Papers

We study uniform high-frequency localization for the Laplacian on compact metric graphs through the least $L^2$-mass that eigenfunctions must place in a prescribed measurable observation set. We first identify this asymptotic localization constant with the minimum of a linear functional over the attainable edge-intensity set; in the generic standard-Kirchhoff setting, this set is governed by the regular Gauss image of the secular manifold. Primitive cycles and exterior-to-exterior paths consequently determine the positivity threshold, but not, in general, the positive numerical value. We introduce a boundary-aware singular-completion cone and prove that it contains all regular secular edge-energy vectors for trees, unicyclic graphs, and closed graphs of cycle rank two. We then construct a cycle-rank-two graph with two Dirichlet leaves for which this completion principle fails. An exact rational separator, combined with a validated Krawczyk enclosure, yields a nonsingular scalar secular state lying outside every boundary-compatible singular sector. A positive radial derivative identity and recurrence in the compact orbit closure convert this local separation into an exact high-frequency eigensequence for a single fixed metric. For a suitable measurable observation set, the true high-frequency localization constant $C_\infty(\omega;\ell)$ and its singular-completion counterpart $C_{\mathrm{sing}}(\omega;\ell)$ satisfy $$C_\infty(\omega;\ell)<1/2<C_{\mathrm{sing}}(\omega;\ell)$$. Thus, singular completion captures the quantitative localization geometry in several low-complexity classes but does not, in general, determine the high-frequency variational problem on a fixed quantum graph.

Population-level heterogeneities, combined with temporal fluctuations in sexual partnerships, shape the structure of sexual contact networks and can substantially influence the spread of sexually transmitted infections (STIs). Traditional static network models, which assume fixed attributes of partnerships, such as count and duration, may not adequately capture the effects of partnerships on STI transmission. In contrast, agent-based dynamic network models offer a flexible framework for incorporating individual and population-level heterogeneities. We developed an agent-based dynamic network model in which partnership formation and dissolution probabilities, stratified by age, sex, and sexual orientation (including bisexual individuals), govern the formation of monogamous and concurrent partnerships and their dissolution via a duration-dependent hazard. Partnership statistics from the National Survey of Sexual Attitudes and Lifestyles (NATSAL-3) were used as model calibration targets, and Latin Hypercube Sampling (LHS) was used to generate candidate parameter combinations. Parameter estimation was performed by selecting the combination that produced the lowest Mean Squared Error (MSE) between the model outputs and the calibration targets. Our study addresses three questions: (1) how well can the observed characteristics of sexual partnerships in NATSAL-3 be reproduced using an agent-based model; (2) how does concurrency shape the structure of dynamic sexual contact networks; and (3) how do concurrent partnerships affect the dynamics of STI transmission. In this study, we find that interactions between individual characteristics such as age, sex, and sexual orientation, and partnership attributes such as count, duration, and concurrency play a critical role in shaping the population-level sexual contact network and, in turn, the dynamics of STI transmission.

Galactic foregrounds represent a major contamination to the measurement of primordial $B$-modes from observations of the Cosmic Microwave Background polarisation. Even after the application of component separation algorithms, foreground residuals may potentially still bias the estimate of the tensor-to-scalar ratio $r$, causing a false detection. In this work, we present the methodology of a robustness test for the validation of an eventual detection of primordial $B$-modes, as obtained by a future, LiteBIRD-like satellite experiment. The goal of the test is to identify the foreground residuals contamination by looking for non-Gaussian properties in the CMB $B$-modes map, recovered through blind component separation algorithms. We adopt scattering transforms (ST) as our summary statistics sensitive to the non-Gaussian features of foreground residuals and to their correlation with foregrounds tracer maps. We characterise and validate the methodology on realistic sky simulations with different levels of foregrounds complexity. The proposed test is able to identify a bias on the tensor-to-scalar ratio of $\gtrsim 10^{-3}$ in $\sim 90\%$ of our simulations, with this bias value being of the same order of the accuracy targeted by LiteBIRD. Additionally, for our particular experimental configuration, the test is passed when the bias is lower than the sensitivity on the $r$ parameter, and no warning is raised. These results provide an important step forward in the development of statistical tools for validating future measurement of cosmological parameters, against foregrounds contamination.

