Long-term chemical durability of glass, crucial for immobilizing nuclear waste, is governed by glass properties such as composition, surface geometry, as well as external factors like thermodynamic conditions and surrounding medium. Despite decades of research, there are no models that account for these intrinsic and extrinsic factors to predict the dissolution rates of glass compositions. To address this challenge, we evaluate the role of natural language embeddings capturing the synthesis and testing conditions in enhancing the predictability of glass dissolution. Evaluating the approach on hand-curated ~700 datapoints extracted from the literature, we reveal that the machine learning (ML) model including natural language embeddings (NLP-ML) outperforms classical ML model in predicting glass dissolution rate. Furthermore, we developed a generalizable ML model by transforming the compositional features to structural descriptors of glass alongside NLP-derived features, enabling extrapolation capability to glass compositions with completely new elements absent in the training data. Evaluating this model on a completely new dataset of glass compositions 34 chemical components in contrast to the training dataset that had only 28 components, we demonstrate that the model indeed exhibits generalizability to glass compositions that are out-of-distribution. Altogether, this integrated approach offers a pathway towards high-fidelity glass dissolution prediction and accelerate the discovery of novel glass compositions with tailored durability for sustainable nuclear waste management.

The idea of a $\bigvee$-system was introduced by Veselov in the study of rational solutions of the WDVV equations of associativity. These are algebraic/geometric conditions on the set of covectors that appear in rational solutions to the WDVV equations. Here, this idea is generalized to open WDVV equations, which are an additional set of PDEs originating from open Gromow-Witten Theory. We develop -- for rank-one extensions -- algebraic/geometric conditions on the covectors that supplement the $\bigvee$-system to give rational solutions to the open WDVV equations. Examples, and the relation to superpotentials and to Dubrovin almost-duality, are given.

We present a model for sticky particles in which cluster sizes after a reaction have $\ell$ fewer total particles than the sum of their reactants. The finite particle system is modeled as a Markov process under a mean-field assumption for selecting reactants. The limiting kinetic equations form an infinite system of nonlinear differential equations similar to the Smoluchowski coagulation equations with multiplicative kernel. We show existence and uniqueness for systems whose cluster sizes are either bounded above or below by the emission size $\ell$. When clusters have at most $\ell$ particles, well-posedness can be extended until an exhaustion time in which certain cluster fractions vanish. For clusters with more than $\ell$ particles, we prove short-time well-posedness, along with explicit formulas for cluster sizes and moments. We also conduct numerical experiments which suggest these formulas hold until a gelation time, at which an infinite-sized cluster forms.

Iterators are a fundamental programming abstraction for traversing and modifying elements in containers in mainstream imperative languages such as C++. Iterators provide a uniform access mechanism that hides low-level implementation details of the underlying data structure. However, iterators over mutable containers suffer from well-known hazards including invalidation, aliasing, data races, and subtle side effects. Immutable data structures, as used in functional programming languages, avoid the pitfalls of mutation but rely on a very different programming model based on recursion and higher-order combinators rather than iteration. However, these combinators are not always well-suited to expressing certain algorithms, and recursion can expose implementation details of the underlying data structure. In this paper, we propose persistent iterators -- a new abstraction that reconciles the familiar iterator-based programming style of imperative languages with the semantics of persistent data structures. A persistent iterator snapshots the version of its underlying container at creation, ensuring safety against invalidation and aliasing. Iterator operations operate on the iterator-local copy of the container, giving true value semantics: variables can be rebound to new persistent values while previous versions remain accessible. We implement our approach in the form of LibFPP -- a C++ container library providing persistent vectors, maps, sets, strings, and other abstractions as persistent counterparts to the Standard Template Library (STL). Our evaluation shows that LibFPP retains the expressiveness of iterator-based programming, eliminates iterator-invalidation, and achieves asymptotic complexities comparable to STL implementations. Our design targets use cases where persistence and safety are desired, while allowing developers to retain familiar iterator-based programming patterns.

