Software vulnerabilities pose critical security threats, with nearly 50,000 CVEs reported in 2025. While Large Language Models (LLMs) show promise for automated vulnerability detection, three key challenges remain. First, LLM-generated vulnerability reports suffer from high false positive rates and lack reproducible verification. Second, existing LLM-based approaches use suboptimal granularities for vulnerability localization: function-level analysis overlooks bugs when context becomes extensive, while line-level analysis lacks sufficient context. Third, existing approaches have difficulty reasoning about vulnerabilities with complex cross-function dependencies and triggering conditions. We present FuzzingBrain V2, a multi-agent system that addresses these gaps through four key contributions: (1) fully automated vulnerability analysis built on Google's OSS-Fuzz, ensuring all reported vulnerabilities are fuzzer-reproducible; (2) Suspicious Point, a novel control-flow-based abstraction for precise vulnerability localization at the optimal granularity; (3) logic-driven hierarchical function analysis with dual-layer fuzzing enhancing function coverage under resource constraints; (4) MCP-based static and dynamic analysis tools with context engineering enhancing complex vulnerability reasoning. On the AIxCC 2025 Final Competition C/C++ dataset, FuzzingBrain V2 achieved 90% detection rate (36 of 40 vulnerabilities). In real-world deployment, FuzzingBrain V2 discovered 29 zero-day vulnerabilities across 12 open-source projects, all confirmed and fixed by maintainers, with 2 assigned CVE IDs.

This paper introduces four types of subdivision products for simple directed graphs extending those from the undirected case, in particular, the subdivision-vertex join, subdivision-arc join, subdivision-vertex corona and subdivision-arc corona. Structural and spectral properties of these constructions are analyzed, with a focus on adjacency, Laplacian and signless Laplacian spectra.

Most hot subdwarfs (sdO/B) are low-mass core-helium-burning stars formed through binary interaction. A subgroup of intermediate He-rich sdOBs shows extreme heavy-metal (Z>30) enrichments exceeding $10^4$ times solar, especially in Zr or Pb. We analyse the first ultraviolet spectra of the "heavy metal" subdwarfs LSIV-14 116 (Zr-rich) and EC22536-5304 (Pb-rich) to determine their abundance patterns and test nucleosynthesis models. Both stars show exceptionally rich heavy-element spectra dominated by ions in stages III-VI, many absent from standard line lists. We compiled literature energy levels, wavelengths, and oscillator strengths and implemented them in the SYNSPEC code. In addition, we computed new oscillator strengths for As III, Se III, Hf IV, and Tl IV. New photoionisation cross-sections for Pb III-VI enabled the first non-LTE models of multiply ionised Pb. In LSIV-14 116 we detect 16 light and 24 heavy metals (Ga-Bi); Br, Nb, Mo, Pd, In, Sb, Te, and Xe are measured in an sdO/B star for the first time. In EC22536-5304 13 light and 26 heavy metals are detected, including first detections of La, Ce, Pr, Nd, Er, Yb, Lu, Hf, Ta, W, Os, Pt, Hg, Tl, and Bi. LSIV-14 116 peaks at ~4.3 dex for Sr-Sn relative to solar, declining to 3.1 dex at Pb and 2.3 dex at Bi, whereas EC22536-5304 reaches 6.2 dex for Pb and 5.4 dex for Bi. Both stars are Fe-poor. The abundance patterns cannot be explained by atomic diffusion alone and retain a clear nucleosynthetic signature. EC22536-5304 closely matches predictions of i-process nucleosynthesis, providing strong evidence for i-process self-enrichment in hot subdwarfs. EC22536-5304 likely formed via Roche-lobe overflow, whereas LSIV-14 116 likely originated from the merger of two low-mass white dwarfs, which may explain differences in its enrichment pattern. These results suggest that heavy metals in other He-sdO/Bs may also be self-synthesised.

