-adjacent respectively, and is $0$ , if $v_i=v_j.$ The Seidel energy of $G$ is the sum of the absolute values of the eigenvalues of its Seidel matrix. We present here some graph families which are Seidel equienergetic.

Europium plays a key role in studies of nucleosynthesis in the rapid (r-) process of neutron capture nuclear reactions and the evolution of the r-process element abundances in galaxies. We refine the method for analyzing the Eu~II lines in stellar spectra by updating the Eu~II model atom with recent data on the rate coefficients for inelastic processes in the Eu II + H I collisions. The method was tested by deriving abundances from the Eu~II 4129 A and 6645 A lines in the Sun and five reference stars with well determined atmospheric parameters and high-resolution spectra available. It was shown that abandoning the local thermodynamic equilibrium (LTE) assumption allows the abundances from the two lines to be matched within the error bars, while the difference in the LTE abundances amounts to -0.09 dex for the Sun and -0.07 dex to -0.18 dex for the metal-poor stars. Accounting for the departures from LTE (non-LTE effects) for Eu~II leads to reducing the statistical errors of the derived stellar Eu abundances. The non-LTE abundance corrections for 11 lines of Eu~II were calculated for a grid of the plane-parallel MARCS model atmospheres with effective temperatures, surface gravities, and metallicities relevant to F-G-K type stars. They are publicly available and can be applied for improving stellar Eu abundances in studies of the galactic chemical evolution.

We investigate the vacuum expectation value of a complex scalar field on a two-dimensional torus with quantized magnetic flux $M$. A characteristic feature of this system is the emergence of a critical area: when the area of the torus exceeds this critical value, the vacuum expectation value becomes nonvanishing. Furthermore, any nonzero vacuum expectation value necessarily exhibits nontrivial dependence on the coordinates of the torus. Employing the lowest-mode approximation, we find a single vacuum configuration for $M=1$, whereas two and six degenerate vacuum configurations arise for $M=2$ and $M=3$, respectively. We then analyze the symmetry properties of these vacuum configurations and determine whether they preserve or spontaneously break the symmetry of the underlying system.

In this short note, we show that, assuming a conjecture of Arcara and Miles, a line bundle on a smooth complex projective surface admits a deformed Hermitian-Yang-Mills metric if and only if it is stable in the ``large scaling limit" with respect to a generic Kähler form. The same statement for toric surfaces was recently proved by Stoppa. The purpose of this note is to remark that this equivalence holds for arbitrary smooth projective surfaces.

While Large Audio Language Models (LALMs) achieve strong performance on short audio, they degrade on long-form inputs. This degradation is more severe in temporal awareness tasks, where temporal alignment becomes increasingly inaccurate as audio duration grows. We attribute these limitations to the lack of data, benchmarks, and modeling approaches tailored for long-form temporal awareness. To bridge this gap, we first construct LAT-Chronicle, a 1.2k hour long-form audio dataset with temporal annotations across real-world scenarios. We further develop LAT-Bench, the first human-verified benchmark supporting audio up to 30 minutes while covering three core tasks: Dense Audio Caption, Temporal Audio Grounding, and Targeted Audio Caption. Leveraging these resources, we propose LAT-Audio, formulating temporal awareness as a progressive global-to-local reasoning paradigm. A global timeline is first constructed as an aligned temporal-semantic context,and the Think-With-Audio Chain-of-Thought (TWA-CoT) is then introduced to perform iterative reasoning by incorporating local audio information via tool use. Experiments show that LAT-Audio surpasses existing models on long-form audio temporal awareness tasks and improves robustness to input duration. We release the dataset, benchmark, and model to facilitate future research at https://github.com/alanshaoTT/LAT-Audio-Repo.

Let $P$ be a compact hyperbolic Coxeter truncation polytope of dimension $d\ge 3$, and let $Γ$ be the orbifold fundamental group of the associated Coxeter orbifold $\mathcal{O}_P$. Let $\mathscr{G}(Γ,G)$ be the geometric component containing the holonomy representation in $\operatorname{Hom}(Γ,G)/G$. $\mathscr{G}(Γ,G)$ is identified with the deformation space of properly convex real projective structures on the Coxeter orbifold $\mathcal{O}_P$. We prove that $\mathscr{G}(Γ,G)$ contains only finitely many integral representations. The same conclusion holds more generally for irreducible, large, $2$-perfect truncation polytopes.

We describe the Bandicoot GPU linear algebra toolkit, a C++ based library that prioritises ease of use without compromising efficiency. Bandicoot's API is compatible with the popular Armadillo CPU linear algebra library, enabling easy transition for existing CPU-based codebases. Unlike other GPU-focused toolkits, Bandicoot uses template metaprogramming to generate fused GPU kernels directly at compile time, yielding efficient kernels that are often able to saturate memory bandwidth. This removes the need for runtime overhead or JIT infrastructure. Empirical results show that Bandicoot outperforms (sometimes by considerable margins) commonly-used linear algebra toolkits including PyTorch, TensorFlow, and JAX.

