We present a Lanczos tau method for the approximation and optimization of the $H^2$-norm of time-delay systems described by semi-explicit delay differential algebraic equations. The soundness of this approach is proven under the assumption of a finite strong $H^2$-norm. Furthermore, we prove convergence if the rational approximation of the exponential underlying the discretization is well-behaved and the discretization is stability preserving. Numerical results suggest that, for multiple delays, the method converges at cubic rate in the discretization degree for systems of retarded type and linearly for those of neutral type. In the single delay case, we note geometric convergence of the $H^2$-norm for systems of both retarded and neutral type when a symmetric basis is chosen. Explicit formulas are derived for the gradient of the approximation with respect to system parameters and delays. These allow us to compute the entire gradient using only about double the computational time of approximating the $H^2$-norm alone. We illustrate how these can be used to synthesize robust feedback controllers and stable approximate models. The article is concluded by a discussion of how the presented results extend and improve for approximations based on splines. We note acceleration of the convergence rate by about two orders for such a choice. Finally, we prove that a Lanczos tau method using a spline based on Legendre orthogonal polynomials preserves stability and guarantees convergence of the $H^2$-norm.

Full-physics modeling of multiphase flow in porous media, e.g., for carbon storage and groundwater management, requires the nonlinear coupling of various physical processes. Industry standard nonlinear solvers, typically of Newton-type, are not unconditionally convergent and computationally expensive. Homotopy continuation solvers have recently been studied as a robust and versatile alternative. They tackle challenging nonlinear problems by first solving a simple auxiliary problem and then tracing a solution curve towards the more complex target problem. Robustness and efficiency of the method depends on the iterative numerical curve tracing algorithm as well as on careful design of the auxiliary problem. We assess the traceability of the solution curve for different choices of the auxiliary problem. For the Buckley-Leverett equation, modeling two-phase flow in one dimension, we exemplarily compare the previously introduced vanishing-diffusion and linear constitutive laws homotopy continuation, and a new approach based on the entropy solution of the problem. This provides insight toward systematically and robustly designing homotopy continuation methods for solving complex multiphase flow in porous media.

A \emph{fractal} is an object exhibiting complexity at arbitrarily small scales. In order to study and characterise fractals, one is often interested in quantifying how they fill up space on small scales. This gives rise to various notions of \emph{fractal dimension}. However, even for the simplest examples, the different definitions of dimension may completely disagree about the answer. In this expository article I will examine this phenomenon and use it to discuss and motivate \emph{dimension interpolation}. Dimension interpolation views these classical notions as boundary points of continuous families of dimensions, thus transforming isolated numerical answers into a coherent geometric picture.

We prove that the leading and penultimate leading coefficients in $u_3$ of the ``error" terms of NRS(2) applied to a cubic polynomial $f(z) =\sum_{i=0}^3 a_i z^i=\prod_{i=1}^3 (1-u_iz)$ with starting point $(-\frac{a_1}{a_2}, -\frac{a_1}{a_2})$ are positive-coefficient polynomials in $u_1$ and $u_2$. Our proof for the leading coefficients simplifies that of \cite{DeFranco} and extends to the penultimate leading coefficients as well.

Energy extraction from compact objects has been a central topic in general relativity since the introduction of the Penrose process. In this work we present a unified analysis of rotational and electromagnetic energy extraction in Kerr, Reissner-Nordstrom, and Kerr-Newman spacetimes. Using particle energetics and the irreducible mass formalism, we compare the efficiencies of these mechanisms and examine their consequences for horizonless objects. While purely rotational extraction in Kerr spacetime is fundamentally limited by geometric constraints, electromagnetic interactions enlarge the region of negative energy orbits through an effective ergoregion, allowing significantly higher efficiencies. In Kerr-Newman geometry, the combined effect of rotation and charge further enhances the extractable energy. We then study the long-term evolution of over-extremal cases under continuous extraction. By deriving coupled evolution equations for the mass, spin, and charge parameters, we show that continuous extraction can gradually drive a naked singularity toward the extremal bound. For astrophysically realistic luminosities, the characteristic evolution timescale is of order about 10^9 years. These results suggest that energy extraction provides an energetic indication of instability in Reissner-Nordstrom, Kerr, and Kerr-Newman naked singularities and may lead to horizon formation as a long-term stabilizing outcome.

