We establish quantum uncloneable encryption with unconditional security, preventing two non-communicating adversaries from simultaneously decrypting a single ciphertext $-$ even when both are given the key. Our construction achieves security that approaches the ideal limit at a rate that is exponentially small in the security parameter, without employing any assumptions. Our proof invokes unitary invariance of the shared entangled state and simplifies the adversarial strategies by enforcing this symmetry. Crucially, it then rules out the sender being highly correlated with two non-communicating adversaries at once by an approximation property that we develop, for such unitarily invariant states, which yields a near-optimal bound on the probability of cloning. Consequently, no coordinated strategy beats random guessing of the encrypted bit, establishing unconditional uncloneability. This reveals the existence of an uncloneable bit in Nature and delineates a fundamental, physically enforced cryptographic primitive unavailable in classical settings.

The Kuramoto model is the paradigmatic model to study synchronization in coupled oscillator systems. In its classical formulation, the oscillators move on the unit circle, each characterized by a scalar phase and a natural frequency, by interacting through a sinusoidal coupling. In this work, we propose a d-dimensional generalization in which oscillators are represented as unit vectors on the (d-1)-sphere and interact through a matrix-weighted network (MWN), a recently introduced framework where links are endowed with a matrix weight instead of a scalar one. We derive necessary conditions for global synchronization via a Master Stability Function approach: the existence of a synchronous solution requires identical frequency matrices across nodes and, in the MWN case, a coherence condition on the network structure. Through a suitable change of variables, the stability analysis reduces the full Nd-dimensional problem to a family of d-dimensional eigenvalue problems, each one parametrized by the eigenvalue of a suitable scalar weighted Laplacian, showing that the synchronous solution is locally stable for any positive coupling strength K on any connected network. Analytical results are complemented by numerical simulations.

We present a systematic investigation of native point defects and oxygen impurities in GaAs using hybrid functional calculations. Defects are characterized by their structural, electronic, and optical properties. Under thermodynamic equilibrium, dominant native defects are Ga antisites (Ga$_{\rm As}$), As antisites (As$_{\rm Ga}$), and/or Ga vacancies ($V_{\rm Ga}$) in which As$_{\rm Ga}$ and $V_{\rm Ga}$ are charge-compensating defects under As-rich conditions. On the basis of the defect transition levels, the isolated As$_{\rm Ga}$ can be identified with the $EL2$ center reported in experiments. The defect, however, has a negligible nonradiative electron capture cross section and thus cannot be the ``main electron trap'' as commonly believed. We find that GaAs can have multiple O-related defect centers, especially when prepared under As-rich conditions. The quasi-substitutional O impurity (O$_{\rm As}$) and its complex with two As$_{\rm Ga}$ defects (O$_{\rm As}$-2As$_{\rm Ga}$) both have a metastable and paramagnetic middle (neutral) charge state; however, only the latter can be identified with the experimentally observed Ga--O--Ga or ``OX'' center. These two defects have large nonradiative electron capture cross sections and can be effective carrier traps or recombination centers, which has important implications for materials design.

Coded caching (CC) can transform cache memory at network devices into an active communication resource and significantly enhance the Degrees of Freedom (DoF) of multi-input multi-output (MIMO) systems by jointly exploiting global caching and spatial multiplexing gains. Existing linearly decodable MIMO-CC designs, however, largely rely on symmetric stream allocation, where all scheduled users receive the same number of streams, which induces coarse DoF granularity and may leave spatial dimensions unused. This letter studies one-shot linearly decodable MIMO-CC delivery with arbitrary per-user stream allocations. We derive a sufficient stream-count decodability condition, expressed through per-user stream counts and multicast-codeword multiplicities, that generalizes the symmetric common-stream feasibility rule. Building on this condition, we develop a greedy multicast scheduling procedure with certified linear decodability, which redistributes coded multicast messages across transmission intervals to realize asymmetric stream allocations. Numerical results show that the proposed scheduler fills DoF-granularity gaps and improves finite-SNR symmetric rates over the state of the art.

