Physics-informed neural networks (PINNs) have emerged as a powerful framework for modeling physical systems and solving inverse problems. In such settings, sensors are deployed to capture observable system responses; however, the quality of reconstruction critically depends on how these sensors are selected. Existing sensor selection strategies for PINNs are closely related to active learning and experimental design, typically relying on iterative refinement schemes that sequentially add sensors and retrain the model. While effective under limited data regimes, these approaches incur substantial computational cost due to repeated retraining and primarily focus on selecting subsets of sensors, without providing a global characterization of sensor importance. In this work, we propose FOSSA, a first-order optimality-based sensor selection algorithm for inverse PINNs. Unlike existing methods, FOSSA evaluates sensor importance in a post-training manner, requiring only a single trained PINN. FOSSA assigns importance scores to all candidate sensing locations based on the first-order optimality condition at convergence. To improve robustness, a refinement scheme is further proposed to handle instability in the inverse solver. FOSSA facilitates a global assessment of the contribution of each sensor to reconstruction. We validate the proposed approach on the inverse electrocardiography (ECG) modeling and show that not all sensors contribute positively to predictive performance. Incorporating low-importance sensors can, in fact, degrade reconstruction accuracy. These findings highlight the need for principled sensor importance evaluation and provide a scalable pathway for guiding sensor deployment in physics-informed inverse modeling.

Predictive runtime monitoring asks whether an execution $σ$ of a concurrent program can be used to \emph{soundly predict} the existence of a reordering $ρ$ of $σ$ that satisfies a property $φ$. Its effectiveness and efficiency depend on two factors: (a) the complexity of $φ$, and (b) the expressive power of the reorderings considered. At one extreme, allowing all reorderings induced by \emph{reads-from equivalence} makes predictive monitoring intractable, even for simple properties such as data races. At the other extreme, restricting to commutativity-based reorderings (Mazurkiewicz trace equivalence) yields efficient algorithms for simple properties, but remains intractable for general regular specifications and offers limited predictive power. We address this tradeoff via \emph{parametrization}. We introduce \emph{sliced reorderings} and their generalization, \emph{$k$-sliced reorderings}. Informally, $ρ$ is a $k$-sliced reordering of $σ$ if $σ$ can be partitioned into $k+1$ ordered subsequences whose concatenation yields $ρ$, while preserving program order and reads-from constraints. Our results are twofold. First, $k$-sliced reorderings form a strictly increasing hierarchy that converges to reads-from equivalence as $k$ grows. Second, for any fixed $k$, predictive monitoring modulo $k$-sliced reorderings against any regular specification admits a constant-space streaming algorithm. Together, these results establish $k$-sliced reorderings as a principled alternative to existing equivalences, enabling a uniform parametrized framework where expressive power can be systematically traded off against computational cost.

We study the $q$-deformation of the Demazure product model from arXiv:2407.21653. Consider the longest element $w_0$ in $S_n$ written as a reduced word in simple transpositions. Independently delete each transposition with probability $1-p$ and apply the $q$-Demazure product to the remaining ones. We show that the law of the resulting permutation converges as $n \to \infty$ to a deterministic permuton, which coincides with the $q=0$ case studied in arXiv:2407.21653 for adjusted probability $p'=p(1-q)/(1-qp)$. This resolves Conjecture 1.13 from arXiv:2407.21653 and identifies the limiting permuton explicitly.

