Generative AI and large language models can produce realistic predictions of human behavior from rich, unstructured inputs with little to no task-specific training data. Recent work uses these ``digital twin'' predictions to supplement human responses in surveys and experiments. We study the special case of using AI-generated predictions to reduce variance in randomized experiments. We argue that doing so requires no new estimators and that researchers can simply include AI predictions as covariates in standard regression adjustment, analogous to adjusting for a prognostic score. A benefit of this approach is a ``do no harm'' property whereby the adjusted estimator reverts to the unadjusted difference in means when predictions are uninformative. Other methods, such as variants of prediction-powered inference, do not have this guarantee. We provide implementation guidance, including how to obtain continuous scores from discrete LLM outputs and how to use LLMs to featurize unstructured inputs as auxiliary covariates. We demonstrate these ideas in simulations and three empirical applications: a survey mega-study, an email marketing A/B test, and a large-scale technology platform experiment. Overall, efficiency gains are real if modest, with greater benefits in studies that contain substantial text and other unstructured data. We also confirm the do no harm property empirically. Given these gains and limited costs, we recommend adjusting for AI-generated predictions as a regular empirical practice.

Exploiting parallelism in modern CPU architectures remains a longstanding challenge in optimizing SMT solvers. We introduce a novel parallel framework that dynamically builds a binary partition tree of the search space by sampling from workers' VSIDS statistics during solving. We leverage the full power of core-based CDCL-style pruning to continuously shrink the partition tree. We further optimize our architecture by incorporating online backbone detection into worker threads, as well as a terminate-on-demand mechanism to eagerly eliminate work on pruned subproblems. The resulting algorithm is highly generalizable and scales effectively with available resources. We implement our approach in the Z3 SMT solver and demonstrate that it outperforms both sequential Z3 and existing state-of-the-art parallel frameworks on challenging benchmarks from six logics in the SMT-COMP 2025 Parallel Track.

Trust and reputation management underpins reliable interactions in distributed networks, yet existing trust models rely solely on forward propagation of interaction-based trust signals. They lack robust mechanisms to enforce accountability for the propagated trust signals when negative interactions occur. In addition, such models often fail to initialize newly joined nodes with sparse interaction history, leading to the cold-start problem. In this paper, we propose RepuLink, a two-layer reputation model that couples an endorsement network with an interaction feedback network. RepuLink integrates two concurrent backward propagation mechanisms: Backward Endorsement Penalty Propagation (BEPP), which recursively penalizes endorsers of misbehaving nodes, and Backward Endorsement Reward Propagation (BERP), which rewards endorsers of well-performing nodes. Together, RepuLink enforces endorsement accountability and incentivizes positive behaviors, which form a positive interaction feedback loop. The endorsement layer further provides explainable, endorser-weighted trust initialization for newly joined nodes. Experiments on real-world datasets against representative trust propagation baselines demonstrate that RepuLink outperforms across four evaluation metrics in both interaction-only and full two-layer settings, while preserving comparable efficiency.

In this paper we review the theory that David Goss developed, starting from 1979, to construct zeta functions around Carlitz zeta values and other remarkable formal series in local fields of positive characteristic. In the description of Goss' theory, we will see how it is primarily motivated by analogies with the classical theory of complex valued zeta and $L$-functions. We compare Goss' theory with another way of constructing zeta and $L$-functions that emerged in more recent times. The functions in the second type have as domains curves over finite fields, with the scalars extended to complete and algebraically closed fields of positive characteristic. The second type of functions interacts with Goss' functions but remains fundamentally different. We shall review a rationality theorem of Ferraro that allows, among others, to introduce some kind of analogue of the function $ξ$ of Riemann. In the path of describing Ferraro's proof, we present some essential tools useful to get into the theory: shtuka divisors and functions, special functions, Anderson motives, Drinfeld modules, among others. We discuss certain relative zeta functions that can be considered as counterparts of Dedekind zeta functions. In particular, we use methods introduced by Goss to prove that these functions extend to entire functions. The paper contains an appendix by Ferraro where the property of entireness of the above relative zeta functions is deduced (in a special case) from the conjunction of a formula by Anglès, Ngo Dac and Tavares Ribeiro and Ferraro's rationality formula. Ferraro also presents a conjecture on the order of vanishing of this function at the canonical point $Ξ$ and some numerical evidences.

