This study investigates the elastic response of a two-dimensional semi-infinite medium subjected to a moving surface load with a prescribed displacement profile. As a fundamental step, we derive analytical Green's functions for the displacement and stress fields generated by a point load traveling at a constant velocity along the surface, explicitly incorporating elastodynamic effects through Mach number dependence. These moving-load solutions serve as building blocks for constructing more general loading scenarios via linear superposition. Based on Green's functions, an inverse problem is formulated to reconstruct the unknown surface traction responsible for a given surface displacement. The inverse analysis is performed through a Fourier-domain inversion with regularization, which enables a direct and computationally efficient determination of the contact pressure without iterative forward simulations. This framework is applied to a rigid wheel-ground contact problem, where the imposed displacement is dictated by the wheel geometry. The reconstructed surface traction exhibits a smooth, symmetric distribution within the contact region, while the resulting subsurface stress fields are obtained in closed analytical form and involve dilogarithm functions. The principal stress difference reveals characteristic spatial patterns similar to photoelastic fringes, and their asymmetry increases with the Mach number, reflecting the dynamic nature of the moving contact.

Two of the most iconic systems of quantum physics are the particle in a box and the Coulomb potential (the third is, of course, the harmonic oscillator). In this expository paper, we consider the quantum solution to the problem of an electron confined between the grounded planes of an infinite capacitor. The potential arises from the image charges that form in the grounded planes, along with the added condition that at x = 0, L, where L is the distance between the planes, the wavefunction must be zero. This effectively couples a hydrogen like system to a particle-in-a-box (PIB) based on L, the distance between the planes. The problem of finding the electrostatic potential of this infinite series of image charges is an old one, going back to at least 1929. Here, we give a short derivation for one of the limiting cases that yields a compact expression and show how the Kellogg infinite summation formula converges to that value. We note here that this potential is a symmetric double well potential, so there will be many familiar properties of its solutions. Then using that potential, we solve Schrödinger's equation using a spectral technique. The limiting forms of a particle in a box for small L (and high E), and that of a (degenerate) bound image charge at large L and small energy are recovered. We also discuss the tunneling level splitting that occurs in the transition from the large L to the small L regime.

Agentic applications are LLMs that iteratively invoke external tools to accomplish complex tasks. Such tool-based agents are rapidly becoming the dominant paradigm for deploying language models in production. Unlike traditional single-turn inference, agentic workloads chain together multiple LLM calls and tool executions before producing a final response, creating a new performance bottleneck that manifests as increased latency in First Token Rendered (FTR) of the final answer. Through analysis of requests at production scale, we reveal three critical challenges: tool calls account for 30-85% of FTR latency, KV cache hit rates collapse despite substantial context reuse across iterations, and sequential orchestration wastes potential intra-request parallelism. These bottlenecks stem from a design gap in which orchestrators and LLM engines operate as decoupled black boxes, preventing cross-layer optimizations. We present Sutradhara, a co-designed agentic inference system that integrates orchestration with LLM serving through a thin API enabling three optimizations: overlap tool execution with subsequent LLM prefill using tool-aware prompt splitting, streaming tool execution to dispatch tools incrementally during decode rather than waiting for complete output, and orchestrator-aware cache management that uses semantic hints to improve hit rates and reduce thrashing. Implemented on vLLM, Sutradhara improves the throughput-latency trade-off in agentic systems, sustains up to 77% higher load at the same median FTR latency, or reduces median FTR latency by up to 15% at the same load while reducing end-to-end latency by upto 11% on A100 GPUs.

We say that $d_3(n)$ has exponent of distribution $θ$ if, for every $\varepsilon>0$, the expected asymptotic holds uniformly for all moduli $q \le x^{θ-\varepsilon}$. Nguyen proved, following earlier work of Banks, Heath-Brown, and Shparlinski, that after averaging over reduced residue classes $a \bmod q$, the function $d_3(n)$ has exponent of distribution $2/3$. Using the Petrow--Young subconvexity bound for Dirichlet $L$-functions, we improve this to $8/11$ when averaging over residue classes modulo a prime $q$.

