Let $\mathbb{F}_{q}$ be a finite field, and $A:=\mathbb{F}_{q}[T]$. In this article, we give explicit criteria, involving concrete valuations, on the coefficients of the Drinfeld $A$-modules of rank $r$ for $r=2,3$, which ensure the surjectivity of the associated $(T)$-adic Galois representation. As a result, we shall calculate the densities of such Drinfeld $A$-modules.

We study flat Friedmann-Lema\^ıtre-Robertson-Walker (FLRW) models with a perfect fluid matter source and a scalar field minimally coupled to matter with power-law-exponential \textquotedblleft hybrid\textquotedblright potential. Using expansion-normalised variables, we formulate the field equations as a constrained three-dimensional dynamical system and determine its equilibrium structure. We show that viable cosmological histories, consisting of a transient matter or radiation era followed by late-time accelerated expansion, arise in restricted regions of parameter space. A central result is that the physically relevant trajectories are confined to an invariant plane, which contains both the transient matter point $\mathcal{B}$ and the accelerated point $\mathcal{C}$. We further show, by centre-manifold analysis, that the accelerated point $\mathcal{C}$ is not a global attractor: it attracts trajectories with $ϕ>0$ and repels those with $ϕ<0$. For dust, a standard matter era requires vanishing coupling of the scalar field to matter, while for radiation the interaction term vanishes identically. Finally, we discuss the issue that the qualitative cosmological dynamics may be independent of the precise functional form of the scalar-field potential.

We consider the application of the Fluctuation Dissipation Theorem (FDT) to the electrodynamics of Aharonov-Bohm (ABE), which differs from Maxwell's in that it allows for local non-conservation of charge. For the case of a system of non-conserved charges at thermal equilibrium we obtain the same spectral distribution of energy of the electromagnetic field as in Maxwell electrodynamics. However, the electric field contribution to that energy doubles that in Maxwell case, while the magnetic contribution is the same as in Maxwell theory, the electric excess energy is compensated by a negative contribution arising form the Aharonov-Bohm (AB) scalar field. For a conductor with local non-conservation of charge described by the $γ$ model, we derive the spectrum of current correlation at first order in $γ$, which results in a violet noise contribution added to the classical Johnson-Nyquist white noise result for the voltage fluctuations in a conductor.

Rydberg atoms, which possess exceptionally large electric dipole moments, offer a promising route for electric field sensing as well as metrology traceable to the International System of Units (SI); however, current research predominantly focuses on the microwave (MW) regime, leaving the quasi-direct current (quasi-DC) and low-frequency bands, ubiquitous in power systems, largely unexplored. In this paper, we present a theoretical investigation into low-frequency electric field detection. To this end, we establish a comprehensive modeling framework incorporating Fisher information (FI) and the Cramér-Rao lower bound (CRLB) to quantify the fundamental precision limits of electromagnetically induced transparency (EIT) readouts. Building upon this framework, we propose a linearized sensing strategy utilizing a DC-biased two-point differential measurement. Numerical validations demonstrate that this approach effectively mitigates the weak-field insensitivity for both DC and AC fields, achieving a CRLB-limited sensitivity bound of approximately $1\times 10^{-4}$ V/m/$\sqrt{\text{Hz}}$. Furthermore, to surpass the single-pass sensitivity limit, we introduce a Fabry-Pérot (FP) cavity-enhanced configuration. This architecture leverages intracavity phase modulation to significantly steepen the transmission slope, boosting the FI by over two orders of magnitude compared to standard free-space configurations. This work provides a rigorous theoretical basis and design guidance for the high-precision quantum monitoring of electromagnetic environments in smart grids.

We consider the three-dimensional incompressible MHD system. Any weak solution satisfying a strong energy inequality is $L^2$-asymptotically stable around a Landau solution. Under an additional integrability assumption on the initial perturbation, we also obtain an explicit algebraic decay rate for the $L^2$-norm of the velocity and magnetic perturbations.

The general position number for graphs ask for largest vertex subsets $S$ such that no three vertices are contained on a common shortest path. We examine this problem in the setting of directed graphs. We provide bounds for the general position number of digraphs, show that the problem is NP-complete for oriented graphs, investigate the problem for some important families of digraphs such as circulant digraphs, Kautz digraphs and permutation digraphs, and study the general position numbers obtained from all orientations of an undirected graph.