We study the classical stability of a non-topological $Z^\prime$ string in the minimal 331 model, which arises from the maximal symmetry breaking pattern of an ${{\mathfrak s}{\mathfrak u}}(6)$ toy model. Two Higgs triplets are introduced according to the emergent global symmetries in the fermionic sector of the ${{\mathfrak s}{\mathfrak u}}(6)$ toy model, which will achieve the sequential symmetry breaking of ${{\mathfrak s}{\mathfrak u}}(3)_c\oplus {{\mathfrak s}{\mathfrak u}}(3)_W \oplus {\mathfrak u}(1)_X\to {{\mathfrak s}{\mathfrak u}}(3)_c\oplus {{\mathfrak s}{\mathfrak u}}(2)_W \oplus {\mathfrak u}(1)_Y$. By analyzing small perturbations around the string background and solving the coupled Helmholtz equations numerically, we find that the string is stable only near the semilocal limit of $\vartheta_S \approx \fracπ{2}$, even when Higgs self-couplings are tuned to minimize instabilities. This suggests that such non-topological strings are unlikely to exist in unified theories based on ${{\mathfrak s}{\mathfrak u}}(N>5)$ Lie algebras.

We study a lightweight ledger protocol for intermittent and noisy networks, motivated by IoT and mobile settings in which partitions are common and full-history verification is impractical. Our design centers on an \emph{operational} notion of \textbf{contextual authentication}: each node decides whether a chain extension is acceptable in its current local context, using checkpoint-first fork choice, a local branch score derived from recent proposer behavior, and an inconsistency-driven \emph{quarantine} signal. To improve recovery after partitions, we combine this acceptance rule with \textbf{adaptive synchronization}, which increases gossip effort only when inconsistency becomes prevalent. We evaluate the protocol with a discrete-event simulator under controlled partitions and two network regimes (clean and noisy). Across 500 seeds at $N=20$, the main result is that quarantine alone does not materially improve agreement or recovery under noisy conditions, whereas increased synchronization (\texttt{Gossip\_only} and \texttt{Both}) substantially improves both final agreement probability and recovery-time tails after partition rejoin. Longer-horizon experiments show that low-synchronization failures are not removed simply by waiting longer, and scaling experiments at $N=50$ and $N=100$ show that parameters that work at small scale do not automatically generalize. These results indicate that, under noisy partition/rejoin dynamics, recovery in the current design is limited primarily by information availability, making synchronization policy a first-class design problem.

The field of high-dimensional quantum photonics involves the use of multimode photonic degrees-of-freedom such as the spatial, temporal, or spectral structure of light to encode multi-level quantum states. Recent years have seen rapid progress in the development of methods to generate, manipulate, and distribute such quantum states of light and their use in a range of quantum technology applications that offer practical advantages over conventional qubit-based approaches. High-dimensional quantum states of light encoded in photonic time-bins, frequency-bins, transverse-spatial modes, waveguide paths, and temporal modes have enabled noise-robust fundamental tests of quantum mechanics, error-resilient and high-capacity quantum communication protocols, andas well as efficient approaches for quantum information processing, to name just a few examples. However, research in this field has progressed fairly independently, with little exchange across different photonic degrees-of-freedom or between experiment and theory and no comprehensive comparison between degrees-of-freedom. This roadmap aims to bridge this gap by surveying progress in each area and identifying shared challenges and opportunities that cut across two or more photonic degrees-of-freedoms. We review early work and state-of-the-art experimental techniques under development for high-dimensional quantum states encoded in single and entangled photons, as well as theoretical tools for their measurement and certification. We outline the main outstanding challenges for theory and each experimental degree-of-freedom, identifying promising future directions of research that may enable these to be overcome. We end by discussing interconnections and shared challenges centered around their distribution, measurement, and manipulation, with a view towards their integration into next-generation quantum technology platforms and applications.

This work constructs a new class of traversable wormhole solutions with a double-throat topology, modeled as a localized perturbation of the Ellis-Bronnikov metric in a string cloud background. Embedding diagrams and the analysis of curvature invariants, including the Kretschmann scalar and the Weyl invariant, illustrate the geometric transition from single to double-throat structures as a function of the perturbation amplitude. By imposing the zero-tidal condition, we derive analytical expressions for the energy density and pressures, showing an asymptotic $r^{-2}$ decay characteristic of a string cloud, endowed with the topology of a global monopole. A key finding is that the energy density converges to a positive constant at the center, with the radial pressure becoming negative. This local behavior provides the repulsive support necessary to inflate the inter-throat region with non-exotic matter, concentrating Null Energy Condition violations to the throat vicinities. These results suggest that multi-throat geometries offer a natural mechanism for localizing exotic matter while maintaining a physical asymptotic background.