A complex matrix is called \emph{coninvolutory} if $T\overline{T}=I$. In this paper, we study decompositions of affine transformations in $\mathrm{Aff}(n,\mathbb{C})=\mathrm{GL}(n,\mathbb{C})\ltimes \mathbb{C}^n$ into products of coninvolutions. We prove that an affine transformation $g$ is a product of two coninvolutions in $\mathrm{Aff}(n,\mathbb{C})$ if and only if its linear part $L(g)$ is $c$-reversible; that is, $L(g)$ is conjugate to $\overline{L(g)}^{-1}$ in $\mathrm{GL}(n,\mathbb{C})$. Equivalently, $g$ is conjugate to $\overline{g}^{-1}$ in $\mathrm{Aff}(n,\mathbb{C})$. We further characterize elements that are products of three coninvolutions via consimilarity and show that every $g=(A,v)\in \mathrm{Aff}(n,\mathbb{C})$ with $|\det(A)|=1$ can be expressed as a product of at most four coninvolutions.

We investigate the upper critical field and superconducting anisotropy of epitaxial La2.82Sr0.18Ni2O7 thin films, which show a sharp superconducting transition at Tc=31.6 K. Near Tc, superconductivity exhibits thickness-limited two-dimensional characteristics. Upon cooling, the out-of-plane coherence length decreases below the sample thickness of 6 nm, corresponding to a 3-unit-cell film, indicating a crossover to intrinsic three-dimensional bulk superconductivity. High-field transport measurements reveal large upper critical fields with a small anisotropy ratio gama~1.34, comparable to bulk Ruddlesden-Popper nickelates. At low temperatures, the in-plane (ab) upper critical field Hc2(ab) is strongly suppressed by spin-paramagnetic pair breaking and approaches the Pauli limit (Hc2(Pauli)=58 T), while Hc2(c) remains largely unaffected. This anisotropic Pauli limitation accounts for the reduced upper critical field anisotropy and supports the conclusion that superconductivity in these films is fundamentally three-dimensional bulk like. Our results highlight the essential role of spin-paramagnetic effects in shaping the high-field superconducting phase diagram of Ruddlesden-Popper nickelates.

Ground-state properties of rare-earth based 1/1 periodic approximants of icosahedral quasicrystal are clarified theoretically on the basis of an effective model for magnetism taking into account uniaxial anisotropy arising from crystalline electric field. By performing numerically-exact calculation on the 1/1 approximant crystal with a lattice constant $a$=14.725 Å, we have determined the ground-state phase diagram for ferromagnetic interactions. The result shows that eight kinds of noncollinear and noncoplanar magnetic structures are stabilized, whose magnetic space groups are identified as $I_{\rm P}m'\bar{3}'$, $C2'/m'$ and $R\bar{3}$. We have clarified the degeneracy of each ground state, which is expected to be reflected in the numbers of the domains. By analyzing each state, the magnetic as well as topological properties are revealed. Our results are shown to explain the measured magnetic structures in the 1/1 approximants and the effective model is discussed to be useful for understanding the magnetic structures and their topological properties in broad range of rare-earth based 1/1 approximants.

Early detection of cancer is essential for timely diagnosis and improved patient outcomes. Among emerging technologies, intra-body nanoscale communication offers an innovative solution to identify molecular cues within the human bloodstream. This study investigates a minimally invasive approach for early-stage cancer biomarker detection using nanomachines introduced into the bloodstream. To assess the feasibility of this approach, computational simulations are used to emulate the vascular environment and evaluate biomarker detection performance under different physiological conditions. Current modeling approaches often fail to capture essential vascular characteristics, including non-uniform flow structures, size-dependent particle mobility, and particle margination driven by red blood cell interactions. To address these limitations, our study incorporates these factors into the simulation framework and quantifies their individual and combined effects on biomarker detection efficiency. Baseline detection performance is first obtained under uniform flow assumptions, after which introducing realistic vascular transport mechanisms progressively reduces detection probability for all vessel types and nanomachine sizes. Among the considered vessels, capillary consistently achieves the highest detection probability across all nanomachine sizes.

