Ceramic solid-state batteries with sodium (Na) metal electrodes promise enhanced safety and energy density compared to contemporary secondary batteries. However, the critical delamination of the Na metal electrode during discharge - when vacancies accumulate at the Na/ceramic interface - remains to be understood and avoided. The study investigates the underlying mechanism by applying a linear current ramp between two Na metal electrodes separated by a ceramic solid electrolyte to provoke vacancy buildup. Above a critical current density $j_\mathrm{crit}$ the anode voltage no longer increases linearly but in an exponential fashion. Arrhenius analysis of $j_\mathrm{crit}(T)$ for the three solid electrolytes $\mathrm{Na_{1.9}Al_{10.67}Li_{0.33}O_{17}}$, $\mathrm{Na_{3.4}Zr_2Si_{2.4}P_{0.6}O_{12}}$, and $\mathrm{Na_5SmSi_4O_{12}}$ yields an activation energy $E_\mathrm{A}$ of $0.13$ to $0.15\,\mathrm{eV}$. This exceeds the activation energy of $0.053\,\mathrm{eV}$ for the diffusive vacancy migration in bulk Na significantly. Further, $E_\mathrm{A}$ is insensitive to anode microstructure variation. Both observations rule out bulk diffusion as the transport bottleneck. A thin tin-sodium alloy interlayer lowers $E_\mathrm{A}$ to $(0.10\pm0.01)\,\mathrm{eV}$, implicating interfacial thermodynamics as rate-limiting. Sodiophilic, Na-conducting interlayers and low-tension interfaces emerge as key pathways to stable, high-rate Na-SSBs at practical stack pressures.

Ultralight bosonic dark matter with masses in the meV range, corresponding to terahertz (THz) Compton frequencies, remains largely unexplored due to the difficulty of achieving both efficient signal conversion and single-photon-sensitive detection at THz frequencies. We propose a hybrid detection architecture that integrates a dielectric haloscope, Rydberg-atom transducer, and superconducting nanowire single-photon detection within a unified cryogenic platform operating at $\lesssim 1\,\text{K}$. The dielectric haloscope converts dark matter into THz photons via phase-matched resonant enhancement, achieving form factors $C \sim 0.4$ and loaded quality factors $Q_L \sim 10^4$. A cold $^{87}$Rb ensemble then coherently up-converts the THz signal to the optical domain through six-wave mixing among Rydberg states. The intrinsic directionality and narrow bandwidth ($Δν_{\mathrm{atomic}} \sim 1\,\text{MHz}$) of this process provide extra suppression of isotropic thermal backgrounds. With 10 days of integration at $0.3\,\text{K}$, we project sensitivity to the axion-photon coupling $g_{aγγ} \sim 10^{-13}\,\mathrm{GeV}^{-1}$ at $m_a \sim 0.4\,\text{meV}$, reaching the QCD axion band and opening the THz window for searches of both axion and dark photon dark matter.

Bohr's last problem (1952) asks whether every ordinary Dirichlet series with nonzero Lindelöf order function $μ$ has $μ'(ω_μ{-}0)\le-1$; a negative answer would imply Lindelöf for $ζ$. Kahane (1989) refuted this with half-plane counterexamples. We study the refinement for series with entire continuation of order $\le 1$: the Analytic Lindelöf Hypothesis that $μ$ is piecewise linear with integer slopes. Deforming the Mellin integral to the strip boundary reduces $μ_L$ to a residue sum over singularities of the generating function on $|x|=1$, giving $μ_L(σ)=\max(0,\tfrac12-σ+ρ)$. For classical $L$-functions this sum is the functional-equation dual, and bounding it is Lindelöf; for self-similar or random singularities it is a Rajchman Fourier transform. We show Kahane's half-plane examples fail entirety, his entire random examples have integer slopes a.s., and Lerch-Lindelöf implies ALH. Our central construction is the Cantor Dirichlet series $L(s)=\sum\hatν(n)n^{-s}$, with $ν$ the ternary Cantor measure. Its Kaczorowski--Perelli twist spectrum is empty; we prove $μ_L(\tfrac12)\le\tfrac18$ unconditionally via a Montgomery--Vaughan argument on the product variable $(m_1+α)(m_2+α)$, where a Vieta identity guarantees distinct frequencies. A Cantor-weighted Hurwitz second-moment conjecture would give $μ_L(\tfrac12)=0$.

