We study conductance fluctuations in random resistor networks with hyperuniform bond disorder, where the fluctuations of the number of bonds present in a test volume $V$ scale as $V^{-a}$ with $a > 1/2$. Since small changes in the concentration of bonds present in a local region give rise to a proportionate increase in the locally averaged conductance, one may expect that in hyperuniform disorder, conductance fluctuations will also show suppressed fluctuations. We argue that this is not the case: conductance fluctuations scale as $L^{-d/2}$ for a sampling size $L$. We show numerical results for $d=2$.

Final FIPS and PKIX standards for ML-KEM and ML-DSA settle the normative floor, yet they do not by themselves provide assurance. In practical post-quantum X.509 deployments, failures still emerge at certificate-profile semantics, SubjectPublicKeyInfo representation, and private-key container import, while current PQ public-key linting does not yet provide a reproducible workflow that says which checks belong to the certification authority, which belong to the artifact importer, and how those checks should act under deployment-facing policy. We present an operational post-quantum X.509 assurance framework for ML-KEM and ML-DSA in a narrow executable profile, pkix-core. The framework reifies 17 final-standards requirements into an assurance registry indexed by owner, stage, detector kind, normative strength, and mode-specific action; packages those requirements into three operator gate packs; spans certificate/profile, SPKI/public-key, and private-key-container/import surfaces; and evaluates them through a frozen mutation-based corpus backed by bounded public-appendix and cross-tool supporting evidence. Across a controlled corpus of 48 artifacts, comprising 21 valid and 27 invalid cases, the artifact detects all expected invalid artifacts in both strict and deployable modes with zero false positives. Strict blocks all 17 active requirements; deployable preserves the same underlying detection coverage while downgrading exactly one exercised ML-KEM canonicality condition from block to warning. On the importer-owned private-key surface, all 7 active requirements are covered, with 7/7 expected invalid detections and no open detector gaps. On a comparable certificate subset, a frozen JZLint baseline meets 5/10 expected invalid detections and fatally rejects 3 valid ML-KEM certificates, whereas the local artifact meets 10/10 with no fatal valid rejections.

Software systems generate massive, evolving, semi-structured logs that are central to reliability engineering and AIOps, yet difficult to analyze at scale under drift and limited labels. Recent advances in pretrained Transformer models and instruction-tuned large language models (LLMs) have reshaped log analysis by enabling semantic generalization and cross-source evidence integration, but also introducing deployment risks such as context limits, latency and cost, privacy constraints, and hallucinations. This paper presents LLM4Log, a systematic review of LLM-based log analysis across the end-to-end pipeline, from upstream logging-statement generation and maintenance to log parsing/structuring and downstream tasks including anomaly detection, failure prediction, root cause analysis, and log summarization. Following a structured search and manual screening protocol, we completed literature collection in November 2025 and identified 145 unique papers across seven logging tasks. We organize the research area through a unified, task-driven taxonomy, summarize common design patterns (prompting/ICL, retrieval grounding, fine-tuning, tool/agent augmentation, and verification), and analyze evaluation practices, datasets, metrics, and reproducibility. Based on these cross-paper analyses, we summarize key lessons and open challenges for reliable real-world adoption. We emphasize robustness under drift and long-tail events, grounding and faithfulness for operator-facing outputs, and deployment-oriented designs with verifiable behavior.

In this paper, we study the portfolio utility maximization in the case where the risky asset is driven by a Brownian motion and an independent homogeneous Poisson measure, with strategies that may include jump signals. This means that the allowed strategies are no longer predictable but also include the information given by a process driven by the Poisson measure. Using the results of Bank and K{ö}rber [1], we first express the considered portfolio as semi-martingale processes. We then present the martingale optimality principle for the exponential utility maximization. This allows to derive an original BSDE with jumps and to express the optimal value and an optimal strategy using the solution to this original BSDE. We then prove existence of a solution to the considered BSDE. We finally present some numerical experiments to quantify the gain of utility given by the information from the jump signals.