The ethanimine molecule, CH3CHNH, is one of the prebiotic molecules detected by astronomers in chemically-rich molecular clouds in the Galactic Center. The observations indicate a non-equilibrium distribution of rotational state populations in both the E- and Z-isomers of ethanimine, resulting from the competition between radiative processes and collisions with background gases such as He and H2. Accurate interpretation of these observations requires the use of radiative transfer models with collisional state-to-state transition processes included. Here, in order to compute cross sections for state-to-state transitions in both ethanimine isomers, accurate potential energy surfaces for their interaction with a He atom were constructed and three complementary methods for inelastic scattering were utilized: full-quantum coupled-channel and coupled-states methods, and the mixed quantum/classical theory. Strong propensities of transitions toward $Δj = 0$ and either $Δk_a = 0$ (with $Δk_c = \pm 1$) or $Δk_c = 0$ (with $Δk_a = \pm 1$) are reported and the origin of this effect is identified. Small but non-negligible differences between energy transfer in the two isomers, on the order of 10%, were found. The utility of the mixed quantum/classical approach to collisional energy transfer at higher collision energies is discussed.

The information-theoretic concept of identification describes a sender-receiver architecture in which the receiver only checks whether a particular message was sent or not, thereby promising a low-energy receiver design. In low received-energy regimes, quantum receivers are a promising tool for studying the system limits. However, the known information-theoretically optimal identification codes typically assume perfect synchronization. In this work, we study deterministic identification in a satellite setting under explicit synchronization constraints, where a satellite broadcasts the signature of a specific User Equipment (UE) which it assumes to be attached to one out of several possible Ground Station (GS), with the goal of establishing communication with the target UE. Within the proposed design, and assuming a specific phase-encoded coherent-state clock scheme in which the discrete time index is represented by equidistant phase rotations on the unit circle, our results reveal a fundamental asymmetry: At any transmission power, identification performance improves with blocklength, whereas synchronization accuracy degrades. In particular, the energy needed for transmitting the satellite clock to the GS can be several orders of magnitude higher than the one needed for the identification signal. This indicates that synchronization strongly impacts identification performance and motivates the investigation of the error-correcting capabilities of bosonic codes under jitter.

The real projective line $\mathbb{R}\mathbf{P}^1$ is the boundary of $\mathbf{HP}=\{z\in \mathbb{C}\colon \Im(z)>0\}$, a model of the hyperbolic plane whose space of geodesics identifies with $\mathcal{G}(\mathbf{HP})=\mathbb{R}\mathbf{P}^1 \times \mathbb{R}\mathbf{P}^1 \setminus \mathrm{diagonal}$. The modular group $Γ=\operatorname{PSL}_2(\mathbb{Z})$ acts on $\mathbf{HP}$ with quotient the modular orbifold $\mathbf{M}=Γ\backslash \mathbf{HP}$. Consider a finite-index subgroup of the modular group $Γ^\prime \subset Γ= \operatorname{PSL}_2(\mathbb{Z})$ corresponding to a finite cover $\mathbf{M} \to \mathbf{M}^\prime$. A geodesic $(ξ^-,ξ^+)\in \mathcal{G}(\mathbf{HP})$ projects $\bmod{Γ^\prime}$ to a geodesic $ξ^\prime \subset \mathbf{M}^\prime$. We conjecture that if $ξ^\prime$ is simple, then $ξ^+$ is either rational or quadratic or transcendental. We prove this conjecture for leaves of minimal geodesic laminations. We explain why the conjecture is known for all simple geodesics in the modular torus cover associated to the derived subgroup $Γ^\prime = [Γ, Γ]$.