We establish finite-step probabilistic upper bounds on the contraction ratios $ρ_k = Δ_{k+1}/Δ_k$ for iterated Pearson correlation dynamics. Let $(P_k)_{k\ge 0}$ be the sequence generated by the Pearson update. Define $Δ_k := \|P_{k+1}-P_k\|_F$, $ρ_k := Δ_{k+1}/Δ_k$ for $Δ_k > 0$, and $δ_k := Δ_k/n$. Although $Δ_k \to 0$ along convergent trajectories, the ratios $ρ_k$ may exceed unity in finitely many steps. This behavior is invisible to local linearization. Our main contribution is a probabilistic bounding framework that captures these finite-step expansions. We initialize $P_0$ with i.i.d. $\mathcal{U}[-1,1]$ entries and let $\mathbb{P}$ be the induced measure. For $k \ge 2$, we construct state-dependent bounds $B_p : \mathbb{R}_+ \to \mathbb{R}_+$ satisfying $\mathbb{P}(ρ_k \le B_p(δ_k)) \ge p$. The functions $B^{\mathrm{q}}_p(δ)$ are empirical conditional $p$-quantiles of $\log ρ_k$ given $δ_k$ under logarithmic binning. Larger families $B^{\mathrm{TC}}_{p,τ}(δ)$ and $B^{\mathrm{tol}}_{p,τ}(δ)$ are obtained via multiplicative adjustments, yielding pointwise larger bounds that preserve the $δ$-dependence. Validation on held-out trajectories confirms the bounds hold with empirical coverage matching nominal levels for all $n \in [3,2000]$. The baseline $0.95$-quantile bound $B^{\mathrm{q}}_{0.95}(δ)$ yields two concrete results: $\mathbb{P}(ρ\le 1 \mid δ\le 0.03) \ge 0.95$ uniformly in $n$, and $\mathbb{P}(ρ\le 1.7) \ge 0.95$ for 21 of 22 dimensions. The exception $n = 69$ attains $2.35$, revealing a rare extreme upper tail discontinuity not captured by asymptotic analysis. These are the first finite-step probabilistic bounds for Pearson correlation dynamics. The framework is fully reproducible with provided code and data.

Governance opacity over AI systems shifts in kind as capability asymmetry grows, and the strongest forms defeat the disclosure-based remedies governance ordinarily relies on. This paper applies a six-dimension framework from political theory (legitimacy, accountability, corrigibility, non-domination, subsidiarity, institutional resilience) to six AI governance arrangements already in operation, ordered by increasing capability asymmetry between system and overseer. Proprietary secrecy yields to disclosure at the low end, but at the high end the governed system either games its own evaluation or sits inside the governance process, and transparency remedies lose traction. Legitimacy and non-domination strain more consistently across the sample than corrigibility and resilience, which respond more readily to institutional design quality. The sample cannot separate institutional design maturity from capability asymmetry, and the patterns are offered as hypotheses for multi-rater validation.

In this paper, we study non-reflexive Banach spaces $X$ for which the quotient space $X^{**}/X$ is reflexive. Such spaces were first introduced by James R.~Clark, where they were called coreflexive spaces. We show that a space $X$ is coreflexive if and only if every separable subspace $Y\subseteq X$ is coreflexive, provided that $X$ is w$^*$-sequently dense in its bidual $X^{**}$. We show that coreflexive spaces are stable under $\ell^{p}$-sum for $1<p<\infty$. We show that if $X$ is a coreflexive space such that $X^{**}/X$ is separable, then the space of Bochner $p$-integrable functions, $L^{p}(μ,X)$ is coreflexive for $1<p<\infty$. We conclude by providing an alternative proof of the fact, in a quasi-reflexive space $X$, w-PC's of the unit ball $X_{1}$ continue to have the same property in all the higher even-order dual unit balls of $X$.