Post-quantum migration in TLS 1.3 couples signature-algorithm choice with certificate-hierarchy structure, chain exposure during the handshake, and role-dependent cryptographic cost. In certificate-based authentication, the practical effect of a signature family depends on where it appears in the certification hierarchy, how much of that hierarchy is exposed during the handshake, and how the resulting cryptographic cost is distributed across client and server roles. Post-quantum TLS migration must therefore be evaluated as cryptographic design within authenticated key establishment, with algorithm selection assessed in its deployment context. This paper presents a local experimental study of TLS 1.3 authentication strategies implemented with OpenSSL 3 and oqsprovider. Using a reproducible laboratory setting, it compares ML-DSA and SLH-DSA across multiple certificate placements, hierarchy depths, and key-exchange modes, including classical, hybrid, and pure post-quantum configurations. The analysis is organized into four complementary campaigns: a leaf-only comparison, a full hierarchy strategy matrix, a depth comparison, and a key-exchange exploration. Across the experimental matrix, the main discontinuity appears when SLH-DSA is placed in the server leaf certificate. In that configuration, handshake latency and server-side compute cost increase by orders of magnitude, whereas strategies that confine SLH-DSA to upper trust layers and preserve ML-DSA in the interactive leaf remain within a more plausible operational range. The results also show that transport size alone does not explain the heavy regime: outside leaf-SLH scenarios, transferred bytes and observed chain size track latency closely, but once SLH-DSA reaches the leaf, server-side cryptographic cost becomes dominant.

We study driven-dissipative activated random walk with sleep probability $p$ on an $n$-vertex complete graph with a sink that traps jumping particles with probability $q_n$. We show that the number of sleeping particles $S_n$ left by the stationary distribution has a Gumbel scaling limit for $\exp(-n^{1/3}) \ll q_n \ll n^{-1/2}$. The particular scaling implies that $S_n$ is hyperuniform and thus the stationary configuration law has negative correlations and is not a product measure. We also prove that $S_n/n$ converges to $p$ if and only if $q_n = e^{-o(n)}$, and that, when $q_n=0$, the number of jumps to stabilization undergoes a phase transition at density $p$.

Nonlinear underactuated systems such as two-wheeled inverted pendulums (TWIPs) exhibit a limited region of attraction (RoA), which defines the set of initial conditions from which the closed-loop system converges to the equilibrium. The RoA of nonlinear and constrained systems is generally nonconvex and analytically intractable, requiring numerical or approximate estimation methods. This work investigates the estimation of the RoA for a TWIP stabilized under three model-based control strategies: saturated linear quadratic regulator (LQR), linear model predictive control (MPC), and constraint tightening MPC (CTMPC). We first derive a Lyapunov-based invariant set that provides a certified inner approximation of the RoA. Since this analytical bound is highly conservative, a Monte Carlo-based estimation procedure is then employed to obtain a more representative approximation of the RoA, capturing how the controllers behave beyond the analytically guaranteed region. The proposed methodology combines analytical guarantees with data-driven estimation, providing both a formally certified inner bound and an empirical characterization of the RoA, offering a practical way to evaluate controller performance without relying solely on conservative analytical bounds or purely empirical simulation.

We introduce RFOX (Rotated-Field Oscillatory eXchange), a parameter-free quantum algorithm for combinatorial optimization that combines an almost constant non-stoquastic $XX$ catalyst with a weak harmonic $ZX$ counter-diabatic term. Using the Floquet-Magnus expansion, we derive an effective Hamiltonian whose leading-order $\mathcal{O}(δ/ω)$ corrections yield local $Y$ fields, field-modulated 2-body terms, and poly-local 3-body topological interactions driven by graph connectivity. This structure ensures a nearly flat instantaneous spectral gap, preventing the unpredictable gap collapses typical of conventional $X$ (stoquastic), $XX$, and $X+sXX$ (non-stoquastic) driver schedules. Extensive noiseless simulations and physical hardware experiments on IBM Quantum processors (up to 20 qubits) validate our spectral predictions. RFOX consistently attains near-optimal or exact ground states in the random-field Ising model using up to an order of magnitude fewer Trotter slices, with an advantage that grows alongside problem disorder. These results suggest that fixed-gap, non-stoquastic drivers augmented with analytically derived counter-diabatic terms offer a scalable, tuning-free route for quantum optimization.