Context: Open Source Software (OSS) is a crucial component of over 90\% of digital infrastructure underpinning industry and public digital services, facilitating collaborative software development and dissemination. Its significance in the European public sector has been emphasised through various Ministerial Declarations, highlighting its potential to accelerate digitalisation, transform businesses, and foster a digitally skilled population. Research Aim: This study aims to explore how the adoption, development, and collaboration on OSS can be enabled through organisational support functions or centres of competency, also known as Open Source Programme Offices (OSPOs) within Public Sector Organisations (PSOs) in the European Union, Norway, Liechtenstein, and Iceland. Methodology: A qualitative research approach was adopted, involving an interview survey of 18 OSPO representatives across 16 cases of public-sector OSPOs. These cases were cross-analysed and categorised into six OSPO archetypes. The findings were validated and enriched through two follow-up focus groups that included earlier interviewees and additional experts. Results: The study identified six distinct OSPO archetypes, providing insights into their organisational structures, responsibilities, and contributions to OSS adoption. The archetypes, along with policy recommendations, offer guidance on how PSOs can design their own OSPOs, taking into account their specific context, resources, and policy goals. Conclusions: The findings enhance the understanding of OSPOs as strategic endeavours aimed at promoting OSS adoption. The study offers practical guidance for PSOs and policymakers on leveraging OSS to achieve strategic objectives, foster digital sovereignty, drive economic growth, and improve the interoperability and quality of digital services.

We define a finite-volume lattice-QCD density-matrix observable for the vacuum-subtracted spatial R'enyi response of a source-sink-prepared, momentum-projected hadron. At fixed regulator, integer R'enyi index $n>1$, spatial region $B_R$, spin projection, gauge-theory cut prescription $\mathcal{C}$, and after the usual double-sided source-sink projection, the central result is an exact source-sink replica identity: the response is obtained from the logarithm of a replicated hadron correlator on the cut geometry normalized by the corresponding power of the ordinary one-sheet correlator. This identity makes the natural first numerical target the two-sheet $n=2$ measurement of the replicated source-sink correlator ratio, together with a finite-volume test of whether the response scales as $L^{-3}$ at fixed physical $R$. The exponent is a lattice output to be tested, not an input theorem for the nonlinear R'enyi functional. The construction is prescription-defined in gauge theory, and full QCD requires the replicated sea-quark determinant and valence contractions on the replicated cut graph; quenched and partially quenched calculations are therefore pilots. Large-$N_c$ two-dimensional QCD provides an interacting benchmark in which the matched one-meson response is suppressed by the inverse spatial volume, with the short-interval coefficient controlled by light-front PDF moments.

We demonstrate a turbulence mechanism that reconciles high plasma confinement with efficient heat exhaust -- a central challenge for fusion energy. Global two-fluid turbulence simulations of the reactor-relevant Quasicontinuous Exhaust regime on the ASDEX Upgrade tokamak reveal that a quasicoherent mode drives mesoscopic oscillations of the pedestal boundary across the magnetic separatrix and ejects ballistic filaments (blobs), reproducing both the mean profiles and turbulent fluctuations observed experimentally. This behavior arises from a synergistic interplay between kinetic ballooning modes and resistive X-point modes straddling the separatrix. These first-principles results place extrapolations to future fusion reactors on a firm physical footing.

We revisit the problem of bounding the expected supremum of a canonical Gaussian process indexed by a convex set $T \subset \mathbf{R}^d$. We develop two decompositions for the Gaussian width, based on the geometry of the index set. The first decomposition involves metric projections of Gaussians onto rescaled copies of $T$. The second involves fixed points arising from a quadratically penalized variant of the local width. Neither decomposition directly invokes generic chaining constructions. Our results make use of recent work in geometric analysis and Gaussian processes. The work of Chatterjee [Ann. Statist., 2014] characterizes the behavior of the metric projection of a Gaussian random vector onto rescaled copies of $T$ with a variational problem involving localized Gaussian widths. We use these bounds to develop decompositions of the Gaussian width using the local metric structure of $T$. Second, we leverage the work of Vitale [Ann. Probab., 1996] to form a connection between the Wills functional (and hence the intrinsic volumes of $T$) and the first terms that appear in our decompositions. Finally, invoking recent work by Mourtada [J. Eur. Math. Soc., 2025] on the logarithm of the Wills functional, we show that the width is controlled by a single, ''peak index'' of the intrinsic volumes. In the worst case, our bound recovers a local form of the classical Dudley integral.