We study physical (near-kernel of constraints) states of 4-d Euclidean loop quantum gravity in Smolin's weak coupling limit on the complete graph $K_5$ using variational Monte Carlo with neural network quantum states. We investigate the Hamilton constraint $\hat{H}$ in the ordering proposed by Thiemann, as well as $\hat{H}^\dagger$ and $\hat{H}+\hat{H}^\dagger$. We find that the variational optimisation selects distinct solution families for $\hat{H}$ and $\hat{H}^\dagger$ across several considered cutoffs on the kinematical degrees of freedom. The solution family of $\hat{H}$ is flat on all minimal loops and has non-vanishing volume expectation values. Its edge-charge marginals delocalise with increasing cutoff, which indicates they are approximations to solutions that are non-normalisable in the kinematical inner product. The solution family for $\hat{H}^\dagger$ is normalisable, shows non-trivial charge correlations, lies in the kernel of volume and is not flat. $\hat{H}+\hat{H}^\dagger$ turns out to be much harder to solve and yields quasi-solutions combining features of both previous families. We characterise all solutions using chromaticity 1- and 2-point functions, minimal loop holonomies, geometric area and volume observables and show that the two families can be interpreted as, on the one hand, a family of states close to the Ashtekar-Lewandowski vacuum and the Dittrich-Geiller vacuum with some numerical noise on the other hand. We also present some results that link solutions of the truncated theory to solutions of the continuum theory.

We study the effect of assortative and disassortative mixing on the robustness of networks under random node failures. For ordinary (dyadic) networks, by using the generating function technique and stochastic simulations, we show that the relationship between the Pearson assortativity coefficient $r$ and the percolation threshold $p_c$ is not always monotonic. More specifically, in certain regions of the parameter space of our model, moderately disassortative networks can be more fragile than either strongly disassortative or uncorrelated networks. We observe this nonmonotonic behavior for trimodal networks as well as for networks with Poisson and power-law degree distributions. We then extend our analysis to hypergraphs with correlations between node hyperdegree and hyperedge cardinality. For this case, we find that positively correlated hypergraphs tend to be more fragile than negatively correlated ones. Additionally, as in the dyadic case, the relationship between $r$ and $p_c$ is nonmonotonic, and the most fragile configuration does not correspond to the most assortative hypergraph.

We propose novel particle swarm optimization (PSO) variants incorporated with deep neural networks (DNNs) for particles to pursue globally optimal positions in dynamic environments. PSO is a heuristic approach for solving complex optimization problems. However, canonical PSO and its variants struggle to adapt efficiently to dynamic environments, in which the global optimum moves over time, and to track them accurately. Many PSO algorithms improve convergence by increasing the swarm size beyond potential optima, which are global/local optima but are not identified until they are discovered. Additionally, in dynamic environments, several methods use multiple sub-population and re-diversification mechanisms to address outdated memory and local optima entrapment. To track the global optimum in dynamic environments with smaller swarm sizes, the DNNs in our methods determine particle movement by learning environmental characteristics and adapting dynamics to pursue moving optimal positions. This enables particles to adapt to environmental changes and predict the moving optima. We propose two variants: a swarm with a centralized network and distributed networks for all particles. Our experimental results show that both variants can track moving potential optima with lower cumulative tracking error than those of several recent PSO-based algorithms, with fewer particles than potential optima.

The first dedicated observation of an off-limb prominence by the Spectral Imaging of the Coronal Environment (SPICE) instrument took place on April 15, 2023. We aim to create parameter maps on the prominence region, including temperature, pressure, and column mass, by studying the integrated intensity of the Lyman $β$ and Lyman $γ$ lines from SPICE data. After constraining the altitude and radial velocity in the prominence, we use a 1D non-LTE radiative transfer code to generate 1000 random models and compute the Lyman $β$ and Lyman $γ$ line profiles. The computed intensities are compared with observed integrated intensities from SPICE. Then, we create models which simultaneously give a reasonable match with the observed intensities in both lines. Unlike previous approaches, our method uses contribution functions to guide the optimisation of temperature and pressure profiles. Our approach enables a physically constrained and consistent match to both spectral lines. The method in this paper enables us to generate models from pixels on the prominence region and use this information to generate parameter maps. The results obtained have potential for future research.

