The exponential growth of financial research has rendered traditional systematic literature reviews (SLRs) increasingly impractical, as manual screening and narrative synthesis struggle to keep pace with the scale and complexity of modern scholarship. While the existing artificial intelligence (AI) and natural language processing (NLP) approaches often often produce outputs that are efficient but contextually limited, still requiring substantial expert oversight. To address these challenges, we propose LR-Robot, a novel framework in which domain experts define multidimensional classification taxonomies and prompt constraints that encode conceptual boundaries, large language models (LLMs) execute scalable classification across large corpora, and systematic human-in-the-loop evaluation ensures reliability before full-dataset deployment.The framework further leverages retrieval-augmented generation (RAG) to support downstream analyses including temporal evolution tracking and label-enhanced citation networks. We demonstrate the framework on a corpus of 12,666 option pricing articles spanning 50 years, designing a four-dimensional taxonomy and systematically evaluating up to eleven mainstream LLMs across classification tasks of varying complexity. The results reveal the current capabilities of AI in understanding and synthesizing literature, uncover emerging trends, reveal structural research patterns, and highlight core research directions. By accelerating labor-intensive review stages while preserving interpretive accuracy, LR-Robot provides a practical, customizable, and high-quality approach for AI-assisted SLRs.

We study the behaviour of the solution $u_\varepsilon$ to the Navier-Stokes equations with vanishing viscosity and a non-slip condition in a randomly perforated domain. We consider the space $\mathbb{R}^3$ where we remove $N$ holes that are i.i.d. distributed. The behaviour depends on the particle size $\varepsilon^α=N^{-α/3}$ and the viscosity $\varepsilon^γ=N^{-γ/3}$ of the fluid. We prove quantitative convergence results to a function $u$, provided that the local Reynolds number is small, in the subcritical ($α+γ>3$) and critical ($α+γ=3$) regime. In the first case, $u$ solves the Euler equations, whereas in the second case $u$ solves the Euler-Brinkman equations. This extends the results of https://doi.org/10.1088/1361-6544/acfe56 from the periodic to the random setting. We only treat the case $α>2$ so that the particles do not overlap with overwhelming probability.

We present the first empirical evaluation of techniques for encoding distributions of quantitative edge values within adjacency matrices. In many real-world networks, edges represent not a single value but a set of measurements. While adjacency matrices preserve structural clarity, their compact cells limit the simultaneous display of multiple values. To address this, we explore edge encodings that represent distributions by two values: a measure of central tendency (mean, median, mode) and a measure of dispersion (standard deviation, variance, IQR). We select four possible encodings for evaluation that prior work has suggested are suitable for the limited space available in matrices: a bivariate color palette, embedded bar charts, and two overlaid-mark designs mapping the primary attribute to color and the secondary attribute to area or angle. In a preregistered crowdsourced study with 156 participants, we assessed performance of these encodings across eight analytical tasks and collected readability and aesthetic ratings. Results reveal clear performance regimes: area-based overlaid marks and bar charts achieved the highest overall performance; angle-based marks show moderate but less stable performance,and bivariate color consistently underperforms these alternatives. These findings clarify how visual channels behave under strict constraints and delineate the strengths and limitations of key design choices for multivariate edge visualization.

The origin of enhanced reactivity in aqueous microdroplets remains debated, with interfacial electric fields (IEFs) often invoked as catalytic drivers. Here, we provide a quantum-mechanical, spatially resolved characterization of the electric field at air-water interfaces by combining deep-learning molecular dynamics with \emph{ab initio} re-sampling. Across planar interfaces and nanodroplets of varying curvature and charge state, we find an outward-oriented field of $\sim 1.0$--$1.2$ V/Å along the intrinsic surface normal. Crucially, its magnitude scales linearly with the average number of hydrogen bonds per interfacial molecule, directly tying the field to the local hydrogen-bond network. Despite its large magnitude and contrary to common expectations, we find that curvature and pH exert only a minor influence on the IEF, becoming negligible at experimentally relevant droplet sizes and pH. Consequently, the reactivity differences observed in $μ$m-sized droplets cannot be ascribed to variations in the IEF, which changes by a factor of only $\sim10^{-5}$ between $3$ and $40μ$m-sized droplets. Moreover, the IEF is localized inside the interfacial region and rapidly vanishes within a few Å. This strong spatial confinement renders the IEF strongly tied to the local electronic structure, identifying it as a local property of the air-water boundary rather than an independent physical driver of ``on-water'' catalysis.