This paper presents a new explicit infinite family of 2-quasi-perfect $p$-ary Lee codes of length $\frac{q-1}{2}$ and dimension $\frac{q-1}{2}-2k$ for $q = p^k \ge 14$, $p\geq 5$ a prime. Our codes are derived from the generating set $H_q = \{(a, a^3) \mid a \in \mathbb{F}_q^*\}$ of the additive group of the finite field $\mathbb{F}_{q^2}$. Furthermore, we bridge between 2-quasi-perfect Lee codes constructed by Mesnager, Tang, and Qi and well-known abelian Ramanujan graphs, specifically Li's graphs and finite Euclidean graphs, providing a unified theoretical framework for these families.

Time-varying dielectric metasurfaces that support sharp optical resonances with nontrivial electromagnetic field distributions constitute a unique platform for realizing temporal interfaces for metasurface-guided waves (MGWs). Rapidly changing metasurface resonance enables frequency conversion and temporal scattering of a concurrently propagating MGW. Using analytical methods and electromagnetic simulations, free carriers are generated locally to create frequency-shifted infrared MGWs. Such time interfaces can be utilized to generate large, highly localized quasistatic magnetic fields within the metasurfaces. The resulting nanoscale magnetization, supported by the residual circulating currents, persists for several optical cycles after the departure of the time-scattered MGWs. During the rectification process, the initial electromagnetic energy of the injected MGWs is partitioned between the temporally scattered MGWs, the residual motion of the free carriers, and a quasistatic magnetic field.

Click-fraud is commonly seen as a key vulnerability of pro-rata revenue sharing rule on music streaming platforms, whereas user-centric is largely immune. This paper develops a tractable non-cooperative model in which artists can purchase fraud activity that generates undetectable fake streams up to a technological limit. We defend pro-rata by showing that it is fraud-robust: when fraud technology is weak, honesty is a strictly dominant strategy, and an efficient fraud-free equilibrium obtains; when fraud technology is strong, a unique fraud equilibrium arises, yet aggregate fake streams remain bounded. Although fraud is inefficient, the resulting redistribution may improve fairness in some cases. To mitigate fraud without abandoning pro-rata, we introduce a parametric weighted rule that interpolates between pro-rata and user-centric, and characterize parameter ranges that restore a fraud-free equilibrium under technology constraint. We also discuss implications of Spotify's modernized royalty system for fraud incentives.

We investigate the behavior of curvature invariants for a large ensemble of neutron stars built with equations of state (EOSs) that satisfy constraints from nuclear theory and perturbative QCD, as well as measurements of neutron-star masses, radii, and gravitational waves from binary neutron-star mergers. Surprisingly, our analysis reveals that stars with negative Ricci scalar $\mathcal{R}$ are rather common and about $\sim 50\%$ of our EOSs produce one or more stars with Ricci curvature that is negative somewhere inside the star. The negative curvature is found mostly but not exclusively at the highest densities and pressures, and predominantly for stiff EOSs and for the most compact and most massive stars. Furthermore, we improve the quasi-universal relation between the stellar gravitational mass $M$ and the baryonic mass $M_\mathrm{b}$, which allows us to express analytically one in terms of the other with a maximum variance of only $\sim 3\%$. Finally, using the relation between the Ricci scalar and the trace anomaly $Δ$, we determine the conditions under which $Δ$ vanishes or becomes negative in neutron stars.

Extended ultraviolet (XUV) emission in nearby disk galaxies supports the inside-out growth scenario through low-efficiency star formation in their outer regions. However, such detections have largely been limited to the local Universe ($z \sim 0$) due to the need for deep, high-resolution UV imaging. We report the detection of a clumpy XUV disk in a massive, isolated spiral galaxy ($\log(M_*/M_\odot) \approx 11.04$) at $z=0.67$, observed with AstroSat/UVIT. The intrinsic rest frame FUV surface brightness profile, corrected for the instrument PSF, shows a more extended disk than its optical and IR counterparts. The XUV disk reaches nearly twice the optical radius and includes a large UV-bright low surface brightness (LSB) region ($S_{LSB}/S_{K80}\approx15,\ μ_{FUV}-μ_K\approx0.8$), consistent with the Type II XUV definition. Additionally, the detection of UV clumps without optical counterparts supports a Type I classification, suggesting gravitational instabilities and recent star formation. These features point to recent cold gas accretion onto the outer disk. From the asymmetric light profile, we estimate a gas accretion rate of $\sim11\ M_\odot$ yr$^{-1}$, providing evidence of active disk growth at intermediate redshift.