We give an abstract framework to transfer generalized amalgamation from a simple theory to another, and we apply it to theories of bounded PAC structures, of fields with operators and of lovely pairs. We show in particular that bounded pseudo-algebraically closed fields have generalized amalgamation, regardless of their imperfection degree.

We search for the weak decays $ψ(2S)\to D_s^-π^+ + c.c.$ and $ψ(2S)\to D_s^-ρ^+ + c.c.$ for the first time. The search is based on $(2712.4\pm14.3)\times 10^6$ events containing the charmonium state $ψ(2S)$ collected at the center-of-mass energy $\sqrt{s}=3.686\ \rm{GeV}$ with the BESIII detector. This search offers a unique opportunity to test the Standard Model and search for new physics. Since no signal excess above the background is observed, the upper limits on the branching fractions at the 90\% confidence level are set to be $1.4\times 10^{-6}$ and $7.0\times 10^{-6}$ for $ψ(2S)\to D_s^-π^+ + c.c.$ and $ψ(2S)\to D_s^-ρ^+ + c.c.$, respectively.

High-quality dielectric films are essential for fabricating advanced electronic devices, but their direct deposition often degrades the films and their underlying interfaces, which compromises device performance, especially on sensitive or low-adhesion surfaces. To overcome these limitations, film transfer methods enable the integration of high-quality dielectric films onto such surfaces without damaging the underlying interfaces. However, existing transfer methods have predominantly focused on high-dielectric-constant (high-$κ$) materials, leaving a critical gap for transferable, high-quality low-$κ$ alternatives, which are required for enabling low-power and high-speed electronics. Herein, we address this need by demonstrating a method to integrate freestanding low-$κ$ fluoropolymer dielectric films with smooth surface morphology onto diverse substrates, including low-adhesion surfaces like hydrogen-terminated diamond. The transferred films revealed high breakdown fields of ${8.0}\pm{1.2}$ MV cm$^{-1}$, with leakage current density remaining typically below ${10}^{-7}$ A cm$^{-2}$ before the breakdown. The incorporation of these fluoropolymer films as gate dielectrics in p-channel hydrogen-terminated diamond field-effect transistors resulted in transfer and output characteristics with negligible hysteresis, high channel mobility (${\approx}400$ cm$^{2}$V$^{-1}$s$^{-1}$) and a low interface trap density (${\le}3{\times}10^{11}$ cm$^{-2}$eV$^{-1}$). These findings highlight the versatility of the transfer method and position freestanding fluoropolymers as a promising platform for forming high-quality dielectric/semiconductor interfaces for advanced electronics.

Measuring the phase of light is fundamental to optical imaging, sensing, and signal processing applications. Conventional optical phase measurements rely on multipath configurations, bulky interferometric setups, and computationally intensive data pipelines, limiting scalability, robustness, and practicality. We introduce a technique that allows for reference-free in-line phase retrieval of abrupt phase transitions in optical pulses directly from spectral measurements. Theory, simulations, and experiments concurrently explain the effect as a result of a Kerr-mediated interference between a projected linear wave component and the high-intensity residual of the phase-altered pulse. Utilizing this phenomenon, we demonstrate algorithm-free phase measurements of up to π/385 sensitivity and shot-to-shot signal prominence at 13 dB above noise at 80 MHz rates and 50 pJ pulse energies. This approach offers new paths toward the use of femtosecond pulses as broadband data carriers for optical communications, information processing, and direct high-throughput phase imaging.

For $p>1$, we introduce the cutoff Sobolev inequality on general metric measure spaces, and prove that there exists a metric measure space endowed with a $p$-energy that satisfies the chain condition, the volume regular condition with respect to a doubling scaling function $Φ$, and that both the Poincaré inequality and the the cutoff Sobolev inequality with respect to a doubling scaling function $Ψ$ hold if and only if $$\frac{1}{C}\left(\frac{R}{r}\right)^p\le\frac{Ψ(R)}{Ψ(r)}\le C\left(\frac{R}{r}\right)^{p-1}\frac{Φ(R)}{Φ(r)}\text{ for any }r\le R.$$ In particular, given any pair of doubling functions $Φ$ and $Ψ$ satisfying the above inequality, we construct a metric measure space endowed with a $p$-energy on which all the above conditions are satisfied. As a direct corollary, we prove that there exists a metric measure space which is $d_h$-Ahlfors regular and has $p$-walk dimension $β_p$ if and only if $$p\leβ_p\le d_h+(p-1).$$ Our proof builds on the Laakso-type space theory, which was recently developed by Murugan [Ann. Probab., to appear].