The vanilla scotogenic model (VSM) featuring three right-handed neutrinos and an inert scalar doublet, offers a unified explanation of neutrino masses, dark matter (DM), and the baryon asymmetry of the Universe through leptogenesis. The typical mass scale of such a scenario lies in the vicinity of $\sim$ 10 TeV and above, whereas enhanced second-generation Yukawa couplings lower the leptogenesis scale to $\sim 1$ \TeV, allowing the model to be probed at the future muon colliders. Adhering to DM, neutrino mass, Leptogenesis, and flavour dependent constraints, the charged scalar is likely to be a long-lived particle (LLP). We analyse both the prompt and displaced vertex signatures of the model to find that, prompt mono-photon signals remain challenging, but LLP searches offer a promising avenue to probe such a framework, subject to the timing resolutions, and displaced-vertex reconstruction efficiency.

For any fixed $k$, we prove a lower bound on the $k$th largest modulus of an eigenvalue of the non-backtracking matrix $B$. Specifically, consider any deterministic or random family of graphs that converges locally to the unimodular Galton-Watson tree with root degree distribution $D$, and set $\kappa:=\mathbb E[D(D-1)]/\mathbb E[D]$. Given $\kappa>1$ and an exponential-moment bound on the empirical degree distributions, we show that $|\lambda_k(B)|\geq\sqrt{\kappa}-o_N(1)$, where $N$ is the number of vertices. When restricted to locally tree-like regular graphs, this recovers a well-known consequence of the Ihara-Bass formula. In the specific case where the graph is generated through the Erdős-Rényi model with expected degree $d>1$, this proves a conjecture of Bordenave, Lelarge, and Massoulié. To do this, we show that the normalized log-determinant of the Bethe-Hessian of the graph is bounded by that of the Bethe-Hessian of its local limit. This bound is violated if the eigenvalues of the non-backtracking matrix are too small. We establish this using an effective-conductance interpretation of the tree Green's function recursion.

We obtain two families of neutral planar black branes in a potential-free dilaton-coupled Lovelock–Horndeski theory. Heterotic compactification relates higher-dimensional curvature to scalar dynamics and motivates the interaction structure. At fixed scalar zero mode, the horizon radius and temperature vary while the complete stationary Wald entropy remains constant and positive. The exponential scalar factor at the horizon exactly compensates the area growth, giving this behavior a direct geometric explanation. An exact coefficient analysis determines the two four-dimensional branches and their continuation to every higher dimension through closed coupling relations. The linear family is conformally flat and leaves the AdS scale free at fixed couplings; the fractional family is Weyl curved and fixes that scale. The common kinetic relation also excludes their realization through a real one-scalar flat-torus reduction of a metric–dilaton parent.

An agentic society is a collection of AI agents that coordinate autonomously across trust boundaries on behalf of different principals. We show experimentally that in such societies even honest, competent agents often fail to reach satisfactory outcomes when using current harnesses and messaging primitives; and faulty or malicious agents can completely stall progress, influence outcomes, and pursue harmful goals by exploiting communication vulnerabilities. We argue that agentic societies need a social harness. Unlike a personal harness, which manages private context and communication with the principal, a social harness manages interactions with other agents. We propose a layered architecture for social harnesses which (i) prevents classes of communication failures outright, (ii) enables agents to detect invalid messages, and (iii) supports post-facto investigation and consequences.

