We study global uniqueness of competitive equilibrium in two-good pure-exchange economies with heterogeneous impatience types and a common HARA Bernoulli utility. The paper connects the CRRA sorting result of \citet{GeanakoplosWalsh2018} with the line of HARA uniqueness results developed in \citet{LoiMatta2022,LoiMatta2024}. In the CRRA case, ordered endowments provide a sorting mechanism for uniqueness. In the HARA case, uniqueness is known to hold for arbitrary endowments under the curvature bound $γ\le I/(I-1)$, where $I$ is the number of impatience types. For two types, the curvature restriction can be removed under a monotone sorting condition linking patience and endowment composition. The present paper shows that this high-curvature HARA sorting mechanism is not specific to the two-type case. Our main result proves global uniqueness for any finite number of impatience types and any $γ>1$. If types can be ordered so that more patient agents hold weakly more of the first good and weakly less of the second, then the equilibrium price is globally unique. Thus the paper extends the two-type high-curvature HARA result to a genuinely multi-type setting and complements the arbitrary-endowment low-curvature result by replacing the low-curvature restriction with an economically interpretable sorting restriction. In the CRRA subcase ($b=0$), the ordered-endowment condition coincides with that of \citet{GeanakoplosWalsh2018}, and our corollary recovers their uniqueness result. The contribution of the present paper is therefore not the sorting condition itself but its reach: the same ordered heterogeneity in patience and endowment composition rules out multiplicity throughout the shifted HARA case ($b>0$), for any finite number of types and any $γ>1$, through a global coefficient-ratio argument.

In this paper, we apply the I-method to establish global well-posedness for the fractional nonlinear Schrödinger equation with initial data u_0 \in H^s(R^d) for s <α/2, i.e., below the energy threshold. Moreover, for radial initial data, we combine a modiffed Morawetz estimate-recovered via Balakrishnan's formula-with the I-method to obtain improved results. In the same spirit, we employ the "upside-down" I-method to derive polynomial-in-time growth bounds for the higher-order Sobolev norm. The main difffculty stems from the fact that Strichartz estimates for the fractional Schrödinger equation has a loss of derivatives, and the problem is always L^2-supercritical, thereby requiring more delicate analysis.

The quasar Eigenvector-1/Main Sequence (E1/MS) provides a physically motivated empirical framework to organize the spectroscopic diversity of type~1 active galactic nuclei (AGN). In its optical plane, the full width at half maximum of H$β$ and the Fe\,II strength ratio $R_{\mathrm{FeII}}$ define a sequence that is primarily driven by Eddington ratio, with important secondary roles played by black-hole mass, orientation, spectral energy distribution, and chemical enrichment. The E1/MS framework is therefore well suited to identify highly accreting and possibly super-Eddington (SE) sources, usually associated with the extreme Population~A (xA) spectral types. We discuss why E1/MS is a useful tool to search for SE accretors among jetted AGN and, conversely, to place $γ$-ray-detected AGN in the broader context of quasar phenomenology. We summarize two complementary results: (1) some candidate SE accretors show radio properties such as high brightness temperature non-thermal cores or radio lobes} consistent with jet activity; and (2) a subset of low-redshift $γ$-ray narrow-line Seyfert~1 galaxies exhibit optical spectra consistent with xA or borderline-xA classification. We also expand the discussion of recent developments in E1/MS studies, including metallicity trends, the spectral energy distribution of xA quasars, and the role of highly accreting quasars as discovery tools for extreme accretion states, as probes of quasars at the reionization epoch, and as possible cosmological probes.

Although symmetricity in the converter controller is desirable for robust stability margins, a direct link between system-level asymmetricity and instability has yet to be clearly established. Converter control introduces three-phase asymmetricity through loops such as DC-link voltage control, a phase-locked loop , and a power synchronization loop. Furthermore, the inherently asymmetric topology of the two-level voltage-source converter, which converts a DC voltage into a three-phase balanced set, acts as the underlying origin of the asymmetries that propagate into the control structure. Consequently, establishing a direct relationship between system asymmetricity (rather than control asymmetricity alone) and the stability margin is essential for understanding the underlying instability mechanisms. In this work, asymmetricity is quantified using the Asymmetricity Quantification Index (AQI), derived from the sequence-domain representation of the interconnected converter-grid impedance. Within this domain, symmetricity is identified through the definition of symmetrical matrices, which serve as the benchmark against which asymmetricity is measured. A robust and generalized analysis correlates AQI with the stability margin, including both grid-following and grid-forming control structures connected to the power grid. It is found that instability arises from increased asymmetricity in the combined converter-grid system, which is dominated by asymmetric control loops and operating points. Thus, reducing asymmetricity without compromising controller functionality can improve stability margins. The analysis is validated in both control-hardware-in-the-loop and power-hardware-in-the-loop environments.

We report the fabrication and mechanical characterization of a "bubble" geometry for accessing local strain gradients using freestanding, single-crystalline manganite nanomembranes: a switchable bistable nanodrum, with opposite strain gradient polarities. By leveraging epitaxial strain as a source of pre-strain and with control of geometrical and mechanical boundary conditions, the fabricated device can support strain gradients with strain variation ranging from 0.01% to 1%. Switching energetics can be designed to configure the bubble morphology. By providing a mechanical framework for sustained strain gradients, this platform supports scalable oxide membrane applications such as the mechanical manipulation of magnetism, coupled to local probes.

We study stochastic interacting particle systems whose interaction structure is described by dense weighted directed graphs converging to a graphon. In the thermodynamic limit, we prove a law of large numbers for the empirical measure process and derive a deterministic nonlinear master equation describing the macroscopic evolution. The limiting equation retains the heterogeneous interaction structure of the microscopic system through the limiting graphon, allowing for spatially non-homogeneous behaviors such as localized or community-type interactions.