We show that for any closed surface $S$ there is an explict neighborhood $V$ of the fuchsian locus in quasifuchsian space $\mathsf{QF}(S)$ such that for every representation $ρ\in V$ which is not fuchsian, there is a proper affine action on $\mathfrak{sl}(2,\mathbb{C})$ with linear part $\mathsf{Ad}(ρ)$. We further show that there is a larger neighborhood $U$ of the Fuchsian locus so that every critical point of the entropy function in $U$ lies on the Fuchsian locus.

Deep Brain Stimulation (DBS) is an effective treatment for neurological disorders but requires invasive surgery. This work presents a method for non-invasive DBS, based on microwave focusing of amplitude-modulated electric fields using an external antenna array of magnetic point dipoles. The proposed method combines iterative time reversal (iTR) and temporal interference (TI) optimization to jointly address electromagnetic field focusing and physiologically relevant neural stimulation. Antenna element positions, orientations, frequencies, amplitudes, and phases are optimized to localize stimulation within a target region. The method is evaluated in an anatomically realistic voxel head model with heterogeneous and lossy tissue properties. Systematic numerical studies, including perturbation analysis and statistical evaluation, demonstrate consistent spatial localization and robustness across all reported configurations. Safety is quantified using specific absorption rate (SAR), ensuring compliance with exposure limits. The study further provides insight into the influence of key parameters on field behavior and the associated trade-offs between focality, penetration, and safety in physiologically relevant stimulation. To the authors knowledge, this is the first study to combine iTR and TI optimization for microwave-based DBS in a realistic voxel head model, establishing a promising framework for safe non-invasive deep brain stimulation.

Nodal-line semimetals (NLSs) can display unconventional quasiparticle dynamics and charge transport properties due to their extended band degeneracy and the peculiar geometry of their Fermi surface. We consider electron-acoustic phonon scattering as the dominant relaxation mechanism and compute the quasiparticle decay rate and dc conductivity by solving the linearized semiclassical Boltzmann equation in a minimal model of a doped circular NLS. We find that the toroidal geometry of the Fermi surface gives rise to two parametrically distinct Bloch-Grüneisen temperatures, associated with momentum transfers along the poloidal and toroidal directions, respectively. As a result, an intermediate temperature window opens between these two scales, in which the decay rate follows $Γ\propto T^2$, while the conductivity follows $σ\propto T^{-2}$. We also obtain the low- and high-temperature asymptotic behaviors, and discuss implications for ARPES and transport measurements in candidate NLS materials.

This paper presents VaN3Twin-the first open-source, full-stack Network Digital Twin (NDT) framework for simulating the coexistence of multiple Vehicle-to-Everything (V2X) communication technologies with accurate physical-layer modeling via ray tracing. VaN3Twin extends the ms-van3t simulator by integrating Sionna Ray Tracer (RT) in the loop, enabling high-fidelity representation of wireless propagation, including diverse Line-of-Sight (LoS) conditions with focus on LoS blockage due to other vehicles' meshes, Doppler effect, and site-dependent effects-e.g., scattering and diffraction. Unlike conventional simulation tools, the proposed framework supports realistic coexistence analysis across DSRC and C-V2X technologies operating over shared spectrum. A dedicated interference tracking module captures cross-technology interference at the time-frequency resource block level and enhances signal-to-interference-plus-noise ratio (SINR) estimation by eliminating artifacts such as the bimodal behavior induced by separate LoS/NLoS propagation models. Compared to field measurements, VaN3Twin reduces application-layer disagreement by 50% in rural and over 70% in urban environments with respect to current state-of-the-art simulation tools, demonstrating its value for scalable and accurate digital twin-based V2X coexistence simulation.

Starting from a generalized direct category $R$, we construct an absolutely dense functor $\mathbf{D}_r \to R$ with domain a strict direct category. Given any tribe $\mathcal{T}$, we leverage this construction to provide a tribe structure on a subcategory of fibrant diagrams in $\mathcal{T}^{R^{op}}$, assuming some finiteness condition on $R$.

