In the shuffle model of DP (Differential Privacy), a shuffler randomly permutes users' data to achieve high accuracy and privacy. Recent studies show that most existing shuffle protocols are vulnerable to collusion attacks by the data collector and users. They address this issue by introducing the augmented shuffle model that incorporates random sampling and dummy data addition into the shuffler. However, it remains open how to ensure the shuffler follows the protocol and does not collude with the data collector in this model. We address this trust issue by thoroughly exploring the augmented shuffle model with TEEs (Trusted Execution Environments). We first introduce a new privacy notion, FODP (Fully Oblivious DP), which strengthens DP to prevent various TEE side-channel attacks based on external/internal memory access patterns and control flows. We propose a general framework for FODP algorithms based on memory-size obfuscation and three concrete algorithms within it. We also improve the efficiency of our algorithms by using the count-min sketch and optimizing the number of hashes. We evaluate our algorithms on Intel SGX and demonstrate their effectiveness through comparisons with nine baselines.

Let $A$ be a bounded non positive commutative differential graded algebra $A$. Let $\mathbf{D}(A)$ its derived category of DG-modules. If $\mathbf{D}(A)$ is generated by the DG-modules corresponding to the residue fields of the ordinary ring $H^0(A)$ then its localizing subcategories and its colocalizing subcategories are in bijection with the subsets of $\textrm{Spec}(H^0(A))$. These results generalize well-known theorems by A. Neeman (from 1992 and 2011, respectively), because any Noetherian ring satisfies this condition.

LLM-generated outputs in software engineering rarely exist in isolation. They must plug into toolchains, APIs, and data pipelines that impose strict, often organization-specific structural contracts. A semantically correct output that violates the expected format is, from the consuming system's perspective, indistinguishable from a wrong answer, making structural fidelity an operational prerequisite for deploying LLMs in practice. Yet current models routinely produce syntactically invalid or structurally non-compliant outputs. Unlike encoders, autoregressive decoders generate text token-by-token with a local rather than global focus, amplifying structural fragility whenever the target format deviates from familiar training distributions. We present a systematic evaluation of structural reliability across four representative SE tasks, categorizing failures into syntax, structural, and semantic errors. We benchmark ways of mitigation targeting the decoder: grammar-constrained decoding, regex-based validation, and a strict template-driven control (Template Token Match Generation, TTMG) to isolate the sources of these failures. TTMG nearly eliminates syntax errors, yet substantial structural and semantic errors persist, demonstrating that the core bottleneck lies beyond syntax formatting. A detailed case study further illustrates how residual errors cascade in downstream workflows. Our findings show that current structure-enforcing tools are necessary but insufficient, and highlight the need for approaches that jointly ensure structural fidelity and semantic correctness in LLM-driven workflows.

Scientific knowledge advances through within-country and cross-border scientific activities and collaborations, influenced by funding and strength of research enterprise. Sudden declines in research funding, for example from Federal sources in the United States (US) 2024-25, adversely impact on scientific collaboration. How rapid declines in funding affect the science enterprise and the magnitude of impact need to be analysed. Past studies have modelled the global scientific system as complex collaborative networks of entities and studied its topology and dynamics. However, these studies have not undertaken compensation analysis to real-world shocks that have produced rapid declines in scientific research funding. In this study we examine the effect of the sharp declines in the US Federal funding on cancer science research enterprise globally. We model the cancer science ecosystem as a 5-layer multiplex network of collaborative linkages between 233 countries and territories in grants and clinical trial co-investigations, paper co-authorships, co-inventions and patent co-ownerships. We quantify information flow in the multiplex system through network efficiency. Proposing a framework for compensation analysis, we show that sharp declines in US Federal funding for research degrade global information exchange in science, imposing outsized compensatory burdens on country groups such as the European Union (EU) and BRICS (Brazil, Russia, India, China and South Africa). However, we also show that if other countries provide more support for international collaborations, there is an opportunity to remodel the cancer science system to be more resilient to future shocks.