The nature of the finite temperature phase transition of QCD depends on the particle density and the mass of the dynamical quarks. We discuss the properties of the phase transition at high density, considering an effective theory describing the high-density heavy-quark limit of QCD. This effective theory is a simple model in which the Polyakov loop is a dynamical variable, and the quark Boltzmann factor is controlled by only one parameter, $C(μ,m_q)$, which is a function of the quark mass $m_q$ and the chemical potential $μ$. The Polyakov loop is an order parameter of $Z_3$ symmetry, and the fundamental properties of the phase transition are thought to be determined by the $Z_3$ symmetry broken by the phase transition. By replacing the Polyakov loop with $Z_3$ spin, we find that the effective model becomes a three-dimensional three-state Potts model ($Z_3$ spin model) with a complex external field term. We investigate the phase structure of the Potts model and discuss QCD in the heavy-quark region. As the density varies from $μ=0$ to $μ=\infty$, we find that the phase transition is first order in the low-density region, changes to a crossover at the critical point, and then becomes first-order again. This strongly suggests the existence of a first-order phase transition in the high density heavy-quark region of QCD.

Interfacial interactions in two parallel-stacked hexagonal boron-nitride (hBN) layers facilitate sliding ferroelectricity, enabling novel device functionalities. Additionally, when Bernal or twisted bilayer graphene is aligned with an hBN layer, unconventional ferroelectric behavior was observed, though its precise origin remains unclear. Here, we propose an alternative approach to engineering such an unconventional ferroelectricity in graphene-hBN van der Waals (vdW) heterostructures by creating specific types of hBN boundaries and interfaces. We found that the unconventional ferroelectricity can occur--without the alignments at graphene-hBN or hBN-hBN interfaces--when there are hBN edges or interfaces with line defects. By systematically analyzing the gate dependence of mobile and localized charges, we identified key characteristics of localized states that underlie the observed unconventional ferroelectricity, informing future studies. These findings highlight the complexity of the interfacial interactions in graphene/hBN systems, and demonstrate the potential for defect engineering in vdW heterostructures.

Computer simulations of complex population genetic models are an essential tool for making sense of the large-scale datasets of multiple genome sequences from a single species that are becoming increasingly available. A widely used approach for reducing computing time is to simulate populations that are much smaller than the natural populations that they are intended to represent, by using parameters such as selection coefficients and mutation rates whose products with the population size correspond to those of the natural populations. This approach has come to be known as rescaling, and is justified by the theory of the genetics of finite populations. Recently, however, there have been criticisms of this practice, which have brought to light situations in which it can lead to erroneous conclusions. This paper reviews the theoretical basis for rescaling, and relates it to current practice in population genetics simulations. It shows that some population genetic statistics are scaleable while others are not. Additionally, it shows that there are likely to be problems with rescaling when simulating large chromosomal regions, due to the non-linear relation between the physical distance between a pair of separate nucleotide sites and the frequency of recombination between them. Other difficulties with rescaling can arise in connection with simulations of selection on complex traits, and with populations that reproduce partly by self-fertilization or asexual reproduction. A number of recommendations are made for good practice in relation to rescaling.

We present a next-to-leading order QCD sum rule analysis of $J^{PC}=1^{-+}$ light tetraquark states. By investigating various compact tetraquark and molecular configurations, we determine the mass spectrum of these states. Our calculations exclude the possibility that $π_{1}(1400)$ is a tetraquark or hybrid-tetraquark mixture. This suggests that it may not exist, which is consistent with recent experimental results. In contrast, we obtained multiple $1^{-+}$ states around $2.0\,\text{GeV}$ that match well with $π_{1}(2015)$, which makes us confident that $π_{1}(2015)$ is a tetraquark candidate. As for $π_{1}(1600)$, our results indicate that the tetraquark currents tend to couple to heavier states, reducing the possibility of it being a tetraquark, while earlier studies suggested the opposite.