Prediction markets are powerful mechanisms for information aggregation, but existing designs are optimized for single-event contracts. In practice, traders frequently express beliefs about joint outcomes - through parlays in sports, conditional forecasts across related events, or scenario bets in financial markets. Current platforms either prohibit such trades or rely on ad hoc mechanisms that ignore correlation structure, resulting in inefficient prices and fragmented liquidity. We introduce ParlayMarket, the first automated market-making design that supports parlay-style joint contracts within a unified liquidity pool while maintaining coherent pricing across base markets and their combinations. Our main result is a convergence characterization of the resulting system. Under repeated trading, the AMM dynamics converge to a unique fixed point corresponding to the best approximation to the true joint distribution within the model class. We show that (i) parameter error remains bounded at stationarity due to a balance between signal and noise in trade-induced updates, and (ii) pricing error and monetary loss scale with this parameter error, implying that aggregate market-maker loss remains controlled and grows at most quadratically in the number of base markets. These results establish explicit limits on the information-retrieval error achievable through the trading interface. Importantly, parlay trades play a structural role in this convergence: by providing direct constraints on joint outcomes, they improve identifiability of dependence structure and reduce steady-state error relative to markets that rely only on marginal trades. Empirically, we show both in controlled simulations and in replay on historical Kalshi parlay data that this design achieves the intended scaling while remaining effective in realistic market settings.

A perturbative expansion of knot invariants is derived using quantum cluster algebras. By interpreting the $R$-matrix of $U_q(\mathfrak{sl}_2)$ as a cluster transformation and introducing an auxiliary parameter $ε$, we derive a perturbed $R$-matrix expressed in terms of Heisenberg algebra generators arising from the representation theory of the quantum cluster algebra. The resulting knot invariant has a zeroth-order term equal to $Δ_K(T)^{-1}$, the reciprocal of the Alexander polynomial, while higher-order terms in $ε$ produce perturbed-Alexander invariants in line with the construction by Bar-Natan and Van der Veen. Our construction combines the Schrödinger representation of the quantum torus algebra with cluster mutation combinatorics and is illustrated with a Mathematica implementation and explicit examples.

Many statistical problems can be addressed by applying a multiple testing procedure (MTP) that controls either the Family-wise Error Rate (FWER) or False Discovery Rate (FDR) under unknown arbitrarily-interdependent $p$-values, without explicitly modeling these inter-correlations. They include the FWER-controlling Bonferroni (1936) MTP and Holm (1979) MTP; the FDR-controlling Benjamini and Yekutieli (2001) MTP; and the DP-MTP (Karabatsos, 2025), based on a Dirichlet process (DP) prior distribution supporting the entire space of MTPs that control either the FWER or FDR. For such an MTP, this study introduces a new and congenial method for Bayesian predictive power analysis, for power calculation and sample size determination for any given planned future (e.g., replication or interim) study. This novel MTP predictive power analysis method is based on a joint prior distribution defining a scale matrix mixture of asymmetric multivariate normal mean-variance mixture distributions, factorized as a general prior distribution for effect sizes (e.g., obtained from expert judgment or results of prior studies), and a uniform prior distribution for correlation matrices representing arbitrary dependencies between $p$-values of test statistics of given multiple hypothesis tests under their alternative hypotheses. The new MTP power analysis method also results in $p$-value weights which can be used to minimize the relative impacts of and assess for significance-chasing biases (e.g., publication bias, $p$-hacking, etc.) in multiple testing, without needing to assume that $p$-values (effect sizes) are independent. The new simulation-based MTP predictive power analysis method is illustrated through the analysis of $p$-values obtained by a famous study of lead exposure and re-analyzed by the previous MTP literature, using R package bnpMTP.