We introduce the Parabolic Mellin Transform (PMT), defined by ${P}_σ[f](z)=\int_{-\infty}^{\infty}w^{2z}f(w^2)dt$, where $w=σ+it$ and $σ>0$. Under the substitution $u=w^2$, the vertical line $\operatorname{Re}(w)=σ$ is mapped to the parabolic contour $C_σ$ in the $u$-plane. For the Gaussian kernel, the PMT yields $\int_{-\infty}^{\infty}w^{2z}e^{w^2}dt=π/Γ(\tfrac{1}{2}-z)=\cos(πz)Γ(z+\tfrac{1}{2})$, a parabolic-contour form of the classical Hankel representation for the reciprocal Gamma function. The advantage of this parametrization is that the contour integral becomes a Gaussian-damped vertical-line integral. We develop scaling, differentiation, and Dirichlet-composition identities for the PMT and use them to derive integral representations of the Hurwitz zeta, Riemann zeta, and Dirichlet eta functions. The framework provides a unified transform dictionary for Gamma-type and zeta-type special functions and yields equivalent reformulations of the Riemann hypothesis and the Lindelöf hypothesis in terms of zeros and growth of parabolic-contour integrals.

We present results from imaging observations of three quadruply lensed quasars by Hubble Space Telescope (HST) and James Webb Space Telescope (JWST) at redshifts $z = 2.550$, 2.975, and 1.500. We model our targets assuming a singular isothermal ellipsoid mass profile and an elliptical SÃ\c{opyright}rsic profile for the lensing galaxies, and reconstruct the geometric configuration of each system with measured Einstein radii of 0.44$'$, 0.58$'$, and 0.49$'$. While no spectroscopic measurements are available for the lenses, we constrain the redshift of each lens to $0.5 < z < 1.2$, $1.0 < z < 1.5$, and $0.4 < z < 0.9$. For all three lenses, the best-fit light model yield a typical de Vaucouleurs $n_{\rm S\acute{e}rsic} \sim 4$ profile and an effective radius $R_e$ around $\sim 1.5 - 3.5$ kpc. We accordingly classify the three lenses as early-type galaxies at an intermediate to high redshift, a common type for strong lensing galaxies. Compared to other known quadruple lenses, the lensing galaxies in this work are at the lower end of the distribution of Einstein radii and upper end of the distribution of the lens redshifts. They represent an interesting quadrant of subarcsecond-separation lenses in the population of single-galaxy strong lensing which have been largely unexplored yet and will be great targets of interest in upcoming high-resolution lensing surveys.

We compute the canonical, or brick-wall, entropy of a massless scalar field in a quantum black hole model whose strong field exterior is described phenomenologically by the static $q$-metric, also known as the Zipoy-Voorhees metric. This geometry is an exact vacuum deformation of Schwarzschild with a small quadrupolar distortion parameter, $q$. Using WKB counting of trapped near horizon cavity modes, we show that this deformation changes the near horizon density of states so that the usual Schwarzschild brick-wall ultraviolet divergence is self-regularized, eliminating the need for an ad hoc proper distance cutoff within the perturbative regime studied here. Treating the Hawking temperature and Bekenstein-Hawking entropy of a Schwarzschild black hole of the same mass as external thermodynamic benchmarks, we obtain an analytic entropy-motivated deformation scale, $|q|\sim 0.2$, across the stellar-to-supermassive black hole mass range. Through a stationary extension, this scale maps phenomenologically onto percent-to-tens-of-percent violations of the Kerr multipole relations, providing observational targets for ngEHT imaging, LISA extreme mass ratio inspirals, and third generation ground based gravitational wave tests.

X-ray reflection spectroscopy is a powerful tool for testing the Kerr hypothesis and probing the strong gravity regime around accreting black holes. Most tests of General Relativity (GR) assume that the spacetime around a black hole is circular, meaning the metric possesses a specific symmetry structure common to the Kerr solution. However, deviations from circularity are predicted by various modified gravity theories and non-vacuum General Relativity solutions. In this work, we test a specific non-circular metric constructed based on a locality principle, where the deviation from the Kerr spacetime is driven by the local spacetime curvature. To accurately model the reflection spectrum in this background, we implement a relativistic ray-tracing code in horizon-penetrating (ingoing Kerr) coordinates, which are favored for their ability to avoid introducing curvature singularities at the horizon in non-circular spacetimes. We apply this model to the high-quality \textit{NuSTAR} spectrum of the Galactic black hole binary EXO 1846--031. Our spectral analysis reveals a source with a high inclination angle ($ι\approx 76^{\circ}$) and a near-extremal spin parameter ($a_* \approx 0.98$). While we identify a global minimum in the parameter space suggesting a non-zero deformation ($\ell_{\mathrm{NP}} \approx 0.12$), the 99\% confidence interval fully encompasses the Kerr limit ($\ell_{\mathrm{NP}}=0$). We conclude that the current X-ray reflection data for EXO 1846--031 are consistent with the Kerr hypothesis. This work demonstrates the feasibility of using X-ray reflection spectroscopy to constrain non-circular metrics and establishes a framework for future tests.