We study uniform recursive directed acyclic graphs with freezing. Here, a graph is built by adding vertices one-by-one and connecting a new vertex to $m\in\mathbb N$ uniformly selected vertices already present. At certain steps vertices can also be frozen, and arriving vertices are not allowed to connect to frozen vertices. This model generalises the uniform attachment tree with freezing, introduced by Bellin et. al (which corresponds to the case $m=1$) as well as the uniform recursive directed acyclic graph model (where no vertices are frozen). Under mild assumptions on when vertices are frozen, we study the empirical degree distribution, large degrees in the graph, and other properties of large-degree vertices such as their label and distance to the first vertex in the graph. Our work improves and/or extends various results from the literature on uniform attachment trees (with freezing) and uniform recursive directed acyclic graphs without freezing. In particular, our results show that statistics that are determined `locally' (e.g. the empirical degree distribution and maximum degree) are essentially unaffected by the freezing of vertices, whereas statistics that are determined `globally' (e.g. the length of paths between vertices) are highly affected by introducing freezing. The analysis relies on adapting the Kingman coalescent construction for uniform attachment trees to the non-tree setting.

This chapter introduces the fundamental principles of metrology and the concept of measurement uncertainty. It explains the role of measurement in engineering and manufacturing, outlines the distinction between error and uncertainty, and presents standard methods for evaluating uncertainty, including the GUM framework, uncertainty budgets, and Monte Carlo simulation. Practical examples and industrial standards are discussed to illustrate real-world applications.

We suggest that quantum algorithms can be used to model classical stochastic simulations as the measurement process is inherently random. To illustrate, we solve the classical Lorenz system with stochastic behavior using a Python random number generator. We compare the classical stochasticity of the Lorenz system with the measured output of the system obtained using quantum algorithms.

Momentum-based acceleration of iterative hard thresholding (IHT) can dramatically speed up sparse signal recovery from linear measurements, but its effectiveness hinges on careful parameter tuning -- a task complicated by the frequent support changes inherent to hard thresholding. We propose CosMIHT(Consecutive Support Matching Induced Momentum IHT), which resolves this difficulty through a simple adaptive rule: start with the conservative parameters and whenever two consecutive iterates share the same support, estimate the extreme eigenvalues of the support restricted Gram matrix via a lightweight power method and switch to the corresponding optimal heavy-ball parameters. This mechanism allows CosMIHT to automatically interpolate between cautious MIHT-like behavior during support discovery and near-optimal accelerated convergence after support identification. Under standard restricted isometry assumptions, we develop a two-phase convergence theory. In the \emph{wandering phase}, we establish a linear contraction of the recovery error up to a noise floor and derive an explicit upper bound on the number of iterations required to identify the correct support. In the \emph{lock-in} phase, we establish that, with a randomly initialized power method based eigenvalue estimates that depend on the number of power iterations, the algorithm enjoys, with high probability, a near-optimal accelerated convergence rate akin to the heavy ball method. We corroborate the theoretical findings with extensive numerical experiments on both noiseless and noisy measurements demonstrating that CosMIHT achieves faster convergence than state-of-the-art iterative sparse recovery techniques without compromising the recovery performance.

Entanglement-assisted (EA) stabilizer codes enhance the rate of error correction in relation to codes with no pre-shared entanglement. Meanwhile, bosonic error-correcting codes, such as the Gottesman-Kitaev-Preskill (GKP) code, can be concatenated with qubit stabilizer codes to significantly reduce the logical failure probability of those stabilizer codes. First, we combine the above two concepts to propose an EA version of the qubit-into-oscillators concatenated code that chains an EA-stabilizer (outer) code with a GKP (inner) code. As an example we present a three-qubit EA-repetition concatenated with a GKP code. Second, we propose an EA version of the non-Gaussian oscillator-into-oscillators concatenated code that chains a GKP (outer) code with an EA-stabilizer (inner) code. As an example we present a GKP code concatenated with a three-qubit EA repetition code that uses two maximally entangled modes (emodes) and suppresses the variances of both position and momentum quadrature errors of a data mode. Furthermore, we generalize the latter example to a family of GKP code concatenated with a $n$-qubit EA repetition code that uses ${n-1}$ emodes and suppresses the variances of both position and momentum quadrature errors of a data mode by a factor ${1/n}$.