A $t$-all-symbol PIR code and a $t$-all-symbol batch code of dimension $k$ consist of $n$ servers storing linear combinations of $k$ information symbols with the following recovery property: any symbol stored by a server can be recovered from $t$ pairwise disjoint subsets of servers. In the batch setting, we further require that any multiset of size $t$ of stored symbols can be recovered from~$t$ disjoint subsets of servers. This framework unifies and extends several well-known code families, including one-step majority-logic decodable codes, (functional) PIR codes, and (functional) batch codes. In this paper, we determine the minimum code length for some small values of $k$ and $t$, characterize structural properties of codes attaining this optimum, and derive bounds that show the trade-offs between length, dimension, minimum distance, and $t$. In addition, we study MDS codes and the simplex code, demonstrating how these classical families fit within our framework, and establish new cases of an open conjecture from \cite{YAAKOBI2020} concerning the minimal $t$ for which the simplex code is a $t$-functional batch code.

Uranium digermanide UGe$_2$, the first ferromagnetic superconductor, represents a key composition in the U-Ge system dominated by U-5$f$ states. To examine the impact of controlled stoichiometric deviations on the electronic structure, UGe$_{2\pm x}$ thin films ($0 \le x \le 1$) were prepared by triode sputtering and studied on pristine surfaces by X-ray (XPS) and Ultraviolet (UPS) photoelectron spectroscopy. XPS and UPS reveal a robust metallic valence band with a dominant U-5$f$ contribution at the Fermi level and a broad incoherent feature at higher binding energies, without qualitative changes in spectral line shape across the composition range. The experimental spectrum of UGe$_2$ thin films is well reproduced by DFT+U(ED) valence-band calculations combining density functional theory with exact diagonalization of the multiconfigurational U-5$f$ shell. These results demonstrate that the overall U-Ge electronic framework of UGe$_2$ thin films remains resilient to moderate stoichiometric deviations, providing a reliable electronic baseline for future studies of interface- and heterostructure-driven phenomena in uranium-based systems.

This paper presents three main results on coloring discrete $d$-pseudomanifolds: $(1)$ the general chromatic bounds $d+1 \leq X(K) \leq 2d+2$ for any $d$-pseudomanifold $K$; $(2)$ an improved bound $X(K) \leq 2d+1$ for pseudomanifolds expressible as a Zykov join $K = S^k + K'$; $(3)$ the optimal bound $X(K)\leq\lceil 3(d+1)/2\rceil$ under the additional assumptions that the spherical join factor $S^k$ is built from even-cycles and its dimension $k$ is close to $d$.

We develop a kinetic-theory framework to investigate the steady rheology of a dilute gas interacting via a repulsive potential under uniform shear flow. Starting from the Boltzmann equation with a restitution coefficient that depends on the impact velocity and potential strength, we derive evolution equations for the stress tensor based on Grad's moment expansion. The resulting expressions for the collisional rates and transport coefficients are fitted with simple analytical functions that capture their temperature dependence over a wide range of shear rates. Comparison with direct simulation Monte Carlo (DSMC) results shows excellent quantitative agreement for the shear stress, temperature anisotropy, and shear viscosity. We also analyze the velocity distribution functions, revealing that the system remains nearly Maxwellian even under strong shear.

Let $ν_1,ν_2,\dots$ be a sequence of probabilities on the nonnegative integers, and $X=(X_1,X_2, \dots)$ be a sequence of independent random variables $X_i$ with law $ν_i$. For $λ>0$ denote $Z^λ_i:= \sum_x λ^xν_i(x)$ and $λ^{\max}:= \sup\{λ>0: Z^λ_i<\infty \text{ for all }i\}$, and assume $λ^{\max}>1$. For $λ<λ^{\max}$, define the tilted probability $ν_i^λ(x):= λ^xν_i(x)/Z^λ_i$, and let $X^λ$ be a sequence of independent variables $X^λ_i$ with law $ν^λ_i$, and denote $S^λ_n:= X^λ_1+\dots+X^λ_n$, with $S_n=S^1_n$. Choose $λ^*\in(1,λ^{\max})$ and denote $R^*_n:= E (S^{λ^*}_n)$. The Gibbs Conditioning Principle (GCP) holds if $P(X\in\cdot|S_n>R^*_n)$ converges weakly to the law of $X^{λ^*}$, as $n\to\infty$. We prove the GCP for log-concave $ν_i$'s, meaning $ν_i(x+1)\,ν_i(x-1) \le ( ν_i(x))^2$, subject to a technical condition that prevents condensation. The canonical measures are the distributions of the first $n$ variables, conditioned on their sum being $k$. Efron's theorem states that for log-concave $ν_i$'s, the canonical measures are stochastically ordered with respect to $k$. This, in turn, leads to the ordering of the conditioned tilted measures $P(X^λ\in\cdot|S^λ_n>R^*_n)$ in terms of $λ$. This ordering is a fundamental component of our proof.