We present the discovery of TIC-65910228 b / NGTS-38 b, a giant exoplanet with a radius of $1.081\pm0.047$ R$_\text{J}$ and a mass of $4.78_{-0.37}^{+0.39}$ M$_\text{J}$ on a long-period ($180.52797\pm0.00036$ day), moderately eccentric ($e=0.3086\pm0.010$) orbit transiting a bright (V=$10.230\pm0.020$ mag) metal rich ([Fe/H]=$0.33\pm0.09$, 'dex') F6V-F7V type host star. The planet was initially detected from a single transit in TESS Sector 33. A photometric monitoring campaign of 228 nights with NGTS detected a transit egress of the planet, which together with spectroscopic radial velocity monitoring with CORALIE and HARPS identified an orbital period of ~180.5,d. These radial velocity measurements also showed the mass of the companion to be planetary. Additional transit observations coordinated by the TESS follow-up observing program allowed further confirmation and refinement of this period. With its relatively cool equilibrium temperature of $457\pm11$ K, NGTS-38 b joins a small but growing population of well characterised transiting warm-Jupiters and has one of the longest periods of any discovered to date. The target is situated in the LOPS2 field of the upcoming PLATO mission which will allow for greater refinement of the system parameters and potential for the discovery of additional companions too small and/or too long-period to be seen by TESS or NGTS. NGTS-38 b's bright host star and wide orbital separation make it an attractive target for further study, including potential measurement of its spin-orbit alignment or targeted exomoon/ring searches.

We provide an explicit realization of the Corner Proposal for Quantum Gravity in the case of spherically symmetric spacetimes in four dimensions, or equivalently, two-dimensional dilaton gravity. We construct coherent states of the Quantum Corner Symmetry group and compute the entanglement entropy relative to these states. We derive the classical corner charges and relate them to operator expectation values in coherent states. For a subset of coherent states that we call classical states, we find that the entanglement entropy exhibits a leading term proportional to the area, recovering the Bekenstein-Hawking area law in the semiclassical limit.

Quantum gravity theories often modify spacetime symmetries. In particular, Lorentz invariance may be violated when approaching the Planck scale. Although the scales at which interactions occur in extensive air showers induced by ultra-high-energy cosmic rays in the atmosphere are many orders of magnitude below the Planck scale, these violations might still be observable. In this work, the fluctuations in the number of muons in the extensive air showers measured at the Pierre Auger Observatory are exploited, for the first time, to constrain Lorentz invariance violations. The bounds derived in the hadronic sector are the strongest ever obtained, and do not rely on assumptions about the mass composition of ultra-high-energy cosmic rays. The fluctuations in the number of muons constitute a new and powerful observable to further explore Lorentz invariance in a region of the parameter space not accessible to other observables.

The aim of this paper is to study categorified algebraic structures and their pseudo- and lax homomorphisms using the framework of Lawvere $2$-theories, and more generally, (enhanced) $2$-dimensional sketches. The key notion we focus on is that of $2$-dimensional commutativity. As one of the main results, we prove that if a Lawvere $2$-theory $\mathbb{T}$ is equipped with such a structure, then the $2$-category $\mathsf{Mod}_l(\mathbb{T},\mathbf{Cat})$ of $\mathbb{T}$-models, lax homomorphisms, and modifications admits a natural structure of a closed $2$-multicategory. From this, we deduce a generalization of Fox's theorem. We also discuss the analogue in the higher setting for Lawvere $(\infty,2)$-theories. As a result of independent interest, we construct a multicategory (or $\infty$-operad) structure on the hom-category $\mathsf{Hom}_{\mathbb{V}}(\mathcal{M},\mathcal{N})$, where $\mathbb{V}$ is a monoidal $(\infty,2)$-category and $\mathcal{M},\mathcal{N}$ are monoids therein.