Traditionally, the disc is believed to evolve under the influence of turbulent viscosity, although the importance of this mechanism has recently been questioned. Alternatively, magnetic disc wind or gravitational instability could be considered, but which of these three mechanisms contributes the most at a given evolutionary stage remains an open question. We present global numerical hydrodynamic simulations of protoplanetary disc evolution in the thin-disc limit on disc lifetime timescales, including all three mechanisms of mass and angular momentum transport. We calculate the gravitational, viscous, and magnetic torques to assess the contribution of each mechanism. We found that these transport mechanisms occupy distinct zones of influence in the disc depending on the stage of evolution: the dominance of disc self-gravity during the early phase is replaced by the prevalence of magnetic disc wind and viscosity, with the latter being especially relevant at the disc periphery. We show that a noticeable decrease in disc mass occurs only after the termination of the embedded phase. The suppression of disc viscous spreading is achieved only for the most intense wind; otherwise, the disc continues to grow in size till the end of simulations. The spiral structure contributes to the temporary retention of dust in the disc. However, this is insufficient to prevent the depletion of dust on long timescales. The results emphasize the importance of a comprehensive approach to long-term simulations of protoplanetary discs with no single mechanism of mass and angular momentum transport regarded as exclusive.

Kernel-level anti-cheats are effective against malicious player behavior in competitive video games, but raise significant user privacy concerns regarding installing unverifiable components at privileged modes (i.e., ring-0 in x86). While existing research has focused on improving the effectiveness of anti-cheats, the user privacy concern has been largely ignored. Tirith is an anti-cheat architecture that addresses this problem using two key ideas. First, instead of running video games within regular processes that players (as root admins) have control over, Tirith executes video games in Protected Virtual Machines that naturally sandbox computations from untrusted admins. Second, to monitor user behavior outside the sandbox (e.g., see if they are running malicious drivers), Tirith leverages a virtualization monitor that is trusted by both players and developers. Together, these ideas remove the need to run untrusted kernel-level anti-cheats, while providing the same level of protection compared to such solutions against a wide-range of common cheating mechanisms. The main challenge we face in implementing these ideas, however, is that the existing software stack for virtual machines is not designed to run video games and creates significant security and performance problems. We address these problems by proposing a security-focused Library OS kernel for games and an efficient graphics sharing pipeline for near-native rendering and display performance. In summary, without compromising on cheating behavior detection or performance, this work makes user privacy a first-class citizen in personal computers.

World-action models (WAMs) jointly model future observations and actions, typically predicting the future as RGB images. Other visual modalities such as depth, pretrained visual features, and point tracks can more efficiently capture geometric, semantic, and motion features. However, how best to combine these modalities within WAMs remains an open question. We introduce ModAR, the first WAM to autoregressively denoise multiple future modalities before predicting actions. This allows each prediction to condition on previously generated modalities. We train from scratch to systematically study how training-data mixtures, predicted modalities, and WAM formulations affect performance. In our evaluations, WAMs benefit from predicting point tracks, DINO features, and depth maps, while additionally predicting future RGB does not provide a consistent benefit. We also find that ModAR's sequential generation outperforms existing WAM formulations, with the highest average success rate at all evaluated data scales. We also fine-tune the video-model-initialized WAM Flex-$\pi$ on the same data; ModAR achieves a slightly higher observed average success rate (75% vs. 72%) while using approximately $20\times$ fewer training FLOPs and no pretraining. On three real-world bimanual tasks, ModAR outperforms baselines and improves with human videos.

We introduce and release ScienceBuddy, an interactive scientific research workspace that brings continually improving scientific agents into researchers' everyday workflows. ScienceBuddy supports researchers in carrying out scientific tasks while transforming their requests, feedback, and execution evidence into tasks and evaluation rubrics for continual learning. At its core is recursive-in-recursive self-improvement, a paradigm that couples harness evolution with model reinforcement learning: the inner recursion improves the harness with the model fixed, while the outer recursion trains the model under the improved harness. Harness evolution shapes training experience, and model learning creates new opportunities for harness adaptation. We present case studies of researcher interaction, harness refinement, and model learning, with the benchmark cases spanning four scientific task families. By releasing ScienceBuddy as a research product, we make this paradigm available to the scientific community and take a step toward discovery intelligence: scientific AI that advances through sustained collaboration with researchers and evolves alongside the research it supports. Website: http://science-buddy.io