Low-order virtual element methods (VEM) compute a consistent finite-strain contribution through polynomial projections and rely on stabilization to control the unresolved modes in the projector kernel. In current hyperelastic VEM practice, stabilization is often defined by integrating a nonlinear surrogate energy over an auxiliary sub-triangulation and scaled through modified Lamé parameters and incompressibility factors; this can introduce sensitivity to the arbitrary internal tessellation, complicate consistent Newton linearization, and, most critically, inject bulk-dependent proxies into shear-type kernel penalties, artificially stiffening isochoric missing modes in the nearly incompressible regime. This work develops a submesh-free, kernel-only stabilization that decouples deviatoric and volumetric channels and is explicitly designed to scale like the current Newton tangent energy on the kernel: the deviatoric term is scaled solely by a shear measure and enhanced by bounded geometry-driven directional weights, while the volumetric term is scaled by an independent bulk measure and can be capped or suppressed as $ν\to 1/2$. A spectral framework is established in which the canonical VEM stability requirement on the kernel is characterized by generalized Rayleigh quotients and eigenvalue bounds, and it is shown under standard polygon regularity assumptions that the deviatoric stabilization is uniformly equivalent to $μ_E|\cdot|_{1,E}^2$ on the kernel with constants independent of mesh size and Poisson ratio. Element-level diagnostics confirm that classical surrogate-based stabilizations assign bulk-driven energy to isochoric kernel modes as $ν\to 1/2$, whereas the proposed decoupled stabilization remains shear-scaled; kernel spectra and Cook's membrane simulations in the nearly incompressible regime further support improved robustness across polygonal mesh families.

Zero-error recovery under deterministic partial views is graph recovery for the induced confusability relation. A finite family of coordinate-subset observations determines a graph on latent states; $T$-ary exact recovery is graph $T$-colorability, block composition is strong powering, and asymptotic recoverability is Shannon capacity. Coordinate structure gives tractable certificates inside the graph semantics. For affine realized state families with explicit linear presentations, restricted coordinate ranks form a representable matroid certificate giving polynomial-time upper bounds on one-shot confusability and asymptotic capacity, with rank additivity matching direct-sum block composition. In the full tuple-space coordinate model, the realizable confusability relations are exactly the upward-closed coordinate-agreement families. Transitive confusability is equivalent to intersection closure of the generated agreement family, yielding a cluster graph whose capacity is determined by connected components. Host-level realizability determines when the latent state family is canonical. Verifiable rate-$1$ realizability for structural facts holds if and only if the host provides zero-delay synchronization and structural side-information; eleven representative host architectures instantiate the criterion. The same clique-size bit-budget bound governs both the graph-level and host-level layers. All cited results are mechanized in Lean 4 against a shared formalization library.

We show that the normalized Kähler-Ricci flow on a compact Kähler manifold with semiample canonical bundle converges in the Gromov-Hausdorff topology to the metric completion of the twisted Kähler-Einstein metric on the canonical model, as conjectured by Song-Tian's analytic mimimal model program.

We develop an $\mathrm{L}^p$-theory for Dolbeault-Dirac operators on compact Kähler manifolds with coefficients in a Hermitian holomorphic vector bundle $E$. For each $p \in (1,\infty)$ we consider the closed $\mathrm{L}^p$-realization $\mathcal{D}_{E,p}$ of the Dolbeault-Dirac operator $\mathcal{D}_{E}$ on the Banach space $\mathrm{L}^p(Ω^{0,\bullet}(M,E))$. We prove that $\mathcal{D}_{E,p}$ is bisectorial and admits a bounded $\mathrm{H}^\infty$ functional calculus. We establish a Gaffney-type estimate controlling covariant derivatives in $\mathrm{L}^p$, and also obtain $\mathrm{L}^p$-Hodge decompositions. As an application, we show that the closed operator $\mathcal{D}_{E,p}$ yields a compact Banach spectral triple, and we identify the index of the associated Fredholm operator with the holomorphic Euler characteristic, proving in particular that it is independent of $p$. This work initiates a connection between complex geometry, $\mathrm{L}^p$-analysis and Banach noncommutative geometry, beyond the Hilbert space setting.