We utilize JWST/MIRI IFU observations from the Galaxy Activity, Torus and Outflow Survey (GATOS) to investigate the diverse range of ionized outflow rates of obscured AGN with similar bolometric luminosity and explore potential associations with AGN feedback. We explore spatial correlations between ionized emission potentially associated with fast shocks ([Fe II]5.34μm) and the excitation of H2. We further constrain our investigation to the inner 400 pc (the nuclear and circumnuclear regions r < 200 pc), and estimate the excitation temperature and column density of H2 assuming local thermodynamic equilibrium (LTE) and using the S(1) to S(8) rotational H2 emission lines visible to JWST/MIRI spectroscopy. We report the molecular gas temperature of the deprojected 400 pc nuclear region to correlate with the ionized mass outflow rate. We also observe the stronger degree of spatial correlation between [Fe II]5.34um emission and H2 gas temperature. We observe regions of enhanced [Fe II]5.34μm / [Ar II]6.99μm spatially coincident with the ionization cones of objects with higher ionized outflow rate and [Fe II]5.34μm / [Ar II]6.99μm in the deprojected 400 pc nuclear region to scale positively with both ionized outflow rate and estimated molecular gas temperature. We do not observe the estimated jet cavity power within the central 400 pc to strongly correlate with the ionized mass outflow rate or molecular gas temperature of the nuclear region. We take the preceding observations to suggest a higher degree of interaction between AGN outflows and the circumnuclear disk.

Automated matching engines execute millions of orders per session, yet systematic asymmetries in latency, order size, and market access compound into persistent execution disparities that erode participant trust. We formulate provably fair order matching as a Constrained Markov Decision Process and propose CPO-FOAM (Constrained Policy Optimization with Feedback-Optimized Adaptive Margins). An inner loop computes an analytic trust-region step on the Fisher information manifold; a PID-controlled outer loop dynamically tightens safety margins, suppressing the sawtooth oscillations endemic to Lagrangian methods under non-stationary dynamics. Group fairness (demographic parity, equalized odds) enters the CMDP cost vector while individual Lipschitz fairness is enforced deterministically via spectral normalization. We prove BIBO stability and that the integral term drives steady-state violations to zero. On LOBSTER NASDAQ data across six market regimes, CPO-FOAM recovers 95.9% of unconstrained throughput at 2.5% constraint violation frequency; on crypto-asset LOB data under MEV injection it captures 98.4% of the reward envelope at 3.2% CVF. The method scales sub-linearly to M=8 constraints, settles on-chain within one Ethereum block, and yields a 2.1X reward improvement on Safety-Gymnasium, confirming domain-agnostic generalization.

What is the smallest size of a family of subsets of $[n]$ such that it does not contain an induced copy of $Q_2$ as a poset (known as the \textit{diamond}), but adding a new set creates such a copy? It is easy to see that a maximal chain has this property, and thus the answer is at most $n+1$. Despite the simplicity of the diamond structure, the lower bound stagnated at $\sqrt n$ for quite some time, until recently the authors obtained a linear lower bound. In this paper, we fully solve this question showing that such a family must have size at least $n+1$.