As artificial intelligence (AI) becomes increasingly integrated into workflows, humans must decide when to rely on AI advice. These decisions depend on general efficacy beliefs, i.e., humans' confidence in their own abilities and their perceptions of AI competence. While prior work has examined factors influencing AI reliance, the role of efficacy beliefs in shaping collaboration remains underexplored. Through a controlled experiment (N=240) where participants made repeated delegation decisions, we investigate how efficacy beliefs translate into instance-wise efficacy judgments under varying contextual information. Our explorative findings reveal efficacy beliefs as persistent cognitive anchors, leading to systematic "AI optimism". Contextual information operates asymmetrically: while AI performance information selectively eliminates the AI optimism bias, data or AI information amplify how efficacy discrepancies influence delegation decisions. Although efficacy discrepancies influence delegation behavior, they show weaker effects on human-AI team performance. As these findings challenge transparency-focused approaches, we propose design guidelines for effective collaborative settings.

We propose a hybrid photonic quantum reservoir computing (QRC) framework for swaption surface prediction. The pipeline compresses 224-dimensional surfaces to a 20-dimensional latent space via a sparse denoising autoencoder, extracts 1,215 Fock-basis features from an ensemble of three fixed photonic reservoirs, concatenates them with a 120-dimensional classical context, and maps the resulting 1,335-dimensional feature vector to predictions with Ridge regression. We benchmark against 10 classical and quantum baselines on six held-out trading days. Our approach achieves the lowest surface RMSE of~$0.0425$ while maintaining sub-millisecond inference. The quantum layer has zero trainable parameters, sidestepping barren plateaus entirely. Variational quantum methods (VQC, Quantum LSTM) yield negative $R^{2}$ on test data, confirming that fixed quantum feature extractors paired with regularised readouts are more viable for low-data financial applications.

Shock tubes provide well-controlled high-temperature and high-pressure conditions for chemical kinetics studies, yet the region behind the reflected shock is seldom perfectly homogeneous. Axial and radial gradients arise from shock formation, attenuation, and the interaction of the reflected shock wave with the boundary layer, and these variations influence chemical kinetic measurements such as ignition delay time. The present study combines experimental diagnostics and numerical simulations to quantify these gradients in a single-diaphragm shock tube. A coupled RANS-LES framework implemented in CONVERGE CFD incorporates realistic diaphragm opening profiles and is validated using pressure histories and shock velocity profiles for argon, nitrogen, and carbon dioxide. The results show that incident shock attenuation strongly influences the thermodynamic state of the reflected-shocked region, with test gas-dependent differences: a nearly uniform core with modest axial gradients is maintained in argon, whereas substantial axial gradients due to reflected-shock and boundary-layer interactions is seen in nitrogen and carbon dioxide. The analysis provides a foundation for quantifying test-gas homogeneity in shock-tube experiments and potential extrapolation to improving interpretation of ignition data acquired under non-ideal flow conditions.

Life sciences research depends heavily on open-source academic software, yet many tools remain underused due to practical barriers. These include installation requirements that hinder adoption and limited developer resources for software distribution and long-term maintenance. Jupyter notebooks are popular because they combine code, documentation, and results into a single executable document, enabling quick method development. However, notebooks are often fragile due to reproducibility issues in coding environments, and sharing them, especially for local execution, does not ensure others can run them successfully. LabConstrictor closes this deployment gap by bringing CI/CD-style automation to academic developers without needing DevOps expertise. Its GitHub-based pipeline checks environments and packages notebooks into one-click installable desktop applications. After installation, users access a unified start page with documentation, links to the packaged notebooks, and version checks. Code cells can be hidden by default, and run-cell controls combined with widgets provide an app-like experience. By simplifying the distribution, installation, and sharing of open-source software, LabConstrictor allows faster access to new computational methods and promotes routine reuse across labs.