Weather regimes provide a useful framework for describing large-scale atmospheric variability and its impacts on regional weather. Despite extensive study, there is still no universally accepted definition or method for identifying weather regimes. Recent work has shown that weather regimes can be interpreted geometrically as topological structures in the phase space of the atmospheric system. In this approach, regimes are identified using a density--radius bifiltration combined with persistent homology, a well-established tool from Topological Data Analysis (TDA). This topological perspective provides a unifying view of regimes and, unlike traditional methods, does not require the number of regimes to be specified in advance. However, the method relies on density estimation techniques (typically Gaussian kernel density estimation), which can over--smooth weakly populated but dynamically important regions of the phase space.

Why do non-axisymmetric stellarators avoid ballooning crashes that afflict tokamaks? Three-dimensional geometry induces Anderson localization of ballooning modes, converting a global instability into a Ginzburg--Landau network of isolated wave packets. Global stability reduces to a percolation problem: below a critical threshold, instability is arrested; above it, a crash occurs. This explains benign stellarator saturation, predicts vulnerability in quasisymmetric designs, and introduces the critical threshold as a nonlinear stability metric for reactor optimization, pending experimental validation.

The impact of the most recent cosmic microwave background (CMB) data from the Atacama Cosmology Telescope (ACT) is studied for a model of cosmic inflation which predicts a non-zero vacuum expectation value (VEV) $M$ for a large-field regime. Since lower values of $M$ are compatible with the higher spectral index $n_s$ provided by the ACT+Planck joint analysis, we establish new limits on this parameter while also considering further CMB data from the latest BICEP/Keck Array release for CMB polarization modes. We find $\log_{10}M/M_{Pl}=-2.5^{+1.1}_{-1.3}$ at 68\% confidence level, compatible with $M/M_{Pl}\simeq 0.003$, which is interesting for post-inflationary processes, such as preheating. We conduct a lattice simulation for the inflaton field for the first few e-folds, as the model is compatible with the production of relics such as oscillons, which are possible candidates as sources of gravitational waves and primordial black holes. We find that the model indeed produces localized, quasi-spherical structures compatible with oscillons, which might lead to signatures detectable by future experiments. However, in agreement with recent works, we find that although the abundance of gravitational waves that could be generated in this regime has an amplitude well within the sensitivities of these detectors, the frequency range is on the GHz limit, away from the expected frequencies. Finally, we estimate the impact of a coupling of the type $yϕχ^2$ to the inflaton, in the realization of perturbative reheating, directly impacting the predictions of the model, as lower values of $M$ are consistent with both the entire allowed temperature range, and the limits imposed by BICEP/Keck Array+Planck+ACT.