Advanced air mobility operations will require reliable coordination mechanisms for managing dense traffic near vertiports. However, sequencing decisions may become vulnerable when they rely on potentially falsified self-reported information such as estimated time of arrival. Self-interested vehicles may misreport their arrival times to obtain favorable landing priority, while malicious actors may spoof information to disrupt sequencing decisions or induce unnecessary congestion. This paper studies secure coordination for vertiport sequencing under sensing uncertainty. We consider a coordinator that combines self-reported Remote-ID information with externally obtained surveillance measurements to check reports and assign separation-feasible arrival schedules. Since surveillance-based estimates are uncertain, falsified reports may remain consistent with the sensing uncertainty region and cannot always be rejected outright. We therefore formulate sequencing as a robust design problem over this uncertainty region. Self-interested misreporting is modeled as a strategic deviation that improves the reporting vehicle's own sequencing outcome, whereas malicious spoofing is modeled as an adversarial disturbance that degrades the system-level objective. The final paper will develop robust sequencing rules over surveillance-consistent uncertainty sets and evaluate their performance in representative vertiport sequencing scenarios.

We predict an antipolar instability in hexagonal LaN using first-principles density functional theory. Starting from a nonpolar hexagonal phase, we identify competing polar and antipolar zone-center phonon instabilities. Condensation of the polar and antipolar modes stabilizes, respectively, dynamically stable wurtzite (WZ) phase and an hexagonal antipolar (AP) phase which is characterized by alternating local polarization and zero net macroscopic polarization within the unit cell. At ambient conditions, the AP phase is metastable with respect to the WZ phase, and a finite energy barrier exists between these phases, suggesting a possible polarization-switching pathway via the AP intermediate state. The energy barrier between the WZ and AP phases decreases with increasing pressure, indicating enhanced tunability between polar and antipolar states. The sublattice polarization increases with pressure in the AP phase, while it decreases in the WZ phase. We further find that, with increasing pressure, the rock-salt and tetragonal phases of LaN become more stable than the hexagonal phases (AP and WZ). Consequently, the realization of the AP phase is more favorable in the low-pressure regime, where hexagonal phases remain energetically competitive. These results demonstrate pressure-driven competition between polar and antipolar phases in LaN and point toward antiferroelectric-like behavior in this binary nitride system.

This paper establishes quasi-optimal and lower-order error estimates for weak Galerkin, discontinuous Galerkin, and hybrid-high order finite element methods for the biharmonic equation under minimal regularity assumptions on general polytopal meshes. Furthermore, it is shown that the stabilization is an efficient contribution in a~posteriori error estimators.

We show that every $C^2$ minimal action of Thompson group $T$ on the circle is ergodic with respect to the Lebesgue measure. If such action is not minimal then the Lebesgue measure of the exceptional minimal set is zero.

Short-packet communication alters the fundamental performance limits of reconfigurable intelligent surface (RIS)-assisted systems, making conventional analyses based on the infinite blocklength regime insufficient. This work investigates RIS-assisted transmission in the finite blocklength (FBL) regime while explicitly incorporating thermal noise generated by passive RIS elements, an effect commonly neglected in existing models. A unified analytical framework is developed to characterize the block-error rate (BLER), its asymptotic behavior, and the resulting goodput under both uniform and non-uniform RIS reflection coefficients. Our results show that ignoring RIS thermal noise leads to a pronounced overestimation of reliability with the mismatch increasing as the number of reflecting elements grows. Furthermore, increasing the RIS size does not always improve performance, particularly in the low transmit power regime where accumulated noise becomes dominant. Overall, the results highlight fundamental limitations of idealized RIS models and demonstrate the need for incorporating thermal noise for accurate system evaluation.

We study a class of dynamically consistent risk measures that robustify a time-homogeneous Markovian reference model by allowing for distributional uncertainty in its transition laws. We start from one-step convex risk evaluations in which ambiguity is captured by penalized worst-case expectations over alternative transition laws. Imposing time consistency then yields a convex monotone semigroup on bounded continuous payoff functions, and this semigroup represents the associated dynamic risk measure. The semigroup is uniquely characterized by its risk generator. Under a lower bound on the family of penalties in terms of suitable optimal transport costs relative to the reference laws, we identify the generator on smooth test functions. For optimal transport bounds with linear small-time scaling, this produces a first-order, drift-type correction given by a convex Hamiltonian acting on the gradient. Under martingale transport constraints and a different scaling, however, the leading correction is genuinely of second order and is described by a convex monotone functional acting on the Hessian. We illustrate both regimes for Wasserstein and martingale Wasserstein penalizations and derive explicit formulas via convex conjugates of the underlying transport costs. The associated dynamic risk measures admit stochastic control representations in which the control acts on the drift in the first-order case and on the volatility in the second-order case.