We investigate the properties of heat conduction in a network of harmonic oscillators interacting with heat baths, described by a generalized model of Brownian motion. This model includes noise and dissipation terms in both the momentum and position equations. This generalization is motivated by the requirement of consistency with the Gorini-Kossakowski-Sudarshan-Lindblad (GKSL) equation. Because standard definitions of heat current based on velocity become mathematically inconsistent in this framework, we derive an analytical expression for the steady-state heat flow based on an extended framework of stochastic energetics. We confirm that Fourier's law (linear thermal response) is satisfied and that the model naturally captures microscopic thermal boundary resistance, analogous to Kapitza resistance. This demonstrates that our generalized model functions as a valid phenomenological framework for simulating non-equilibrium processes, marking a crucial step toward a unified formulation of stochastic and quantum thermodynamics. Furthermore, we analyze the time evolution of heat conduction by numerically solving the corresponding differential equations for the correlation functions. Unlike standard Brownian motion, the generalized model generates continuous and nowhere differentiable trajectories for both momentum and position (as is characteristic of overdamped dynamics). Finally, we show that the heat current exhibits characteristic transient behavior when the inter-particle interaction is switched on. Specifically, an instantaneous heat flow emerges, whose direction is strictly governed by whether the interaction is attractive or repulsive, significantly differing from the predictions of the standard model.

Direct detections of gravitational waves provide a unique opportunity to probe the astrophysical origin of compact binary mergers. The formation channels of these systems remain highly debated, and a fraction may originate in dynamical environments or active galactic nuclei. Binaries formed in such environments are expected to experience line-of-sight acceleration from their surroundings, which can imprint characteristic signatures on the observed gravitational-wave signal. Here, we re-derive the line-of-sight acceleration effects and implement them in state-of-the-art quasi-circular waveform models with precession and higher-order modes. We also implement the corrections in eccentric waveform models, applying them consistently to all contributing harmonics. Using this model, we investigate the impact of these effects on the inference of line-of-sight acceleration and analyze a few interesting GWTC events observed during the third observing run of LIGO and Virgo. We find no substantial evidence for line-of-sight acceleration in these events. We also show that an inconsistent treatment of line-of-sight acceleration between higher harmonics can lead to biased conclusions. Our model provides a robust framework for uncovering line-of-sight acceleration in current and future gravitational-wave observations, enabling more accurate probes of environmental signatures in compact-binary formation.

In this paper, we investigate the relationship between the long time behaviour of solutions to the Kahler-Ricci flow on an asymptotically conical gradient Kahler-Ricci expander and the asymptotic behaviour of their initial data at spatial infinity.

This paper presents an adaptive model predictive control (MPC) framework for nonlinear urban air mobility (UAM) vehicles operating across the full flight envelope. The proposed approach leverages a linear parameter-varying (LPV) representation to update the predictive model online, enabling accurate capture of strongly nonlinear and time-varying dynamics associated with distributed electric propulsion (DEP) eVTOL aircraft. To systematically address the high-dimensional and coupled nature of MPC tuning, a multi-objective evolutionary optimization strategy based on NSGA-II is employed, incorporating proper normalization of states and control inputs to ensure balanced weighting and meaningful exploration of the design space. The resulting controller explicitly accounts for actuator constraints and enables reconfigurable control allocation for fault-tolerant operation. The framework is evaluated in nonlinear simulations using NASA's Generic Urban Air Mobility (GUAM) model and benchmarked against a robust servomechanism linear quadratic regulator (RSLQR). Results demonstrate that the proposed adaptive MPC achieves improved trajectory tracking and enhanced robustness under both nominal conditions and actuator degradation scenarios, including partial motor failure, while maintaining constraint satisfaction throughout all flight regimes.

We study Dyck paths refined simultaneously by proper area and water capacity, where water capacity is measured above the path and below its lattice-path upper hull. The finite-height ingredients used in the enumeration are classical bounded-height area-polynomial and continued-fraction objects. The upper-hull decomposition produces a coupled area--capacity substitution, which gives an exact four-variable height expansion with denominator branches indexed by the height levels. The full generating function is asymmetric in the two weights, while the height summands admit a symmetric unreduced denominator representation under interchange of the area and capacity weights. In the open square $0<p,q<1$, we prove that the length radius of $G(x,1,p,q)$ is the minimum of the positive real denominator branches. The proof combines uniform normal convergence of the height expansion below this first branch with a Perron-root representation of the branch locations and an interval log-submodularity theorem for spectral radii of weighted paths. On the diagonal $p=q=s$, the classical Chebyshev specialisation gives explicit branch crossings and a $(1-s)^{2/3}$ branch-envelope accumulation law at the Dyck critical point.