While significant advancements have been made in weak magnetic field detection, conventional high-sensitivity techniques are often limited by requirements for cryogenic operation or bulky setups. In this work, we develop a sensitive alternating magnetic field sensor based on a coupled system of an active microwave cavity and yttrium iron garnet (YIG), with the components implemented on printed circuit boards (PCBs). By introducing electrically tunable gain to compensate for cavity losses, we substantially improve both the quality factor and the signal intensity. Under the coupled system, Floquet modulation is induced by the alternating magnetic field, allowing for weak field detection by driving a specific hybrid mode and measuring the resulting Floquet sidebands. This miniaturized device operates at room temperature, achieving a detection limit of 121 pT/\sqrt{Hz}.

Source localization in complex networks is a rapidly advancing field with numerous real-world applications, including determining the source of misinformation. In this work, we model information spread across several real-world and synthetic complex networks using our Generalized Fractional Susceptible-Infected-Recovered (GFSIR) model, which incorporates the information overload (IOL) phenomenon. Then, we use Pearson's correlation algorithm to identify information sources in these networks and investigate how information overload affects localization quality. Numerical simulations have shown that localization effectiveness decreases with the parameter $α$, which controls the strength of the IOL, and increases with the spreading rate $β$. Our comparison across various topologies reveals that localization is generally more effective in synthetic structures, with Erdős-Rényi networks exhibiting greater resilience to IOL than Barabási-Albert models. Furthermore, we identified a critical reversal in the impact of network density: while a higher average degree enhances localization when IOL is negligible, less dense networks perform better under strong overload. This phenomenon represents a significant departure from the behavior observed in standard epidemic models.

Nanofluidic devices prompts unconventional ion transports appealing to energy and information technologies, thanks to the susceptibility of confined electric double layers (EDL) to various external physical fields. Although experimental studies advance rapidly, the rationalization of field-tunable nanofluidic transports has not reached a formalized and unified level. Here we formally reformulate the Poisson-Boltzmann theory and reveal distinct EDL regimes on the parameter space. Based on the regime classification, we establish a formal framework for the tunable nanofluidic transport, which reproduces the observed conductivity-concentration scaling behaviors, rationalizes the ionic transistors with reconfigurable polarities, and predicts two fundamental thermodynamic limits for electrostatic modulation (60 mV/dec and 120 mV/dec). Being accurate, generalizable and extensible, this framework can account for a wide range of ion transports in confined spaces.

Altermagnet-based heterojunctions have demonstrated magnetoresistive effects in experiments, however, a predictive theoretical model for non-ferromagnetic structures has remained elusive. In this work, we develop a tunneling-based spin-transport theory that explicitly incorporates the transverse-wavevector ($\bf{k}_\|$)-dependent spin polarization of an altermagnet's transport channels, enabling the prediction of giant tunneling magnetoresistance (TMR). Based on the theory, we predict that the altermagnet KV$_2$Se$_2$O can reach the extreme limit of magnetoresistance. By performing first-principles transport calculations, we verify that magnetic tunnel junctions using the metallic KV$_2$Se$_2$O as the electrodes and few-layer MgO as the spacer exhibit zero-bias magnetoresistance larger than $7.57\times10^7$\%, which is robust against the bias and thickness of the spacer. Our research provides a quantitative design principle for next-generation spin-electronic devices and establishes KV$_2$Se$_2$O/MgO/KV$_2$Se$_2$O as a leading candidate material system for room-temperature ultra-high-density non-volatile memory.