Multiscale topology optimization (TO) of hyperelastic materials remains computationally prohibitive due to the repeated solution of microscale boundary value problems. In this work, we present a concurrent multiscale topology optimization framework that overcomes this limitation by leveraging physics-augmented neural networks (PANNs) as surrogate constitutive models. The proposed approach enables the simultaneous optimization of macroscale material distribution and microscale descriptors, within a unified nonlinear finite strain setting. The surrogate models are constructed using input-specific neural networks (ISNNs) that enforce key physical principles directly within the architecture, including convexity and material symmetry through invariant-based representations and structural tensors. This ensures thermodynamic consistency and numerical stability while accurately representing homogenized anisotropic hyperelastic responses. The trained PANNs replace the microscale boundary value problem and provide efficient evaluations of stresses and consistent tangent moduli using analytical first and second derivatives of the neural network, enabling tractable large-scale multiscale optimization. The framework is demonstrated on representative microstructures exhibiting transversely isotropic, cubic anisotropic, and nearly incompressible isotropic behavior. The results show that the proposed method captures complex multiscale interactions and enables physically meaningful spatial tailoring of material properties, while significantly reducing computational cost compared to classical FE$^2$ approaches. These findings establish PANNs as a powerful tool for high-fidelity multiscale topology optimization of nonlinear anisotropic materials.

Macroporous silicon is widely employed in sensing and optoelectronic applications due to its large internal surface area and adjustable pore structure. However, quantitative correlations between morphology and functionality require accurately characterizing the three dimensional pore network. In this study, we used focused Ga+ ion beam scanning electron microscopy tomography to reconstruct representative volumes of electrochemically etched macroporous silicon layers. We extracted true three dimensional porosity and surface-to-volume ratios and compared them with two-dimensional estimates obtained from SEM images. Our results demonstrate that surface-based porosity systematically underestimates true volumetric porosity. These discrepancies arise from anisotropy, branching, and variability in pore size. Fractal analysis reveals that the pore network has moderate geometric complexity, consistent with electrochemical macropore formation mechanisms. The results highlight the importance of direct 3D characterization for reliable morphological quantification and provide a robust framework for interpreting structural trends in macroporous silicon.

Donald and Owens introduced two link concordance groups with a marked component and showed that they contain the knot concordance group as a direct summand with infinitely generated complements. While not explicitly posed by Donald and Owens, the problem of determining the structure of these complements arises naturally from their work. In this paper, we completely resolve this problem by proving that both complements are isomorphic to $\mathbb{Z}^{\infty} \oplus (\mathbb{Z}/2\mathbb{Z})^{\infty}$. Moreover, we introduce a notion of prime element and establish a unique prime decomposition theorem. This yields a canonical normal form, providing a complete description of the group structure.

We consider the family of generalized Paley graphs (GP-graphs for short) $Γ(k,q) = Cay(\mathbb{F}_q, (\mathbb{F}_q^*)^k)$, with $q=p^m$ and $p$ prime. We characterize all GP-graphs having real spectrum; namely, $Spec(Γ(k,q)) \subset \mathbb{R}$ if and only if $Γ(k,q)$ is undirected. We then study conditions for integrality in the spectrum and give a general method to produce integral GP-graphs through cyclotomic polynomials. Using this, we construct several infinite families of integral GP-graphs. Next, we focus on directed GP-graphs (GP-digraphs). We show that GP-digraphs always have three or more eigenvalues, and then we prove that there is only one kind of GP-digraphs having three different eigenvalues: the oriented Paley graphs $\vec{\mathcal{P}}_q$ or disjoint unions of copies of them, $\vec{\mathcal{P}}_q \cup \cdots \cup \vec{\mathcal{P}}_q$. Then, we show that generically the GP-digraphs have period 1 (equivalently index of imprimitivity 1) except for $Γ(q-1,q)$ with $q$ odd, which is the disjoint union of oriented $p$-cycles, having period $p$. Finally, as an application, we study weak Waring numbers over finite fields through GP-graphs. In particular, we reduce the computation of the weak Waring numbers over finite fields to the computation of classic Waring numbers over finite fields, a result previously obtained by Cochrane and Cipra in 2012 by other means.