In this contribution, we review the physics and phenomenology of nuclear parton distribution functions (PDFs), with a particular focus on the small-x region of nuclear shadowing. We summarise experimental evidence for nuclear modifications of PDFs and discuss their theoretical explanations; in particular, we contrast different models of nuclear shadowing. We also overview model-agnostic extractions of nuclear PDFs from global data on hard processes with nuclei, emphasizing the validity of collinear factorization and the dominance of leading-twist nuclear PDFs. Finally, we discuss perspectives for present and future precision studies of nuclear PDFs and small-x QCD dynamics, including photonuclear reactions in heavy-ion ultraperipheral collisions at the Large Hadron Collider and lepton-nucleus deep inelastic scattering at the future Electron-Ion Collider.

This paper proposes a novel flexible coupler antenna (FCA) that translates passive coupling elements around a fixed-position active antenna to reshape the induced currents on the passive elements for radiation. A new form of mechanical beamforming is achieved by moving only the passive coupling elements while keeping the active antenna stationary. The proposed design significantly reduces the antenna and radio-frequency (RF) chain costs of conventional active array beamforming with low mechanical control complexity and energy consumption. For the purpose of exposition, we consider a point-to-point communication system with one FCA at the transmitter and one fixed antenna at the receiver. Specifically, based on multi-port circuit theory, we establish both the line-of-sight (LoS) and multipath channel models and derive the mechanical beamforming weights of the passive couplers as functions of their positions. Then, we formulate a new problem to maximize the received signal-to-noise ratio (SNR) by optimizing the positions of passive couplers at the transmitter, subject to coupler movement and transmit power constraints. Solving the resulting problem is inherently difficult because coupled channel and mechanical beamforming create non-linearity in the objective function.To tackle this problem, we propose an efficient block-coordinate conditional gradient method to search for the best positions of all passive couplers by sequentially optimizing the position of each coupler with those of the other couplers fixed in an iterative manner.Simulation results demonstrate that the proposed system significantly outperforms benchmark schemes in terms of achievable rate, but with significantly reduced active antennas and RF chains.

Inertial confinement fusion implosion design requires simultaneous optimisation of strongly coupled target and driver parameters across high-dimensional design spaces. Existing automated design approaches typically rely on non-differentiable radiation-hydrodynamics codes treated as black boxes, making optimisation increasingly expensive as dimensionality grows. In this work, we present a differentiable simulation approach for high-dimensional inverse design of inertial confinement fusion implosions. Automatic differentiation through a differentiable implosion physics model, driven by an external pressure pulse, provides gradients of implosion objectives with respect to design parameters, enabling gradient-based optimisation. The framework is applied to 25 kJ OMEGA-scale direct-drive implosions, optimising 500-parameter laser pulses across sampled target geometries. The optimised pulse recovers a near-isoentropic rise to peak power without that structure being imposed. Neural-network pulse parameterisations are additionally explored as a means of accelerating design-space exploration. These results establish differentiable implosion modelling as a promising tool for ICF design, while motivating further work on adjoint robustness and higher-fidelity differentiable simulators.

When do three-dimensional conformer ensembles improve molecular property prediction beyond two-dimensional fingerprints? We provide the first systematic, mechanistically grounded answer. Through ~1,000 experiments spanning 13 model configurations, 14 regression targets, and 2 classification targets across MoleculeNet, QM9, and MARCEL benchmarks, we discover selective complementarity: conformer ensemble statistics extracted via Distribution Kernel Operators (DKOs) yield statistically significant RMSE reductions on solvation-dependent properties (ESOL -11.0%, p < 10^{-9}; FreeSolv -13.5%, p < 3x10^{-5}; 10-seed paired validation) while providing no benefit for electronic or steric tasks. Three lines of evidence confirm this selectivity has a physical rather than statistical basis: improvement is larger under scaffold splits than random splits (+11.9% vs. +8.5% on ESOL), concentrates on large, flexible molecules (+18.9% for heaviest quartile), and grows monotonically with training data. We establish a four-tier performance hierarchy: end-to-end 3D GNNs (SchNet, PaiNN; 21-42% over fingerprints) >= engineered physicochemical descriptors (PMI/SASA/USR) > Morgan fingerprints + XGBoost > all neural conformer ensemble methods, confirmed by two architecturally diverse GNNs and revealing that the pre-computed feature bottleneck limits ensemble approaches. Feature attribution and mutual information analysis expose the mechanistic asymmetry: conformer mean features carry 2-8x more information per feature than fingerprint bits, yet covariance features contribute <2% of model signal, explaining why five simple scalar invariants outperform all complex covariance architectures (p < 0.001). These findings yield an empirical property taxonomy and a practical decision framework for when conformer generation is worth the investment.