We study a one-dimensional cross-diffusion system for two interacting populations on the torus, with a linear pressure law and different mobilities. For arbitrary bounded non-negative initial data, we show that any good approximation scheme, yields existence of global weak solutions. More precisely, we introduce a notion of \textit{admissible approximation sequence} and show that any such sequence admits a subsequence converging to a weak solution of the system. The strategy relies on entropy estimates and the div--curl lemma, in the framework of Young measures.

Encrypted control employs homomorphic encryption (HE) to protect both the computation and communication stages, making it a promising approach for secure networked control systems. Most existing results pre-design a controller in the plaintext domain and then implement it over encrypted data. However, this can be problematic because HE induces non-negligible communication and computation delays, which typically increase with the security level, potentially degrading control performance and even destabilizing the closed-loop system. To address this issue, we propose a co-design framework for cryptographic parameters and delay-aware feedback gain. We characterize the encryption-induced delay as a function of the cryptographic parameters and derive a sufficient condition for the existence of a stabilizing delay-aware feedback gain, expressed as a finite set of linear matrix inequalities. This leads to a tractable outer-inner design procedure that searches over cryptographic parameters that satisfy a desired security level and, for each such parameter, seeks a stabilizing feedback gain.

We study the finite-size Kuramoto model of all-to-all coupled phase oscillators with heterogeneous natural frequencies and characterize the minimal coupling strength required for the existence of a fully phase-locked equilibrium (in a co-rotating frame). To remove the degeneracy due to uniform phase shifts, we move to a reduced co-rotating frame and assess stability through the Jacobian of the reduced system: a fully phase-locked state is stable when this Jacobian is negative definite. This defines a stability region in the phase space. The Kuramoto vector field maps this region to a convex set in frequency space, so a fully-locked state at coupling $K$ exists exactly when the rescaled frequency vector $\hat{\mathbfω}/K$ lies inside that convex image. The critical coupling $K_{\ell}$ is defined as the smallest coupling strength for which a fully phase-locked equilibrium exists; geometrically, it corresponds to the first intersection of the ray $t\hat{\mathbfω}$ with the boundary of this convex set. Building on this convex-geometric structure, we construct an explicit polytope from analytically computable boundary points of the stability region, providing a closed-form upper bound $K_b \ge K_{\ell}$. The bound is exact for frequencies aligned with polytope vertices and offers a fully explicit outer approximation for general frequency vectors. While not uniformly sharp in a quantitative sense, this construction exposes the underlying geometry of stable fully phase-locking solutions. These results provide a practical use the convex-geometric structure underlying stable fully-locked states in the Kuramoto model.

Phononic silicon structures have emerged as an integrable and scalable nanosystem for tailoring thermal transport. However, their widespread adoption has been limited by their complex fabrication pathways. Alongside, the reliable characterization of thermal properties in suspended nanostructured films remains challenging, as thermal contact resistances often hinder the accuracy of measurements. In this work, we demonstrate a clear and controllable reduction of thermal conductivity in nanopatterned silicon membranes. A block copolymer self-assembly approach is employed to fabricate nanoholed silicon films with a pitch of 63 nm and hole diameters of 35 nm. Additionally, we introduce an extension of the three-probe technique that enables robust, quantitative, and spatially resolved thermal conductivity measurements in complex thin-film systems, accounting for thermal contact artifacts. The method is validated through measurements on unpatterned 40 nm-thick silicon thin films between 30 and 350 K, yielding a room-temperature thermal conductivity of 46.5 W/m.K. Finally, we further show that controlled etching of the nanoholes provides a powerful means to tune thermal transport in the overall studied temperature range, establishing hole etch depth control as an effective parameter in phononic silicon. Specifically, a fivefold reduction in thermal conductivity is achieved, reaching 7.3 W/m.K for fully etched-through membranes at room temperature.