The construction of Quasi-Exactly-Solvable quantum Hamiltonians where only the two first eigenstates $Φ_0(x)$ and $Φ_1(x)$ of energies $E_0$ and $E_1$ are explicit is revisited from the point of view of one-dimensional Markov processes satisfying detailed-balance, whose generators are related to quantum Hamiltonians via similarity transformations. Here the lowest energy vanishes $E_0=0$ and is associated the conservation of probability and to the steady state $P_*(x)$, while $E_1>0$ is the rate that governs the exponential relaxation towards the steady-state, and is associated to the slowest observable $L_1(x)$ that corresponds to the ratio $ \frac{Φ_1(x) }{Φ_0(x)}$ of the two quantum eigenstates. Our main conclusion is that the Markov perspective leads to interesting re-interpretations and that the construction of quasi-exactly-solvable models with $N=2$ explicit levels is more intuitive and technically simpler if one takes the slowest observable $L_1(x)$ as the central object from which all the other properties can be reconstructed. This general approach is then applied to Fokker-Planck generators in continuous space and to Markov jump generators on the lattice.

Symmetry classification of crystal structures has been central to predicting physical properties of materials. While such structural classification identifies which physical responses are symmetry-allowed, the magnitudes of these responses are governed by the degree of symmetry breaking in the electronic state. However, a well-defined quantitative descriptor for the electronic symmetry breaking has been established only in limited cases such as electric polarization and magnetization. No analogous descriptor exists for most other types, including chirality. Here, we propose an experimental framework for quantifying electronic symmetry breaking from the anisotropy of valence electron density distribution. We show that the orbital hybridization phases governing this anisotropy can be uniquely determined under site symmetry constraints. Applying this framework to structurally chiral transition-metal silicides, we determine hybridization phases from their valence electron densities observed by synchrotron X-ray diffraction. From the obtained complex hybridization, we quantify an electronic chirality $χ$ and theoretically demonstrate that it is directly proportional to circular dichroism, establishing $χ$ as a predictive descriptor of chiral responses. This approach is systematically applicable to various point groups, offering a general route to quantifying electronic symmetry breaking and predicting associated physical properties.

The NEXT-DEMO++ detector, a high-pressure xenon gas time projection chamber serving as a prototype for the NEXT-100 experiment, was used to measure the electroluminescence (EL) yield as a function of reduced electric field ($E/p$) across pressures from 2.0 to 9.4 bar, utilizing the 41.5 keV de-excitation peak of $^{83m}$Kr. These measurements were made to examine the pressure dependence of the slope of the reduced EL yield $Y/p$, which has shown inconsistencies in the literature. The reduced yield was fitted with a linear model, revealing a modest ($\sim$5%) change in slope, beginning around 5 bar and increasing with pressure up to 9.4 bar.

The kink observed in the nuclear charge radius of Sn isotopes around neutron number $N = 82$ is investigated within the relativistic mean-field (RMF) framework using the NL3$^*$ parameter set. It is shown that the small components of the Dirac spinors for the neutron single-particle states near the Fermi level play a crucial role in forming the kink through their contribution to the proton central potential. In particular, the significant differences between the radial parts of the small components of spin-orbit partner states make neutrons with $j = l - 1/2$ more efficient in increasing the nuclear charge radius than those with $j = l + 1/2$. However, the effect induced by the small components alone does not fully account for the magnitude of the kink observed in Sn isotopes.

Conveying environmental data has grown interest in encouraging the adoption of eco-friendly lifestyles through data-driven strategies. This scope appeals to data visualizations representing the environmental purpose. For example, previous work has already proposed nature-inspired counters, gauges, and bitmaps, but data series remains to be explored. Therefore, could we design and implement effective plant-like charts? This paper brings answers through a research-through-design approach that explores a design space to maximize readability and aesthetics. It then compares four prototypes of charts over modality and material dimensions by asking users about scenarios involving renewable energy forecasts. The results examine whether implementing physical charts is worth it instead of graphical charts and the advantages of using meaningful materials that evocate sustainability and enhance naturalness. The results also reexamine, with physical charts, the previous results on graphical infographics of slightly lower clarity and readability but higher aesthetics of embellishment. In addition, learnability is examined for encoding rates through folded shapes. This paper shows that physical plant-like charts are worthwhile because of promising performance and best-of-breed naturalness when materials allow low-tech aspects' perception and because being installable in public places without explanations if folded shapes encode rates ranging from 0 to a maximum value.