Increasing connectivity and decreasing qubit-state delocalization without compromising the speed and accuracy of elementary gate operations are topical challenges in the development of large-scale superconducting quantum computers. In this theoretical work, we study a special honeycomb qubit lattice where each qubit inside a unit cell is coupled to every other one via two dedicated tunable couplers and a common central element. This results in an effective multi-mode interaction enabling tunable, on-demand, all-to-all connectivity between each qubit pair within the unit cell. We provide a thorough analysis of the unit cell, including a proposal for a novel and efficient conditional-Z gate scheme which takes advantage of the effective multi-mode coupling. We develop an experimentally viable pulse protocol for a single-step gate implementation which considerably improves the gate speed compared to the previous two-qubit-gate realizations suggested for architectures utilizing a center mode. We also show numerical results on how the presence of spectator qubits affects the average two-qubit-gate fidelity, and analyse how the multi-mode coupling structure mitigates the delocalization-induced crosstalk during simultaneous single-qubit gates within the unit cell. We also provide analytical estimates for the errors caused by relaxation and dephasing during a two-qubit-gate operation, including noise terms for the multi-mode coupling structure. Our multi-mode coupling architecture results in a good balance between increased connectivity and available parallelism, especially when several interacting unit cells form a quantum processing unit. We anticipate that the obtained results pave the way towards high-connectivity quantum processors with efficient and low-overhead quantum algorithms.

Stacked intelligent metasurfaces (SIMs) have emerged as a powerful paradigm for wave-domain signal processing, enabling fine-grained control over electromagnetic (EM) propagation in next-generation wireless systems. However, conventional multi-layer SIMs often suffer from excessive structural complexity, high computational overhead, and significant power attenuation across layers, limiting their performance. In this paper, we first characterize SIMs from the perspectives of functionality, application, and layer configuration, revealing the inherent trade-offs between signal processing flexibility and power efficiency. Then, two representative 2-layer architectures, the meta-fiber-connected SIM (MF-SIM) and the flexible intelligent layered metasurface (FILM), are introduced, each advocating a distinct 2-layer SIM design philosophy. Moreover, we identify several open challenges in topology optimization for MF-SIM, shape control for FILM, and hybrid 2-layer architectures. Finally, case studies considering 2-layer MF-SIM and FILM assisted point-to-point multiple-input multiple-output (MIMO) and multi-user communication systems validate that properly designed 2-layer SIMs can significantly reduce power loss and optimization burden while maintaining good signal processing performance, offering a promising pathway toward practical SIM-enabled 6G systems.

Quantum many-body systems can exhibit distinct regimes where dynamics is either ergodic, dynamically exploring an extensive region of available state-space, or non-ergodic, where the dynamics may be restricted. An example is the many-body localization (MBL) transition, where disorder induces non-ergodic behaviour. Most measures of ergodicity notably rely on global quantities, such as level spacing statistics. We explore the ability for a subsystem to probe the ergodicity of dynamics via measurement of local observables, and use expected results from random matrix theory (RMT) as a benchmark for the ergodic regime. We exploit two predictions from RMT as ergodicity is broken: the time evolution of the quantum Fisher information, and a fluctuation-dissipation relation. These are investigated in three different ergodicity breaking mechanisms, namely, as a consequence of transition to integrability, MBL, and Quantum Many-Body Scars (QMBS). We show that the predicted behaviour from RMT can be used as a potential witness for transition to non-ergodic behaviour from the measurement of local observables alone.

This paper studies the impact of funding market frictions on bond prices and market-wide liquidity. Using proprietary transaction-level data on all gilt-backed repo and reverse-repo trades, we demonstrate how the market power of individual dealers and their linkages generate frictions. Specifically, we show that frictions related to market power account for between 0.5 and 1.3 percentage points of bond yield deviation, while the transmission of heterogeneously persistent shocks between dealers accounts for between 2 and 4 percentage points of yield deviation.