We present an analytical framework for the emergence of nonclassical radiation in strongly laser-driven quantum systems, with a focus on high-order harmonic generation (HHG). Starting from a Pauli-Fierz description, we employ a parametric factorization of the coupled light-matter wavefunction that reduces the dynamics to coupled equations for a field-driven electronic state and a quantized light mode. Within this framework, we identify a simple and predictive mechanism for nonclassicality: it originates from the nonlinear dependence of the electronic dipole response on the light-mode coordinate. An approximately constant dipole yields coherent radiation, a linear dependence produces squeezing, and higher-order nonlinearities give rise to Wigner-function negativity. We illustrate this mechanism for atomic and molecular model systems and analyze its scaling in multi-emitter configurations, indicating routes toward high-photon-number nonclassical radiation in HHG. Our results provide a transparent connection between strong-field dynamics and quantum-optical properties of emitted light, offering a basis for engineering nonclassical states in intense laser-matter interactions.

Cellular organization and mechanotransduction pathways are crucial regulators of tissue morphogenesis, whereas their dysregulation contributes to pathologies. Overactive myofibroblasts are key drivers of fibrosis, yet how their presence alters collective cellular ordering remains unclear. Owing to steric interactions, elongated cells exhibit local order. Topological defects, where alignment is disrupted, have been postulated to serve as mechanical centers. In this study, we examine how incorporating slower moving myofibroblast phenotype impacts defect relaxation in monolayers consisting of co-cultured fibroblasts and myofibroblasts. In this system, myofibroblasts act as the less active component. Increasing their fraction increases disorder strength and slows defect recombination. On microgrooved surfaces, higher myofibroblast concentrations lead to worse alignment, suggesting single-cell mechanosensing and cell-cell interactions act jointly. Furthermore, we found that myofibroblasts preferentially localize at negatively charged -1/2 defects, whereas fibroblasts localize at +1/2 defects. Consequently, the slowdown of recombination dynamics can be partially attributed to myofibroblasts' preferential association with the less mobile -1/2 defects, increasing local friction and impeding defect mobility. This localization may also reduce compressive stress on myofibroblasts, as indicated by immunofluorescence of a downstream mechanotransducer. This work provides insights into possible connections between topological defects and cell motility in mixed phenotype monolayers.

Experiments using intermediate- to high-energy radioactive nuclear beams present numerous findings. Extracting important properties of physical observables relies on a firm theoretical analysis. Though Glauber theory is believed to work well, no convincing calculation has so far been done. We perform ab initio Glauber theory calculations of both elastic differential cross sections and total reaction cross sections for p+12C, 12C+12C, and 6He+12C systems. The wave functions of both 6He and 12C are generated by variational Monte Carlo calculations with spatial and spin-isospin correlations induced by realistic two- and three-nucleon potentials. Glauber's phase-shift function is computed by Monte Carlo integration up to all orders of nucleon-nucleon multiple scatterings. We show an excellent performance of the Glauber description to the selected data on the above systems. We also find that the cumulant expansion of the phase-shift function converges rapidly up to the second order for the above systems. This finding will open up interesting applications for the analysis of high-energy nuclear experiments.