The extragalactic background light (EBL) fluctuations in the optical/near-IR encode the cumulative integrated galaxy light (IGL), diffuse intra-halo light (IHL), and high-$z$ sources from the epoch of reionisation (EoR), but they are difficult to disentangle with auto-spectra alone. We aim to decompose the EBL into its principal constituents using multi-band intensity mapping combined with cosmic shear and galaxy clustering. We develop a joint halo-model framework in which IHL follows a mass- and redshift-dependent luminosity scaling, IGL is set by an evolving Schechter luminosity function, and EoR emission is modelled with Pop II/III stellar emissivities and a binned star-formation efficiency. Using mock surveys in a flat $Λ$CDM cosmology with ten spectral bands spanning 0.75-5.0$\rm μm$ in the NEP deep fields over about 100$°^2$ with source detections down to AB=20.5 for masking, and six redshift bins to $z=2.5$, we fit auto- and cross-power spectra using a MCMC method. The combined SPHEREx$\times$Euclid analysis recovers all fiducial parameters within 1$σ$ and reduces 1$σ$ uncertainties on IHL parameters by 10-35% relative to SPHEREx EBL-only, while EoR star-formation efficiency parameters improve by 20-35%. Cross-correlations reveal a stronger coupling of IHL than IGL to the shear field, enhancing component separation; conversely, the EoR contribution shows negligible correlation with cosmic shear and galaxy clustering, aiding its isolation in the EBL. Relative to the SPHEREx EBL-only case, the inferred IHL fraction as a function of halo mass is significantly tightened over $10^{11}-10^{14} M_{\odot}$, with uncertainties reduced by 5-30%, and the resulting star-formation rate density constraints extend to $z\sim 11$, with uncertainty reductions of 22-31%.

Metallic quantum ferromagnets in the absence of quenched disorder are known to generically undergo a first-order quantum phase transition, avoiding the quantum critical point that had originally been expected. This is due to soft modes in the underlying Fermi liquid that lead to long-ranged correlations. These correlations in turn yield a nonanalytic dependence of the free energy on the magnetization even at a mean-field level that results in a fluctuation-induced first-order transition. Kirkpatrick and Belitz [Phys. Rev. Lett. {\bf 124}, 147201 (2020)] have pointed out that one notable exception are non-centrosymmetric metals with a strong spin-orbit interaction. In such materials the spin-orbit interaction gives the relevant soft modes a mass, which inhibits the mechanism leading to a first-order transition. Miserev, Loss, and Klinovaja [Phys. Rev. B {\bf 106}, 134417 (2022)] have claimed that this conclusion does not hold if electron-electron interactions in the particle-particle channel, or 2$\kF$ scattering processes, are considered. They concluded that this interaction channel leads to soft modes that are not rendered massive by the spin-orbit interaction and again lead to a first-order quantum phase transition. In this Comment we show that this conclusion is not correct in three-dimensional magnets if the screening of the interaction is properly taken into account.

Motivated by the necessity of developing theoretical models for studying the electroweak structure of baryons in a nuclear medium, we apply a covariant quark model to study interactions of baryons with nuclear matter. The electromagnetic and axial form factors of the octet baryons are determined by combining a covariant quark model that takes into account the meson cloud dressing of the baryon cores, developed for free space, with the quark-meson coupling model in the extension to the nuclear medium. We discuss the medium modifications on the electroweak form factors of octet baryons for the range of densities from $ρ=0$ up to $ρ=2 ρ_0$, where $ρ_0= 0.15$ fm$^{-3}$ is the normal nuclear matter density. We also study how the shape of the form factors is modified in finite nuclei due to the profile of the nuclear density distributions compared with calculations using the average density of the nucleus

Python is widely used for agent-based modelling because it is accessible and has a mature scientific ecosystem, but object-per-agent execution incurs interpreter overhead that restricts the population sizes feasible in interactive modelling, calibration, and parameter sweeps. This paper presents AMBER, a Python framework that stores agent state in a Polars-backed columnar table and exposes population operations through a compact view API. The framework preserves conventional model and agent abstractions while translating common population updates into compiled column operations; behaviours that do not vectorise remain expressible through a buffered object-oriented path. We evaluate AMBER on wealth transfer, random walk, and spatial SIR benchmarks against Mesa, AgentPy, SimPy, Melodie, Agents.jl, and AMBER's own loop path, using invariant checks to verify comparable model outputs before timing. Across the tested workloads, AMBER has the lowest execution time among Python-hosted implementations and achieves speedups of up to $1118\times$ over Mesa; on the largest SIR benchmark it is also faster than the Julia-based Agents.jl implementation.