Future 6 G networks are envisioned as a network of networks (NoN) ecosystem, integrating communication and computing resources across multiple domains. At the deep edge, IoT and end-user devices will form subnetworks for local communication and distributed task processing. These subnetworks will seamlessly integrate into the NoN ecosystem, creating an IoT-edge-cloud continuum. The unified resources across this continuum facilitate dynamic and scalable task offloading, unlocking new possibilities to support emerging services, including critical vertical services with stringent reliability and deterministic service level requirements. In this context, this paper demonstrates that a deterministic approach to task offloading and resource (communication and computing) allocation in the IoT-edge-cloud continuum not only ensures deterministic service levels but also enhances scalability compared to existing task offloading and resource allocation methods. By flexibly managing task completion deadlines while maintaining deterministic (i.e. bounded latency) service levels, deterministic policies achieve a more balanced workload and resource distribution across the continuum, ultimately improving scalability.

As energy communities move from policy design to implementation in Switzerland, understanding their performance in practice has become increasingly important. A techno-economic assessment of a regulation-compliant LEC is presented under the new Swiss legal framework in this study. A reference case without local electricity exchange is compared to a LEC scenario with internal electricity sharing. Results show that LEC participation increases local renewable utilization, reduces grid exports, and delivers economic benefits to both consumers and prosumers. A sensitivity analysis further indicates that internal electricity pricing plays a critical role in shaping trade-offs between overall efficiency and fairness in benefit distribution. This exploratory study provides practical insights to support informed decision-making and the future development of LEC in Switzerland.

High-Resolution Electron Backscatter Diffraction (HR-EBSD) has advanced rapidly in recent years, significantly improving elastic strain measurements and dislocation density evaluation with submicron spatial resolution. To achieve better accuracy in the measurements, high-quality dynamical simulation patterns are required to be matched with experimental ones. Currently, the most widely used pattern simulation method, the Bloch Wave method (BW), can accurately predict the positions and brightness of Kikuchi poles and bands, but is intrinsically limited to perfect crystal structures. Another simulation scheme, the multi-slice method (MS), follows the evolution of electron waves as they travel through the sample. MS is advantageous in simulating various defect structures with more diffraction details. Yet, it is mainly considered for theoretical developments and has not been compared to experimental data. This paper optimizes the MS method by abandoning the high-energy hypothesis and utilizing higher-order Taylor expansions to approach the forward-only Schrodinger equation. Experimental EBSD patterns of polycrystal Al-Mg alloys are used to challenge MS simulations as a reference for indexation. It is demonstrated that the 5th-order expansion of MS, referred to as MS5, achieves a good balance between computational cost and pattern precision. A tailored isotropic distortion correction model and standard stereographic triangle reconstruction enhance the precision of MS5 to be comparable with BW. To the best of our knowledge, this study provides the first comparison of MS EBSD simulations with experimental data. It opens new possibilities for EBSD characterization, such as reproducing diffraction patterns of crystals with various defects.

We investigate the properties of neutral and charged mesons in magnetic fields, from weak-field to strong-field regimes. To develop analytic insights, we employ a non-relativistic quark model with a confining potential of the harmonic oscillator type. Short-range correlations, such as Coulomb and color-magnetic interactions, are treated as perturbations. In particular, we focus on the magnetic field dependence of the relative and the center-of-mass motions. The qualitative trends differ significantly between neutral and charged mesons: for neutral mesons, the transverse momenta are conserved and continuous, while charged mesons exhibit quantized transverse dynamics. The Zeeman effects, arising from intrinsic spins and orbital angular momenta, are carefully examined. In particular, for charged mesons with spins $s\ge 1$, we discuss how the zero-point energy in the internal quark motion cancels the Zeeman energy from the orbital angular momentum, ensuring the energetic stability of mesons with high spins. The effectively reduced dimensionality of these mesons in the strong-field limit is also discussed.