The Hamiltonicity and related subjects of split graphs, and in particular $K_{1,r}$-free split graphs with $r\ge 3$ received much attention. Dai et al. [Discrete Math. 345 (2022) 112826] conjectured that every $(r-1)$-connected $K_{1,r}$-free split graph is Hamiltonian. They proved the case when $r=4$, and earlier Renjith and Sadagopan [Int. J. Found. Comput. Sci. 33 (2022) 1--32] proved the case when $r=3$. Recently, Liu, Song, Zhang and Lai [Discrete Math. 346 (2023) 113402] proved that a split graph is Hamiltonian if and only if it is fully cycle extendable. So for $r=3,4$ every $(r-1)$-connected $K_{1,r}$-free split graph is fully cycle extendable. We give tight spectral sufficient conditions for a $K_{1,r}$-free split graph to be Hamiltonian for $r=3,4$.

Superluminous supernovae (SLSNe) are one of the most luminous stellar explosions known, yet they remain poorly understood. Because they are intrinsically rare, efficiently identifying them in the large alert streams produced by modern time-domain surveys is essential for enabling spectroscopic follow-up. We present NOMAI, a machine learning classifier designed to identify SLSN candidates directly from photometric alerts in the ZTF stream, using light curves accumulated over at least 30 days. It does not require any spectroscopic redshift and is running in real time within the Fink broker. ZTF light curves are transformed into a set of physically motivated features derived primarily from model-fitting procedures using SALT2 and Rainbow, a blackbody-based multi-band fitting framework. These features are used to train an XGBoost classifier on a curated dataset of labeled ZTF sources constructed using literature samples of SLSNe, along with TNS and internal ZTF labeled sources. The final training dataset contains 5280 unique sources, including 225 spectroscopically classified SLSNe. On the training sample, the classifier reaches 66% completeness and 58% purity. Deployed within the Fink broker, NOMAI has been running continuously since 18/12/2025 on the ZTF alert stream and publicly reports SLSN candidates every night by automatically posting them to dedicated communication channels. Based on this, we also report the first two-month as an evaluation period, where the classifier successfully recovered 22 of the 24 active SLSNe reported on the Transient Name Server. The achieved performances demonstrate that the classifier provides a valuable tool for experts to efficiently scan the alert stream and identify promising candidates. In the near future, NOMAI is intended to be adapted to operate on the Legacy Survey of Space and Time conducted by the Vera C. Rubin Observatory.

We establish Grauert--Riemenschneider vanishing for $F$-pure threefolds over a perfect field $k$ of characteristic $p>5$. We apply this to prove Steenbrink vanishing for three-dimensional sharply $F$-pure pairs in characteristic $p>5$. As a consequence, we obtain the logarithmic extension for one-forms in this setting.