We present a sample of 2081 sources selected at photometric redshift $z_{\mathrm{phot}} > 8$ across the JADES DR5 data release in GOODS-S and GOODS-N over a total area of 469 square arcmin. These sources range from $M_{\mathrm{UV}} = -22$ to $M_{\mathrm{UV}} = -16$, with 19 objects at $z_{\mathrm{phot}} > 14$. We estimate the UV slopes for the full sample from fits to the photometry and find evidence for a steepening of the relationship between the UV continuum slope and $M_{\mathrm{UV}}$ to higher redshifts, a result that differs from prior analyses of brighter samples in the literature. We provide evidence that over one quarter of our sources have evidence for being morphologically extended, with many galaxies showing multiple bright knots or clumps even out to $z \sim 13 - 14$, an indication of how galaxies at Cosmic Dawn are growing and evolving. We discuss JADES-GN+189.15982+62.28899, a GOODS-N F200W dropout galaxy at $z_{\mathrm{phot}} \sim 15 - 18$ which has been observed spectroscopically with JWST/NIRSpec in prism mode, resulting in a very low signal-to-noise spectrum that is consistent with the photometry and rules out a number of low-redshift solutions for the source. Finally, we use a subsample of 123 objects in our sample with spectroscopic redshifts to explore the usage of alternate fitting templates and a prescription for Ly-$α$ damping wing absorption, finding that both produce significant improvements to the estimated photometric redshifts.

AI tools are suggested as solutions to assist public agencies with heavy workloads. In public defense -- where a constitutional right to counsel meets the complexities of law, overwhelming caseloads, and constrained resources -- practitioners face especially taxing conditions. Yet, there is little evidence of how AI could meaningfully support defenders' day-to-day work. In partnership with the New Jersey Office of the Public Defender, we develop the NJ BriefBank, a retrieval tool which surfaces relevant appellate briefs to streamline legal research and writing. We show that existing retrieval benchmarks fail to transfer to real public defense research, however adding domain knowledge improves retrieval quality. This includes query expansion with legal reasoning, domain-specific data and curated synthetic examples. To facilitate further research, we release a taxonomy of realistic defender search queries and a manually annotated evaluation dataset for public defense retrieval. This benchmark is highly correlated with a proprietary retrieval dataset annotated by experienced public defenders. Our work improves on the status quo of realistic legal retrieval benchmarking and illustrates one approach to applying AI in a real-world public interest setting.

Realizing Chern insulators with Chern numbers greater than one remains a major goal in quantum materials research. Such platforms promise multichannel dissipationless chiral transport and access to correlated phases beyond the conventional C = 1 paradigm. Here, we discover a family of high-Chern-number orbital magnets in twisted monolayer-multilayer rhombohedral graphene, denoted (1+n) with n = 3, 4, and 5. Magnetotransport measurements show pronounced anomalous Hall effects at one and three electrons per moiré unit cell when they are polarized away from the moiré interface. Across the (1+n) systems, we observe a clear topological hierarchy C = n, revealed by the Středa trajectories and the quantized Hall resistance. Our experimental observations are supported by self-consistent mean-field calculations. Moreover, we realize both electrical and magnetic switching of the high-Chern-number states by flipping the valley polarization. Together, these results establish a tunable hierarchy of orbital Chern magnets in twisted rhombohedral graphene, offering systematic control of Chern number and topology through layer engineering in pristine graphene moiré systems.

An extension of the Standard Model with $Γ_2\simeq S_3$ modular flavor symmetry is presented. We consider the construction of the lepton sector, augmented by two right-handed neutrino states, in the vicinity of the fixed points $τ= i\infty $, $τ= i$ and $τ\!=\!ω\!=\!-\frac{1}{2}\!+\!i\frac{\sqrt{3}}{2}$. Due to the residual symmetries at these points, and with the aid of nonholomorphic modular forms (which constitute representations of $S_3$) and by assigning specific transformation properties to the fermion fields, highly economical models (without flavon fields) are constructed with interesting Yukawa textures. All presented models strongly prefer the inverted ordering for the neutrino masses.