Spherical p-spin models provide a mean-field framework for glassy dynamics. Coupling such systems opens a controlled way to probe how they evolve jointly, develop cross correlations, and possibly share common aging scales. We study spherical p-spin systems with site-independent inter-system couplings and generally correlated quenched disorders. We derive closed multi-subsystem two-time equations for correlations, responses, and spherical constraints. A marginal one-step replica-symmetry-breaking construction provides static benchmarks for overlap plateaux, aging crossover scales, and effective temperatures. We then specialize to two ferromagnetically coupled p=3 systems and compare dynamical data with marginal 1RSB predictions. Independent quenched disorders reduce the equal-time correlation between the systems below its disorder-free value, while correlated disorders enhance it. For sufficiently strong coupling, finite-time fluctuation-dissipation estimates within and between the systems are compatible with a common effective temperature even when one or both subsystems would equilibrate as a paramagnet in isolation. This common value lies above the effective temperatures that the constituent systems would have separately and increases with disorder correlation and coupling strength. The marginal 1RSB value T/m captures these trends but is slightly below the finite-time dynamical estimate. For weak coupling, the dynamical results instead suggest that two aging regimes develop for each system, with partial equilibration within each. We perform a marginal replica analysis with two-step breaking, whose predictions compare favorably with the numerical measurements. Our numerical accuracy is insufficient to determine whether the observed finite-time crossover will eventually become a sharp transition.

Interactive control for video generation is moving from coarse prompts toward fine-grained, physically meaningful manipulation of dynamic scenes. Yet existing controllable methods either require the full control schedule before generation starts, or use pixel-space signals that dictate object positions rather than physical dynamics. To address these limitations, we propose PhysStream, an autoregressive model for physics-grounded image-to-video synthesis that incorporates structured scene memory—positional maps and object tracking maps derived online from previously generated frames—and supports fine-grained motion control via sparse velocity-increment signals that encode physical quantities, letting the model learn the underlying dynamics. We train our model in two stages: a bidirectional model is first finetuned with motion-control conditioning, then a causal autoregressive model is trained with additional structured scene memory, further improving physical consistency. PhysStream enables interactive, mid-generation control over multi-object tabletop rigid-body scenes—a capability not supported by prior methods—reducing motion distribution distance (FVMD) by 33% and trajectory error by 12% over the strongest baselines on synthetic benchmarks, and is preferred by human evaluators in over 85% of in-the-wild comparisons. Please check our website for more details: https://czzzzh.github.io/PhysStream

Consider a branching random walk (BRW) of depth $n$ with standard Gaussian increments, conditioned on all endpoints lying in an interval of radius $r$ (which may depend on $n$), i.e. a small ball event. We prove that this conditioning results in exponential decay of correlations between the endpoints, with correlation length $O(r)$. Our proof is based on the renormalization group, which in this context captures the effect of the endpoint conditioning on earlier steps in the walk. This effect can be separated into so-called relevant and irrelevant parts, and in our setting the relevant part makes the conditioned BRW behave like a branching Ornstein-Uhlenbeck walk for the first $n-O(r)$ steps, leading to the correlation decay. The irrelevant part shrinks in a nontrivial manner, and the simplest argument to bound it uniformly only yields correlation length $O(r^2)$. To achieve the optimal $O(r)$ bound, we establish that the irrelevant part shrinks horizontally in space before decaying uniformly. The BRW is a prototypical example of a log-correlated Gaussian field, and it forms the basis of many hierarchical field theories in the mathematical formulation of quantum field theory. As such, we present our results in a general form which is applicable to other hierarchical field theories with confining potentials, of which the small ball conditioned BRW is an example. We apply our general result to two other models: first, the sinh-Gordon model which has a strictly convex potential, so at the level of covariances the model behaves like one with a quadratic potential, i.e. the model has a positive mass. Second, we consider generalizations of the $\phi^4$ model with any power $\alpha \geq 2$; as $\alpha$ increases from $2$ to $\infty$, these power potentials naturally interpolate between the massive (quadratic) potential and the infinite square well potential of the small ball event.