This work addresses the challenge of analyzing geometric structures using Kendall's 3D Shape Space. While Riemannian geometry provides a robust framework for shape analysis (independent of scale, position, and orientation) the transition from theoretical manifolds to practical computational workflows remains difficult. Although Geomstats is currently the leading Python library for manifold-based statistics, it lacks specific utilities required for advanced 3D shape analysis. This article introduces tools designed to bridge this gap, translating complex mathematical abstractions into efficient, accessible software solutions for researchers.

Background: Subgroup analyses and meta-regression are commonly used to investigate heterogeneity in diagnostic test accuracy (DTA) meta-analyses (MA), but adherence to methodological guidance is unclear. This methodological review summarizes investigations of heterogeneity (IoH) in DTA-MAs, examining their frequency, characteristics, and alignment with recommendations. Methods: We included DTA-MAs published in 2024 reporting at least one pair of summary sensitivity and specificity. Non-DTA reviews, narrative syntheses, studies reporting only alternative measures, and overviews of systematic reviews were excluded. MEDLINE (via Ovid) was searched for English-language publications, with the final search in January 2025. Results: From 403 records, the most recent 100 DTA-MAs were included, each contributing one index test. IoH were reported in 61 analyses. The number of primary studies was positively associated with conducting an investigation (OR 1.66; p = 0.008). Subgroup analyses were used in 35/61 (57%), while 26/61 (43%) applied meta-regression alone or with subgroup analyses. Subgroup analyses examined fewer variables than meta-regression (p < 0.001). Among 44/61 (72%) analyses with sufficient detail to identify a statistical model, the bivariate model was used in 28/44 (64%), univariate random-effects models in 14/44 (32%), and the HSROC model in 5/44 (11%). Formal tests for subgroup differences were reported in 37/61 (61%). Protocols were available for 43/61 (70%) analyses, of which 19/43 (44%) fully prespecified IoH. Discussion: IoH were common and more likely when more primary studies were available, although individual subgroups were often supported by limited data. Reporting of statistical models and model choice was frequently unclear. Greater prespecification of IoH in protocols may reduce spurious findings and improve transparency in diagnostic research.

Nonuniform exponential dichotomy serves as an important characteristic of nonuniform hyperbolicity, while admissibility of function classes is often used to characterize nonuniform exponential dichotomy. In this paper, we investigate the preservation of nonuniform exponential dichotomy under certain nonlocal perturbations. By utilizing the concept of admissibility of a pair of function classes, we establish sufficient conditions to ensure that the dichotomy results are consistent with those in the homogeneous situation. These results need to satisfy a smallness integrability condition.

Agile software development evolves so rapidly that research struggles to remain timely and transferable - an issue heightened by the swift adoption of generative AI and agentic tools. Earlier discussions highlight theory and time gaps, leading to results that often lack clear reuse conditions or arrive too late for practical decisions. This paper introduces a project-based, AI-integrated agile education platform as a collaborative research environment, positioned between controlled studies and real-world industry. The platform enables rapid inquiry through sprint rhythms, quality gates, and genuine stakeholder involvement. We present a framework specifying iteration structures, recurring events, and quality gates for AI-assisted engineering artifacts. Early results from several semesters - covering project pipeline, cohort growth, and stakeholder participation - show the platform's potential to generate practice-relevant evidence efficiently and with reusable context. Finally, we outline future steps to enhance governance and evidence capture.

In statistics, forecast uncertainty is often quantified using a specified statistical model, though such approaches may be vulnerable to model misspecification, selection bias, and limited finite-sample validity. While bootstrapping can potentially mitigate some of these concerns, it is often computationally demanding. Instead, we take a model-agnostic and distribution-free approach, namely conformal prediction, to construct prediction intervals in high-dimensional functional time series. Among a rich family of conformal prediction methods, we study split and sequential conformal prediction. In split conformal prediction, the data are divided into training, validation, and test sets, where the validation set is used to select optimal tuning parameters by calibrating empirical coverage probabilities to match nominal levels; after this, prediction intervals are constructed for the test set, and their accuracy is evaluated. In contrast, sequential conformal prediction removes the need for a validation set by updating predictive quantiles sequentially via an autoregressive process. Using subnational age-specific log-mortality data from Japan and Canada, we compare the finite-sample forecast performance of these two conformal methods using empirical coverage probability and the mean interval score.