This paper develops an agent-based model of climate-related human migration that links repeated environmental shocks to individual migration decision-making through the joint evolution of perceived risk, aspirations to migrate, and migration capability. Building on the aspirations-capabilities framework, the model represents migration as an emergent outcome of two opposing dynamics: shocks increase perceived risk and raise aspirations to move, while simultaneously eroding wealth and reducing the capability to do so. This interaction generates non-linear mobility patterns, including immobility under rising climate stress. Agents are embedded in a spatially heterogeneous shock environment, and their migration capability is further shaped by local conditions and diaspora support. Results show that more frequent shocks can initially increase migration pressure but eventually trap vulnerable agents in place as resources decline. Climate shocks amplify existing income inequalities in mobility outcomes, with lower-income agents more likely to become trapped or remain acquiescently immobile, while higher-income agents retain greater flexibility to migrate or choose voluntary immobility.

We investigate the asymptotic behavior of the complex roots of Rayleigh-Lamb dispersion relations arising in elastic waveguides. We consider Neumann, Dirichlet, and fluid boundary conditions and derive explicit asymptotic expansions of the associated wavenumbers as their modulus tends to infinity. In the Neumann case, we provide a rigorous justification of asymptotic formulas that have long been used in the literature without proof, together with higher-order terms and explicit constants. Similar results are obtained for Dirichlet and fluid boundary conditions. The analysis relies on a reformulation of the dispersion relations as zeros of holomorphic functions and on asymptotic properties of the Lambert function. We also show how these asymptotic expansions can be used to establish modal decompositions and well-posedness results for elastic waveguide problems. Numerical experiments confirm the accuracy of the proposed formulas.

We study optimal quantization of probability measures on Carnot groups equipped with a left-invariant homogeneous distance. We prove two main results. First, we establish a Zador-type asymptotic formula for the quantization error: after the natural rescaling, the error converges as the number of centers tends to infinity, and the exponent is determined by the homogeneous dimension of the group. The limiting constant is a Carnot cell constant, defined through the quantization problem on a reference cell. Second, we prove weak convergence of the empirical measures associated with optimal centers, and describe the limit in terms of the density of the absolutely continuous part of the measure. The proof combines a tiling of Carnot groups by exponential cubes with a sub-Riemannian version of Pierce's lemma, which allows us to treat measures with non-compact support.

We introduce and study the class of $t$-$g$-radical supplemented modules, which unifies two independent generalizations of the classical supplemented module condition: $g$-radical supplements and $t$-sum terms. A module $M$ is $t$-$g$-radical supplemented if every submodule $N \leq M$ has a $g$-radical supplement that is simultaneously a $t$-sum term of $M$. We establish closure properties under $t$-sums, quotient modules, and homomorphic images, prove inheritance by $t$-sum terms, and classify the standard module classes (simple, semisimple, local, hollow, and Prüfer groups) within this framework. A key observation is that the class strictly contains the class of supplemented modules: both $\mathbb{Q}$ and $\mathbb{Z}_{p^{\infty}}$ are $t$-$g$-radical supplemented but not supplemented.

We study paired multiplication operators associated with orthogonal decompositions of $L^2(\mathbb{T})$ arising from Hardy spaces and Sz.-Nagy--Foias model spaces. For a non-constant inner function $θ$, we characterize $\mathcal{K}_θ$-paired and triply paired operators by finite-rank commutator identities with the bilateral shift $M_z$. We also apply these ideas to sums of truncated Toeplitz and truncated Hankel operators on $\mathcal{K}_θ$. Using the displacement characterizations of Sarason and Gu--Ma, we derive a second-order finite-rank displacement formula for such sums and describe the ambiguity of the decomposition in terms of $\mathcal{I}_θ=\mathcal{T}_θ\cap \mathcal{H}_θ$. In the finite-dimensional case $θ(z)=z^n$, the framework recovers the classical Toeplitz-plus-Hankel matrix recurrence of Bevilacqua--Bonanni--Bozzo.