Spatial crowdsourcing (SC) enables the assignment of location-based tasks to mobile users who must travel to specific locations to perform sensing or service activities. However, SC systems often operate in strategic environments where both task requesters and task executors possess private valuation information, posing challenges for designing efficient and truthful incentive mechanisms. To address these issues, this paper proposes a truthful multi-task double Auction for quality-aware spatial crowdsourcing (TRUST-SC). The proposed framework adopts a three-tier architecture. First, task executors are grouped into spatial clusters to improve scalability and reduce allocation complexity. Second, reliable executors are identified through a majority-voting-based quality evaluation process. Third, tasks are allocated, and payments are determined through a multi-unit double-auction mechanism that guarantees incentive compatibility and individual rationality. Theoretical analysis and simulation results demonstrate that the proposed mechanism achieves efficient task allocation, reliable executor selection, and improved performance compared with existing benchmark mechanisms.

Modern ASIC design is becoming increasingly complex, driving up design costs while limiting productivity gains from existing EDA tools. Despite decades of progress, current tools rely on fixed heuristics and offer limited control via tool hyperparameters, requiring extensive manual tuning to achieve an acceptable quality of results (QoR). While prior work has explored learning-based optimization and design-specific hyperparameter tuning, these approaches operate within the constraints of static tool algorithm implementations and do not adapt the underlying algorithms to individual designs. To address this limitation, we introduce the concept of design-adaptive EDA tooling, in which the internal algorithms of EDA tools are automatically specialized to the characteristics of a given design. We instantiate this paradigm through GR-Evolve, a code evolution framework that leverages an agentic large language model (LLM) to iteratively modify global routing source code using QoR-driven feedback. The framework equips the LLM with persistent contextual knowledge of open-source global routers along with an integrated toolchain for QoR evaluation within the OpenROAD infrastructure. We evaluate GR-Evolve across seven benchmark designs across three technology nodes and demonstrate up to 8.72% reduction in post-detailed-routing wirelength over existing baseline routers, highlighting the potential of LLM-driven EDA code evolution for design-adaptive global routing.

Device-Independent Quantum Key Distribution (DIQKD) provides information-theoretic security by relying solely on the violation of Bell inequalities, eliminating the need to trust the quantum devices. However, practical implementations of DIQKD are highly sensitive to noise. Efficient error correction during the classical post-processing stage is important for improving the fidelity. This work investigates the impact of noise on the Clauser-Horne-Shimony-Holt (CHSH) value and evaluates the effectiveness of Cascade error correction. The protocol is applied iteratively to correct errors via parity checking and binary search procedures. Simulation results show that noise significantly degrades the CHSH value, reducing the strength of nonlocal correlations required for secure DIQKD. Nevertheless, Cascade reduces the error ratio, and most corrections occur within the first several rounds. These findings highlight the importance of classical error correction in improving DIQKD systems.

Capillary rise is one of the classical problems in fluid mechanics and is traditionally described by Jurin's law, which balances capillary suction against hydrostatic pressure. Here we extend this classical result to active fluids, materials that generate internal stresses through microscopic energy consumption. Using the continuum theory of active nematics, we show that activity modifies the normal stress balance at the liquid-gas interface through an additional active normal stress contribution. This leads to a generalized active Jurin's law, which can be written in dimensionless form as \(H_{\infty} = 1 - \mathrm{Ja}_a ξ_0\), where \(H_{\infty}\) is the dimensionless active Jurin height at equilibrium, \(\mathrm{Ja}_a\) is an active Jurin number comparing active stress to capillary pressure, and \(ξ_0\) characterizes the alignment of active constituents at the meniscus. The theory predicts that extensile and contractile active fluids can either enhance or suppress capillary rise depending on the magnitude of activity and the interfacial alignment state. From this relation we construct a phase diagram in the \((\mathrm{Ja}_a,ξ_0)\) plane that delineates regimes of activity-enhanced rise, activity-suppressed rise, and complete suppression of the classical capillary state. When orientational order depends on confinement and flow, the coupling between activity and capillarity produces nonlinear equilibrium conditions that may admit multiple steady heights; linear stability analysis reveals that the overdamped dynamics selects a single stable state, whereas the inertial extension allows the possibility of activity-induced bistability. These results show that internally generated stresses fundamentally reshape one of the most classical capillary transport problems.

QAssemble is a pure-Python package for the quantum many-body problem. It implements various functional approaches, such as tight-binding, Hartree-Fock, and GW approximations within a unified object-oriented architecture. Each physical concept--crystal structure, Hamiltonian, Green's function, self-energy, polarizability, screened Coulomb interaction--is represented as a distinct class. The modular design prioritizes code clarity and extensibility, leveraging NumPy, SciPy, and libdlr for numerical operations. Performance-critical kernels, including the polarizability bubble, Dyson equation inversion, and lattice Fourier transforms, are systematically vectorized and combined with the discrete Lehmann representation to achieve practical efficiency within a pure-Python environment. We validate QAssemble on the electronic structure of graphene with local and non-local interactions. Furthermore, benchmarks on a five-orbital extended Hund-Hubbard model demonstrate that this strategy delivers up to a 60x speedup over traditional loop-based Matsubara implementations. QAssemble supports both batch execution for production calculations and interactive workflows for method development.