The temperature sensitivity of a probe in equilibrium can be gauged by its thermal quantum Fisher information (QFI). It is known that probes exhibiting degeneracy in their energy-level structure can achieve larger sensitivities, while probes with a more uniform spectrum may remain sensitive over a broader temperature range. Here, we study the thermometric performance of a multilevel quantum Rabi model in which two well-separated atomic manifolds of near-degenerate levels couple to a single cavity mode. We generalise the standard quantum Rabi treatment in the adiabatic regime to find an approximate closed-form expression for the thermal QFI. We then characterise two complementary limits. On the one hand, a large dark-state manifold (dark-manifold saturation) produces a robust peak in thermal sensitivity due to bright--dark population transfer. Such increase in sensitivity is further maximised at an intermediate light--matter coupling strength. Maximising instead the number of bright states (bright-manifold saturation) generates a broadband thermal response that becomes increasingly stable under random light--matter couplings as the number of levels is increased. The rich spectral structure of our cavity-QED model thus makes it a versatile and sensitive equilibrium thermometer over a broad range of temperatures.

This paper proposes asymmetric perturbation, where only one player's payoff function is perturbed, for solving bilinear saddle-point optimization problems, commonly arising in minimax problems, game theory, and constrained optimization. Symmetric perturbation is known to require decreasing its strength to ensure convergence to a solution, i.e., an equilibrium in the original game, resulting in a slower rate. First, with asymmetric perturbation, we show that, for a sufficiently small perturbation strength, the equilibrium strategy of the asymmetrically perturbed game coincides with an equilibrium strategy of the original unperturbed game. Second, building on this coincidence, we construct a learning algorithm with a linear last-iterate convergence rate. Third, motivated by the fact that the coincidence relies on the perturbation strength being sufficiently small, we also provide a parameter-free variant, retaining the linear rate. Finally, we empirically demonstrate fast convergence toward equilibria in both normal-form and extensive-form games.

This work presents a two-stage physics-informed, data-driven constitutive modeling framework for hyperelastic soft materials undergoing progressive damage and failure. The framework is grounded in the concept of hyperelasticity with energy limiters and employs Gaussian Process Regression (GPR) to separately learn the intact (undamaged) elastic response and damage evolution directly from data. In Stage I, GPR models learn the intact hyperelastic response through volumetric and isochoric response functions (or only the isochoric response under incompressibility), ensuring energetic consistency of the intact response and satisfaction of fundamental principles such as material frame indifference and balance of angular momentum. In Stage II, damage is modeled via a separate GPR model that learns the mapping between the intact strain energy density predicted by Stage I models and a stress-reduction factor governing damage and failure, with monotonicity, non-negativity, and complete-failure constraints enforced through penalty-based optimization to ensure thermodynamic admissibility. Validation on synthetic datasets, including benchmarking against analytical constitutive models and competing data-driven approaches, demonstrates high in-distribution accuracy under uniaxial tension and robust generalization from limited training data to compression and shear modes not used during training. Application to experimental brain tissue data demonstrates the practical applicability of the framework and enables inference of damage evolution and critical failure energy. Overall, the proposed framework combines the physical consistency, interpretability, and generalizability of analytical models with the flexibility, predictive accuracy, and automation of machine learning, offering a powerful approach for modeling failure in soft materials under limited experimental data.

Coupled-cluster (CC) theory and Green's function many-body perturbation theory (MBPT) have long evolved as distinct yet complementary frameworks for describing electronic correlation. While CC methods employ exponential wavefunction parametrizations that guarantee size extensivity and systematic improvability, Green's function approaches such as the $GW$ approximation describe quasiparticle and optical excitations through diagrammatic resummations. Recent analyses have established a formal correspondence between these frameworks: the $GW$ approximation is equivalent to an equation-of-motion (EOM) treatment of the direct-ring coupled-cluster doubles (drCCD) method. Within this context, the extended CC (ECC) ansatz offers a unified framework connecting CC and MBPT. This formulation bridges CC-based and Green's function-based methods, providing novel avenues for incorporating vertex corrections within a CC framework that preserves a sum-over-state representation of the self-energy and lead to potentially systematically improvable Green's function approaches.