We present a model calculation to reproduce the differential mass distribution for the $D^*π$ system in the reactions $B^- \to D^{*+} π^- π^-$ and $B^{+}\to D_s^+D^{*-}π^{+}$ analyzed by the LHCb Collaboration, which shows a dominant signal for $D_1(2420)$. %\textbf{We} (The idea is to) We consider a model based on coupled channel meson-meson interactions that can describe the properties of $D_1(2420)$ in terms of the underlying dynamics, use it to determine the invariant mass distribution of the $D^*π$ system, and compare the results with the experimental data. We also determine the $D^*π$ scattering length, for which different values are available from different sources, leading to a controversy. To our knowledge, this is the first attempt to reproduce the mentioned data using model calculations. Our formalism relies on the hadronization of different mesons through a weak decay, allowing for the final-state (strong) interactions among the relevant constituents. We benefit from our previous work when obtaining the amplitudes corresponding to the strong interactions. We hope that our findings can be useful in further investigations of the properties of $D_1(2420)$.

We consider various possible consequences of time-varying dark energy due to a quintessence scalar field whose energy density is partially converted to particles as the field evolves down its potential. This particle production acts as a source of thermal friction on the field that can make it difficult to distinguish whether dark energy is due to a radiating field rolling down a steep potential, a purely self-interacting field moving down a flatter potential, or a cosmological constant. By reducing the acceleration of the scalar field, thermal friction increases the amount of accelerated expansion and can cause a sizable bump in the quintessence equation of state. We take special interest in the case where a steep potential rapidly changes from positive to negative as the field evolves, resulting in the end of cosmic expansion and the beginning of contraction. Even in this case, we find that thermal friction lengthens the period of accelerated expansion and consequently delays the end of cosmic expansion, making it challenging to detect the impending transition to contraction using conventional cosmological tests. However, particle production can also provide alternative avenues for detection by generating a background of thermal dark radiation, partly comprised of neutrinos or other particles, whose energy density exceeds the remnant photon energy density.

Building on the approach of Bar-Natan and Van der Veen to universal knot invariants using (perturbed) Gaussian functions, we develop a Gaussian model to compute the Alexander polynomial $Δ_{\mathcal{K}}(T)$ of an oriented knot $\mathcal{K}$ in $S^3$. Using the Heisenberg algebra and a tensor-contraction formalism, we associate to a knot a Gaussian function whose partition function recovers $Δ_{\mathcal K}(T)$. Here, a presentation matrix of the Alexander module plays the role of a precision matrix of the Gaussian function.

Two-phase sampling offers a cost-effective way to validate error-prone covariate measurements in biomedical databases. Inexpensive or easy-to-obtain information is collected for the entire study in Phase I. Then, a subset of patients undergoes cost-intensive validation (e.g., expert chart review) to collect more accurate data in Phase II. When balancing primary and secondary analyses, competing models and priorities can result in poorly defined objectives for the most informative Phase II sampling criterion. Extreme tail sampling (ETS), wherein patients with the smallest and largest values of a particular quantity (like a covariate or residual) are selected, can offer great statistical efficiency in two-phase studies when focusing on a single analytic objective by targeting observations with the biggest contributions to the Fisher information. We propose an intuitive, easy-to-use approach that extends ETS to balance and prioritize explaining the largest amount of variability across multiple models of interest. Using principal components analysis, we succinctly summarize the inherent variability of all models' error-prone exposures. Then, we sample patients with the most extreme values of the first principal component for validation. Through extensive simulations and an application to the National Health and Nutrition Examination Survey (NHANES), the proposed strategy offered simultaneous efficiency gains across multiple models of interest. Its advantages persisted across various real-world scenarios, including correlated or heterogeneous measurement error. When designing a validation study, concentrating on a single model may be short-sighted. Strategically allocating resources more broadly balances multiple analytical goals simultaneously. Employing dimension reduction before sampling will allow this strategy to scale up well to big-data applications with many error-prone exposures.