We show that the maximum expected inner product between a random vector and the standard normal vector over all couplings subject to a mutual information constraint or regularization is equivalent to a truncated integral involving the rate-distortion function, up to universal multiplicative constants. The proof is based on a lifting technique, which constructs a Gaussian process indexed by a random subset of the type class of the probability distribution involved in the information-theoretic inequality, and then applying a form of the majorizing measure theorem.

Wavelength shifting (WLS) fibers are widely used in particle physics for light collection from scintillators. Light production by charged particles directly in WLS fibers is traditionally ignored. In this study, light produced by charged particles in WLS fibers is clearly observed. The light yield of different batches of Y11(200) 1 mm diameter WLS fibers is as large as 23 $\pm$ 2% with respect to the light yield of the Bicron BCF-12 1 mm diameter scintillating fiber. In clear fibers of the same diameter, no scintillation light is produced, while Cherenkov light is clearly seen at the 45-degree crossing angle. The observed amount of light produced by charged particles in the WLS fibers is not small and should be taken into account in advanced detector simulations.

A first search is presented for BSM resonances in four top quark production in the 2 lepton channel, using $138\mathrm{fb}^{-1}$ $pp$ data collected at $\sqrt{s}=13$ TeV, and $35\mathrm{fb}^{-1}$ $\sqrt{s}=13.6$ TeV $pp$ data. No significant excess is observed; limits are set on vector Z', scalar, pseudoscalar and ALP mediators. Z' mediators with 50% width are excluded up to 850 GeV (1000 GeV expected).

Recently, Dunjko et al.(PRL, 2018) proposed an algorithm for accelerating the solution of 3-satisfiability problems using a small-scale quantum computer. In this paper, we design a distributed quantum-classical hybrid algorithm for solving K-satisfiability problems. Under resource-constrained conditions, our algorithm achieves a significant acceleration in the core term of the exponential time complexity. The proposed algorithm is a generalization of the algorithm by Dunjko et al. Compared with their algorithm, our algorithm requires a smaller number of qubits. More importantly, the proposed algorithm does not rely on any quantum communication.

We investigate the thermal responses of a harmonic oscillator chain coupled at its boundaries to heat baths held at different temperatures. This setup sustains a steady energy flux, continuously dissipating heat into both reservoirs. By introducing slow variations in the bath temperatures, we quantify the resulting excess heat currents and thereby obtain the nonequilibrium heat capacity matrix at fixed but arbitrary temperature differences. We demonstrate the existence of a well-defined thermodynamic limit for long chains. The specific heat associated with energy exchanges with a single bath depends on the difference in friction coefficients governing the system-bath couplings. That thermokinetic effect is typical for nonequilibrium response. When the couplings with the thermal baths acquire temperature dependence, the specific heat correspondingly inherits a nontrivial temperature dependence, in sharp contrast with equilibrium. Our results provide the first explicit determination of specific heat(s) in a locally interacting, spatially extended driven system. Beyond its exact solvability, the model may offer a natural nonequilibrium extension of the Dulong-Petit law, capturing the high-temperature behavior of driven molecules.

We define 2-indexed $(q,p)$-Schatten quasi-norms for any $q,p > 0$ on operators on a tensor product of Hilbert spaces, naturally extending the norms defined by Pisier's theory of operator-valued Schatten spaces. We establish several desirable properties of these quasi-norms, such as relational consistency and the behavior on block diagonal operators, assuming that $|\frac{1}{q} - \frac{1}{p}| \leq 1$. In fact, we show that this condition is essentially necessary for natural properties to hold. Furthermore, for linear maps between spaces of such quasi-norms, we introduce completely bounded quasi-norms and co-quasi-norms. We prove that the $q \to p$ completely bounded co-quasi-norm is super-multiplicative for tensor products of quantum channels for $q \geq p>0$, extending an influential result of [Devetak, Junge, King, Ruskai, 2006]. Our proofs rely on elementary matrix analysis and operator convexity tools and do not require operator space theory. On the applications side, we demonstrate that these quasi-norms can be used to express relevant quantum information measures such as Rényi conditional entropies for $α\geq \frac{1}{2}$ or the Sandwiched Rényi Umlaut information for $α< 1$. Our multiplicativity results imply a tensorizing notion of reverse hypercontractivity, additivity of the completely bounded minimum output Rényi-$α$-entropy for $α\geq\frac{1}{2}$ extending another important result of [Devetak, Junge, King, Ruskai, 2006], and additivity of the maximum output Rényi-$α$ entropy for $α\geq \frac{1}{2}$.