Tropical Pacific sea-surface-temperature (SST) variability spans interacting timescales, with the ENSO as its dominant interannual expression. Yet the dynamical structure organizing this variability and underpinning extended-range predictability remains difficult to extract from high-dimensional observations. Koopman operator learning offers spectral coordinates for nonlinear dynamics, yet finite geophysical records often produce dense, sampling-sensitive spectra whose physical content is ambiguous. We show that this apparent redundancy reflects coherent operator-level structure. Combining kernel Extended Dynamic Mode Decomposition with residual minimization and pseudospectral analysis, we use the Koopman eigenvalue relation as a physics-informed consistency test to organize learned spectra. Applied to ERA5 and HadISST tropical Pacific SST anomalies, the residual landscape identifies 19 robust residual-minimum frequencies with coherent spatial modes that persist across products and sampling realizations. Together, these modes define a compact Koopman backbone spanning low-frequency modulation through quasi-biennial components, including ENSO-band variability. The surrounding spectral cloud is structured by integer powers and nonlinear combinations of this backbone, forming a residual-ordered Koopman hierarchy. The backbone reconstructs substantial Nino3.4 variance and enables skillful out-of-sample forecasts, with greatest gains at 8-18-month leads. By embedding dynamical consistency into physics-informed operator learning, the framework turns opaque spectra into robust, interpretable and predictive representations of tropical Pacific variability.

Urban populations are increasingly exposed to extreme heat events such as heatwaves, which can be exacerbated in cities due to the urban heat island (UHI) effect. With the aim of developing adaptation strategies, recent years have seen a growing interest in deploying high-resolution measurement networks using low-cost devices (LCDs), which enable the evaluation of intra-urban temperature distribution and its impacts at an unprecedented spatial resolution. However, the reliability of LCD measurements has been called into question, especially regarding potential overheating due to inadequate radiation shielding. In this study, we develop a statistical method to correct temperature biases based on short-wave radiation using a generalized additive model (GAM) and then apply it to LCD measurements in the urban climate networks of the cities of Bern, Lausanne, Neuchatel and Zurich (Switzerland). To that end, we first calibrate the correction procedure to the LCD models used in each city using an intercomparison field study, in which the LCD models are collocated next to a professional automated weather station (AWS) operated by MeteoSwiss in the rural surroundings of Bern. Then, we evaluate how these corrections can influence two climate indices, namely the number of tropical nights and the number of heat warnings issued in each city according to MeteoSwiss heat warning system. The findings suggest that the current AWS underestimate the heat warnings, whereas some LCD models likely overestimate them due to radiative errors. Nevertheless, uncorrected LCD measurements still provide a more reliable estimate of urban temperatures than AWS located outside urban settings. The insights can guide selection of LCD models for new monitoring networks and support the application of model-specific radiative bias corrections to existing LCDs, enabling more accurate assessments of heat and its impacts.

In this paper we derive a framework for topological expansions of shape functionals with respect to multiple holes based on the expansion of one hole. Our strategy is similar to deriving a Taylor expansion of order two of functions in $\mathbf R^d$ by applying $d$-times a Taylor expansion in $\mathbf R$. For shape functionals defined on subsets of $\mathbf R^2$ we relate the topological expansion with multiple holes to a Taylor expansion with respect to the ball volumes where usual derivatives are replaced by topological state derivatives. The first topological state derivative was introduced in a previous paper and relates the first topological derivative of cost functionals. The second topological state derivative at two distinct points is introduced, similar to a second directional derivatives of functions defined on Banach spaces, as the topological state derivative of the topological state derivative. The second topological state derivative at the same point is defined as the "far-away" component of the compound layer expansion of the state variable. In dimension three the obtained topological expansion still involves first and second topological state derivatives, but it does not follow the same pattern of a Taylor expansion in the ball volumes. As we will show this dimension dependent behaviour is rather of geometrical nature and already appears in cost functionals without PDE constraints.