While the classical Critical Depth Hypothesis (CDH) effectively explains the onset of blooms as transient instabilities, it does not fully capture the seasonal decoupling of biological rates and the long-term persistence of phytoplankton communities in fluctuating thermal environments. To address these limitations, we introduce a parsimonious framework that leverages the theory of non-autonomous dynamical systems to diagnose the stability of phytoplankton communities throughout the entire annual cycle. By linearizing the dynamics around the extinction equilibrium, we identify the invasion growth rate -formally the Floquet exponent-and derive the critical nutrient requirement ($γ$crit) as a bifurcation point for uniform persistence. Using end-of-the-century projections from the GFDL-ESM4 model under a high-emission scenario (SSP5-8.5), we identify a global regime shift characterized by a widespread expansion of metabolic-driven regimes, which increasingly displace regions where stability was historically governed by physical mixing. Relevance to Life Sciences. Quantitative analysis of system stability challenges CDH by demonstrating that metabolic constraints increasingly modulates phytoplankton persistence in a changing ocean. Our results, based on high-emission projections, reveal a profound physical-biological decoupling at the poles: while warming reduces the critical nutrient requirement ($γ$crit) facilitating persistence in previously marginal waters, this metabolic expansion is offset at poles. A 1:4 ratio between newly viable niches and ice-free deserts suggests that cryospheric retreat does not guarantee a proportional expansion of life. In addition, we identify the North Atlantic Subpolar Gyre as a ''metabolic refuge'' where mixing dynamics still anchor the ecosystem against global thermalization. By providing a ''radiography'' of the future ocean's complexity, this methodology offers a mechanistic basis to deconstruct how the dynamic balance between environmental energy and metabolic demands may determine the functional integrity of the marine biosphere under extreme anthropogenic forcing. Mathematical Content. The temperature dependence of biological rates is modeled using a thermodynamic equation, coupling population dynamics with seasonal variations in mixed layer depth and temperature. Given the non-autonomous nature of the system under annual forcing, we characterize the stability of the extinction equilibrium through its associated invasion growth rate. This rate is analytically derived as the Floquet exponent $λ$P , which provides a rigorous condition for uniform persistence (Theorem 3.2). The numerical analysis of this exponent, projected onto a global scale, quantifies the relative influence of environmental drivers on the stability threshold $γ$crit. This allows for the definition of the thermal dominance index (DT ), a metric that identifies the geographic transition from mixing-driven to metabolic-driven ecological control.

We leverage a quasi natural experiment from India on introduction of free bus schemes for women across five states to study it's impact on women's workforce participation. We use two rounds of the representative Time Use Survey and a triple difference estimation strategy, complemented by an event study framework to identify the causal relationship of interest. Findings reveal that the bus scheme was successful in improving women's paid work participation and duration of employment. We confirm that these results are not merely a continuation of prior trends. The scheme's effects are concentrated among early adopters like Punjab and Tamil Nadu, two states with historically different levels of women's workforce participation. We also find disproportionately higher effects for women residing in more patriarchal districts with higher mobility restrictions. We argue that the scheme works through easing of non-financial binding constraints, which lowers the barriers to women's mobility and workforce participation.

We introduce a general witness-based framework for quantifying and operationally activating continuous-variable (CV) resources into discrete-variable (DV) bipartite entanglement or Einstein- Podolsky-Rosen (EPR) steering. For the three standard CV resource theories associated with Wigner negativity (WN), genuine non-Gaussianity (GNG), and standard non-Gaussianity (SNG), we define infinite families of bounded-witness monotones indexed by box constraints on the witness operators. For closed convex free sets, these monotones are faithful, strongly monotonic under free instruments, Lipschitz continuous, and convex. For closed nonconvex free sets, we show that faithfulness requires a two-copy lift and formulate the corresponding strong-monotonicity statement in the lifted theory. We further construct witness-dependent completely positive trace-preserving (CPTP) measure-and-prepare channels whose outputs are two-qubit Werner states. For the representative case n = m = 1, the optimal entanglement and EPR steering attainable within this witness-dependent activation family are exactly proportional to the underlying monotones. We illustrate the framework with odd-parity states, pure-loss single-photon states, and Gottesman- Kitaev-Preskill (GKP) states, and derive explicit lower bounds for pure-state GNG and SNG. More broadly, our results show that closed CV free sets admit witness-based quantifiers with a direct operational interpretation in terms of experimentally accessible DV correlations.

Subsurface properties are essential for hazard assessment, energy and environmental management, and infrastructure resilience, but direct observations are sparse and uneven, motivating the use of surface observations as indirect constraints. Here we explore whether AlphaEarth embeddings can be applied to subsurface estimation despite indirect and non-unique physical links between surface and depth. We test this idea in two conterminous U.S. applications: shallow seismic site characterization using $V_S 30$ with embedding features alone and with conventional covariates (topographic slope and a tectonic-status indicator), and subsurface temperature reconstruction using embedding-based nonlinear regression. Across both applications, embedding-informed models recover spatially coherent, physically plausible patterns and outperform simpler baselines. The comparison also highlights a key difference: domain covariates materially stabilize $V_S 30$ regression, whereas temperature mapping relies primarily on embedding features. Overall, the results support the feasibility of foundation-model surface representations for regional surface-to-subsurface inference, while emphasizing the need for robust spatial validation under heterogeneous labels and uneven data coverage.