Extreme ultraviolet (EUV) waves are global waves in the solar corona which can accelerate particles. The efficiency of the acceleration depends on local plasma characteristics e.g. Alfvén speed and the geometry of the magnetic field. This shock-driven particle acceleration can produce radio signatures such as Type II radio bursts and herringbone emission. Here we investigate signatures of particle acceleration by a weak coronal shock on 10 March 2024. In particular, we combine EUV images with radio imaging and spectral observations to determine how and where this weak shock could accelerate energetic particles. A potential field source surface extrapolation was used to examine the pre-eruption ambient magnetic field while the evolution of the global wave was probed using running difference and base difference EUV images. The EUV images enabled the speed and Alfvén Mach number of the EUV wave to be characterised. The combination of radio images and dynamic spectra provide evidence of beams of shock-accelerated electrons localised to a dimming region at the time the EUV wave passes through it. The speeds and energies of these electrons were estimated from the drift rates of their herringbones. The EUV wave initially propagated West, channelled by loop systems, before changing direction northward. From the EUV intensity jump at the wavefront, the Alfvén Mach number was estimated to be approximately 1.005 at the time that the herringbones were produced. The herringbone drift rates revealed accelerated electron energies of 75-122 keV, using Newkirk density models with scaling factors of 1.3-2.6. These observations suggest that the weak lateral shock impacted quasi-perpendicular open field in a dimming region, enabling localised particle acceleration. This indicates that the geometry of the ambient magnetic field relative to the shock strongly governs where particles can be accelerated.

In the 1980's Serre asked how many points of bounded height can lie in a thin set. This has motivated significant research ever since, culminating in a series of recent breakthroughs. It is a good time to take stock of the central questions that have been resolved, and also to highlight remaining open questions. First, we survey recent progress on counting points of bounded height in the four types of thin sets, according to the projective/affine and type I/type II designations. Second, we turn to questions of uniformity. Famously, in the setting of type I thin sets, the best-known upper bound for the number of points of bounded height is independent of the maximum size, say $\|F\|$, of the coefficients of the polynomials that define the thin set; such an upper bound is called uniform. A uniform upper bound in the setting of type II thin sets is not known. For type II thin sets, we explore the dependence on $\|F\|$ via several strategies, and construct counterexamples that suggest the question of uniformity is quite subtle in the setting of type II thin sets.

Molecular orientation techniques are becoming available in the study of elementary chemical processes, in order to highlight those structural and dynamical properties that would be concealed by random rotational motions. Recently successful orientation was achieved for asymmetric-top and chiral molecules of much larger complexity than hitherto. In this work, we report and discuss the correlation between the vectors photofragment recoil velocity v, transition dipole moment μ, and permanent dipole moment d in a dissociation experiment on hexapole oriented 2-bromobutane, photoinitiated by a linearly polarized laser. The sliced ion images of the Br* (2P1/2) and Br (2P3/2) photofragment were acquired at 234.0 and 254.1 nm, respectively, by (2+1) resonance-enhanced multiphoton ionization technique. A detailed analysis of the sliced ion images obtained at a tilting angle 45o of the laser polarization provides the information on correlation of the three vectors, which are confined by two polar angles α, \c{hi} and one azimuthal angle ϕμd in the recoil frame. The sliced ion images of Br fragments eliminated individually from the enantiomers at 254.1 nm yield the asymmetric factor close to zero; for this reason the photofragment angular distributions do not show significant differences. The elimination of Br* fragment at 234.0 nm is mainly correlated with a parallel transition, giving rise to a large anisotropy parameter of 1.85, and thus can be considered as a single state excitation. The resulting recoil frame angles are optimized to 163.8° and 164.1° for α and \c{hi}, respectively, whereas ϕμd approaches close to 0o for the best fit. Since in the present case, the three vectors have an only slight spatial arrangement, the photofragment angular distributions of the two enantiomers do not show appreciable differences...