Nonreciprocal structures play an important role in optical physics and applications. Conventional approaches for designing nonreciprocal optical structures rely heavily on extensive numerical simulation and parameter tuning, leading to high computational cost and low efficiency. Here, we apply deep learning to the design of nonreciprocal multilayer photonic structures. Three neural-network models-a forward neural network (FNN), an inverse design network (IDN), and a variational autoencoder (VAE)-are employed to learn the complex mapping between structural/material parameters and nonreciprocal spectral characteristics. We show that the FNN can rapidly and accurately predict the nonreciprocal electromagnetic response of a given structure, while the IDN can directly generate suitable structural parameters for target spectral responses. Both approaches substantially reduce computational cost and design time while improving nonreciprocal performance. Furthermore, the VAE can generate band-limited inverse design under practical performance constraints, facilitating efficient exploration of multiple feasible structures that meet different threshold requirements within specified frequency bands. Our work highlights the potential of deep learning for the advanced design of nonreciprocal optical structures and devices.

Trigger waves are self-regenerating propagating fronts that emerge from the coupling of nonlinear reaction kinetics and diffusion. In cells, trigger waves coordinate large-scale processes such as mitotic entry and stress responses. Although the roles of circuit topology and feedback architecture in generating bistability are well established, how nonequilibrium energetic driving shapes wave propagation is less well understood. Here, we employ a thermodynamically consistent reaction--diffusion framework to investigate trigger-wave dynamics in ATP-dependent phosphorylation--dephosphorylation systems. We first recapitulate general expressions for trigger-wave speed in the bistable regime and analyze curvature-induced corrections that determine the minimum critical nucleus required for sustained propagation in higher dimensions. We then apply this framework to two representative systems, treating ATP concentration and the nonequilibrium parameter $γ= [ATP]/(K_{\mathrm{eq}}[ADP][P_i])$ as independent control variables to examine how energetic driving regulates wave propagation. Our results show that ATP and $γ$ not only modulate wave speed, but can also reverse the direction of propagation and reshape the parameter regime supporting trigger waves. The critical excitation radius also depends on both ATP concentration and phosphorylation free energy. These findings identify the intracellular energetic state as a regulator of trigger-wave behavior, linking metabolic conditions to the spatial dynamics of wave propagation. More broadly, this framework connects classical reaction--diffusion theory with ATP-driven biochemical regulation and provides a general perspective on related energy-dependent cellular decision-making processes.

We investigate the interplay between phase lag and adaptive learning rules in a network of identical pendulum oscillators, where the coupling strengths evolve dynamically in response to the oscillators' states. Specifically, we examine two biologically inspired adaptation mechanisms, Hebbian and spike-timing-dependent plasticity (STDP), and their influence on the emergence of collective dynamical patterns. Under Hebbian adaptation, the network exhibits a wide range of organized behaviors, including two-cluster, solitary, multi-antipodal, and chimera states. In contrast, STDP coupling induces splay, splay-cluster, and splay-chimera configurations. Importantly, we find that the solitary state arises spontaneously in this adaptive network without requiring delays, nonlocal coupling, or external perturbations; instead, it is induced purely by variations in the phase-lag parameter. To the best of our knowledge, such delay-free and symmetry-preserving emergence of solitary behavior has not been reported previously in adaptive oscillator systems. To systematically characterize the resulting dynamical transitions, we employ two complementary incoherence measures based on the local standard deviation of (i) time-averaged frequencies and (ii) instantaneous phases across spatial bins, enabling the construction of detailed two-parameter phase diagrams. Analytical stability analysis of the two-cluster state shows strong agreement with numerical simulations, revealing regions of pronounced multistability. These findings establish adaptive pendulum networks as a minimal yet powerful framework for studying self-organized synchronization, chimera formation, and multistable transitions driven by diverse adaptation mechanisms.