To mitigate the residual interference from imperfect successive interference cancellation (SIC) in Rate-Splitting Multiple Access (RSMA), this paper incorporates improper Gaussian signaling (IGS) into the downlink RSMA framework. Unlike existing RSMA--IGS works that embed impropriety within IQ-imbalanced frameworks, we show that IGS alone effectively counters SIC-induced residual interference. For a basic SISO setup with IGS on the common stream and PGS on private streams, we establish three key results: the optimal impropriety degree for private rate maximization attains its maximum; closed-form optimal solutions with rigorous monotonicity conditions are derived for common rate maximization; and a soft actor-critic (SAC) algorithm is developed for the non-convex sum rate problem. Numerical results show that IGS consistently outperforms PGS, with the gain widening as SIC imperfection increases.

A review of recent multiboson and vector boson scattering (VBS) measurements from the ATLAS and CMS Collaborations at the LHC is presented. Results are reported from precision diboson cross-section measurements, novel CP-sensitive and polarisation observables in $Wγ$ production, VBS observations in semileptonic and fully leptonic final states including the first measurements at $\sqrt{s}$ = 13.6 TeV, and observations of triboson processes. These results constitute a comprehensive test of the electroweak gauge sector of the Standard Model, and provide stringent constraints on anomalous gauge couplings in the effective field theory framework.

We consider a class of stochastic damped semilinear wave equations, in the small-mass limit. It has previously been established that the solution converges to the solution of a stochastic semilinear heat equation. In this work we exhibit strong and weak rates of convergence in this Smoluchowski--Kramers approximation result. The rates depend on the regularity of the driving Wiener process. For instance, for trace-class noise the strong and weak rates of convergence are $1$, whereas for space-time white noise (in dimension $1$) the strong and weak rates of convergence are $1/2$ and $1$ respectively.

Mound formation on flat and miscut crystal surfaces exhibits distinct growth behaviors. While mound structures are the predominant feature on flat surfaces, miscut surfaces display a smooth transition from meandered patterns to three-dimensional mounds, depending on both internal and external conditions. We investigate this morphological evolution-from meander-like surface patterns to faceted pyramidal structures-using a vicinal Cellular Automata modeling framework. The transition is shown to be governed by the competition between the Ehrlich-Schwoebel barrier and adatom mobility on terraces. Under moderate barrier strengths and sufficiently high terrace diffusivity, the system demonstrates a reversible transition from mounded configurations to regular step meandered patterns. This reveals a complex interplay between kinetic barriers and mass transport. Our simulations cover a wide range of growth conditions, including variations in deposition flux, surface diffusion rates, temperature, and miscut angle. By applying the height-height correlation function, we calculate the correlation lengths along and across the steps and analyze their scaling behavior. These results offer insight into the continuum pathways that connect distinct classes of surface structures and provide a unified framework for describing pattern evolution across different crystal growth regimes.

We present a theoretical study of Compton scattering of X- and $γ$-rays by a $K$-shell electron. Special attention is paid to the double-differential cross section and polarization of the scattered photons for linearly polarized incident photons. To investigate these observables, we employ the scattering matrix (S-matrix) approach based on relativistic Green's functions. The S-matrix results are moreover compared with predictions of the free-electron and impulse approximations, allowing us to assess the role of electron binding effects. Detailed calculations are carried out for hydrogen-like Ne$^{9+}$ and Pb$^{81+}$ targets over a wide range of incident photon energies and scattering angles. The calculations reveal kinematic regimes in which the impulse approximation agrees reasonably well with the S-matrix results. We also explore the polarization of scattered photons for slightly depolarized incident radiation, including the highly sensitive case of scattering at $90^\circ$.