In the context of 5G, 3GPP introduced New Radio vehicle to everything (NR-V2X) for direct vehicle-to-vehicle communication. However, starting from Release 18 the focus of the standard has been expanded from vehicles to any device and use case that can benefit from direct communication. In 3GPP terminology, the standard is now referred to simply as Sidelink communication. This standard allows direct communication between devices based on synchronous resource scheduling. Users can rely on controlled scheduling when in network coverage or, in the absence of coverage, autonomously select resources for transmission via a distributed resource allocation mechanism. Focusing on the autonomous resource allocation, this paper investigates the possibility of applying Release 18 Sidelink communication to Air-to-Air (A2A) links between airborne entities. The paper outlines the main challenges and required modifications to adapt the current standard for longer links in the order of kilometres. The analysis identifies the propagation delay as a critical limitation. Communications at distances over 42.4 km require a restriction of the user's transmitting opportunities. However, sidelink communication remains feasible for distances below this threshold without modifications to the standard.

Parallel applications with irregular and time-varying workloads often suffer from load imbalance. Dynamic load balancing techniques address this challenge by redistributing work during execution. We present a new type of distributed diffusion-based load balancing targeted at communication-intensive applications with persistently communicating objects. Leveraging the application's communication graph, our strategy reduces across-node communication while simultaneously distributing load effectively. We also propose an algorithmic variant for cases where the communication patterns are not readily available. We explore optimizations to our algorithm, and comparisons with other related load balancing strategies in simulation and on a Particle-in-Cell benchmark on up to 8 nodes of Perlmutter at NERSC.

A $3$-dimensional nowhere-zero flow on a graph $G$ is a flow where each edge is assigned a $3$-dimensional vector with unit norm (which corresponds to the points of a $2$-dimensional unit sphere $S^2$). K. Jain posed two conjectures related to this idea. First one suggests that such a flow exists for all bridgeless graphs. The second conjecture states that we can assign values $\{-4,-3,-2,-1,1,2,3,4\}$ to the points of $S^2$, such that antipodal points get opposite values, and values of any three equidistant points on great circles sum to zero. If both conjectures would be true, together they would imply Tutte's 5-flow conjecture. We show 2 counterexamples to the second conjecture, by constructing sets of points each of which additionally requires values $\{-5, 5\}$. Github: https://github.com/gexahedron/unit-vector-flows

Multi-access Edge Computings (MECs) enables low-latency services by executing applications at the network edge. To fulfill low-latency requirements of mobile users, providers have to keep multiple edge servers running at multiple locations, even when, in low-load phases, their capacity is not needed. This significantly increases energy consumption. Multi-state sleep mechanisms mitigate this issue by allowing servers to enter progressively deeper sleep states, trading energy savings for longer wake-up delays. At the same time, service execution depends on non-instantaneous lifecycle operations that cannot be performed while servers are asleep, tightly coupling energy management with service continuity. This paper introduces PowerNap (PNap), a lifecycle-aware orchestration framework that jointly manages server sleep states and service lifecycle states. By leveraging traffic forecasting, PNap jointly minimizes the number of active edge servers and service disruptions. We compare PNap against baselines approaches and a state-of-the-art approach. Results validate PNap, showing how it can reduce energy consumption by up to 14.9% with respect to a state-of-the-art solution while matching its service availability results.

Let $G$ be a graph and $I(G)$ its edge ideal. In this paper, we give a complete characterization of the graphs $G$ for which $\reg(R/I(G)) = 3$.