Charmonia are often supposed to provide simple hydrogen-like ``atomic'' systems that can be used to obtain insights into heavier-quark QCD. We use continuum Schwinger function methods to analyse this hypothesis in connection with ground-state scalar and pseudoscalar charmonia and find that a more complex picture of these states may be necessary. For instance, considering orbital angular momentum, the $χ_{c0}$ is not a simple $P$-wave system; similarly, the $η_c$ wave function contains more than merely $S$-wave contributions. The distribution amplitudes (DAs) and distribution functions (DFs) of these mesons are also nontrivial. For instance, the $χ_{c0}$ DA is not positive definite: owing to QCD symmetries, it possesses domains of balanced negative and positive support. This feature is also expressed in the $χ_{c0}$ DF, but differences between $χ_{c0}$ and $η_c$ DFs diminish under scale evolution. Notably, the light-front momentum fraction carried by glue is the same in both states: it is 10\% less than the in-pion glue momentum fraction. Whilst experimental confirmation of the predictions herein is unlikely, our results should serve as benchmarks for complementary theory attempts to understand local and global structural features of heavier-quark hadrons.

Neutrino telescopes employ multi-level reconstruction chains, where computationally expensive high-quality reconstructions are applied only to events that survive initial quality cuts based on fast, coarse directional estimates. Currently, event selection between reconstruction levels is source-agnostic, giving no priority to events from directions of known neutrino source candidates. We propose a simple modification to inter-level event selection: preferentially retain events whose early-level reconstruction places them within an angular tolerance of pre-specified candidate source directions from established multi-messenger catalogs, while continuing to subsample remaining events at the baseline rate. Using a realistic two-level detector model with energy-dependent angular resolution, we show that this source-informed selection can improve median point source sensitivity by factors of $\sim 2$--$3$ compared to uniform subsampling, with the improvement depending on the baseline selection efficiency, angular tolerance, and correlation between reconstruction qualities at different levels. For catalogs of $\mathcal{O}(100)$ sources, the additional computational overhead is modest ($\sim 7$--$14\%$). This approach offers a path to substantially enhance the discovery potential of current and future neutrino telescopes without requiring new detector capabilities.

In H-mode tokamak and stellarator plasmas, edge localized modes (ELMs) lead to the expulsion of heat and particles beyond the edge transport barrier. ELMs cause a loss of energy and have the potential to damage the divertor and other plasma facing components, which motivates efforts to forecast such events to work alongside mitigation systems. In this paper, we use the Doppler backscattering (DBS) diagnostic data as input to train a neural network model, adapted from DeepHit [Lee et al., Deephit, AAAI 2018], to forecast the first ELM crash of H-mode discharges in DIII-D. The model takes 50 ms of DBS spectrogram data and predicts the probability of an ELM crash occurring within set time windows. Training and testing on shots found in the DIII-D database, we find the initial results promising, with the model reliably forecasting the first ELM 100 ms before it occurs. This successful proof-of-concept lays a strong foundation for a predictive tool that can deploy ELM-mitigation techniques before an ELM crash occurs. Future work will expand the training set with carefully selected shots and refine the neural network architecture to improve model robustness to noise and data variation.

Symbolic execution detects vulnerabilities with precision, but applying it to large codebases requires harnesses that set up symbolic state, model dependencies, and specify assertions. Writing these harnesses has traditionally been a manual process requiring expert knowledge, which significantly limits the scalability of the technique. We present Static Analysis Informed and LLM-Orchestrated Symbolic Execution (SAILOR), which automates symbolic execution harness construction by combining static analysis with LLM-based synthesis. SAILOR operates in three phases: (1) static analysis identifies candidate vulnerable locations and generates vulnerability specifications; (2) an LLM uses vulnerability specifications and orchestrates harness synthesis by iteratively refining drivers, stubs, and assertions against compiler and symbolic execution feedback; symbolic execution then detects vulnerabilities using the generated harness, and (3) concrete replay validates the symbolic execution results against the unmodified project source. This design combines the scalability of static analysis, the code reasoning of LLMs, the path precision of symbolic execution, and the ground truth produced by concrete execution. We evaluate SAILOR on 10 open-source C/C++ projects totaling 6.8 M lines of code. SAILOR discovers 379 distinct, previously unknown memory-safety vulnerabilities (421 confirmed crashes). The strongest of five baselines we compare SAILOR to (agentic vulnerability detection using Claude Code with full codebase access and unlimited interaction), finds only 12 vulnerabilities. Each phase of SAILOR is critical: Without static analysis targeting confirmed vulnerabilities drop 12.2X; without iterative LLM synthesis zero vulnerabilities are confirmed; and without symbolic execution no approach can detect more than 12 vulnerabilities.