Modern biomedical survival studies with high-dimensional genomic and clinical predictors are challenged by missing covariates. Existing methods conduct inference through penalization and debiasing when the number of covariates diverges with sample size, but they are typically developed with fully observed covariates. Conversely, substantive-model-compatible multiple imputation methods, particularly substantive-model-compatible fully conditional specification (SMC-FCS), provide principled handling of missing covariates while preserving compatibility with the Cox model, yet current methodology and theory remain largely restricted to fixed-dimensional settings. To address these limitations, we propose a semiparametric multiple imputation framework for inference in Cox regression with missing covariates of a diverging dimension. Missing covariates are imputed through a high-dimensional SMC-FCS procedure driven by Cox-model likelihood contributions, with rejection sampling used to enforce substantive-model compatibility and ridge-regularized posterior draws used to stabilize the imputation models. The algorithm stabilizes the Cox estimator through an imputation-regularized optimization iteration and then generates multiply imputed datasets from a stabilized chain. Inference for low-dimensional linear functionals or contrasts, $c^\top β$, is obtained by combining debiased estimators and within-imputation variance estimates through Rubin's rules. We establish consistency and asymptotic normality of the resulting pooled estimator under a diverging-dimensional regime. Simulation studies demonstrate favorable finite-sample performance, and an application to the Boston Lung Cancer Survival Cohort illustrates the practical utility of the proposed method for high-dimensional survival studies with incomplete covariates.

In this study, we examine an innovative framework towards implementing quantum decision trees utilizing a laser-driven four-level system. We discuss a diamond-shaped atomic configuration, in which we apply Lie-algebraic formalisms to analyze the dynamics of the system. The system is perturbed by a Stokes pulse, represented as $β_j(t)$ (for $j=1,2$), which interacts with the atomic states $|0\rangle, |3\rangle$ and $|1\rangle, |2\rangle$. In addition, a pump laser, denoted as $α_j(t)$, couples the states $|0\rangle, |1\rangle$ and $|2\rangle, |3\rangle$. By employing pulse profiles that possess identical temporal behavior but differ in amplitude, one can effectively redistribute the population from the initial ground state to the other energy levels. This technique facilitates the mimicry of a quantum decision tree. We highlight that the proposed methodology is scalable to N-level systems, enhancing its adaptability and potential utility in quantum computing and various decision-making applications. We introduce a novel framework for implementing quantum decision trees using a four-level laser-driven atomic system. Employing a diamond-shaped energy configuration, we analyze system dynamics through Lie-algebraic methods. Using pulse profiles with identical temporal structures but varying amplitudes, we achieve controlled population redistribution among energy levels, effectively simulating a quantum decision tree. This methodology is scalable to systems of \(N\) levels, offering potential applications in quantum computing and decision-making processes.

Defects are both physically rich objects and powerful tools in modern quantum field theory. They are extended operators, such as boundaries, impurities, and probe particles, embedded in many-body systems. In this dissertation, we study the universal aspects of defect dynamics from the perspective of symmetry principles. We bring together several themes, including defect renormalization group flows, effective string theory, and impurities in atomic quantum gases.

The Erdős-Ginzburg-Ziv theorem states that every sequence of 2n - 1 integers contains a subsequence of length n whose sum is divisible by n. Choi, Kang, and Lim gave a simple deterministic O(n log n) algorithm for finding such a subsequence, and Leung recently improved this to O(n log log log n). We give a deterministic linear-time algorithm. The core is a linear-time algorithm for the following prime target subset-sum problem: given p - 1 nonzero residues in Z_p and a target residue, find a subset with the prescribed sum. Our algorithm maintains a compact arithmetic-progression representation of reachable sums. When two progressions intersect, a bounded Frobenius interval in their sum allows them to be merged into one longer progression, with enough growth to pay for the update. When the representation either contains a full progression or covers all nonzero residues, the target residue is recovered constructively. The standard multiplicative reduction then extends the prime algorithm to arbitrary moduli.