We prove an equivariant Landweber exact functor theorem for abelian compact Lie groups $G$. For a graded module $N$ over the $G$-equivariant Lazard ring $L_G$, we give necessary and sufficient algebraic conditions on $N$ for the functor \[ X\longmapsto (MU_G)_*(X)\otimes_{L_G} N \] to define a homology theory on the category $\mathrm{Sp}^G$ of genuine $G$-spectra. Our criterion is obtained by varifying the Landweber exactness on each stratum indexed by a closed subgroup of $G$ and then gluing the local flatness data via Euler classes. As an application, we show that for any non-equivariant Landweber exact ring spectrum $E$, $MU_G\wedge_{MU} E$ is equivariantly Landweber exact, thereby proving a conjecture of Wisdom.

A BV structure is constructed on the space of zero modes of a quadratic elliptic higher abelian gauge theory. The associated BV integral is shown to be independent of the choice of zero-mode Lagrangian under mild hypotheses. The construction yields explicit zero-mode partition functions for several $p$-form abelian gauge theories.

Barycentric Rényi divergences were introduced in [Mosonyi, Bunth, Vrana, Linear Algebra and its Applications, 2024] as an alternative to standard Kubo-Ando constructions to define multivariate quantum Rényi divergences. They are defined via a variational expression and depend on a finite collection of quantum relative entropies $D^{q_x}$. When all the relative entropies are monotone under CPTP maps then so are the corresponding barycentric Rényi divergences, and when all the relative entropies are additive then the corresponding barycentric Rényi divergences are subadditive under tensor product. Additivity has only been established before for the case where all $D^{q_x}$ are chosen to be the Umegaki relative entropy, which is also the only case where the barycentric Rényi divergence (called the minimal one) was known to admit an explicit expression. Here we settle the problem of additivity by showing that for any choice of monotone quantum relative entropies, the regularized barycentric Rényi divergence coincides with the minimal barycentric Rényi divergence on invertible inputs. This in turn implies that if at least two of the $D^{q_x}$ are strictly larger than the Umegaki relative entropy (in a precise sense), then the resulting barycentric Rényi divergence is not even weakly additive.

Large language models can produce fluent answers when their factual support is weak. This paper introduces Chain-of-Self-Questioning (CoSQ), a prompt-only framework that makes answer commitment conditional on an explicit assessment of the information required to answer a question. We evaluate three CoSQ variants under seventeen conditions on the 817-item TruthfulQA multiple-choice validation set using eleven open-weight and hosted model families. In the final balanced-option protocol, Grounded-CoSQ at {\tau}=0.90 reduces the mean unconditional wrong-commitment rate from 13.1% under chain-of-thought prompting to 8.9%, a 32.1% relative reduction, while increasing answered accuracy from 86.9% to 89.7% and answering 87.6% of questions. Both improvements hold for all eleven models and at every evaluated threshold. Critical-CoSQ and Adaptive-CoSQ provide neighboring operating points with 88.6% and 86.5% coverage, respectively, while remaining more reliable than the baseline. A secondary Natural Questions Short-Answer evaluation provides convergent open-form evidence. These findings show that self-assessment can support explicit, tunable answer-or-abstain decisions when an unsupported commitment is more costly than referral or review.

Pruning can reduce the deployment cost of large language models (LLMs), but its impact on context-grounded tool calling remains poorly understood. We systematically study pruning-induced degradation in smart-home tool calling across four LLMs spanning dense Transformer, dense hybrid, and mixture-of-experts (MoE) architectures, together with depth, width, hybrid, and expert pruning methods. After post-pruning supervised fine-tuning (SFT), we evaluate more than 19,500 instances from three smart-home datasets. Beyond aggregate task accuracy, we characterize degradation along two dimensions: action components (i.e., operation, device, argument, and value) and task complexity. Our results show that dense models have narrow safe pruning regions followed by sharp degradation, while MoE models tolerate substantially more pruning. Pruning degrades grounded specificity before schema-level intent, and aggressive dense pruning can induce systematic over-refusal. These findings highlight the importance of evaluating pruning beyond aggregate accuracy when selecting pruned LLMs for reliable tool execution.