Incrementality is a fundamental design principle to master the complexity of large, long-lived software systems. This principle has been embraced by agile development processes and it lays at the base of continuous software evolution. A major challenge in this context is to incrementally re-verify the correctness of software artifacts after every change, focusing the verification efforts only on the parts affected by the change. We present an approach to the incremental verification of programs written in KernelC, annotated with properties expressed in matching logic. The approach is based on a syntactic-semantic framework that enables analyzing code chunks in isolation so that, after a change to a program fragment, only the part whose semantics is affected by the change is re-processed. This property is obtained by expressing the language syntax through an operator precedence grammar and by formalizing its semantics through a synthesized attribute schema. We have implemented our technique in a prototype tool and experimentally evaluated its effectiveness. The results show that our approach does not penalize the efficiency of formal verification and can outperform program re-verification after changes, depending on the presence and type of annotations, as well as the position of the change and the program structure.

There is a well known correspondence between geometric curve flows in the Euclidean plane and solutions of the modified Korteweg-de Vries (mKdV) equation. For each type of mKdV travelling wave, the resulting geometric curve flows are derived here through a simple quadrature formula and studied in detail. These curve flows can be divided into two broad types: travelling loops, and rotating loops. Travelling loops are shown to arise from mKdV solitons, cnoidal (Jacobi cn) and dnoidal (Jacobi dn) waves, the latter being periodic. Rotating loops comprise asymptotically circular ones that are obtained from both mKdV solitary waves on a non-zero background and mKdV rational waves, as well as periodic ones that are produced by mKdV rational elliptic (cn and dn) waves. A specialization of periodic loops, both open and closed, is shown to yield rational cosine loops. An explicit description of each of these types of curve flows is used to characterize their main features, including the condition under which closed loops exist.

The execution of accurate simulations of fusion energy systems requires the appropriate representation of critical component geometries as well as the coupling of complex fusion physics codes with one another and with engineering analysis tools. This paper examines the challenges of creating simulation workflows that fully leverage existing fusion research codes while integrating them with commercial computer-aided engineering (CAE) software. Key areas addressed include: (a) the construction and meshing of analysis geometries taking full advantage of available geometric modeling and meshing technologies; (b) the effective coupling of fusion physics and engineering analysis codes; and (c) the support for simulation workflows that couple particle and continuum modeling methods.

Product decompositions of metric spaces are built from coordinate maps, but these maps are not part of the resulting metric space. We recover this missing coordinate structure through equivalence relations whose classes are candidate coordinate fibers, and the resulting quotient metrics reconstruct the coordinate factors. This framework characterizes exactly when a metric space admits a finite product or power presentation. We prove an equivalence of categories showing that these equivalence-relation data preserve exactly the ordered coordinate information of power presentations. For spaces with suitable $\ell^\infty$-prime factorizations, we use prime multiplicities to determine the existence and classification of roots. We also study metric spaces satisfying $X\cong X\times_\infty X$, where repeated coordinate splitting gives a family of metric quotients indexed by infinite binary sequences. We prove that these binary tree structures exactly characterize metric spaces satisfying $X\cong X\times_\infty X$. As an application to persistent homology, we show how to recover filtration parameters whose products or powers form a given space of intervals.

We use symmetry arguments combined with density functional theory to demonstrate that all surfaces of crystalline materials host surface phonons that are chiral. As model system, we study slabs of highly symmetric AB rocksalt compounds, and find surface-localized phonons whose atomic displacements exhibit chiral motion. We further show that these chiral surface phonons generate sheets of in-plane magnetism at the surface. Our results reveal that chiral phonons can emerge in all crystalline materials as a result of reduced symmetry at surfaces or interfaces. These findings establish surfaces as a previously overlooked source of chiral phonons and their associated magnetic moments, which could play a role in a broad range of surface-sensitive measurements.