Mobile molecular communication (MC) links with counting receivers are sensitive to transmitter--receiver geometry especially when nodes are mobile. We study binary detection from within-symbol count observations with unknown finite-memory inter-symbol interference (ISI) and a block-constant multiplicative geometry gain. Under a mixed-Poisson view mobility and geometry uncertainty can randomize the latent received intensity and create extra-Poisson dispersion. We propose a profiled dispersion-domain statistic $T_k^{(Δ)}$ formed after profiling the deterministic mean shape. The statistic subtracts the intrinsic Poisson component and normalizes by the squared profiled mean to target threshold stability under the stated multiplicative-gain model. Activity gating makes conditional and gate-integrated false-alarm probabilities explicit. We characterize $T_k^{(Δ)}$ using a time-series central-limit-theorem (CLT)-motivated Gaussian working approximation with long-run-variance dependence correction yielding Gaussian-approximate receiver operating characteristic (ROC)/bit-error-rate (BER) formulas and separability design metrics. Simulations with symbol-dependent active-Brownian mobility and finite-memory ISI support the proposed mechanism show empirical threshold stability over the tested gain range and indicate usefulness when mean-domain differences are weak unreliable or intentionally suppressed.

Flux-tunable superconducting qubits rely on fast flux control pulses to implement two-qubit entangling quantum gates, a key building block for quantum algorithms. However, distortion effects introduced by non-ideal control electronics, parasitic components, and the cryogenic quantum chip response can all degrade the gate fidelity. We present a digital predistortion (DPD) framework for characterizing and then compensating for these distortions using a combination of infinite impulse response (IIR) and finite impulse response (FIR) filters. Experiments on a flux-tunable quantum processing unit (QPU) demonstrate a successful correction of step-response distortions on the flux-control line, with a compensated control signal showing only sub-percent deviations from the ideal target linear behavior. The demonstrated method enables automated rapid calibration of flux control channels for superconducting QPUs.

We force the existence of a chain of length $ω_3$ in $[ω_1]^{ω_1}$ increasing modulo finite. The construction involves symmetric systems of models of two types as side conditions, introduced by the second author. This improves previous results of Koszmider and Veličković-Venturi.

While host-guest co-crystals are well established, and co-amorphous solids are recognized in materials science, the concept of a host-guest co-amorphous structure remains largely unexplored. A potential analogue is seen in SiO2 glass under high pressure with helium as a pressure medium; the drop in compressibility in this system is ascribed to helium atoms occupying internal voids. In this study, we investigated a semicrystalline polymer, isotactic poly(4-methyl-pentene-1) (P4MP1), which shares key characteristics with SiO2 glass, particularly regarding the first sharp diffraction peak (FSDP). The FSDP in P4MP1 is attributed to internal voids, as evidenced by its suppression under pressure and recovery upon decompression for molten P4MP1. Notably, the response to helium as a pressure medium is also known to parallel the behavior observed in SiO2 glass. Here, we analyzed two-dimensional X-ray diffraction (2D-XRD) patterns of stretched P4MP1 and found a suppression of FSDP when P4MP1 is immersed in decane. The use of stretched samples enabled the clear isolation of the amorphous FSDP from overlapping crystalline diffractions. Our findings reveal the existence of a host-guest co-amorphous system at room temperature and atmospheric pressure, in which decane molecules occupy the amorphous host matrix of P4MP1. Unlike conventional co-amorphous mixtures, this structure is defined by the specific accommodation of guests within the host's inherent voids. Intriguingly, the signature of this structure in diffraction measurements, manifested as changes in the FSDP intensity ratio, may be regarded to parallel the variations in Bragg peak intensity ratios in host-guest co-crystals. Since selective sorption and guest exchange are well-known in co-crystals, hosts capable of forming co-amorphous structures will be promising materials for molecular sieves, or more generally, liquid-phase molecular sieves.

