Order theory is increasingly relevant in applications where data is naturally structured as a partially ordered set (poset), often requiring meaningful notions of distance over posets. In this paper, we introduce a new family of extended metrics on path-connected and fence-connected posets that do not require additional structure. Unlike many existing distances, these metrics are not induced by valuations, but instead arise as a type of shortest-path distance determined by both path length and the number of alternations. For discrete posets, we show that these metrics converge to a type of shortest-fence metric. Our main result establishes that these metrics characterize most discrete path-connected posets up to isomorphism, and up to duality for modular posets. Finally, we prove that this family defines interleaving distances when posets are viewed as thin categories.

As a binary neutron star inspirals due to the emission of gravitational waves, the rising tidal frequency resonantly excites vibrational modes. These oscillations are seismological probes of the rich stellar interior, yet it remains to be established whether gravitational-wave interferometers can measure them. Here, we present the first fully Bayesian study of the capability of the Einstein Telescope to detect tidal resonances. We simulate one year of observations and analyse the 200 loudest signals. We find that the Einstein Telescope can identify resonant modes and is sensitive to gravitational-wave phase shifts as small as $ΔΦ\approx 0.03$ for favourable events. We further show that neglecting resonances can bias the inferred tidal deformabilities. These results establish tidal resonances as a measurable route for asteroseismology with future detectors.

We study the motion of columnar ice crystals that form in clouds over a range of low temperature. Our focus here is on elongated ice crystals, which are smaller than the size of the smallest eddies in the flow, with a moderate aspect ratio comprised between $3$ and $5$. We determine turbulent solutions of the Navier-Stokes equations over a range of turbulent kinetic energy dissipation characteristic of clouds ($4.41\;{\rm cm}^2/{\rm s}^3 \le \varepsilon \le 1120\;{\rm cm}^2/{\rm s}^3$) by using direct numerical simulations, and we follow the motion of crystals using simplified but realistic models for the motion of non-spherical, elongated particles. The influence of the fluid inertia leads to a preferential alignment of the crystals perpendicular to the direction of gravity, the alignment effect being opposed by the turbulent fluctuations. Along with the strong alignment of the crystal axis perpendicular to gravity, we observe only a weak alignment with the vorticity, much weaker than in the absence of gravity. The settling velocity depends only weakly on the orientation of the crystals, but is strongly enhanced when $\varepsilon$ increases, an effect that we attribute to preferential concentration in the flow. As the inertia of the columnar ice crystals considered here is significant, we observe a strong spatial clustering. Finally, we discuss the relevance of the effects identified here on the collision frequency between ice crystals in cloud conditions.

We construct a quantum-statistical analogue of Einstein's fluctuation argument for black-body radiation in the context of causal-diamond geometry. Starting from the phase space of a stretched horizon inside a Minkowski causal diamond, we quantize the Poisson algebra generated by the fields averaged over stretched-horizon time. We then compute the fluctuations of the averaged area density of the transverse two-spheres in a thermal state constructed in analogue with the black-body thermal state. In the null limit, where the stretched horizon approaches the causal-diamond boundary, this yields a thermal fluctuation formula of the boundary area operator that contains two terms, in direct analogue with the black-body radiation. The term quadratic in the expectation value is the ``classical'' contribution, while the linear term has the Verlinde--Zurek scaling characteristic of independent microscopic constituents. In direct analogue with Einstein's interpretation of black-body energy fluctuations as evidence for light quanta, we interpret the linear area-fluctuation term as a statistical signature of discrete quanta of geometry. This provides bottom-up evidence for quantum area degrees of freedom and supports the embadon picture of null quantum geometry.

This work analyses and evaluates a few realistic compact objects in the presence of a gravitational interaction between two particles with a nonmetricity $Q$. In the $f(Q)$ gravity framework, we have selected the anisotropic equation of motion and have determined $f(Q)$ to be a linear function of nonmetricity $Q$. To evaluate the field equations in our work, we have opted to employ the Krori-Barua metric. We calculated the anisotropic factor for each of the four compact objects and found that the anisotropic component is positive and increases monotonically and interpreted that the nuclear force can oppose the gravitational attraction. At last, the relationship between mass and radius has been determined and illustrated visually. We have noted that the compactness of the pulsars LMC X-4, SMC X-4, Cen X-3, and Vela X-1 is inside the Buchdahl's limit for varying values of $a$. This has led to the interpretation that these pulsars are neutron stars in a modified gravity background of $f(Q)$. In addition, we calculated the model mass and, using thirty distinct choices of $a$, ran the Chi-Square test to see if there was a noticeable difference between the observed and model-generated masses. We have also looked at how the surface redshift has changed over time and whether the compact objects in our model that were previously described are compact.