Pulsar timing is a valuable source of high-precision astrophysical measurements which can be used to probe gravitational physics, including by detecting gravitational waves. An important factor limiting the precision of these measurements is pulse jitter; i.e., intrinsic, short-timescale variation in the amplitude and shape of pulses from a given pulsar. Because conventional pulse time-of-arrival (TOA) measurement relies on template matching, which assumes the average pulse shape is stable, such variation gives rise to jitter noise in TOA measurements. Here we introduce a generalization of the template matching technique, making use of principal component analysis, which can account for variations in pulse shape. We compare this technique to other proposals for mitigating jitter noise in pulsar timing, paying particular attention to the possibility of corrections absorbing other astrophysical signals of interest, and demonstrate its effectiveness using simulated data.

In arXiv:1711.05958, arXiv:2103.12673, the authors derive one-dimensional Landau-Ginzburg mirrors of Dubrovin-Zhang Frobenius manifolds constructed on regular orbit spaces of an extension of affine Weyl groups. We generalise the method employed, and classify the resulting Frobenius manifold structures in Dynkin type A. We interpret our results in terms of a stratification on the Hurwitz space boundary, and develop a pole-collision framework to compare the Frobenius structures within different strata. With this, we can prove a structural result at the level of the prepotential, for arbitrary rank and dimension, as a suitable renormalised limit of the formulae in arXiv:2412.05165. As a corollary, a conjecture of Ma and Zuo regarding the form of prepotentials related to doubly-extended affine Weyl groups is proven.

Efficiently realizing logical operations on general stabilizer codes remains a long-standing challenge in fault tolerant quantum computing. While code surgery provides a general framework with provable guarantees by joint logical measurements, existing constructions are largely theoretical and incur substantial ancilla overhead in practice. In this work, we propose GeneCS, a resource-efficient compiler for synthesizing code surgery protocols for arbitrary stabilizer codes. Our approach leverages structure-aware optimizations to eliminate redundancy in graph construction, dynamically balance expansion and congestion, and incorporate code degree constraints. Experimental results show that GeneCS achieves an average reduction of over $85\%$ in ancillary qubits and checks for both single-code and cross-code logical operations, while preserving logical error rates. Moreover, our compiler scales to codes with more than $10^4$ qubits with an amortized compilation time of about one second per instance. These results enable practical logical operations and efficient cross-code communication, thereby supporting the deployment of modern QLDPC codes and heterogeneous quantum architectures.

We derive the sharp return-probability asymptotic for the switch--walk--switch lamplighter walk with lamp group $\mathbb Z_2$ over the infinite $d$-regular tree: \[ p_{2n}(e,e) = ρ_d^{2n} \exp\left[ -\left(π^2(\log(d-1))^2+o(1)\right) \frac{n}{\log^2 n} \right]. \] The proofs were generated by QED, a multi-agent system co-developed by the authors, without human intervention beyond the specification of the problem. This provides a test case for the ability of AI systems to produce rigorous mathematical proofs.

DNA origami is a powerful method to achieve nanoscale folded structures. Despite rapid improvements in folding and purification methods, DNA origami objects are still often produced in small quantities and studied at single molecule scale. Here, we design simple DNA origami-inspired polymers with complex topologies, and study their rheology and viscoelastic properties in dense conditions. First, we designed and purified topologically distinct DNA nanostructures, linear, circular, and "tadpole" polymers, to evaluate how polymer architecture influences entanglement and rheology. Despite their distinct topologies, we observe that all constructs obeyed universal rheological scalings, likely due to their short length. However, upon thermal annealing in the bulk, the DNA origami-like polymers displayed significantly different behaviours. Our results suggest that DNA origami-like polymers could be used to engineer thermoresponsive behaviours in complex fluids by introducing reversible and topology-dependent crosslinking.