Static structure models, which map mass-radius constraints to bulk planet composition, are frequently used to categorise exoplanets due to their computational efficiency and the high-level insight they offer into planetary properties. However, static structure models typically have simplified atmospheric treatments, which may introduce systematic biases when interpreting the structures -- and therefore the climates -- of sub-Neptunes and super-Earths.We present a framework for recovering exoplanet properties using static structure models that accounts for necessary physical-chemical complexity in their atmospheres. We produce a comprehensive library of 504,000 exoplanet simulations that unify deep planetary interior structure with radiative-convective-chemical climate calculations. From these models we demonstrate that a planet's envelope mass fraction -- a critical parameter to infer -- is frequently degenerate with its instellation flux and atmospheric metallicity, and sensitive to the treatment of gravitational acceleration at the mbar level. Such uncertainties have significant implications for inferring planetary processes, as our modelling shows that habitable-zone sub-Neptunes readily host supercritical surfaces or deep magma oceans, despite their temperate irradiation regime. To marginalise over these uncertainties, we introduce a Bayesian retrieval tool that uses our library of self-consistent models. By applying this Bayesian approach to case-studies of Pi Men c and TOI-421 b, we show that robust physical interpretations are achievable through whole-planet mass-radius retrievals. While new data from JWST, Ariel, and PLATO will expand our observational horizon, physically-consistent modelling provides the means to transition from categorical interpretations toward a comprehensive picture of the exoplanet continuum.

Rooted bifurcating trees are mathematical objects used to model evolutionary relationships and arise naturally in both coalescent theory and phylogenetics. Recent numerical representations of tree topologies, known as F-matrices, allow for summarizing a sample of trees via Fréchet means and provide new measures of tree balance. However, the number of ranked unlabelled trees grows super-exponentially with the number of leaves. This makes computation intensive and current methods rely on mixed integer programming and simulation-based methods. Moreover, F-matrices are difficult to interpret, and their distribution is only described in terms of first- and second-order moments under neutral branching. In this paper, we introduce a Markov chain embedding of ranked and unlabelled trees that drastically decreases the size of the state space. Leveraging this embedding, we develop an algorithm that efficiently computes all Fréchet means and use discrete phase-type theory to obtain the joint distribution of tree balance indices. We also use discrete phase-type theory to generalize previous results regarding moments of F-matrices to arbitrary order for any time homogeneous and bifurcating coalescent model. Using this framework, we construct three tests for neutrality and demonstrate their improved power compared to previous methods on simulated data.

We show that whenever a separable subset $S$ of a complete metric space $X$ admits a $d$-dimensional weak tangent field, the set $S$ is close to being $d$-dimensional in the following sense. Whenever $μ$ is a Borel finite measure on $X$ supported on $S$, then a typical $1$-Lispchitz map (in the sense of Baire category) into a Euclidean space maps $μ$-almost all of $S$ into a set of Hausdorff dimension at most $d$. When taking $d=0$, this implies that any $1$-purely unrectifiable set is typically carried into a Hausdorff $0$-dimensional set up to a $μ$-null set. We show that the result is sharp in Euclidean spaces and, more generally, in strictly convex Banach spaces of finite dimension.

Grover's algorithm is a cornerstone of quantum algorithms and is strictly optimal in oracle-query complexity. While the full search problem admits no further improvement, one may trade accuracy for speed in the partial search problem, where the task is to identify only the block containing the target item. The best known quantum algorithm for the partial search problem is the Grover-Radhakrishnan-Korepin (GRK) algorithm, whose optimality has long been conjectured but not proved. In this work, we prove the optimality of GRK in the large-block limit. We formulate partial search as a time-optimal control problem and apply the Pontryagin maximum principle to derive the switching-function dynamics, establish the bang-bang structure of regular extremals, and exclude non-optimal switching patterns. As a result, we show that the optimal regular extremal has the global-local-global form, which yields a control-theoretic proof of the asymptotic optimality of the GRK algorithm in oracle-query complexity.

Gravitational-wave events are interpreted in terms of Bayesian posteriors for their source properties inferred under unphysical reference priors. Though these parameter estimates are important intermediate data products for downstream analyses, across the catalog they provide generically biased sourced properties and are therefore unsuitable for direct astrophysical interpretation. Hierarchical parameter estimation is the solution, where joint analysis of the entire catalog of observations not only reduces statistical uncertainties but actually informs the correct prior. Population-informed source properties from there derived are naturally suited to astrophysical interpretation and catalog statistics, such as identification of exceptional events from previous and ongoing observing runs. Using the latest LIGO-Virgo-KAGRA data, we thus demonstrate that population inference is not optional to interpret gravitational-wave observations.