Modern semiparametric estimation often relies on flexible black-box machine learning methods to estimate nuisance functions, raising a fundamental question: how do nuisance estimation errors propagate into inference for low-dimensional target parameters? The dominant paradigm, exemplified by double machine learning (DML), yields error bounds in which nuisance estimation errors enter multiplicatively. While widely adopted, it remains unclear whether this multiplicative-rate dependence is optimal for black-box models. In this paper, we start by revisiting the partial linear model $Y = μ_0(X)+T\cdotβ_0+\varepsilon$ under a structure-agnostic setting, where the nuisance function $μ_0$ is estimated using a generic machine learning model, with approximation error $δ^a_μ$ and stochastic error $δ_μ^s$. We show that the standard DML rate is not optimal in the regime where the auxiliary function $\mathbb{E}[T|X=x]$ cannot be consistently estimated. We propose a new estimator for $β_0$ that achieves a sharper rate of $n^{-1/2}+δ^a_μ+(δ_μ^s)^2$ and establish a matching lower bound demonstrating its optimality. Our results reveal a new principle: the first-order stochastic error of nuisance estimation can be eliminated without imposing any additional assumptions. This also leads to a revised tuning strategy favoring under-smoothing, where $δ^a_μ\asymp(δ_μ^s)^2$, rather than the classical bias-variance trade-off $δ^a_μ\asymp δ_μ^s$. Under mild additional conditions, the estimator is asymptotically normal with minimal asymptotic variance. The proposed method extends to a broad class of semi-parametric linear functional estimation problems, including average treatment effect estimation. Our results imply that popular orthogonal score methods in semiparametric estimation with black-box nuisance learners can be substantially improved.

In this paper, we study the structure of double cyclic codes of length $(γ,δ)$ over $\mathbb F_q+u\mathbb F_q, u^2=0$. We also study the dual of double cyclic code of length $(γ,δ)$ and give a minimal spanning set of double cyclic codes. Moreover, we study the necessary and sufficient conditions for a double cyclic code to be reversible and reversible-complement double cyclic code and with the help of these codes, we constructed DNA codes over $\mathbb F_4+u\mathbb F_4, u^2=0$. We also constructed some optimal codes to support our results.

Fault-tolerant quantum computation is inherently a spacetime problem, requiring not merely good static quantum error-correcting codes but also low-overhead protocols for protecting and manipulating encoded quantum information over time. Fault complexes provide a homological framework for treating such protocols as single spacetime objects. In this work, we initiate the study of low-overhead fault complexes by introducing {spacetime lifting}, a method that constructs fault complexes from symmetry-reduced product structures beyond standard foliation. We show that spacetime lifting yields fault complexes and in particular {spacetime-lifted} memory experiments with almost-linear fault distance in the total spacetime cost, which substantially outperforms existing constructions. We further interpret fault complexes as measurement-based cluster-state protocols and identify general conditions under which they realize fault-tolerant logical teleportation, showing that spacetime-lifted constructions combine favorable scaling with operational schemes. Our study opens a path toward more efficient quantum fault tolerance through general complex constructions.

We study thermalisation and the possible occurrence of the Mpemba effect in a closed quantum setting that mimics the interaction of a system with thermal reservoirs coupled only at its boundaries. Specifically, we consider a tripartite geometry in which a finite chain, initially prepared at a finite temperature, is suddenly connected on both sides to two semi-infinite chains of the same nature held at a different temperature. These outer chains act as thermal baths, while the full system evolves unitarily under a homogeneous Hamiltonian. This setup provides a simple quantum realisation of a temperature quench and closely resembles the original scenario in which the classical Mpemba effect was first observed. We focus on two paradigmatic free-fermion models, the XX chain and the transverse-field Ising chain, which respectively preserve and break the global $U(1)$ particle-number symmetry. As a probe of relaxation, we consider the Frobenius distance between the time-evolved reduced density matrix of the central subsystem and its stationary state, which is the thermal state at the bath temperature. Exploiting the free-fermionic structure of both models, the dynamics remains Gaussian and the Frobenius distance can be expressed exactly in terms of two-point correlation functions. Combining this representation with generalised hydrodynamics, we derive analytical predictions for the Frobenius distance in the hydrodynamic limit, providing a complete characterisation of the thermalisation process. Using these results, we investigate the possible occurrence of the Mpemba effect. We find that, despite the genuine non-equilibrium dynamics displayed by the system, no Mpemba effect arises in this setting. Our analysis identifies a broad class of boundary-driven thermalisation protocols in which relaxation is fully characterised analytically and exhibits no anomalous acceleration of equilibration.