Cardinality estimators are built to support arbitrary schemas and workloads, forcing them to rely on generic statistics even when the schema and workload is known in advance, leaving optimizers prone to large errors and poor plans. We present Bespoke-Card, an agent-driven system that synthesizes workload-specific cardinality estimators as executable code: a planning agent designs the estimators strategies, a coding agent implements them, and a validator scores the estimates against true cardinalities and PostgreSQL estimates, forming a robust and deterministic harness. Going beyond naive prompting, Bespoke-Card uses structured q-error feedback, regression analysis, concrete outlier subplans, a curriculum isolating join-only, filter-only, and full-subplan errors, and archival selection of the best implementation. Injecting its estimates into the optimizer cuts total PostgreSQL runtime on JOB by 33% and reduces median q-error over all JOB subplans by 41%, while synthesizing a strong estimator in under one hour for less than $10. Bespoke-Card is opening a new avenue for cardinality estimation next to classical generic estimators and learned estimator architectures.

Integrated modeling of ARC H-modes has been conducted to assess the feasibility of high-performance scenarios compatible with divertor detachment. The analysis incorporates self-consistent evolution of impurity radiation and density profiles, demonstrating that fusion power levels approaching a GW can be achieved while maintaining divertor temperatures below 2 eV with Ar seeding. Sensitivity studies reveal a strong dependence of fusion power on the separatrix density, with performance spanning 750-1000 MW, and a weaker dependence on enrichment factor and pedestal density. Alternative seeding strategies using Neon have also been explored. Plasmas with Argon seeding consistently access H-mode, providing the highest fusion power and detached divertor operation, whereas Neon seeding leads to lower performance (600-850 MW) and less robust H-mode access, due to excessive core impurity accumulation. A small W impurity peaking has been found, with decreasing values at higher Zeff. Further analyses incorporate reduced momentum transport modeling, and sensitivity studies of neoclassical impurity transport, confirming the robustness of the results. Overall, these findings support the viability of high-performing H-mode operation in ARC, ensuring divertor protection, enabled through Argon and Neon impurity seeding.

Transformer-based architectures have led to significant improvements in Automatic Speech Recognition (ASR), often at the cost of substantially increased model sizes. A promising approach to address this issue is layer sharing through depth recursion, commonly referred to as the Recursive-Transformer, which involves repeatedly applying the same layers within the model. Despite its potential shown in other fields, this technique remains relatively unexplored in ASR. In this paper, we present an experimental study of the Recursive-Transformer applied to ASR encoder architectures. We systematically investigate the impact of recursion depth and layer allocation within the Recursive-based Transformer. Our results demonstrate that the Recursive-Transformer is a viable alternative, especially when recurrence is applied in the latent space with a restricted number of loops, obtaining comparable performance while reducing the parameter count by 66%.

Polymer simulations are among the most computationally demanding workloads in soft-matter research, often requiring days of execution and high energy consumption to achieve physically meaningful results. In this work, we address these challenges through the coupling and optimization of two complementary simulation frameworks: the Uneyama-Doi Model (UDM) and the SOft coarse-grained Monte Carlo Acceleration (SOMA). UDM efficiently propagates concentration fields at the continuum level, while SOMA resolves chain-scale thermal fluctuations via particle-based Monte Carlo dynamics. Each model was individually optimized for GPU execution using kernel fusion, memory coalescing, asynchronous random-number generation yielding up to 70% (UDM) and 80% (SOMA) performance improvement. The coupling is performed through our proposed coordinator library that orchestrates data exchange and synchronizes time-stepping across multiple GPUs. Further management of coupling workload distribution enabled a 13x overall speedup and 24.5x reduction in total energy usage compared to the SOMA baseline, i. e., 96% energy saving. The proposed hybrid approach maintains the same scientific fidelity while drastically reducing the computational and energy footprint, showcasing the potential of energy-aware, cross-application co-design for sustainable high-performance simulations

In this article, we focus on a MHD model that takes into account the Coriolis force. In this case, the strength of the rotation is measured by the Rossby number $ε$ (positive). Under the assumption that the rotation is strong (that is, when $ε$ goes to zero) and the kinematic viscosity goes to zero as $ε$^$α$ ($α$ positive), we first establish the global convergence of weak solutions, and then prove the global existence and convergence of strong solutions. In particular, the Strichartz estimates used to obtain explicit convergence rates depend on the above parameter $α$ and lead us to identify an admissible interval for $α$.