Phase-change materials (PCMs)-based integrated photonic memory offers a viable pathway for the development of neuromorphic computing chip. The sizable optical contrast in the telecom band between amorphous and crystalline phases of PCM, in particular, Ge2Sb2Te5 (GST), is used for multilevel programming. However, the high extinction coefficient k of crystalline GST leads to high optical loss, posing a serious challenge for scaling up the device array for practical use. In this work, we focus on the atomic understanding and application of the so-called low-loss PCM, Sb2Se3, through multiscale simulations. First, we elucidate the bonding origin of the wavelength dependent optical properties of amorphous and crystalline Sb2Se3 via ab initio calculations. Given the suppressed k in the telecom band, we design a programable mode converter (PMC) waveguide device that utilizes only the contrast in refractive index n between amorphous and crystalline Sb2Se3 to encode multiple optical levels per waveguide device. The finite-difference time-domain simulations show that a single PMC device can achieve 5-bit programming precision (32 levels) via direct laser writing, and the photonic tensor core formed by the PMC array could possibly be scaled to 128*128. Finally, a thorough comparison between low-loss PCM and conventional PCM is provided.

Trilinear mappings appear naturally when performing spatial isogeometric discretizations of degree $p = 1$. Among them, birational maps are characterized by the property that both the mapping and the associated inverse map are rational and thus easy to evaluate. These mappings have recently been analyzed, and a classification over the field of complex numbers has been obtained. The parameter lines of trilinear mappings form three two-parameter families of straight lines, and thus it is promising to analyze these mappings with the tools provided by the field of line geometry, which is a classical branch of higher geometry. Indeed, in the birational case, the three families of lines form space-filling line congruences associated with rational mappings that can be used to parameterize certain algebraic surfaces. Moreover, the three systems are closely related. In this paper, we present a classification, over the field of real numbers, of the parametric line congruences arising from trilinear birational maps.

Efficient optomechanical cooling typically requires high photon occupancy to maximize cooling power, a constraint that generally limits the degree of coherent quantum control available in the few-photon regime. Here, we investigate this trade-off by considering a strongly nonlinear cavity operated as a discrete quantum system. In the weak-coupling limit, we derive a general connection between the optomechanical damping rate and the cavity's dressed-state manifold. This framework reveals that the damping rate (determined by the population imbalance across dressed states) is directly tunable via the coherent manipulation tools which are standard in circuit quantum electrodynamics. We illustrate this framework using a Josephson photonics architecture, where a dc-biased junction induces a photon blockade that truncates the cavity to an $N$-level system. By sacrificing raw cooling (or heating) power, this platform enables full quantum mechanical control over optomechanical properties, offering a versatile avenue for the quantum manipulation of mechanical modes.

While research on AI agents focuses on enabling them to operate graphical user interfaces, the most effective and widely adopted agent tools in practice are terminal-based. We argue that this convergence is not coincidental. It reflects three design properties central to effective human-AI-UI collaboration: representational compatibility between agent and interface, transparency of agent actions within the interaction medium, and low barriers to entry for human participants. We ground each property in established HCI theory, show how terminal-based tools satisfy them by default, and argue that any modality, including graphical and spatial interfaces, must be deliberately engineered to achieve them. Rather than a legacy artifact, the terminal serves as a design exemplar whose properties any agent-facing modality must replicate.

Self-testing--the attractive possibility to infer the underlying physics of a quantum device in a black-box scenario--has gained increased traction in recent years, with applications to device-independent quantum information processing. Thus far, self-testing has been done under the assumption that the settings for the requisite Bell test are chosen freely and independently of the device tested in the experiment. That is, the random number generator used to generate the settings has been assumed to have no correlations with the device tested. Here, we extend self-testing protocols beyond the independence assumption. Surprisingly, we show that all pure bipartite partially entangled states can be self-tested provided that the random number generator obeys a residual randomness constraint strictly weaker than the independence assumption. This in itself provides a semi-device-independent certification of independence between the randomness source and the device.