We study $\mathbb{Z}_3$-symmetric Rabi model that describes a three-level system coupled to two bosonic modes. We derive a mapping of the two-mode $\mathbb{Z}_3$ Rabi model onto a qubit-boson ring. This mapping allows us to formulate a realistic implementation of the $\mathbb{Z}_3$ Rabi model based on superconducting qubits. It also provides context for the previously proposed optomechanical implementation of the $\mathbb{Z}_3$ Rabi model. In addition, we propose a physical implementation of the $\mathbb{Z}_3$ Potts model via a coupled chain of $\mathbb{Z}_3$ Rabi models.

Local life service recommendation is distinct from general recommendation scenarios due to its strong living need-driven nature. Fundamentally, accurately identifying a user's immediate living need and recommending the corresponding service are inextricably linked tasks. However, prior works typically treat them in isolation, failing to achieve a unified modeling of need prediction and service recommendation. In this paper, we propose a novel large language model based framework that jointly performs living need prediction and service recommendation. To address the challenge of noise in raw consumption data, we introduce a behavioral clustering approach that filters out accidental factors and selectively preserves typical patterns. This enables the model to learn a robust logical basis for need generation and spontaneously generalize to long-tail scenarios. To navigate the vast search space stemming from diverse needs, merchants, and complex mapping paths, we employ a curriculum learning strategy combined with reinforcement learning with verifiable rewards. This approach guides the model to sequentially learn the logic from need generation to category mapping and specific service selection. Extensive experiments demonstrate that our unified framework significantly enhances both living need prediction performance and recommendation accuracy, validating the effectiveness of jointly modeling living needs and user behaviors.

We discuss what is, at best, an ambiguity, and possibly an inconsistency of the eikonal Color Glass Condensate (CGC) description of Deep Inelastic Scattering (DIS). In this framework, the Bjorken-$x$ dependence enters the cross section solely through the rapidity cutoff $Λ=x_b$, leading to an all-order cross section independent of $x_b$. To address this issue, we explore a natural modification in which the weight functional depends explicitly on the light-cone momentum fraction $z$, with integration limits determined by $x_b$. This modification is consistent with the physical expectation that the observed non-perturbative structure depends on the probe energy. Our analysis implies that the $x_b$ variation of the cross section is not solely driven by small-$x$ evolution equations. We support this conclusion through an analysis of existing DIS fits and by demonstrating that a similarly good description of the data can be obtained within the modified framework. Finally, we show that the modified formulation is compatible with $k_t$-factorization, unlike the standard one.

Peer review shapes which scientific claims enter the published record, but its internal dynamics are hard to measure at scale because reviewer criticism and author revision are usually embedded in long, unstructured correspondence. Here we use a fixed-prompt large language model pipeline to convert the review correspondence of \textit{Nature Communications} papers published from 2017 to 2024 into structured reviewer--author interactions. We find that review pressure is concentrated in the first round and focused disproportionately on core claims rather than peripheral presentation. Higher average opinion strength is also associated with more reviewer disagreement, while review patterns vary little with broad team attributes, consistent with relatively impartial evaluation. Contrary to the intuition that stronger papers should pass review more smoothly, with greater reviewer--author agreement and less extensive revision, we find that stronger criticism, higher-quality comments, and greater revision burden are associated with higher later citation impact within accepted papers. We finally show that fields differ more in review style than in review length, pointing to disciplinary variation in how criticism is negotiated and resolved. These findings position open peer review not just as a gatekeeping mechanism but as a measurable record of how influential scientific claims are challenged, defended, and revised before entering the published record.