The area compressibility modulus is a key descriptor of lipid membrane mechanics, but the molecular interactions that determine this elasticity are not evident from the total modulus alone. Here, molecular dynamics simulations of a POPC bilayer described by the coarse-grained Martini 3 force field were combined with virial stress analysis to decompose the area compressibility modulus into contributions from molecular groups and their interactions. Partial lateral tensions were evaluated as functions of membrane area strain, and their derivatives at the equilibrium state were used to obtain the corresponding contributions to the area compressibility modulus. Hydrocarbon chains provided the dominant positive contribution, accounting for approximately 70% of the total modulus, whereas water-lipid interactions contributed approximately 30%, predominantly through water-headgroup interactions. Within the bilayer, the headgroup and headgroup-chain contributions were of similar magnitude but opposite in sign and nearly canceled. Direct intermonolayer interactions contributed only about 3% of the bilayer-only modulus, indicating an almost additive elastic response of the two monolayers. The hierarchy of elastic contributions differed markedly from that of equilibrium partial tensions, showing that interactions responsible for static stress balance are not necessarily those governing membrane stiffness. This decomposition provides a microscopic interpretation of lipid bilayer area elasticity.

We study the numerical geography and tangent geometry of very amply polarized Calabi–Yau threefolds $(X,H)$ through the positivity of the first jet bundle $J^1(H)$. Writing $d=\int_X H^3$, $c=\int_Xc_2(X) H$, and $e=\int_X c_3(X)$, we exploit two different positivity properties of this single bundle. Mixed intersections on $\mathbb{P}(J^1(H)^*)$ give $e\ge-5d-c-c^2/(4d)$, while a volume estimate for a perturbed tautological class gives $e\ge40d\left[(1-\frac{c}{10d})^{3/2}-1\right]$; in particular $e+6c\ge0$, improving Sun's inequality $e+10c\ge0$. As consequences, we obtain the uniform Hodge bounds $-4d-80\le h^{1,1}(X)-h^{2,1}(X)\le173d/66$, the lower bound $\mathrm{deg}X^\vee\ge78$ for the dual hypersurface, and, in the critical case $X\subset\mathbb{P}^6$, the upper bound $d\le34$. We also prove that, for every $m\ge2$, the tangent-incidence morphism associated with $|mH|$ is the normalization of the tangent variety, conjecture tangent birationality for complete embeddings $X\subset\mathbb{P}^N$ with $N\ge7$, and verify it for several families.

We prove that every smooth properly embedded free-boundary minimal annulus in the unit ball is congruent to the critical catenoid. We also classify positive solutions of $(\Delta_{\mathbb{S}^2}+2)u=0$ on smooth spherical annuli with $u=0$ and $|\nabla u|=1$ on the boundary; their one-homogeneous extensions are the axially symmetric Alt-Caffarelli cones. Lastly, we also treat the case of free-boundary minimal annuli in spherical caps.