Motivated by fast matrix multiplication and recent connections between asymptotic tensor rank and fine-grained complexity, we revisit classical tools from the matrix multiplication literature and develop a framework for obtaining improved asymptotic rank upper bounds for tensors beyond matrix multiplication. In the 1980s, Coppersmith-Winograd and Strassen discovered a series of speedup theorems for asymptotic rank: in certain regimes, one can extract additional terms from a border rank upper bound on a tensor $T$, and then use these terms to obtain an improved asymptotic rank of $T$. We establish general speedup theorems that subsume these results and enable quantitative improvements. Two representative applications are: (1) The asymptotic rank of the small Coppersmith-Winograd tensor $\mathrm{cw}_q$ is less than its border rank. For instance, we prove the asymptotic rank of $\mathrm{cw}_2$ is smaller than $3.931$, improving on $\underline{\mathrm{R}}(\mathrm{cw}_2)=4$. It is known that if the asymptotic rank of $\mathrm{cw}_2$ equals $3$, this would imply $ω=2$. (2) A general improvement over Strassen's bound: we obtain an upper bound below $d^{2ω/3}$ on the asymptotic rank of any $d\times d\times d$ tensor. To make full use of speedups, we analyze degenerations in which both sides are nontrivial direct sums, a setting where the optimal quantitative bound one can achieve was previously unclear. We do so via an approach we call Strassen calculus: a systematic method for converting such degeneration data into explicit asymptotic rank bounds using Strassen's theory of the asymptotic spectrum.

The element abundances of Milky Way disc stars encode entangled imprints of multiple enrichment processes, making it difficult to uncover the underlying chemical evolution. Here we re-project 16 stellar abundances for 199,290 red giant stars ([Fe/H]$ > -1$) into a set of (4) shared enrichment patterns, providing a generative framework for learning the organising structure of the Milky Way disc. The relative contributions of these patterns vary systematically across the disc, revealing a low-dimensional enrichment basis that responds coherently to global drivers of disc evolution. By grouping stars according to their pattern contributions, we identify coherent enrichment pathways that exhibit strong chemo-spatial correlations and are stratified in both age and height above the plane, linking radial growth to vertical disc structure. Stars occupying similar positions along these enrichment pathways also show coherent vertical deviations across radius, indicating that the low-dimensional chemical structure captures the disc's response to dynamical perturbations. We identify a transition in enrichment behaviour at approximately 6 Gyr, marking the onset of a more chemically mixed regime with increasing contributions from delayed sources. Within this connected system, the observed $α$-bimodality arises within a shared, low-dimensional abundance structure, with stars populating continuous sequences of changing enrichment fractions that are tightly coupled to spatial, temporal, and orbital coordinates across the Milky Way disc.

Let $G$ be a virtually compact special Gromov-hyperbolic group. We prove that the double $G *_H G$ along a quasiconvex subgroup $H$ is virtually compact special. More generally, we show that if a finite graph of groups has constant vertex groups, with each vertex group virtually compact special Gromov-hyperbolic and each edge group quasiconvex in its adjacent vertex groups, then its fundamental group is virtually compact special.

For $w$ in the symmetric group $S_n$, let $\widetilde C_w$ be the corresponding modified, signless Kazhdan--Lusztig basis element of the type-$A$ Hecke algebra $H_n(q)$. An extension [Ann. Comb. 25, no. 3 (2021) pp. 757--787] of a result of Deodhar [Geom. Dedicata 36, (1990) pp. 95--119] implies that any factorization of the form \begin{equation*} \widetilde C_w = \frac1{f(q)} \widetilde C_{v^{(1)}} \cdots \widetilde C_{v^{(r)}}, \end{equation*} with $v^{(1)},\dotsc,v^{(r)}$ maximal elements of parabolic subgroups of $S_n$ and $f(q) \in \mathbb N[q]$ depending on these, provides cancellation-free combinatorial interpretations of the polynomials $\{P_{v,w}(q) \,|\, v \in S_n \}$ appearing in the expansion $\sum_v P_{v,w}(q) T_v$ of $\widetilde C_w$ in terms of the natural basis $\{ T_v \,|\, v \in S_n \}$ of $H_n(q)$. While the set of permutations $w \in S_n$ admitting such a factorization of $\widetilde C_w$ has not yet been characterized, we apply a result of Gaetz -- Gao [Adv. Math. 457 (2024) Paper No. 109941] to describe a set admitting no such factorization.

In this paper, we present new multiplicity fixed point theorems for operators acting on Cartesian products of two normed linear spaces. We show that Leggett-Williams type conditions in each component of the system guarantee the existence of nine distinct fixed points, of which four of them are coexistence fixed points, i.e., points with all components nontrivial. In addition, a hybrid approach combining Leggett-Williams conditions in one component with Krasnosel'skii compression-expansion conditions in the other allows us to obtain three fixed points. As an application, we establish the existence of multiple positive solutions for nonlinear systems of second-order equations with two-point boundary conditions.