RTK augmentation andINS integration are widely used to improve GNSS positioning performance. However, on inland waterways, bridges and surrounding structures can degrade satellite visibility and correction availability, causing RTK augmentation loss, and GNSS/INS fusion transients. Since these effects depend on the local environment and sensor configuration, nominal receiver specifications are insufficient, and deployment-specific characterization is required. This paper presents a benchmarking study of an AsteRx-i3 D Pro+ GNSS/INS receiver installed within the mobile Sensor Box developed at KU Leuven. The study combines a real-world bridge-passage case study, static benchmarking, and closed-loop path-following experiments. The static benchmarking evaluates four receiver configurations: standalone GNSS, standalone GNSS with INS integration, RTK-augmented GNSS, and RTK-augmented GNSS with INS integration. The closed-loop experiments use INS-integrated GNSS as the navigation input and compare path-following operational performance with and without RTK augmentation. Results show that correction loss during bridge passage causes reduced positioning accuracy, increased positioning uncertainty and recovery-induced state jumps exceeding 1 m. Static benchmarking and closed-loop experiments confirm that RTK augmentation substantially improves positioning precision and uncertainty consistency, while INS integration supports short-term continuity during RTK unavailability but may introduce drift, bias, or transient uncertainty variations. By characterizing the deployment-specific receiver behavior with RTK augmentation and INS integration, this study motivates higher-level state estimation as a necessary next step toward spatially continuous and uncertainty-consistent positioning on inland waterway. The experimental data are released at: https://doi.org/10.5281/zenodo.20541733.

We present $\tt BlackHawk$ $\tt v3.0$, a major update of the public code designed to compute Hawking radiation spectra of black holes. Building upon previous versions, this release considerably extends the range of black hole geometries that can be studied by implementing several new spherically symmetric metrics: the Bardeen and Hayward regular black holes, the Simpson-Visser and Peltola-Kunstatter black-bounces, the D'Ambrosio-Rovelli black hole-to-white hole metric, and the Babichev-Charmousis-Lehébel black hole. For each metric, we compute the corresponding Hawking temperatures and greybody factors, enabling the determination of primary Hawking emission spectra for particles of different spins. The greybody factors are obtained through dedicated numerical routines based on the companion code $\tt GrayHawk$. Additionally, $\tt BlackHawk$ $\tt v3.0$ introduces several technical improvements aimed at enhancing precision and efficiency, providing a highly versatile tool. The code is publicly available at https://blackhawk.hepforge.org/

The European Union will introduce the EUDI Wallet by late 2026, which allows users to hold digital credentials (i.e., representations of physical official identity documents) on their devices. This will allow users to securely and privately disclose identity attributes to websites. Although such a system has many benefits, it also introduces risks caused by poor credential disclosure decisions. In this paper, we (i) conduct a large-scale survey on credential disclosure with users and experts and (ii) evaluate the effectiveness and feasibility of our Credential Assistant that displays expert recommendations and user opinions. Our results show that users are likely to overshare (e.g., ~20% of users disclosed their official ID to news websites). This indicates that users struggle to protect their privacy, which will impact the usability of the EUDI Wallet and lead to privacy violations, identity theft, and other abuses of leaked credentials. Finally, we show that our Credential Assistant significantly reduces users' credential disclosure mistakes from ~15% to ~7%. However, it does not fully eliminate poor credential disclosure decisions, indicating that stronger interventions may be necessary, especially for sensitive attributes.

We construct an explicit equivariant quantum Satake map for Grassmannians, which enables us to express their torus-equivariant quantum cohomology in terms of that of projective space. We then consider the exterior algebra of the latter, which admits a canonical identification with a Clifford algebra. We describe the resulting action in several complementary ways: first, from a geometric perspective via push-pull maps, and second, in terms of the shuffle product, which also arises in the simplest cohomological Hall algebra associated with the $A_1$-quiver. Exploiting the Clifford algebra structure, we derive new recurrence relations among equivariant Gromov-Witten invariants, yielding a new method for their computation in terms of Wick's Theorem. As an application, we provide combinatorial proofs of Graham positivity for both equivariant quantum Pieri rules, and in one case extend these results to quantum triple Schubert calculus.