Context . Extremely metal-poor (EMP) stars are formed from gas clouds enriched by one or a few supernova explosions belonging to the first stellar generation and this very limited number of sources of metal enrichment is suitable to produce peculiar chemical patterns that give birth to stars with anomalous chemical composition. Among the EMP stars, r-II stars are characterised by an over-abundance of the heavy elements with respect to iron. Aims . In the search for apparently young, metal-poor stars, we serendipitously selected TYC 170-1218-1, which turned out to be an EMP star, enhanced in neutron capture elements over iron. Our aim is to obtain a detailed chemical inventory for this exceptional object. Methods . We investigated high-resolution spectra observed with UVES at the VLT telescope and Mike at the Magellan Clay telescope. We derived the abundance of 33 elements using the MyGIsFOS code and an ATLAS 9 model atmosphere. Results . The star is an EMP with [Fe/H] = -3.52. It is enhanced in the $α$ elements, as EMP stars usually are. It is an r-II star with [Eu/Fe] = +1.84 and [Th/Fe] = +1.85. The star is also poor in carbon with respect to iron. The quality of the spectra was insufficient for us to detect uranium. Kinematically the star belongs now to the Galactic halo, but it joined the Milky Way during the Sequoia accretion event.

Extensive list of 4+4-dimensional Manin triples that was presented recently can be used to find new solutions of supergravity equations via Poisson-Lie T-plurality. To get the solutions we start with 1+3-dimensional flat backgrounds on Poisson-Lie groups corresponding to semi-Abelian Manin triples. For application of the Poisson-Lie T-plurality we identify Manin triples that form various decompositions of the same Drinfeld double. Beside flat backgrounds and plane-parallel waves solving supergravity equations, plurality transformation also produces curved backgrounds with torsion satisfying (generalized) supergravity equations. Many of the Poisson-Lie transformations can be understood as homogeneous Yang-Baxter deformations. Of special interest are the non-unimodular deformations leading to solutions of generalized supergravity equations.

Holography of Information (HoI) and the island formula are two recent approaches to the black hole information loss paradox that yield different Page curves. The difference between the Page curves has been argued to be rooted in the algebra that each approach focuses on. In this paper, we study the candidate algebras for the CGHS model. Making the usual assumptions that are made in HoI literature, we establish HoI for the CGHS model coupled to a massless scalar by constructing the radiative phase space and asymptotic algebras at future null infinity. We prove that the quantum state of the right-moving modes can be recovered from an arbitrarily small neighbourhood of the right future null infinity. We then argue that if the Hilbert space factorization between left- and right-moving modes holds in the quantum theory of CGHS, then the island entropy cannot be identified with the von Neumann entropy of any one-sided asymptotic algebra, and that this mismatch constitutes a version of the factorization problem for CGHS/RST models. We discuss the possible distinction between the HoI and island approaches for the CGHS model.

Automatic Speech Recognition (ASR) systems are widely deployed across linguistically diverse regions, yet their ability to generalize across fine-grained geographic variation remains underexplored. We present a systematic study of cross-district ASR generalization for Indian languages, analyzing the impact of regional variation on performance. Using finetuning as a controlled probe, we train models on speech from a single district and evaluate them on other districts within the same language. We examine trends across multiple train test district pairs and quantify performance differences. To assess geographic effects, we analyze the correlation between WER and inter district distance using two distance measures. Our results show consistent correlations between geographic distance and WER, highlighting the challenges of regional generalization and the need for geographically diverse speech data in ASR development and evaluation in India.