We study the singular limit $p \downarrow 1$ for positive radial entire solutions $u_p$ of $$ -\Delta_p u_p=F_p\left(|x|, u_p,\left|\nabla u_p\right|\right) u_p^{-\beta_p} \quad \text { in } \mathbb{R}^n, $$ where $n \geq 2,1<p<\min \{2, \sqrt{n}\}$, and $0 \leq \beta_p \leq p-1$. Assuming that $$ F_p \rightarrow F_1 \quad \text { locally uniformly }, \quad \frac{\beta_p}{p-1} \rightarrow \mathbf{c} \in[0,1] \quad \text { as } p \downarrow 1, $$ we prove that, after passing to a subsequence, $u_{p_j} \rightarrow u$ in $C_{\text {loc }}\left(\mathbb{R}^n\right)$ and $\nabla u_{p_j} \stackrel{*}{\rightharpoonup} \nabla u$ in $L_{\text {loc }}^{\infty}\left(\mathbb{R}^n ; \mathbb{R}^n\right)$, where $u \in W^{1, \infty}\left(\mathbb{R}^n\right)$ is radial, and solves $$ -\Delta_1 u=\mathtt{K}(|x|) \quad \text { in } \mathbb{R}^n . $$ On $\left\{x \in \mathbb{R}^n \mid \mathtt{G}(|x|)<1\right\}$, we prove that $\mathtt{K}(|x|)=w^{-\mathbf{c}} F_1(|x|, u(x), 0)$ and that $\nabla u=0$ a.e., where $u_{p_i}^{p_i-1} \rightarrow w$. On the other hand, we show that if $\rho \mapsto F_1(r, t, \rho)$ is affine for every $r$ and $t$, then $\mathtt{K}(|x|)=$ $w^{-\mathbf{c}} F_1(|x|, u(x),|\nabla u(x)|)$ a.e. in $\mathbb{R}^n$. For $n=1$ and $1<p<2$, we study $$ \frac{\mathrm{d}}{\mathrm{~d} x}\left(\left|u_p^{\prime}\right|^{p-2} u_p^{\prime}\right)=\mathtt{F}_p\left(|x|, u_p,\left|u_p^{\prime}\right|\right) u_p^{-\beta_p} \quad \text { in } \mathbb{R} $$ and obtain analogous results as $p \downarrow 1$.

We present a complete analytic expression for the $N$-body Hamiltonian of nonspinning point particles at second post-Newtonian (2PN) order in the Arnowitt-Deser-Misner (ADM) gauge. Recent work reduced the general $N$-body Hamiltonian to a form containing a single unresolved integral term, which prevented a fully explicit closed-form representation. Here, we evaluate this integral analytically and thereby obtain a fully explicit closed-form expression for the general 2PN $N$-body Hamiltonian. We outline the main steps of the derivation and validate the analytic expression through direct numerical comparisons with the original integral representation.

Neural audio codecs are a key component in speech language modeling. However, their high frame rates lead to long sequence lengths, increasing computational costs. Dynamic frame rate codecs mitigate this by reducing the effective frame rate using a compression step to merge multiple frames together. However, most prior methods either operate on single-codebook codecs or apply a single compression step before multi-layer quantization. This forces all quantization layers to share the same segmentation boundaries, despite the residual embeddings at different quantization layers exhibiting different rates of change over time. We propose LACE (Layer-Adaptive Codec Encoding), a dynamic frame rate codec that applies an independent compression step at each quantization layer, enabling layer-specific segmentation boundaries. To use LACE tokens in downstream text-to-speech (TTS), we further introduce union alignment and boundary anchor mechanisms to make durations consistent across layers while preserving compression benefits. Experiments on LibriTTS show that LACE offers a better rate-quality tradeoff than prior dynamic frame rate methods on the reconstruction task and improves TTS inference efficiency while maintaining competitive synthesis quality. Our code is released as part of the ESPnet3 codec recipe.

Normally strong and tough, steel$\unicode{x2014}$with iron as its base$\unicode{x2014}$falls prey to severe embrittlement when infiltrated by hydrogen; the insights into why are not well understood. This work explores how hydrogen affects bond strength in iron during fracture and why it reduces cohesion between fracture surfaces, laying bare the central role of electrostatic repulsion.