This paper develops a unified probabilistic framework based on distributional derivatives and Dirac delta representations for the analysis of conditional and transportation-related quantities. General identities are established for arbitrary random variables, encompassing absolutely continuous, discrete, and mixed distributions. The proposed approach yields unified formulas for conditional expectations, conditional distributions, hazard functions, and improper distributions, revealing a common localization mechanism underlying these classical concepts. The framework is further combined with copula methods to investigate transportation and dispersion functionals through dependence structures. Exploiting the extremal properties of the Fréchet--Hoeffding bounds together with expectation inequalities induced by $Δ$-antitonic functions, sharp bounds are derived for absolute difference moments under fixed marginals. These results lead to concise derivations of quantile representations for the Wasserstein distance and a corresponding upper transportation functional, as well as survival-function representations and bounds for generalized absolute difference moments. As a particular case, new representations are obtained for the bivariate Gini mean difference and the associated bivariate Gini index. Applications are given to Wasserstein-type functionals arising in the normal approximation of standardized counting distributions, including Poisson, Binomial, and Negative Binomial models, for which explicit quantile representations are derived. Overall, the results establish explicit links among conditional structures, dependence modeling, dispersion measures, normal approximation, and optimal transport, providing a unified perspective on several fundamental constructions in probability and mathematical statistics.

We study deconfined quantum critical points (DQCP) associated with Lieb-Schultz-Mattis (LSM) anomalies in one-dimensional spin chains. Our starting point is a structural characterization of the LSM anomaly in the Lyndon-Hochschild-Serre spectral sequence: $ω_{\mathrm{LSM}}\in E_\infty^{1,2}= H^1(\mathbb Z_{\mathrm{trans}},H^2(G_{\mathrm{int}},\mathrm{U}(1)))\subseteq H^3(G_{\mathrm{int}}\rtimes_ρ\mathbb Z_{\mathrm{trans}},\mathrm{U}(1))$. Physically, this class decorates a translation defect with a projective representation of the internal symmetry $G_\mathrm{int}$. We show that gauging the internal symmetry in the presence of an $E_\infty^{1,2}$-type anomaly necessarily produces a non-invertible dual symmetry. This gives a general mechanism for type-II DQCP: in contrast to type-I examples with $E_\infty^{2,1}$-type anomalies which are dual to ordinary group-like symmetry breaking, type-II transitions are dual to spontaneous breaking of a non-invertible symmetry. We illustrate the mechanism using a spin-$1/2$ chain with an anomalous $D_8$ LSM symmetry. We construct a dimer-to-ferromagnet DQCP candidate, provide numerical evidence for a critical theory with central charge $c\approx 1$, and show, using both category theory and explicit lattice constructions, that gauging the internal symmetry yields the non-invertible $\mathrm{Rep}(H_8)$ dual symmetry.

The dynamics of open quantum systems is commonly described by quantum master equations derived under the assumption of weak system-bath coupling and a separation of timescales between system and bath. When the system is additionally subjected to a periodic driving, the validity of the resulting Floquet master equations is further restricted to regimes of weak or high-frequency driving. Here, we benchmark a set of commonly used Floquet master equations for a model of two locally driven spins coupled to a shared Ohmic reservoir at finite temperature. We systematically probe the accuracy of the equations as a function of the driving parameters, thus identifying limits of their applicability. Dynamical maps predicted by each master equation are compared against numerically exact non-Markovian simulations, tracking the full relaxation dynamics. We find that the accuracy of each master equation closely reflects the assumptions underlying its derivation. For the Floquet-Lindblad equation, errors can be strongly amplified near resonances where the secular approximation breaks down, while approaches that avoid the secular approximation perform better and exhibit a more systematic dependence of the error on driving frequency and amplitude.