Sorted $\ell_1$ Penalized Estimation (SLOPE) models, that perform either variable or group selection, control the false discovery rate (FDR) under orthogonal settings with known noise, but such settings are rare in practice. Under general conditions, cross-validation is the default model selection approach for SLOPE, yet it targets predictive performance rather than FDR control. We address this gap for the SLOPE family of models by proposing new Bayesian approaches, Bayesian Group SLOPE (BGSLOPE) and Bayesian Sparse-group SLOPE (BSGS). BGSLOPE and BSGS embed group-based SLOPE models into a spike-and-slab framework, with BSGS providing a continuous spike-and-slab framework for sparse-group models. We further introduce Two-step Orthogonal (TSO), which transforms a general setting into an orthogonal one to recover SLOPE's FDR control properties. Through extensive synthetic and real data studies comparing all major model selection strategies for SLOPE models, the proposed Bayesian models consistently control FDR, achieve higher power, and outperform competing methods in prediction.

Clapeyron's Theorem of classical linear elasticity provides a way to explicitly express the energy stored in an equilibrium configuration in terms of the work of the forces applied on the boundary. We derive several new integral relations which can be viewed as nonlinear analogs of this classical result, reinterpreting them as rather general statements within Calculus of Variations. These relations reflect specific properties of Lagrangians, that we call ``partial variational symmetries'', since they are more general than classical variational symmetries. In the framework of nonlinear elasticity, partial variational symmetries, such as scale invariance, or scaling homogeneity, lead, via Noether's analysis to different nonlinear generalizations of Clapeyron's Theorem that combine naturally the work of physical and configurational forces. We present a series of illuminating examples showing the effectiveness of the obtained general results in different problems of nonlinear elasticity.

We present a low-variance randomised numerical linear algebra approach for multi-query finite element systems arising from parametric elliptic partial differential equations with applications to digital twins and online model calibration. The method relies on Galerkin subspace projection for reducing the dimensionality, and then combines parameter-oblivious leverage-score Bernoulli sampling with a control variates scheme to yield a reduced-variance `forward' sketch and an invertible `inverse' sketch that are then fused to a single efficient regularised estimator. Effectively, this reduces the computational cost in computing the projected system of equations while preserving the structure, stability, and accuracy of the underlying FEM formulation. We derive probabilistic bounds for the sketching error, invertibility, and estimator variance, and then validate the method on large-scale example problems. The results show that when the parameter fields do not vary too sharply, the synergy of control variates together with the sketch fusion can largely offset the loss incurred by the sub-optimal parameter-oblivious sampling. In this regime, our method achieves substantial savings in time, memory, and communication while maintaining accuracy levels that are acceptable for scientific simulation.

This study aims to identify cell microenvironment parameters that can be robustly estimated from IMPULSED diffusion MRI signals and to develop a reliable mapping-based estimation framework. Diffusion MRI signals were simulated using the established IMPULSED model with one pulsed gradient spin echo sequence and two oscillating gradient spin echo sequences at different frequencies. Five cellular parameters were considered: cell diameter ($d$), intracellular diffusion coefficient ($D_{in}$), intracellular volume fraction ($V_{in}$), extracellular diffusion coefficient ($D_{ex}$), and the frequency-dependent slope of $D_{ex}$ ($β_{ex}$). Parameter uncertainty was quantified using Jacobian-based sensitivity analysis at an SNR of 30, representing clinically achievable conditions on a 1.5T MRI scanner. To enable direct parameter mapping, signals were logarithmically transformed, reduced in dimension using principal component analysis, and then used to estimate parameters with linear regression, fourth-order polynomial regression, and a fully connected four-layer neural network. Model validation was performed in vitro using MC38 cell lines. Uncertainty analysis identified $d$, $V_{in}$, and $D_{ex}$ as robustly derivable parameters, each with relative uncertainty below 1.0. Among the tested models, the four-layer neural network performed best, with mean absolute errors of 1.7 $μ$m for $d$, 5.06% for $V_{in}$, and 0.28 $μ$m$^2$/ms for $D_{ex}$. In vitro validation showed a 6.7% error in cell diameter estimation. These results demonstrate that IMPULSED dMRI can support robust estimation of key cell microenvironment parameters and provide a practical framework for noninvasive assessment of tumor microenvironment changes during radiation therapy response monitoring.