We investigate thermosphere responses to non-orographic gravity waves (GWs) using wind measurements from the Neutral Gas and Ion Mass Spectrometer onboard the Mars Atmosphere and Volatile EvolutioN mission, alongside simulations from the Mars Planetary Climate Model. We focus on zonal jets in high-latitude regions of the upper atmosphere. Jet acceleration and deceleration (280 m/s ) arise from momentum divergence (1,300 m/s/sol ) driven by wave saturation and wind filtering. Simulations and observations indicate that GWs modulate these jets in the hemisphere associated with the descending branches of the Hadley Cell, due to the absence of wave critical layers in the middle atmosphere. Interactions between GWs and the mean flow can shape the circulation and dynamics of the upper atmosphere of Mars.

Achieving effective uplink bistatic ISAC over an OFDM waveform gives rise to challenging interference structures. These are mostly due to unequal direct- and echo-path contributions and Doppler-induced ICI, rendering orthogonal resource separation and fixed SIC strategies inadequate. To address this problem, we propose a RS-inspired framework where the transmitter splits each communication message into a robust and a supplementary stream, which are jointly superposed over a sensing signal. Furthermore, we present the design of a staged sensing-communication receiver. Based on this framework, we derive tractable per-subcarrier SINR expressions and establish the relation between sensing accuracy and communication reliability based on the Fisher information. Building on these, we formulate a joint power-allocation problem for SE maximization under sensing-performance and power constraints. The resulting non-convex formulation is solved using convex surrogates and fractional programming. Numerical results demonstrate that, compared to NOMA-inspired baselines, the proposed framework provides more effective IFI management and improved robustness to Doppler-induced ICI.

Phylogenetic networks and, more generally, directed acyclic graphs (DAGs) represent hierarchical structure beyond trees, for instance in the presence of reticulate evolutionary events such as hybridization or horizontal gene transfer. A central question is which parts of such graphs are essential with respect to leaf-observable information, and which parts can be removed without changing this information. Resolving this question can lead to principled simplification methods for phylogenetic networks, such as the recent normalization approach of Francis et al. In this paper, we study this question from three related perspectives: clusters displayed by a DAG $G$, least common ancestors (LCAs) of subsets of its leaf set, and visibility, a path-based property of vertices. We first introduce an LCA-based simplification procedure called $i$-regularization. For a DAG $G$ and $i\geq 1$, the DAG $\reg_i(G)$ retains precisely those vertices that occur as unique LCAs of leaf subsets of size at most $i$, removes the remaining non-leaf vertices by a graph-editing operation $\ominus$, and then deletes shortcuts. We show that $\reg_i(G)$ preserves all such LCAs, is $i$-lca-relevant, and admits a cluster-level description: it is regular, i.e., isomorphic to the Hasse diagram of the corresponding lca-clusters. We then compare LCA-based regularization with normalization. Using the same $\ominus$-operator, we describe the cover construction underlying normalization, identify visible vertices that are nevertheless removed, and characterize when regularization and normalization coincide. Together, these results provide a unified framework for cluster-based, LCA-based, and visibility-based simplifications of DAGs and phylogenetic networks.

The relation $M_H^2\simeq M_ZM_t$, previously proposed as a non-trivial Higgs mass coincidence, is reconsidered with present electroweak inputs and with a scheme-consistent matching analysis. With the 2025 PDG values for $M_Z$, $M_W$ and $M_H$, and the ATLAS-CMS direct top-mass combination, the pole-level ratio is $ρ_{Zt}=M_ZM_t/M_H^2=1.00362\pm0.00261$. Thus an exact pole-level geometric relation predicts either $M_H=125.426\pm0.120\,\mathrm{GeV}$ or $M_t=171.898\pm0.302\,\mathrm{GeV}$, which is still a $1.4σ$ test rather than an exclusion. By contrast, the companion arithmetic relation gives $ρ_{Wt}=(M_W+M_t)/(2M_H)=1.00994\pm0.00159$ and is not a viable exact mass sum rule. We then evaluate the complete NNLO weak-scale $\overline{\mathrm{MS}}$ matching formulae at $μ=M_t$. In the standard convention one obtains $\widehatρ_{Zt}(M_t)=\sqrt{g_2^2+g_Y^2}\,y_t/(4\sqrt2λ)=0.96714\pm0.00361$. Consequently, the exact running-coupling boundary condition $λ=g_Zy_t/(4\sqrt2)$ at the top scale would predict $M_H=123.19\pm0.20\,\mathrm{GeV}$, or equivalently $M_t=177.81\pm0.50\,\mathrm{GeV}$ when $M_H$ is held fixed. This is incompatible with the measured point. A possible symmetry explanation must therefore act on pole-level threshold quantities, or provide a finite matching factor $κ_{\rm th}=1.0340\pm0.0039$ at the electroweak scale. We formulate this requirement as a target for custodial/top-Higgs or triality-like symmetry extensions.