Proliferation is a defining feature of life. Through growth, division, and death, living systems consume energy and inject mass, breaking conservation laws and driving collective phenomena from biofilm formation to embryonic development. Yet, while active matter physics has advanced our understanding of self-propelled agents, quantitative frameworks for proliferating systems are still emerging, and most work focuses on simplified settings. Here, we study \textit{E.coli} bacteria growing inside a network of single-file microchannels as a minimal model of structured environments. Competition for free volume drives the spontaneous emergence of coherent growth patterns that persist across generations but vanish when the channel links exceed the typical cell size at birth. Despite the strongly out-of-equilibrium character of the dynamics, the observed phenomenology can be quantitatively captured by an effective equilibrium description in which the flow state at each node is represented by a spin variable with ferromagnetic interactions. Simulations of growing elastic cells show that this coupling arises from internal stress accumulated at network nodes due to dynamical constraints. Our results reveal a surprising correspondence between proliferating active matter and equilibrium statistical mechanics, highlighting open fundamental questions and offering a first step toward describing growth phenomena in real-world complex environments.

Class II protoplanetary discs feature numerous non-axisymmetric substructures like spirals and the underlying mechanisms for their formation are still highly debated. Coincidentally, early stage, massive discs are subject to the gravitational instability that causes them to collapse into denser substructures. However, like for most instabilities, real systems usually remain marginally stable, here with Toomre parameter $Q \gtrsim 1$. We study how the self-gravity of the gas triggers the growth of spiral structures in the disc. We specifically focus on discs that are considered stable, that is, with respect to the gravitational instability (with $Q > 1$), as these discs remain unstable to non-axisymmetric perturbations like spirals. After a linear stability analysis, we produce high-resolution 2D shearing sheet simulations with the GPU-accelerated code \idefix of self-gravitating discs. We probe different initial densities and thermodynamical models of Toomre-stable discs. The initial transient growth of the spiral wave matches the linear theory provided we take into account the time dependency of the amplification. The spirals are then rapidly non-linearly amplified with growth rate $\approx 10$ orbital time scale. After this time spiral large scale mode are amplified up to 1000 times more than linear theory predicts. At later times, low density discs reach a weak gravito-turbulent state with $α\approx 10^{-3}$ and discs with higher density undergo runaway collapse of the spiral arms. All discs exhibit dominant large-scale spirals.

Hanika, Schneider, and Stumme introduced geometric data set as a generalization of metric measure space for the computation of the observable diameter, and extended the observable distance between metric measure spaces to that between geometric data sets. In this paper, we begin by proving the non-separability of the observable distance between geometric data sets. We then extend the box distance between mm-spaces to that between geometric data sets and prove its completeness and non-separability.

Superconductivity and nematicity coexist in the phase diagram of many correlated systems, including iron-based superconductors. We investigate how Hund-driven correlations reshape boson-mediated superconductivity in a multiorbital nematic metal. We find that dynamical correlation effects beyond a quasiparticle-only description are essential to capture the robustness of superconductivity in the Hund regime. In the nematic phase, Hund correlations simultaneously enhance the orbital differentiation of the superconducting gaps and inhibit the most extreme nematic-driven orbital polarization and coherence collapse that would otherwise suppress pairing at strong coupling. A controlled cutoff analysis reveals a nontrivial, orbital-dependent buildup of the gaps, indicating that different frequency windows of the correlated spectrum contribute unevenly to pairing in the nematic Hund regime. This implies that pairing mechanisms with different characteristic boson energies can lead to distinct gap structures and trends.

The hydrogen \lya\ line and the white-light (WL) continuum are two key diagnostics of energy transport in the lower atmosphere during solar flares, yet their relationship remains poorly understood. Here we present a statistical analysis of 69 white-light flares (WLFs) to investigate the relationships among the \lya, soft X-ray (SXR), and WL continuum emissions using the data from GOES and the Helioseismic and Magnetic Imager (HMI) on the Solar Dynamics Observatory. We find that the \lya\ contrast in these WLFs ranges 0.8--28.5\% with a mean value of 7.0\%. Positive power-law relationships exist among peak enhancements in SXR, \lya, and WL. For most events, the \lya\ peak is nearly co-temporal with the peak of SXR time derivative, whereas the WL peak is either co-temporal with or lags those of \lya\ and SXR derivative. The \lya\ and WL rise times are similar ($\sim$3--4 min) and correlated. We also find that the radiated energy in \lya\ and HMI narrow-band WL has a positive power-law relationship with duration. In particular, the power-law index for the narrow-band WL is very close to 1/3 as predicted by magnetic reconnection theory. On average, the radiated energies in GOES \lya\ and SXR bands are approximately three orders of magnitude greater than the energy emitted in the continuum near 6173 Å with a bandwidth of 1 Å. Our findings provide new constraints on lower-atmosphere energy transport in solar flares and can serve as valuable references for modelling and interpreting the flares on solar-type stars.