Within the wide variety of topological solitons supported by Yang--Mills theory, merons occupy a particularly distinguished role. Despite their simplicity, they represent genuinely non-Abelian configurations that can be regarded as the fundamental building blocks of instantons, and they provide a qualitatively accurate picture of confinement. In this work, we show that such configurations are, in fact, supported by a broad class of non-Abelian gauge theories beyond Yang--Mills, provided that suitable physical conditions are satisfied, thereby rendering them universal. Taking into account their gravitational backreaction, we further demonstrate that both black holes and Euclidean wormholes sourced by merons admit natural extensions within this generalized framework, which regularizes the singular behavior they exhibit in constant--curvature backgrounds. As a byproduct, we construct a regular black hole solution supported by genuinely non-Abelian gauge fields, based on a non-Abelian generalization of the Ayón--Beato--García nonlinear electrodynamics. As a consequence of this universality, physical effects intrinsic to merons are likewise expected to be universal. A notable example is the spin from isospin effect, whereby bosonic excitations charged under the gauge group can effectively behave as fermionic degrees of freedom.

The supercurrent diode effect (SDE), characterized by unequal critical currents in opposite directions, has been observed with or without magnetic fields, yet mechanisms enabling zero-field SDE without explicit symmetry breaking remain underexplored. Here we investigate a Josephson junction with strong electron-electron interaction modeled by a Hubbard $U$ term and an odd number of electrons. We find that strong correlations induce spontaneous breaking of time-reversal and mirror symmetries, forming a $φ$-junction with degenerate energy minima at $\pmφ$, resulting in zero-field Josephson diode effect (JDE) without magnetic order. Spin-orbit coupling breaks SU(2) symmetry but does not determine diode polarity, contrasting with magneto-chiral mechanisms. We further show that applying a tiny Zeeman field enables controllable JDE with sizable efficiency due to the enhancement by the strong magnetic correlation, and the JDE strength peaks when the field induces a level-crossing transition. These findings establish strong electron correlation as a distinct mechanism for nonreciprocal superconducting transport, broadening the understanding of SDE origins.

The first dedicated observation of an off-limb prominence by Solar Orbiter took place on April 15, 2023. Our aim is to determine the range of different physical parameters of this prominence and to examine how these parameters affect the formation of the Lyman $β$ and Lyman $γ$ lines of hydrogen. We have found a way to refine key physical parameters by observational data. We will test the method by this prominence observation. We generate 200 random non-LTE models using these observational constraints and compute the Lyman $β$ line and the Lyman $γ$ line profiles. We use the Spectral Imaging of the Coronal Environment (SPICE) full-disk mosaic from November 13, 2023 to constrain the incident radiation. We present the parameters and results of 200 random models using parallel coordinate plots to explore how different parameters affect the results. This allows us to infer the key physical parameters (e.g., central pressure, column mass and temperature gradient) that impact the formation of the Lyman $β$ line and the Lyman $γ$ line in this observation.

This work is concerned with the fundamental scaling laws of quasi-complementary sequence sets (QCSSs) by understanding how large the set size (denoted by $M$) can grow with the flock size ($K$) and the sequence length ($N$). We first establish a geometric framework that transforms a QCSS into a complex unit-norm codebook, through which and by exploiting the density thresholds of the codebooks, certain polynomial upper bounds of the QCSS set size are obtained. Sharp quadratic and cubic scaling laws are then introduced. Specifically, we show that asymptotically optimal QCSSs with tightness factor $ρ=1$ satisfy $M \le (1+o(1))K^2N$, while asymptotically near-optimal QCSSs satisfy $M \le (1+o(1))K^3N^2$ for $ρ< {(1+\sqrt{5})}/{2}$. To validate these upper bounds, we further propose explicit additive-character and mixed-character based constructions for QCSSs that achieve $M = K^2N + K$ and $M = K^3N^2 + 2K^2N + K$, respectively, thereby showing that the quadratic and cubic scaling laws are asymptotically tight. Our proposed constructions admit flexible parameter choices, and their maximum correlation estimates are shown to be tight through explicit extremal examples. Additionally, it is conjectured that the cubic scaling law is universal for all $1<ρ\le 2$, i.e., any asymptotically near-optimal QCSSs should satisfy $M \le (1+o(1))K^3N^2$. This identifies a fundamental cubic barrier for QCSS scalability.