Recent developments in the unification of quantum mechanics and relativity have emphasized the necessity of generalizing classical phase space into a relativistic quantum phase space which is a framework that inherently incorporates the uncertainty principle and relativistic covariance. In this context, the present work considers the derivation of linear and quadratic Casimir operators corresponding to representations of the Linear Canonical Transformations (LCT) group associated with a five-dimensional spacetime of signature (1,4). This LCT group, which emerges naturally as the symmetry group of the relativistic quantum phase space, is isomorphic to the symplectic group Sp(2,8). The latter notably contains the de Sitter group SO(1,4) as a subgroup. This geometric setting provides a unified framework for extending the Standard Model of particle physics while incorporating cosmological features. Previous studies have shown that the LCT group admits both fermionic-like and bosonic-like representations. Within this framework, a novel classification of quarks and leptons, including sterile neutrinos, has also been proposed. In this work, we present a systematic derivation of the linear and quadratic Casimir operators associated with these representations, motivated by their fundamental role in the characterization of symmetry groups in physics. The construction is based on the relations between the LCT group and the pseudo-unitary group U(1,4). Three linears and three quadratics Casimir operators are identified: two corresponding to the fermionic-like representation, two to the bosonic-like representation, and two hybrid operators linking the two representations. The complete eigenvalue spectra and corresponding eigenstates for each operator are subsequently computed and identified

The advent of the Cherenkov Telescope Array Observatory (CTAO) and recent advances in reconstruction of gamma-ray photons with Cherenkov telescopes are bound to push the limit of angular resolution to an unprecedented precision of less than one arcminute at tens of TeV. Naturally, such instrumental improvements open up possibilities for new and interesting scientific studies. We aim to show that the study of pulsar wind nebulae (PWNe) in particular is bound to profit from these high-resolution measurements. This is because PWNe are the dominant Galactic source population at TeV energies, exhibit hard spectra up to hundreds of TeV and from X-ray observations are known to possess plentiful structure on arcminute scales. Using HESS J1813-178 and MSH 15-52 as examples, we create simple leptonic models of the TeV morphology of these sources based on X-ray observations and existing gamma-ray measurements. Then, assuming different models for the exposure and point spread function of the observatory, we create mock observations with the future CTAO southern array. We use these to assess the ability of these observations to differentiate between models and study the physics of these sources, in particular to infer the structure of the magnetic field and electron distributions. We find that future observations with the CTAO southern array at multi-TeV energies - in combination with existing X-ray measurements - will likely be able to constrain the distributions of magnetic field and high-energy electrons in these sources. We demonstrate that the sensitivity of these measurements can be significantly enhanced with the improved angular resolution achievable with novel reconstruction algorithms. However, we also show that in the relevant multi-TeV regime, signal-photon statistics remain a limitation and trading event statistics for improved angular resolution is not necessarily advantageous.

We discuss the quantum geometric contribution to the diffusion constant and the DC conductivity in metals and semimetals with linear Dirac dispersion. We demonstrate that, for systems with perfectly linear dispersion, there exists a clear and rigorous separation of the quantum geometric from the ordinary band velocity contributions to the diffusion constant, which turns out to be directly related to the separation of a rank two tensor into transverse and longitudinal parts. We also demonstrate that, within the self-consistent Born approximation and for Gaussian-distributed disorder, the diffusion constant of three-dimensional Dirac fermions at charge neutrality is entirely quantum geometric in origin, which is not the case for two-dimensional Dirac fermions. This is the result of an accidental perfect cancellation of the band velocity contribution in three dimensions.

The mean-field yrast spectrum of an SU(2)-symmetric two-component Bose gas confined to a ring geometry is known to exhibit an intricate nonanalytic structure that is absent in single-component systems. In particular, due to the interplay between the species concentration and the atomic interactions, a sequence of plane-wave states can emerge as yrast states at fractional values of the angular momentum per particle. This behavior stands in sharp contrast to the single-component case, where plane-wave states occur only at integer angular momenta. In this paper, we investigate how the structure of the yrast spectrum in a two-component Bose gas is modified by interaction asymmetry. By numerically solving the coupled Gross-Pitaevskii equations for propagating soliton states, we compute the mean-field yrast spectrum and, in particular, determine the critical curves associated with the emergence of various plane-wave yrast states. We find that both the behavior of these critical curves and the mechanisms by which plane-wave yrast states arise depend sensitively on the relative strengths of the inter- and intra-component interactions. When the intra-component interaction is weaker, the plane-wave yrast states replace soliton states through a continuous evolution, as in the SU(2)-symmetric case, although the conditions for their existence become more restrictive. In contrast, when the intra-component interaction is stronger, plane-wave yrast states may emerge by overtaking soliton states via branch crossings, and their stability is significantly enhanced. Our results have important implications for the existence and stability of persistent currents in asymmetric, two-component Bose gases.