Time-invariant finite-dimensional systems, under reasonable continuity assumptions, exhibit the property that if solutions exist for all future times, the set of vectors reachable from a bounded set of initial conditions over bounded time intervals is also bounded. This property can be summarized as follows: forward completeness implies bounded reachability sets. By contrast, this property does not necessarily hold for infinite-dimensional systems in general, and time-delay systems in particular. Sufficient conditions for this property to hold that can be directly tested on the function defining the system dynamics are only known in the case of systems with pointwise (or discrete) delays. This paper develops novel sufficient conditions for the boundedness of the reachability sets of time-delay systems involving mixed pointwise and distributed delays. Broad classes of systems satisfying these conditions are identified.

Autonomous vehicles generate large volumes of data for applications such as fleet monitoring, model retraining, and high-definition map updates. Existing studies often rely on generic traffic traces, which do not capture the characteristics of autonomous driving workloads. This paper proposes a system-level workload modeling framework for vehicle-to-cloud data. We classify offloaded data into three types: telemetry, event-driven fleet learning, and high-definition map updates, while we model their generation using a parameterized formulation based on empirical data. Using a real-world mobility trace from Munich, we analyze the resulting workloads over time and space. The results show that workload scales with vehicle penetration, exhibits temporal structure and spatial imbalance across access points, and is distinguished from baseline traffic models.

Extreme quantile treatment effects (eQTEs) measure the causal impact of a treatment on the tails of an outcome distribution and are central for studying rare, high-impact events. Standard QTE methods often fail in extreme regimes due to data sparsity, while existing eQTE methods rely on restrictive tail assumptions or on interior-quantile theory. We propose the Tail-Calibrated Inverse Estimating Equation (TIEE) framework, which combines information across quantile levels and anchors the tail using extreme value models within a unified estimating equation approach. We establish asymptotic properties of the resulting estimator and evaluate its performance through simulation under different tail behaviours and model misspecifications. An application to extreme precipitation in the Austrian Alps illustrates how TIEE enables observational causal attribution for very rare events under anthropogenic warming. More broadly, the proposed framework establishes a new foundation for causal inference on rare, high-impact outcomes, with relevance across environmental risk, economics, and public health.

Topological pumping is conventionally governed by single-particle band topology. Here we show that promoting tunneling to a dynamical, occupation-conditioned variable fundamentally reshapes this paradigm, leading to occupation-selective topological pumping. In a periodically driven one-dimensional superlattice with density-dependent hopping, two-body bound states (doublons) acquire Chern numbers distinct from those of single particles and exhibit quantized transport even when the single-particle pump is trivial, including counter-propagating responses. We identify a dynamical-gauge-field mechanism that induces topological phase transitions in the bound-state sector absent from the single-particle spectrum. Furthermore, the gauge field concentrates Berry curvature into sharply localized resonant regions without compromising adiabatic quantization. A Floquet realization with ultracold atoms is proposed to realize such occupation-selective pumping. Our results reveal a mechanism for occupation-selective topological responses that can persist across higher-occupancy bound states.

We study infinite paths of Markoff $m$-triples, that is, solutions to the generalised Markoff equation \[ x^2+y^2+z^2=3xyz+m, \] with $m>0$, with at least two $k$-Fibonacci components. First, we obtain a complete classification of Markoff $m$-triples whose last two entries are $k$-Fibonacci numbers and that are not roots of any Markoff trees. We then prove that every such infinite path is contained in a branch, starting at a triple of the form \[ \left(\frac{F_k(4r)}{3F_k(2r)},\,F_k(\ell+2r),\,F_k(\ell+4r)\right), \] where $r$ is an odd integer, $\ell\in\{1,2,\ldots, 2r\}$ and $3\nmid k$. These branches are distributed among exactly $2r$ distinct trees.