We prove a quantitative averaging lemma for spatially dependent vector fields. Our proof is based on an iteration of the regularizing operator and some elementary considerations about the local inversion theorem.

We develop new techniques for the construction and classification of representations of row-finite and locally convex higher-rank graph C*-algebras O. This class includes Cuntz--Krieger algebras associated to row-finite directed graphs. Our approach relies on the representation theory of a certain non-self-adjoint algebra and a lifting process of representations. We introduce a novel dimension vector for representations of O yielding a countable partition of the spectrum. Given a Cuntz--Krieger algebra and a finite dimension vector, we construct a smooth manifold parametrising the corresponding spectral component. Our techniques are both explicit and functorial.

This paper studies optimal insurance design under asymmetric information in a Stackelberg framework, where a monopolistic insurer faces uncertainty about both the insured's risk attitude, captured by a risk-aversion parameter, and the insured's risk type, characterized by the loss distribution. In particular, when the risk type is unobservable, we allow the risk-aversion parameter to depend on the risk type. We construct a menu of contracts that maximizes the mean-variance utilities of both parties under the expected-value premium principle, subject to a truth-telling constraint that ensures the truthful revelation of private information. We show that when risk attitude is private information, the optimal coverage takes the form of excess-of-loss insurance with linear pricing in terms of the risk loading (defined as the premium minus the expected loss), designed to screen risk preferences. In contrast, when risk type is unobserved, we restrict the coverage function to an excess-of-loss form and derive an ordinary differential equation that characterizes the optimal risk loading. Under mild conditions, we establish the existence and uniqueness of the solution. The results show that equilibrium contracts exhibit nonlinear pricing with decreasing risk loadings, implying that higher-risk individuals face lower risk loadings in order to induce self-selection. Finally, numerical illustrations demonstrate how parameter values and the distributions of unobserved heterogeneity affect the structure of optimal contracts and the resulting pricing schedule.

We consider the discretization of the $p$-Laplacian equation with an interior penalty discontinuous Galerkin method. We prove novel trace-type inverse estimates, leading to unconditional stability of the method. Further, $hp$-version a priori norm and quasi-norm error estimates are established, subordinate to available polynomial approximation results. The analysis is extended to discontinuous Galerkin methods, based on meshes with essentially arbitrarily-shaped, curved polygonal/polyhedral elements. This extension requires the proof of new $hp$-version weighted inverse estimates on essentially arbitrarily-shaped elements. Numerical experiments are also presented, highlighting the relevance of the theoretical findings.

This paper is devoted to the study of the compressible boundary layer equations in the Gevrey-2 solution space. Compared to the classical Prandtl equation, the additional complexity arises from the strong interaction between viscous layer and thermal layer. By introducing new auxiliary functions and observing the cancellation mechanism to overcome the loss of derivatives, we show the local existence and uniqueness of the solution in the Gevrey-2 space in the tangential variable and Sobolev regularity in the normal variable by using a direct energy method.

Gas infrastructure datasets are essential inputs for energy system planning to support strategic decision-making toward decarbonization. However, relevant data are typically scattered across heterogeneous sources, including geospatial datasets, image-based infrastructure plans, and tabular data, making it complex, time-consuming, and error-prone to create topology-consistent network representations with existing tools.This paper presents QGas, an interactive toolkit for visualizing, creating, and collaboratively extending georeferenced gas infrastructure datasets. QGas integrates GIS-based geometry editing with topology-preserving graph operations in a unified web-based environment, enabling users to digitize infrastructure plans, edit network elements, manage attributes, and perform topology-consistent modifications while maintaining a georeferenced representation of the system. The toolkit is implemented using a modular architecture based on Python, JavaScript, and the Leaflet mapping library. An illustrative example demonstrates its application in extending a natural gas dataset to include hydrogen and CO2 infrastructure, highlighting QGas's capability to support the preparation of consistent multi-carrier gas infrastructure datasets for energy system planning.