Close quasar pairs are rare products of galaxy mergers in which both supermassive black holes (SMBHs) are actively accreting, offering strong constraints on merger-driven active galactic nuclei (AGN) evolution. Identifying close quasar pairs at $z\gtrsim4$ is challenging due to the declining quasar number density in the early Universe. Here we report the confirmation of a close quasar pair at $z=5.7$, J2037--4537, utilizing high-resolution Atacama Large Millimeter/submillimeter Array (ALMA) observations. The quasar host galaxies exhibit tidal disturbed features in both the far-infrared continuum emission and the {\cii} line emission, ruling out the doubly-imaged lensed quasar scenario. The two quasar hosts are massive $(M_\text{dyn}\gtrsim10^{10}M_\odot)$ and star-forming (SFR $\gtrsim500 M_\odot~ \mathrm{yr^{-1}}$). The confirmation of J2037--4537 puts a lower limit on the quasar pair fraction at $5.5<z<6$, $F_\text{pair}>1.2\%$, which is much higher than the quasar pair fraction at $z\lesssim4$. J2037--4537 is expected to form a gravitationally-bound SMBH binary within $\lesssim2$ Gyr. The elevated quasar pair fraction at $z>5.5$, as indicated by J2037--4537, likely contributes to the high gravitational-wave background reported by recent Pulsar Timing Array experiments.

In this paper, we study closed densely defined unbounded truncated Toeplitz operators on model space, where u is an inner function, that commute with modified compressed shifts. The work also establishes properties related to their invertibility and self-adjointness.

Protecting individual privacy is essential across research domains, from socio-economic surveys to big-tech user data. This need is particularly acute in healthcare, where analyses often involve sensitive patient information. A typical example is comparing treatment efficacy across hospitals or ensuring consistency in diagnostic laboratory calibrations, both requiring privacy-preserving statistical procedures. However, standard equivalence testing procedures for differences in proportions or means, commonly used to assess average equivalence, can inadvertently disclose sensitive information. To address this problem, we develop differentially private equivalence testing procedures that rely on simulation-based calibration, as the finite-sample distribution is analytically intractable. Our approach introduces a unified framework, termed DP-TOST, for conducting differentially private equivalence testing of both means and proportions. Through numerical simulations and real-world applications, we demonstrate that the proposed method maintains type-I error control at the nominal level and achieves power comparable to its non-private counterpart as the privacy budget and/or sample size increases, while ensuring strong privacy guarantees. These findings establish a reliable and practical framework for privacy-preserving equivalence testing in high-stakes fields such as healthcare, among others.

Turbulence in inviscid quantum fluids offers unparalleled access to the universal principles of non-equilibrium dynamics, spanning a vast range of length scales from macroscopic flow down to the individual vortex core. In the zero-temperature limit, the microscopic mechanism by which the turbulent energy cascade terminates in the absence of viscosity remains a foundational challenge in quantum hydrodynamics. While prevailing theoretical descriptions prioritize phonon emission, they fail to account for the strong interatomic correlations that give rise to the roton minimum in superfluid $^4\mathrm{He}$. Here, we report the direct observation of roton emission from a single quantized vortex using a high-quality-factor nanomechanical resonator at 10 mK. We identify a sharp onset of dissipation at a critical velocity, and measure the energy loss per cycle, which corresponds quantitatively to the roton gap energy. Our findings address the long-standing mystery of zero-temperature energy relaxation by establishing roton emission as the primary dissipation channel in strongly correlated quantum liquids.