Recent observations have identified a new class of long-duration gamma-ray bursts (GRBs) likely produced by compact binary mergers. Using radio observations and lightcurve modelling, we investigate whether a magnetar remnant can power the long-lasting prompt emission observed in this merger-driven GRB sample. We derive constraints on the magnetars' rotational energy and magnetic-field strength, and assess whether the magnetar central-engine model is viable for the observed events. We conducted 2.1 GHz radio observations of seven nearby merger-driven GRBs ($z<0.25$) using the Australia Telescope Compact Array (ATCA), obtaining sensitive upper limits on late-time radio emission 520-6900 days post-burst. We modelled the expected radio light curves from magnetar-energized ejecta interacting with the circumburst medium and compared them to our observations. We separately tested the magnetar hypothesis against the extended gamma-ray emission using a fallback-accreting magnetar model. No radio counterpart is detected in any of the observed GRBs, with 3$\sigma$ flux density upper limits of 33-72 $\mu$Jy at 2.1 GHz. Modelling the expected synchrotron emission from magnetar-energized ejecta interacting with the circumburst medium, we find that the radio non-detections remain compatible with energetic outflows in low-density environments. The analysis of the prompt gamma-ray emission provides complementary constraints on the spin period and magnetic field of the magnetar engine. Once fallback accretion and jet baryon-loading are considered, the parameter space is narrowly confined.

Let $\mu$ be a finitely supported probability measure on $\mathrm{SL}_2(\mathbb{R})$ whose support generates a Zariski-dense discrete subgroup. We prove that its stationary probability measure on $\mathbb{P}^1(\mathbb{R})$ is singular with respect to the $\mathrm{SO}(2)$-invariant probability measure. The proof compares winding variances on finite covers of a closed hyperbolic surface and uses a topological obstruction.

Measuring M dwarf ages is a central challenge in stellar astrophysics. These stars evolve so slowly that isochrone fitting gives little constraint, requiring alternative methods based on rotation, activity, and kinematics. Reliable ages help constrain the formation and evolution of planetary systems around M dwarfs, including the temperate sub-Neptunes now being characterised with the James Webb Space Telescope (JWST). We present an age analysis of six nearby M dwarf planet hosts (TOI-732, TOI-736, TOI-270, TOI-1468, TOI-1231, and K2-18) using lithium absorption at 6708 Å, rotation periods, and Galactic kinematics. The Li I 6708 Åfeature is absent above 3$\sigma$ in all targets, implying substantial depletion and ages exceeding 200 Myr. Rotation periods of 39-145 days yield ages of 2.8-8.6 Gyr, calibrated against open cluster M dwarfs and including the intrinsic dispersion of the rotation-age relation. Kinematic ages span 0.8-13 Gyr with uncertainties of 4-6 Gyr. These are less precise per star but help identify outliers such as TOI-1231 (~13 Gyr) and K2-18 ( ~1-2 Gyr) and place the stars in Galactic context. Rotation yields age constraints 2-6 times tighter than kinematics where periods are measured, and comparable constraints where periods must be inferred from chromospheric activity. Combining multiple indicators enables more secure classification of these stars' evolutionary states, providing reference points for future comparative studies.

$\text{SiGeSn}$ alloys are promising silicon-compatible semiconductors for monolithic infrared photonics. However, their metastable nature limits the thermal budgets available for post-growth device processing, and the mechanisms governing their thermal degradation remain unresolved. Here, we investigate the thermal stability of $\text{Si}_{0.08}\text{Ge}_{0.83}\text{Sn}_{0.04}$ alloys using in situ spectroscopic ellipsometry (SE) during isothermal annealing at 550 {\deg}C. We show that adding an ultrathin oxide cap kinetically suppresses Sn exchange with the free surface while leaving bulk diffusion pathways largely unaffected. Uncapped films undergo phase separation after 50 min, accompanied by void formation, a 60% thickness reduction, and a 400 meV blueshift of the $E_{2}$ critical point (CP) transition, consistent with substitutional Sn depletion from the probed volume through surface segregation. In contrast, oxide-capped films exhibit a small compositional change (<1 at.% Sn) and optical shift (<20 meV) over the same period, with suppressed void formation, strain relaxation, and alloy decomposition. This surface-kinetic control additionally yields a 25-fold reduction in contact resistivity relative to annealed uncapped alloys. These results identify surface Sn transport as the dominant degradation pathway in SiGeSn and demonstrate that an ultrathin oxide cap extends the thermal stability of metastable group-IV alloys, providing a practical route toward their integration into advanced silicon photonic and electronic platforms.