Speech foundation models enable strong general-purpose ASR and are attractive for downstream adaptation. However, their size and the catastrophic forgetting induced by sequential fine-tuning demand parameter-efficient and regularized training methods, motivating parameter-efficient continual learning (PECL). While PECL has been widely studied in NLP and vision, it has received less attention in ASR. In this paper, we propose a simple yet effective PECL method based on recent advances in parameter-efficient fine-tuning for ASR. We partition pretrained weight matrices into head and tail subspaces according to singular values and restrict adaptation to approximate rotations within the low-energy tail subspace, preserving dominant components and reducing forgetting. For subsequent tasks, rotations are combined via weight averaging to further improve retention. Experiments on two benchmarks demonstrate reduced forgetting and superior overall performance compared to recent PECL baselines.

The palladium-hydrogen system is a prototype for hydrogen-metal interactions and underpins technologies such as hydrogen storage, catalysis and purification. Yet its nanoscale behaviour -- where surface and interface energetics, elastic coherency strain and size-dependent thermodynamics govern phase separation -- has eluded accurate atomistic simulation. Empirical potentials misrepresent the energetics of interstitial hydrogen, while existing machine-learning models are restricted to bulk phases at low-hydrogen environments. Here we introduce an atomic cluster expansion (ACE) for Pd-H that reproduces formation energies, phonon spectra, elastic constants, hydrogen migration barriers and surface adsorption with near-DFT accuracy, benchmarked directly against neutron-scattering, high-pressure and lattice-expansion experiments. Its near-linear scaling and CPU efficiency make molecular dynamics of PdH$_x$ nanoparticles exceeding 28,000 atoms ($\sim$12 nm in diameter) tractable over nanosecond timescales. These simulations resolve, at the atomic scale, the kinetic separation of $α$- and $β$-PdH$_x$ into a core-shell architecture, reproduce the experimentally observed size dependence of the lattice parameter, and uncover a pronounced hydrogen-induced lowering of the nanoparticle melting temperature. The potential brings experimentally relevant scales of metal-hydride dynamics within quantitative reach.

Although Raman scattering in magnetic materials exhibits rich experimental phenomena, the symmetry constraints on Raman tensors have not been fully elucidated. In this work, we use Onsager reciprocity relation, other than the conventional corepresentation method, to deal with the mathematical structures of Raman tensors in magnetic groups. Using this approach, we generate Raman tensor tables for all magnetic point groups, and present a comprehensive understanding of the Raman selection rules in magnetic materials with direct product representations method. Our theoretical and numerical results match previous experiments well, and resolve a puzzle in the Raman spectroscopy of CrSBr. Moreover, we identify a common but overlooked phenomenon: the magneto-Raman vector can be orthogonal to the magnetic moment direction. Our method and associated Raman tensor tables will be helpful for the Raman studies in both experimental and theoretical domains.

Arithmetic terms are finite fixed compositions of additions, subtractions, multiplications, divisions with remainder and exponentiations, containing variables interpreted as natural numbers. They build a well-defined notion of closed formula. It is known that every Kalmar elementary function can be expressed as an arithmetic term. In this paper, one studies the power of expression of the arithmetic terms. By interpreting Hilbert's Tenth Problem in arithmetic terms, it is shown that it is undecidable whether one-variable arithmetic term takes the value $0$, or whether two such terms take or not the same values. An algorithm constructs the arithmetic term representing an arbitrary function, which has been defined by a recurrence rule. This construction has various applications. Functions with chaotic behavior, like the Logistic Map, can be expressed as arithmetic terms. Finally, we construct a Turing complete arithmetic term and we express a Turing universal function by an arithmetic term. A somewhat unexpected application: there is a {\it wise} arithmetic term. It gets (the code of) a sentence, (the code of) a formalized theory and a bound $B$, and after performing a constant number of operations, it outputs (the code of) a proof of the sentence using the given theory if such a proof does exist and its length is less than $B$. Otherwise, it outputs $0$.