Spatiotemporal chaos in fluid systems exhibits severe parametric sensitivity, rendering classical adjoint-based optimal control intractable because each operating regime requires recomputing the control law. We address this bottleneck with hyperFastRL, a parameter-conditioned reinforcement learning framework that leverages Hypernetworks to shift from tuning isolated controllers per-regime to learning a unified parametric control manifold. By mapping a physical forcing parameter μ directly to the weights of a spatial feedback policy, the architecture cleanly decouples parametric adaptation from spatial boundary stabilization. To overcome the extreme variance inherent to chaotic reward landscapes, we deploy a pessimistic distributional value estimation over a massively parallel environment ensemble. We evaluate three Hypernetwork functional forms, ranging from residual MLPs to periodic Fourier and Kolmogorov-Arnold (KAN) representations, on the Kuramoto-Sivashinsky equation under varying spatial forcing. All forms achieve robust stabilization. KAN yields the most consistent energy-cascade suppression and tracking across unseen parametrizations, while Fourier networks exhibit worse extrapolation variability. Furthermore, leveraging high-throughput parallelization allows us to intentionally trade a fraction of peak asymptotic reward for a 37% reduction in training wall-clock time, identifying an optimal operating regime for practical deployment in complex, parameter-varying chaotic PDEs.

We develop a theoretical framework for Floquet resonant X-ray scattering, using Floquet theory combined with the ultrashort core-hole lifetime expansion. We obtain a compact expression for the Floquet components of the resonant inelastic X-ray scattering operator, which shows that Floquet X-ray scattering provides direct access to bond and current correlations that do not directly produce charge Bragg peaks in conventional diffraction. Applying this framework to charge-ordered states on the Kagome lattice, we demonstrate that different symmetry-breaking orders exhibit distinct polarization fingerprints in the Floquet Bragg peaks. Moreover, the relative weight of bond and current contributions can be tuned through the drive frequency. These results establish Floquet X-ray scattering as a symmetry-resolved probe of hidden electronic order or fluctuations in quantum materials.

Resonant heavy-neutrino mixing and sterile neutrino oscillations are two prominent mechanisms to realize low-scale leptogenesis, with singlet neutrino masses below TeV energies that could be probed in current and future laboratory experiments. In their minimal settings, both mechanisms require a significant degree of degeneracy in the singlet neutrino masses to compensate for the suppression that results from the small neutrino Yukawa couplings. After further developing the flavour-covariant Kadanoff-Baym formalism, we study in detail a novel dominant mechanism for low-scale leptogenesis which becomes greatly enhanced by resonant thermal lepton-flavour coherences at the two-loop level. This mechanism works successfully for both Dirac and Majorana singlet neutrinos, and it does not rely on whether these singlet neutrinos are quasi-degenerate or not. In particular, it implies that successful low-scale leptogenesis in the type-I seesaw framework can be naturally realised with heavy neutrino masses that could be as low as GeV.

Authoring realistic haptic textures typically requires low-level parameter tuning and repeated trial-and-error, limiting speed, transparency, and creative reach. We present a language-driven authoring system that turns natural-language prompts into multimodal textures: two coordinated haptic channels - sliding vibrations via force/speed-conditioned autoregressive (AR) models and tapping transients - and a text-prompted visual preview from a diffusion model. A shared, language-aligned latent links modalities so a single prompt yields semantically consistent haptic and visual signals; designers can write goals (e.g., "gritty but cushioned surface," "smooth and hard metal surface") and immediately see and feel the result through a 3D haptic device. To verify that the learned latent encodes perceptually meaningful structure, we conduct an anchor-referenced, attribute-wise evaluation for roughness, slipperiness, and hardness. Participant ratings are projected to the interpretable line between two real-material references, revealing consistent trends - asperity effects in roughness, compliance in hardness, and surface-film influence in slipperiness. A human-subject study further indicates coherent cross-modal experience and low effort for prompt-based iteration. The results show that language can serve as a practical control modality for texture authoring: prompts reliably steer material semantics across haptic and visual channels, enabling a prompt-first, designer-oriented workflow that replaces manual parameter tuning with interpretable, text-guided refinement.