We derive recurrence relations for leading logarithmic all-loop quantum corrections in the case of $SO(N)$ symmetric scalar theory with an arbitrary potential in curved spacetime. On this basis, a system of renormalisation group (RG) equations in the general is obtained approach for the effective potential in the large $N$ limit. As a simple illustration, we analyse the case of power-like potentials in the Jordan frame and discuss their application to inflationary cosmology.

The increasing device heterogeneity and decentralization requirements in the computing continuum (i.e., spanning edge, fog, and cloud) introduce new challenges in resource orchestration. In such environments, agents are often responsible for optimizing resource usage across deployed services. However, agent decisions can lead to persistent conflict loops, inefficient resource utilization, and degraded service performance. To overcome such challenges, we propose a novel framework for adaptive conflict resolution in resource-oriented orchestration using a Deep Reinforcement Learning (DRL) approach. The framework enables handling resource conflicts across deployments and integrates a DRL model trained to mediate such conflicts based on real-time performance feedback and historical state information. The framework has been prototyped and validated on a Kubernetes-based testbed, illustrating its methodological feasibility and architectural resilience. Preliminary results show that the framework achieves efficient resource reallocation and adaptive learning in dynamic scenarios, thus providing a scalable and resilient solution for conflict-aware orchestration in the computing continuum.

Unit-generated orders of a quadratic field are orders of the form $\mathcal{O} = \mathbb{Z}[\varepsilon]$, where $\varepsilon$ is a unit in the quadratic field. If the order $\mathcal{O}$ is a maximal order of a real quadratic field, then the quadratic number field is necessarily of a restricted form, being of narrow Richaud--Degert type. However, every real quadratic field contains infinitely many distinct unit-generated orders. They are parametrized as $\mathcal{O} = \mathcal{O}_{n}^{\pm}$ having quadratic discriminants $Δ(\mathcal{O}) = Δ_{n}^{+} = n^2 - 4$ (for $n \geq 3$) and $Δ(\mathcal{O}) = Δ_{n}^{-} = n^2 + 4$ (for $n \geq 1$). We show the (wide or narrow) class numbers of unit-generated orders satisfy $\log \left|{\rm Cl}(\mathcal{O})\right| \sim \log \frac{1}{2}\left|Δ(\mathcal{O})\right|$ as $\left|Δ(\mathcal{O})\right| \to \infty$, using a result of L.-K. Hua. We deduce that there are finitely many unit-generated quadratic orders of class number one and finitely many unit-generated quadratic orders whose class group is $2$-torsion. We classify all unit-generated real quadratic orders having class number one. We provide numerical lists of quadratic unit-generated orders whose class groups are $2$-torsion for $Δ\leq 10^{10}$, for both wide and narrow class groups. These lists are conjecturally complete for all $Δ$.

This paper studies the efficient implementation of safety filters that are designed using control barrier functions (CBFs), which minimally modify a nominal controller to render it safe with respect to a prescribed set of states. Although CBF-based safety filters are often implemented by solving a quadratic program (QP) in real time, the use of off-the-shelf solvers for such optimization problems poses a challenge in applications where control actions need to be computed efficiently at very high frequencies. In this paper, we introduce a closed-form expression for controllers obtained through CBF-based safety filters. This expression is obtained by partitioning the state-space into different regions, with a different closed-form solution in each region. We leverage this formula to introduce a resource-aware implementation of CBF-based safety filters that detects changes in the partition region and uses the closed-form expression between changes. We showcase the applicability of our approach in examples ranging from aerospace control to safe reinforcement learning.

This letter seeks to clarify the different existing definitions of both instantaneous complex phase and frequency as well as their equivalence under standard modeling assumptions considered for transmission systems, i.e. balanced positive sequence operation, sole presence of electro-mechanical transient dynamics and absence of harmonics and interharmonics. To achieve this, the two fundamental definitions, i.e., those based on either the use of (i) analytic signals or (ii) space vectors, together with the premises used for their formulation, are presented and their relationship shown. Lastly, a unified notation and terminology to avoid confusion is proposed.