We introduce force-kernel extended-system adaptive biasing force (FK-eABF), a force-based kernel reformulation of eABF that replaces the histogram-based mean-force accumulator of conventional eABF with a sparse population of Gaussian kernels storing local running-mean forces. Biasing forces are recovered by Nadaraya-Watson regression, yielding smooth estimates from the earliest stages of a simulation without a minimum-count threshold, while the same kernel population also defines an auxiliary, self-attenuating exploration force that requires no prior knowledge of barrier heights. On N-acetyl-N'-methylalanylamide in explicit water, FK-eABF achieves full free-energy landscape coverage faster than well-tempered metadynamics (WT-MetaD), on-the-fly probability enhanced sampling (OPES), and WTM-eABF, while all four methods converge to comparable accuracy given sufficient time. FK-eABF also retains long-time accuracy: on the DFG-in/out transition of Abl1 kinase, multi-microsecond simulations recover the established near-isoenergetic balance between states. At the opposite extreme, applied to the electrocyclic ring closure of 1,3-butadiene at the ab initio molecular dynamics level, FK-eABF recovers the free-energy landscape within 30 ps. Together, these benchmarks, spanning more than four orders of magnitude in simulation time, establish FK-eABF as more than a kernelized implementation of eABF: A force-based kernel reformulation that delivers faster early-time convergence without sacrificing long-time quantitative accuracy.

Scientific computer simulations cannot represent all scales in realistic applications. To bridge this model-data gap, parameters are injected into models and constrained with noisy data using Bayesian inversion. To reduce the number of simulator evaluations, which can be 10^5 or more, modern approaches employ dimension reduction in conjunction with emulation of the forward map (that contains the simulator). Due to scarcity of model evaluations and data, this dimension reduction becomes very important for posterior sampling performance. Recent work on likelihood-informed subspaces (LIS) truncates to informative directions by optimizing bounds on information loss, and though mathematically well-adapted to sampling, they are often restrictive in practice. In this work, we provably generalize this methodology to facilitate application to $α$-tempered (i.e., annealed, power-posterior) distributions for $α$ in [0,1]. We provide theory to build partially-informed spaces termed $α$-LIS. We show how $α$ < 1 can often produce near-optimal spaces. In addition, we focus on applying $α$-LIS to practical cases, where the available data is severely limited and noisy. We propose and test extensions for utilizing data from the entire sequence of distributions $α$_0 < ... < $α$_k, and use simple approximations of model gradients so that our approach can be used for emulation of forward maps for chaotic or stochastic systems where derivatives are unavailable or uninformative due to noise. In experiments, our accumulated approach is much more robust to these challenging circumstances than the theoretically optimal $α$ = 1.

In this work, we develop a structure-preserving numerical scheme for a Cahn-Hilliard-Darcy model that describes tumor growth in a fluid-saturated porous medium. First, we derive a physically consistent model from the general framework proposed in [29] that guarantees mass conservation and pointwise bounds on the phase-field and nutrient variables, with a decreasing energy law. The resulting model couples the evolution of tumor cells via a Cahn-Hilliard equation with a diffusion equation for the nutrients thro chemotactic interactions and extends the model in [1] by introducing the effect of a surrounding fluid described by Darcy's law. Subsequently, we propose a fully discrete scheme that combines an upwind discontinuous Galerkin method in space and a convex splitting strategy in time, which inherits the fundamental properties of the continuous model: mass conservation, pointwise bounds and discrete energy law. Our theoretical analysis is accompanied by numerical experiments that demonstrate the robustness of the proposed scheme and show the influence of the surrounding fluid on the tumor evolution.