In many real-world settings, problem instances that need to be solved are quite similar, and knowledge from previous optimization runs can potentially be utilized. We explore this for the Traveling Salesperson problem with time windows (TSPTW), which often arises in settings where the travel-time matrix is fixed but time-window constraints change across related tasks. Existing TSPTW studies, however, have not systematically compared solving such task sequences independently with sequential transfer from previously solved tasks. We address this gap using a multi-task benchmark in which each base instance is expanded into five related tasks under two environments: partial time-window expansion and swap-additive time reassignment. We compare a standard from-scratch protocol with an iterative protocol that initializes each task from the best tour of the previous task, using the popular local search approaches LNS, VNS, and LKH-3 under a common penalized-score objective. Our experimental results show that the iterative protocol is consistently superior in the progressive-relaxation setting and generally competitive under swap-additive changes, with improvements increasing on more difficult instances.

Exceptional points (EPs) in non-Hermitian photonic systems enable unconventional control of wave amplitude and phase. However, identifying the EPs in multidimensional parameter space of a system can be nontrivial and, in some cases, even infeasible. Here we propose an inverse-design method to efficiently locate the scattering EPs for a two-port resonant system supporting a single mode. The proposed method provides a direct guide for tuning of geometric parameters to realize scattering EPs, as confirmed by both full-wave simulation and equivalent circuit model. In principle, our method is compatible with multi-mode system, making it broadly applicable to a broad class of resonant systems.

We study the complex Ginzburg-Landau equation posed on possibly unbounded domains, including some singular and saturated nonlinear damping terms. This model interpolates between the nonlinear Schr{ö}dinger equation and dissipative parabolic dynamics through a complex timederivative prefactor, capturing the interplay between dispersion and dissipation. As a continuation of our previous study on the existence and uniqueness of solutions, we prove here some strong stabilization properties. In particular, we show the finite time extinction of solutions induced by the nonlinear saturation mechanism, which, sometimes, can be understood as a bang-bang control. The analysis relies on refined energy methods. Our results provide a rigorous justification of nonlinear dissipation as an effective stabilization mechanism for this class of complex equations where the maximum principle fails.

Collino proved that the fundamental group of a certain Zariski open set of the symmetric square of a hyperelliptic curve is isomorphic to the integral Heisenberg group. We compute the mixed Hodge structure on this fundamental group, and show that the second extension class is expressed by the Abel-Jacobi invariant of the canonical class and the marked points of the hyperelliptic curve, together with a certain F_2-linear map.

We extend the OPE-based renormalization algorithm to composite operators with operator mixing, focusing on scalar operators in $ϕ^4$ and $ϕ^3$ models. Using the OPE of operators with a fundamental field, we show that the $Z$-factors of these composite operators are determined by OPE coefficients of lower-dimensional traceless symmetric tensor operators, and establish a recursive renormalization framework. We report the five-loop anomalous dimensions for operators with $Δ\le5$ in the $ϕ^4$ model and the two-loop anomalous dimensions for operators with $Δ\le10$ in the $ϕ^3$ model. These results further demonstrate the versatility and efficiency of the OPE-based algorithm.

The quantum Mpemba effect (QMpE) describes an anomalous thermalization phenomenon in which quantum states initially far from equilibrium can approach thermal equilibrium faster than states that begin closer to it. While this effect has been extensively studied in various frameworks, its practical implications for quantum information processing remain largely unexplored. We investigate the relationship between QMpE and quantum thermometry, focusing on non-equilibrium scenarios where measurements are performed during early-stage thermalization. In a Markovian model, we rigorously prove that the initial states that are optimal for thermometry exhibit QMpE with high probability and thermalize faster than most initial states. Our results reveal a fundamental connection between quantum thermodynamics and thermometry, suggesting that QMpE can be harnessed to enhance temperature estimation with quantum probes.