We develop a unified geometric framework for dissipative mechanical systems based on uniform $q$-contact manifolds, which provide an extended phase space equipped with multiple contact $1$-forms. Within this setting, we construct both Hamiltonian and Lagrangian formalisms and establish a generalized Noether-type theorem describing the relationship between symmetries and dissipated quantities. We further show that $q$-contact Lagrangian systems admit a genuine variational origin through a generalized Herglotz principle involving multiple action variables. The resulting $q$-contact Euler--Lagrange equations naturally depend on the scalar combination $\sum_{i=1}^q \partial L/\partial z_i$, reflecting the intrinsic structure of uniform $q$-contact geometry. We prove that this variational formulation is fully equivalent to the geometric $q$-contact Hamiltonian dynamics generated by the energy function. Several explicit examples involving multi-parameter dependent dynamics illustrate the effectiveness of the theory and demonstrate its potential to provide geometric insight into complex dissipative systems, thereby extending the scope of classical Lagrangian mechanics beyond symplectic and single-contact structures.

The quantum field theory for a massless scalar field on a two-dimensional non-singular black hole spacetime gives a non-vanishing probability for a particle to tunnel out of the black hole. The black hole spacetime contains an outer and an inner horizon, and the transition amplitude between a one-particle state localized inside the inner horizon, and a one-particle state localized outside the outer horizon is non-zero, even when the regions where the states are localized are causally disconnected. The total tunnelling probability asymptotes to a maximal value that depends on the background spacetime geometry only through the surface gravity of the two horizons, and is polynomially suppressed by the sum of the inverse surface gravities of the inner and outer horizons.

This paper investigates the blow-up of solutions to scale-invariant semilinear wave equations featuring the damping term $\fracμ{1+t} \partial_t u$, the mass term $\frac{ν^2}{(1+t)^2} u$, and a time-derivative nonlinearity $| \partial_t u |^p$. The principal contribution of this work is the demonstration that the sign of the discriminant $δ= (μ-1)^2 - 4ν^2$ is not a structural prerequisite for determining the blow-up range. Indeed, we show that even in the regime $δ< 0$, the blow-up region remains invariant and is uniquely determined by the shifted dimension $n+μ$, aligning with the Glassey-type critical exponent. Our result suggest that the classical restriction $δ\ge 0$ is due to a technical tool rather than an intrinsic feature of the blow-up mechanism.

The realization of blue electroluminescence with high efficiency and lifetime remains a long-standing hurdle for OLED technology to overcome. Divalent Europium [Europium(II)] complexes offer a fundamentally distinct pathway toward this goal, as their atomic 4f-5d transitions yield single-Gaussian, spectrally pure emission with theoretical 100% exciton utilization and no involvement of fragile organic bonds in the emissive process. However, their true potential has never been fully demonstrated before. In this work, we design a rigid aza-crown europium(II) complex (Eu5NHCrown) that achieves near-unity photoluminescence quantum yield with bright, pure-blue emission. The complex sublimes without decomposition and can be vacuum-deposited into a bottom-emitting, single-host OLED architecture, delivering an external quantum efficiency (EQE) of 20.7% with minimal roll-off (19.3% at 1000 cd m-2 ) and a narrowband electroluminescence with CIE coordinates of (0.12, 0.25). These results reveal the true potential of Eu(II) 4f-5d transitions for high-efficiency blue OLEDs, establishing a molecular design concept that bridges atomic-transition efficiency with the processability of organic materials.