Alfvénic turbulence is vital to powering the solar wind and corona, yet eludes a comprehensive understanding of the kinetic processes by which it dissipates. Minor ions are sensitive tracers of these processes, showing extreme perpendicular temperatures and mass-weighted temperature trends that can either correlate or anticorrelate with mass-to-charge ratio, $A_i/Z_i$. We use a combination of quasilinear theory and 3D hybrid-kinetic simulations to explain these features and their correlations with properties of turbulence in the fast solar wind. When Alfvénic turbulence is imbalanced, its cascade to ion-Larmor scales is throttled by the helicity barrier. This barrier ultimately leads to high-frequency proton-cyclotron waves (PCWs), both oblique and parallel, the latter of which produce very flat electric-energy spectra ($\mathcal{E}_{E_{\perp}}\sim k_\parallel^{-η}$ with $η<2$) over the range of scales that are cyclotron resonant with minor ions. While steeper spectra lead to a positive correlation of heating with $A_i/Z_i$, the shallower spectra cause the dependence to invert, with $Q_i\propto Q_{\mathrm{p}}A_i(A_i/Z_i)^{η-2}$. Six simulations of balanced and imbalanced turbulence spanning $β_{\rm p0}=\{1,0.3,1/16\}$ corroborate this prediction, showing minor-ion heating rates that follow $(A_i/Z_i)^a$. Minor-ion heating is strongest and most perpendicular in our lowest $β_{\rm p0}=1/16$ simulation of imbalanced turbulence, reaching $T_{\perp{\rm O}^{5+}}/T_{\perp{\rm p}}\approx40$ and $T_{\perp{\rm O}^{5+}}/T_{\parallel{\rm O}^{5+}}\approx10$, consistent with low-coronal observations. Future minor-ion measurements should test whether intervals in which minor-ion thermal speeds decrease with increasing mass-to-charge ratio are associated with a history of large cross helicity, enhanced power in parallel PCWs, and a steep transition-range spectrum.

We enlarged the capabilities of the publicly available Mathematica-based tool $\tt GrayHawk$. This second version expands the spectrum of metrics that can be considered in two distinct and disjoined directions. First, it enables a fully numerical computation of the tortoise coordinates integral, allowing the user to account for many metrics for which an analytic computation was impractical. Second, it extends the scattering problem to wormhole solutions. The pool of pre-loaded metrics is enriched, enabling immediate testing of the new features, and the code's modular structure is maintained to facilitate easy modification. This implementation proves $\tt GrayHawk$ adaptability and makes it an even more powerful tool for studying black holes, wormholes, Hawking radiation, and other features involving field propagation on curved manifolds. The codes described in this work are publicly available at \href{https://github.com/marcocalza89/GrayHawk-v2}{\faGithub}.

This study examines the evolution of bilateral and multilateral scientific collaboration among EU Member States and between the EU and global partners from 2000 to 2024 using data from OpenAlex and Scopus. The results show that OpenAlex, when restricted to cited articles, yields findings broadly comparable to those obtained from Scopus for assessing country-level research collaboration. Relative Intensity of Collaboration (RIC) values are consistently higher for multilateral than for bilateral partnerships. Increased collaboration intensity during the final years of FP7, the intermediate and later stages of Horizon 2020, and the final years of the study period suggests that EU FP may have strengthened collaboration among participating countries. With regard to European integration, multilateral collaboration intensity increased between the EU-14 and EU-13, between these groups and EU candidate countries, and within the EU-13. Despite this growth, structural asymmetries persist. Bilateral collaboration among EU-14 countries is concentrated within the group and with EU-13, Brazil, Norway, Switzerland, and the United Kingdom, whereas EU-13 countries collaborate more intensively within the group, with EU candidate countries and Russia. EU-14 countries maintain stronger multilateral collaboration with high-income countries such as Australia, Canada, and the United States than do EU-13 countries. For both groups, collaboration with China remains the weakest. Although multilateral collaboration intensity with Russia has declined, it remained above the expected level for the EU-14 in 2024 and was 2.5 times higher than expected for the EU-13. This persistence may reflect the continued participation of Russian researchers in multilateral projects despite Russia's suspension from Horizon Europe in 2022.

Asymptotic e-values are emerging as a powerful alternative to asymptotic p-values, particularly in post-hoc inference and multiple testing, where significance levels may be data-dependent. Existing asymptotic e-values, however, suffer from the ``missing factor,'' a scaling inefficiency resulting in overly conservative inference. Drawing on the framework of near-optimal concentration inequalities developed by Bentkus in the 2000s, we introduce Bentkus-type asymptotic e-values and prove that they successfully eliminate the missing factor. We also demonstrate both theoretically and empirically that Bentkus-type e-values consistently deliver sharper inference than existing alternatives, leading to tighter post-hoc confidence intervals and higher rejection rates in multiple testing procedures.