Financial institutions face increasing cyber risk while operating under strict regulatory oversight. To manage this risk, they rely heavily on Cyber Threat Intelligence (CTI) to inform detection, response, and strategic security decisions. Artificial intelligence (AI) is widely suggested as a means to strengthen CTI. However, evidence of trustworthy production use in finance remains limited. Adoption depends not only on predictive performance, but also on governance, integration into security workflows and analyst trust. Thus, we examine how AI is used for CTI in practice within financial institutions and what barriers prevent trustworthy deployment. We report a mixed-methods, user-centric study combining a CTI-finance-focused systematic literature review, semi-structured interviews, and an exploratory survey. Our review screened 330 publications (2019-2025) and retained 12 finance-relevant studies for analysis; we further conducted six interviews and collected 14 survey responses from banks and consultancies. Across research and practice, we identify four recurrent socio-technical failure modes that hinder trustworthy AI-driven CTI: (i) shadow use of public AI tools outside institutional controls, (ii) license-first enablement without operational integration, (iii) attacker-perception gaps that limit adversarial threat modeling, and (iv) missing security for the AI models themselves, including limited monitoring, robustness evaluation and audit-ready evidence. Survey results provide additional insights: 71.4% of respondents expect AI to become central within five years, 57.1% report infrequent current use due to interpretability and assurance concerns and 28.6% report direct encounters with adversarial risks. Based on these findings, we derive three security-oriented operational safeguards for AI-enabled CTI deployments.

In this article, we establish exponential turnpike theorems for a class of nonlinear deterministic meanfield optimal control problems. We carry out our analysis simultaneously in the so-called Lagrangian and Eulerian frameworks. In the Lagrangian setting, the problem is lifted to a Hilbert space of random variables, and we prove an exponential turnpike theorem by combining first-order optimality conditions, a second-order expansion of the lifted Hamiltonian, and an operator Riccati diagonalization argument. In the Eulerian setting, we derive intrinsic KKT conditions for the static constrained problem, and show how the Eulerian second-order hypotheses split into a horizontal part, transferred by unitary conjugation to the lifted space, and a vertical part which reduces to uniform pointwise stabilizability and detectability conditions on multiplication operators. This yields an exponential turnpike theorem in the Wasserstein space for optimal Pontryagin triples. Along the way, we %provide explicit the link between Wasserstein Hessians and their Lagrangian lifts, and provide several remarks clarifying the role of occupation measures, local Eulerian minimizers, and control constraints in our results.

We study nonparametric covariance function estimation for functional data observed with noise at discrete locations on a $d$-dimensional domain. Estimating the covariance function from discretely observed data is a challenging nonparametric problem, particularly in multidimensional settings, since the covariance function is defined on a product domain and thus suffers from the curse of dimensionality. This motivates the use of adaptive estimators, such as deep learning estimators. However, existing theoretical results are largely limited to estimators with explicit analytic representations, and the properties of general learning-based estimators remain poorly understood. We establish an oracle inequality for a broad class of learning-based estimators that applies to both sparse and dense observation regimes in a unified manner, and derive convergence rates for deep learning estimators over several classes of covariance functions. The resulting rates suggest that structural adaptation can mitigate the curse of dimensionality, similarly to classical nonparametric regression. We further compare the convergence rates of learning-based estimators with several existing procedures. For a one-dimensional smoothness class, deep learning estimators are suboptimal, whereas local linear smoothing estimators achieve a faster rate. For a structured function class, however, deep learning estimators attain the minimax rate up to polylogarithmic factors, whereas local linear smoothing estimators are suboptimal. These results reveal a distinctive adaptivity-variance trade-off in covariance function estimation.