We prove a lower bound on the Calabi functional for degenerations of polarized varieties, involving the difference of CM degrees between generically isomorphic families. This may be viewed as a discretely valued version of Donaldson's lower bound for models, in the sense of non-Archimedean geometry. In particular, this generalizes a result of Donaldson, who considered a single polarized variety. As a main tool, we develop the theory of GIT height, introduced by Wang, and apply it to the family GIT problem of the Chow variety. Using the GIT height, we also give a numerical proof of separatedness of GIT quotients for general and special linear actions, strengthening prior work of Wang--Xu.

The interplay between charge and spin dynamics is at the heart of strongly correlated materials. Inspired by recent quantum simulation experiments, we develop a conserving diagrammatic method to describe the Fermi-Hubbard model for strong repulsion and small hole doping away from the half-filled anti-ferromagnetic ground state. We show that doping leads to four hole pockets in the Brillouin zone formed by magnetic polarons, which become increasingly damped with hole concentration. Likewise, the magnon spectrum of the anti-ferromagnet softens and dampens with doping due to hole-induced magnetic frustration. This gives rise to a suppression of the anti-ferromagnetic correlations in agreement with recent experiments. We then calculate the response of the system to a lattice modulation and recover the qualitative difference between in-phase and out-of-phase modulations seen in experiments, which was interpreted as signs of pseudogap physics. Our results indicate that the complex competition between spin and charge degrees of freedom and the emergence of the pseudogap phase may be usefully analyzed for small dopings, where systematic theories can be developed.

Smart contracts deployed on blockchains such as Ethereum routinely manage large amounts of assets, making their security critical. Empirical studies show that real-world attacks often exploit flaws in the business logic of contracts that unfold across multiple transactions, such as liquidity or front-running attacks. Detecting these attacks requires reasoning about expressive temporal properties beyond the capabilities of existing analysis tools. In this paper, we present an automated approach to the formal verification of smart contracts, enabling the specification and verification of complex temporal properties. Our approach provides a fully automated encoding into Lustre -- the specification language supported by the Kind 2 model checker -- of an expressive subset of Solidity contracts and temporal specifications based on first-order Hennessy-Milner Logic. This encoding allows us to leverage Kind 2 to determine whether the contract respects the specification or not. We implement our approach in a toolchain that integrates the translation and verification steps, and we evaluate its effectiveness and performance on a benchmark of smart contracts and temporal properties capturing complex attack scenarios. Our results show that the proposed approach can effectively verify non-trivial temporal properties of smart contracts and detect violations that are beyond the reach of existing analysis tools.

We study the distribution modulo one of linear recurrent sequences of real numbers. We prove criteria for the finiteness of the set of limit values of the fractional parts of such a sequence and give lower bounds for the maximal distance between two limit values. Our results generalize theorems of Flatto, Lagarias, Pollington, and Dubickas.

We introduce a family of (nonlinear) pairing measures that ensure the validity of the divergence rule for composite functions $\boldsymbol{B}(x,u(x))$, where $\boldsymbol{B}(\cdot,t)$ is a bounded divergence-measure vector field, and $u$ is a scalar function of bounded variation. The elements of the family depend on the choice of the pointwise representative of $u$ on its jump set. Beyond the standard properties, such as the Coarea and Gauss-Green formulas on sets of finite perimeter, this flexibility allows us to characterize the pairings that ensure the lower semicontinuity of the corresponding functionals along sequences converging in $L^1$ with controlled precise values. We show that these lower semicontinuous pairings arise as the relaxation of integral functionals defined in Sobolev spaces.