Modern organizations generate and consume massive volumes of heterogeneous data at high speed. This requires a continuous development of new techniques for more efficient and reliable data management. Designing appropriate data architectures has therefore become a strategic necessity, as they shape how data is integrated, governed, and made available for analytics and decisionmaking. This paper introduces a conceptual framework - Data Architectures and their Technical Requirements (DATER) - to systematically describe and evaluate data architectures based on technical requirements. Six modern architectures are examined: data warehouse, (semantic) data lake, data lakehouse, data fabric, and data mesh. Each is analyzed by historical context, defining features, and conformance to DATER dimensions. The study supports researchers and practitioners in navigating architectural paradigms, clarifying overlaps, and highlighting strengths, limitations, and use-case suitability.

Let $p>3$ be a prime and let $$f_{λ_1,λ_2}(x)=x^{p^2-p+1}+λ_1x^{p^2}+λ_2x^{2p-1}\in\mathbb F_{p^2}[x].$$ We determine all pairs $(λ_1,λ_2)\in(\mathbb F_{p^2})^2$ for which $f_{λ_1,λ_2}$ is a permutation polynomial of $\mathbb F_{p^2}$. The final classification consists of three explicit families. The first one is the binomial case $λ_1=0$. The other two are obtained from the condition $λ_2=cλ_1^3$, with $c\in \mathbb F_{p}^{*}$, and are defined by two simple equations involving the norm $λ_1^{p+1}$. The proof is based on the AGW criterion and on the study of a quartic curve naturally associated with the rational function induced on the unit circle $μ_{p+1}$.

The energy transition in power systems requires flexible assets to offset renewable generation variability across multiple time scales, while supporting the integration of renewables and the electrification of demand without requiring costly grid reinforcement. Energy storage occupies a unique position among these assets: depending on the technology, it can provide short-duration grid services at high ramping rates, such as frequency regulation and voltage support, longer-duration functions such as intra-day peak shaving, or inter-seasonal energy buffering. This multi-service character, combined with the declining costs of energy storage technologies (most notably that of battery energy storage systems), is central to the economic viability of storage investments. The value of a given installation depends strongly on its grid connection point and intended use case: an asset-coupled battery serving a consumer or generation plant faces a different service landscape, and therefore a different business case, than a network-coupled system operating as an independent grid resource. This paper presents a structured taxonomy of grid-connected energy storage applications, discusses the principal application domains, and describes the key challenges that must be addressed to integrate storage effectively into power systems. Services are discussed with special emphasis on the Swiss regulatory context. Finally, the STORE flagship project supported by the Swiss Innovation Agency (Innosuisse), where some of the critical challenges of energy storage integration in power grids are addressed, is introduced.

Large language models (LLMs) are increasingly used to provide automated feedback in introductory programming courses, yet empirical evidence from authentic classroom deployments comparing different feedback modalities remains limited. In this work, we present a large-scale classroom study in which AI-generated feedback was deployed through a randomized protocol in an introductory Python programming course. Students received one of three feedback conditions on incorrect submissions: natural language hints, AI-generated failing test cases, or no AI feedback. We release the resulting dataset, ProgFeed, which captures 6,693 submissions from 215 consenting students across 17 labs, including feedback conditions, execution-based performance measures, and fine-grained temporal information. Using this data, we analyze learning trajectories, feedback quality, and submission behavior over repeated attempts. We find that natural language feedback is significantly associated with higher completion rates and faster convergence to correct solutions. Test case feedback, by contrast, exhibits heterogeneous effects that depend critically on feedback validity. Our results suggest that the form of AI-generated feedback matters, and that evaluating feedback quality -- not just its presence -- is essential for understanding its pedagogical impact.

Dynamical mean-field theory recasts deterministic chaos in random recurrent networks as an effective stochastic process. We show that for analytic nonlinearities with sufficiently fast Fourier decay, this stochasticity is only apparent: the continuous past of a realized mean-field trajectory uniquely determines its future. The mean-field theory is therefore not merely an ensemble description, but a conditional prediction theory for individual trajectories. Unfolding the power spectrum into a Krylov state space exposes how this latent determinism is organized across an infinite hierarchy of temporal modes. The associated Krylov growth rate sets the complexity of finite-resolution prediction and upper-bounds the largest Lyapunov exponent in this class of networks. Thus, microscopic sensitivity and predictive complexity are distinct aspects of mean-field chaos. Our results extend Krylov growth ideas developed for Hamiltonian chaotic dynamics to classical dissipative systems.