The Thomson scattering optical depth to reionisation, $τ$, one of the six parameters of the $Λ$CDM model, is primarily constrained by the large-scale E-mode polarisation of the Cosmic Microwave Background (CMB). In this work, we present the E-mode Likelihood for Cross-Analysis (elica), a multi-frequency, harmonic-space likelihood that combines all currently available large-scale satellite polarisation data, namely the Planck LFI 70 GHz channel, the Planck HFI 100 and 143 GHz channels processed with the SRoll2 map-making algorithm, and the WMAP Ka, Q, and V bands. The likelihood is built on an extension of the Hamimeche-Lewis formalism to multi-field partial-sky observations. We validate the pipeline using 500 realistic simulations and find that retaining all cross-spectra and the WMAP-LFI auto-spectrum eliminates the significant bias present when all spectra are retained, while preserving comparable uncertainties in the recovered value of $τ$. From the low-$\ell$ E-mode power spectrum alone, we obtain $τ= 0.0575_{-0.0058}^{+0.0048}$ (68% CL). Combining elica with the Planck low-$\ell$ temperature likelihood and the CamSpec high-$\ell$ likelihood, we find $τ= 0.0581_{-0.0059}^{+0.0048}$ and $\ln(10^{10}A_{\mathrm{s}}) = 3.048_{-0.012}^{+0.011}$. Including ACT{} DR6 + Planck CMB lensing and DESI DR2 BAO measurements, we derive an upper bound on the total neutrino mass of $\sum m_ν< 0.069$ eV (95% CL). Our results, obtained through careful cross-validation of all available large-scale polarisation datasets, robustly confirm that the optical depth remains relatively low. This severely constrains the possibility of explaining, or even significantly reducing, the tension between DESI-BAO and CMB observations with a high value of $τ$. The elica likelihood is publicly available.

It has been claimed that a fraction of the so-called Little Red Dots (LRDs) are characterised by exponential broad line profiles, which have been ascribed to broadening from electron scattering by an ionised cocoon. In this work, we investigate the H$α$ broad line profiles of 32 AGN, including Little Red Dots (LRDs), Little Blue Dots (LBDs), and X-ray detected sources, using high SNR and resolution spectroscopy. We find that while single Gaussian models are statistically rejected, the exponential model is not universally preferred. Lorentzian and multi-Gaussian profiles provide equally good or superior fits for the majority of the sample, with no statistical preference for exponential profiles in $\sim$60% of cases across all AGN subtypes. There are indications that exponential profiles are preferred more frequently among LBDs, indicating that exponential profiles are not a prerogative of LRDs, which actually seem to more often favour Lorentzian profiles. Furthermore, we demonstrate that exponential wings can emerge naturally from the stratification of BLR clouds in virial motion, without invoking any scattering process. More generally, we also show that stacking multiple broad lines (either from multiple objects, as done in previous works, or from different BLR components within the same object) generally yields an exponential profile, even if none of the individual profiles are exponential. Explaining the exponential profiles in terms of BLR stratification solves various observational tensions with the electron scattering interpretation. While electron scattering may play a role, there is no evidence that it dominates the line profiles and that it significantly affects the inferred black hole masses.

Deploying ML-DSA (FIPS 204) in threshold settings has remained an open problem: the scheme's inherently non-linear rounding step defeats the additive share techniques that underpin practical threshold schemes for elliptic-curve signatures such as FROST. We present TALUS, the first threshold ML-DSA construction that achieves one-round online signing with >99% online success, while producing standard signatures verifiable by any unmodified ML-DSA verifier. We formalise this as the Lattice Threshold Trilemma, proving that no group homomorphism from the ML-DSA nonce space into any abelian group can simultaneously be hiding and binding, ruling out all possible homomorphic commitment schemes. TALUS overcomes this barrier with two techniques. The Boundary Clearance Condition (BCC) identifies nonces whose rounding residuals lie far enough from modular boundaries that the secret key component s2 has no effect on the signature; such nonces (approximately 31.7% of attempts) are filtered during offline preprocessing. The Carry Elimination Framework (CEF) then enables parties to compute the commitment hash input distributedly, without reconstructing the full nonce product. Together, BCC and CEF reduce online signing to a single broadcast round: each party sends one message and the coordinator assembles a valid FIPS 204 signature. We instantiate TALUS in two deployment profiles: TALUS-TEE (trusted execution environment, T-of-N) and TALUS-MPC (fully distributed, malicious security with identifiable abort for T >= 2). Security of both variants reduces to ML-DSA EUF-CMA. A Rust implementation across all three FIPS 204 security levels (ML-DSA-44, ML-DSA-65, ML-DSA-87) shows that TALUS-TEE completes a signing operation in 0.62--1.94 ms and TALUS-MPC in 2.27--5.02 ms (amortised, T=3), competitive with the fastest concurrent threshold ML-DSA proposals.