We investigate the heat transport in porous media convection over a wide Rayleigh--Darcy number range of $26.8\leq Ra\leq 2.62\times 10^5$, and a Darcy number range of $6.18\times10^{-7}\leq Da\leq 1.21\times 10^{-5}$. In the experiments, we employ 3D-printed lattice structures as the solid porous matrix and water as the working fluid. Quantitative analyses of the porous medium Nusselt number $Nu_m$ and local temperature statistics reveal that the present system undergoes a transition through five distinct regimes: I. Conduction, II. Convection, III. Oscillation, IV. Transition, V. Classical Rayleigh--Bénard convection. This transitional process bridges the gap between Rayleigh--Darcy-like behaviour and Rayleigh--Bénard-like behaviour in porous media convection. By varying the permeability of the matrix, we further examine the role of the Darcy number $Da$, which turns out to have a profound impact on the transitional processes across different regimes. Flow field measurements reveal that the flow structures within Regime IV and Regime V evolve from several horizontally stacked convection rolls to a single-roll structure, and the pore-scale Reynolds number both exceeds unity in these two regimes. Finally, we report the corresponding phase diagram in the $Ra$-$Da$ space.

This study explores the evolution of bilateral and multilateral research collaboration of nine EU-14 member states, both within Europe and globally, across six disciplines, between 2010 and 2024, using OpenAlex data. Results indicate that bilateral collaboration rates remained relatively stable and predominantly concentrated within EU-14 countries, followed by the USA, the UK, and China. Multilateral collaboration rates increased significantly across all disciplines, with the highest increase observed in medicine and the highest overall rates maintained in physics & astronomy. The same trend across disciplines was observed for the Relative Intensity of Collaboration (RIC). This reflects the growing importance of large-scale international research consortia in infrastructure-intensive fields that address global scientific challenges. RIC has increased for both bilateral and multilateral collaboration, with stronger growth in multilateral collaboration. Multilateral RIC fell below the expected level most frequently with South Korea, India, and China. Across both collaboration types, increases in collaboration rates were generally associated with increases in RIC. No substantial changes in collaboration rates or RIC with the UK were observed following Brexit. A decline in multilateral collaboration with Russia in physics and astronomy coincided with its suspension from Horizon Europe in 2022, while the collaboration rate in medicine increased.

We determine asymptotic results for the average size of Selmer groups arising from certain isogenies related to Jacobians of hyperelliptic curves of genus $g\geq 2$. We do so by combining Bhargava's geometry-of-numbers methods with new parametrisations coming from Vinberg theory, arising from representations related to the Dynkin diagrams of type $B$ and $C$. We additionally prove some lower bounds on the average size of these isogeny Selmer groups by using a formula of Greenberg--Wiles.

We classify the bulk-to-boundary correlators for general integer-spin $s$ operators in a Poincaré-invariant theory by imposing suitable fall-off conditions near future/past null infinity. Any bulk-to-boundary correlator is a linear superposition of a set of basic tensor structures fixed by the little group \text{ISO}(2) of massless particles. We map the independent tensor structures to all possible non-crossing double-line diagrams. A further mapping of the double-line diagrams to circular diagrams shows that all independent tensor structures are tensor products of loop diagrams. By extrapolating the bulk-to-boundary correlators to boundary-to-boundary correlators, we find a rich structure for general spin-$s$ operators. Furthermore, we show that the extrapolated operator lies in a type Ib spin-$s$ multiplet representation of Carrollian conformal field theory (CCFT). This is a net representation that generated by the Wigner translation generators.

In the evolving landscape of data product exchange platforms, traditional economic valuation models fall short due to the non-rival nature of data and the prevalence of non-monetary data product exchanges. This paper introduces a normative, choice-based metric for valuing data products within intracompany exchanges, where conventional pricing mechanisms are absent. By modeling consumer attention and preferences, the proposed metric quantifies the value of data offerings based solely on user selection behavior, without relying on cost, demand, or competitive pricing data. We show that this metric can be formally cast as a cooperative game with a closed-form Shapley value, providing a principled and fairness-based allocation of value across offerings. The model rewards uniqueness and discriminative consumption, effectively addressing the limitations of popularity-based metrics and incentivizing the creation of high-value, long-tail data products. Through theoretical analysis and illustrative examples, the metric is shown to align with economic principles, support equitable valuation, and contribute to a robust framework for measuring gross data product value. Future research directions include exploring bundling strategies and quantifying product complementarity.