Massive He stars are potential candidates of type Ib/c supernova (SN) progenitors. Understanding their final fates remains a key issue in astrophysics. In this work, we investigate the evolution of He stars with initial masses from 5 $M_\odot$ to 65 $M_\odot$, focusing on the presupernova (pre-SN) core structures to assess their explodability. Our simulations indicate that the final core structure is determined by the CO core mass and the central 12C mass fraction at the end of core He burning, affecting the properties of central C-burning and the locations of convective shells. The location of the last convective C-burning shell sets the mass of the C-free core, constraining the iron core mass and compactness. We found that the final compactness and iron core mass exhibit non-monotonic behavior with initial mass, suggesting that the boundary between neutron star and black hole formation is not a simple mass threshold. This is due to core C/Ne burning becoming neutrino dominated. This process drives stronger core contraction, ultimately increasing the iron core mass and the final compactness. In contrast, earlier core Ne/O/Si ignition and shell mergers inhibit core contraction, reducing both the iron core mass and final compactness. We also discuss the effects of metallicity and overshooting on the pre-SN core structure. These factors potentially affect the explodability of progenitors.

Femtosecond laser micromachining (FLM) fabricated waveguides inherently form elliptical cores due to differences in focal spot size and the Rayleigh range of the microscope objective. Consequently, it is essential to study their propagation characteristics, which differ from those of conventional circular-core waveguides. In this work, we present the results of a parametric optimization of these waveguides to identify fabrication parameters that lead to minimal loss. A propagation loss characterization study revealed that, for a laser wavelength of 1030 nm, a pulse width of $\sim$300 fs, a pulse energy of 600 nJ, a scan speed of 2 mm/s, and a repetition rate of 100 kHz, a transparent and micro-bubble-free waveguide with a propagation loss of $\sim$0.4 dB/cm was formed. The modal analysis further demonstrated that the V-number depends on the core aspect ratio. The waveguide modes were compared with computationally generated modes, revealing a correlation that aligns well with existing literature.

The multiplication of two sparse matrices, known as SpGEMM, is a key kernel in scientific computing and large-scale data analytics, underpinning graph algorithms, machine learning, simulations, and computational biology, where sparsity is often highly unstructured. The unstructured sparsity makes achieving high performance challenging because it limits both memory efficiency and scalability. In distributed memory, the cost of exchanging and merging partial products across nodes further constrains performance. These issues are exacerbated on modern heterogeneous supercomputers with deep, hierarchical GPU interconnects. Current SpGEMM implementations overlook the gap between intra-node and inter-node bandwidth, resulting in unnecessary data movement and synchronization not fully exploiting the fast intra-node interconnect. To address these challenges, we introduce Trident, a hierarchy-aware 2D distributed SpGEMM algorithm that uses communication-avoiding techniques and asynchronous communication to exploit the hierarchical and heterogeneous architecture of modern supercomputing interconnect. Central to Trident is the novel trident partitioning scheme, which enables hierarchy-aware decomposition and reduces internode communication by leveraging the higher bandwidth between GPUs within a node compared to across nodes. Here, we evaluate Trident on unstructured matrices, achieving up to $2.38\times$ speedup over a 2D SpGEMM with a corresponding geometric mean speedup of $1.54\times$. Trident reduces internode communication volume by up to $2\times$ on NERSC's Perlmutter supercomputer. Furthermore, we demonstrate the effectiveness of Trident in speeding up Markov Clustering, achieving up to $2\times$ speedup compared to competing strategies.