LLM-based agents increasingly rely on harnesses that provide execution environments, tool interfaces, context, lifecycle orchestration, observability, verification, and governance. Existing self-improving agents and automatic harness evolution methods mainly improve agents through runtime supervision, prompt optimization, workflow search, or harness modification based on final outcomes. However, they often fail to diagnose where the responsible evidence lies in failed trajectories and which harness layer causes the unreliable behavior, resulting in broad, indirect, or poorly scoped changes. This paper proposes HarnessFix, a trace-guided framework for diagnosing agent failures and repairing agent harnesses. HarnessFix compiles raw execution traces and harness code into a Harness-aware Trace Intermediate Representation (HTIR), which normalizes fragmented trajectory evidence and captures step-level provenance and control-flow relations. It then attributes failures to responsible trajectory steps and harness layers, consolidates recurring diagnoses into actionable flaw records, and maps them to scoped repair operators. Finally, HarnessFix generates and validates harness patches under flaw-specific repair specifications to reduce target flaws without introducing unacceptable regressions. We evaluate HarnessFix on SWE-Bench Verified, Terminal-Bench 2.0 Verified, GAIA and AppWorld. Across these benchmarks, HarnessFix improves held-out test performance over the initial harnesses by 15.2%--50.0%, outperforms human-designed and self-evolution baselines, and reveals recurring harness-flaw patterns across ETCLOVG layers.

A consistent transformation from momentum space to energy space is performed for the diffusion equation within kinetic theory, with particle-number conservation explicitly preserved. Under the assumption of a constant single-particle level density, the equation reduces to a one-dimensional diffusion equation in energy space with consistent kinetic coefficients. The equivalence of the definitions of the equilibrium temperature in momentum space and in energy space is demonstrated. It is established that the inclusion of the energy dependence of the kinetic coefficients leads to an energy-dependent equilibrium temperature and a modification of the distribution function. The obtained results may be used to analyze relaxation processes in atomic nuclei and nonequilibrium dynamics of Fermi systems.

Low and medium spin excitations in $^{146,148,150,152}$Nd isotopes, populated in $β^-$ decay of corresponding Pr isotopes or in prompt-$γ$ fission of $^{252}$Cf have been studied using Gammasphere array of Ge spectrometers. 159 new levels, including two new isomers, 305 new $γ$ transitions and 83 new spin-parity assignments were added in the four studied nuclei. The structure of excited levels in the studied Nd isotopes is discussed using phenomenological classifications and systematics and compared to calculations reported in other works. Particular attention is paid to $0^+$ and $2^+$ excitations related to the emerging quadrupole collectivity and to the role of the 11/2$^-$[505] neutron extruder in the process.

Extracting work from quantum states is a fundamental task in quantum thermodynamics. Previous studies have primarily focused on determining the best achievable rate of work extraction, and remarkably, this characterization appeared to remain unchanged regardless of the choice of allowed processes: whether one considers the operationally motivated class of energy-conserving thermal operations, or the axiomatic class of Gibbs-preserving operations, the optimal extractable work is given by the Helmholtz free energy. Here, we challenge this perspective, showing that a more refined analysis of the asymptotic performance of work extraction reveals significant differences in the performance for the two different classes of free operations. Precisely, we focus on the trade-off between the extraction rate and its reliability, characterized by the optimal asymptotic speed at which the extraction error can be suppressed. We establish that the reliability of Gibbs-preserving operations and of thermal operations are respectively characterized by the Petz and the sandwiched Rényi relative entropies, demonstrating that the former in general strictly outperforms the latter, and providing new interpretations of several information-theoretic divergences. Our analysis reveals that operational constraints such as energy conservation impose stronger limitations on the achievable precision of quantum tasks than can be inferred from their asymptotic rates, thereby questioning the use of Gibbs-preserving operations as a mathematically convenient substitute for the physically realizable thermal processes.

We present a polynomial-time algorithm for computing a $1/e$-approximate Hylland--Zeckhauser (HZ) equilibrium. This establishes the \emph{first} efficient approximation guarantee for HZ equilibria in settings with multi-valued utilities. Our main technical contribution is a novel utility stratification technique that reduces the original multi-valued market to a structured bi-valued instance. This reduction allows us to efficiently compute the approximation by leveraging the exact algorithm of Vazirani and Yannakakis.