Following our previous work constraining interacting dark energy (IDE) models, which showed their potential to alleviate the Hubble tension, in this work we investigate the non-linear effects of the IDE scenario favoured by CMB and DESI observations. The implications of IDE for the $S_8$ tension remain unclear, since current weak-lensing and large-scale-structure analyses either exclude highly non-linear scales or model the non-linear regime using prescriptions calibrated within $Λ$CDM. We address this issue by implementing a fully self-consistent IDE pipeline. We perform N-body simulations of the IDE model with a transfer rate $Q=ξ{\cal H}ρ_x$ using a modified implementation of RAMSES. Since the dark matter Euler equation remains unchanged with respect to $Λ$CDM, the interaction can be incorporated through the modified background evolution and an effective time-dependent dark matter particle mass. We find scale-dependent deviations in the quasi-linear and non-linear regimes of the matter power spectrum, together with modifications to the density-field morphology and halo abundance. Our results show that the impact of IDE on quasi-linear and non-linear structure formation cannot be captured by standard $Λ$CDM-calibrated prescriptions, highlighting the importance of model-consistent non-linear modelling for future weak-lensing and large-scale-structure constraints on interacting dark energy cosmologies.

Hot evolved stars are key objects to reconstruct the various evolutionary pathways of Sun-like stars, to probe binary interactions and the physics of supernovae. They serve as powerful observational constraints to test diffusion, mixing, and mass loss in hot stellar atmospheres. Furthermore, hot stars serve as laboratories to test and derive atomic data for highly ionised trans-iron group elements and to investigate different nucleosynthesis models. Hot evolved stars emit most of their flux in the ultraviolet (UV) and a lot of progress has been made in characterizing their UV-spectra both on the observational and on the modelling side. The unique capabilities of HST to obtain high- and medium-resolution UV-spectra played a crucial role and are needed to further advance this field also in preparation for HWO.

As renewable energy systems expand, inverter availability becomes increasingly important for grid reliability and economics, yet photovoltaic inverter repair logistics remain under-modeled. This paper presents an event-driven Monte Carlo framework for a centralized repair facility with parallel production lines, capturing the full repair cycle from administrative pre-wait and transport to health-driven repair and return-to-inventory. The model incorporates opportunistic scheduling that uses mandatory hold periods to insert additional units onto temporarily idle lines, improving throughput without added capacity. Stage durations are represented by a two-component VaR-style mixture distribution for routine and heavy-tailed delays, while a continuous health score determines repair completion. Calibrated by minimizing the one-dimensional Wasserstein distance between simulated and empirical repair-duration distributions, the model is applied to 43 field-observed repairs, reproducing the empirical bimodal structure with a Wasserstein distance of 53.3 days. Results show that 51.2% of units are accommodated through opportunistic insertion, indicating that hold periods provide a significant recoverable scheduling resource.

Combinatorial memory is a class of memory in which information is encoded in the set of paths through a structured mesh. In this work, we introduce a systematic encoding framework, referred to as the Color-Rule-Function (CRF) approach, for representing information in combinatorial memory. The method consists of four key steps: selecting a sequence of paths in the mesh, assigning values (e.g., colors) to each cell, defining a set of rules based on the values encountered along each path, and constructing a Boolean function that determines the state of each path. . The coding procedure is illustrated by several examples. The design space scales of the CRF scale fundamentally faster compared to conventional memory. This apparent advantage arises from the use of rule-based and functional representations but is accompanied by increased hardware complexity. A possible hardware realization of the CRF framework is discussed. Importantly, the hardware overhead can be substantially reduced through the use of customized modules. The examples of the customized design are described in the text. The combination of CRF coding with customized module design may lead to a practical advantage in data storage density. According to the estimates, the data storage density may exceed Exabit per centimeter squared. A key problem that requires further investigation is related to the minimum Hamming distance between an arbitrary target bit sequence and the closest sequence realizable within the CRF framework under fixed hardware constraints.

Positive longitudinal magnetoconductance (LMC) and planar Hall conductance (PHC) are hallmark transport signatures of the chiral anomaly in Weyl semimetals. Recent theoretical developments have extended Weyl fermions to multifold Fermionic systems with higher-pseudospin quasiparticle excitations, motivating the study of their magnetotransport properties. Here, we employ semiclassical Boltzmann transport theory within the relaxation-time approximation to investigate magnetotransport in pseudospin-1 Weyl semimetals, incorporating momentum-dependent scattering, orbital magnetic moment corrections, and charge-conservation constraints. To obtain a finite PHC, we break azimuthal symmetry through either a generic tilt of the quasiparticle dispersion or a finite misalignment between the electric and magnetic fields. In the untilted case, the PHC is positive and scales quadratically with magnetic field strength. Increasing the scattering strength induces a sign reversal of the PHC, producing a transition from positive to negative values. The PHC further exhibits the characteristic angular dependence $\sin 2γ$, where $γ$ is the angle between the magnetic field and the $x$-axis. Tilt qualitatively alters this behavior: tilt along the $x$- and $z$-directions changes the angular response to $\sinγ$ and $\cosγ$, respectively, generating strong anisotropy in the planar Hall signal. Moreover, the PHC shows a nonmonotonic dependence on tilt magnitude, revealing the interplay between tilt-induced symmetry breaking and chiral-anomaly-driven transport. Our results provide experimentally accessible signatures of multifold fermions and a framework for interpreting magnetotransport measurements in candidate materials of space groups 199, 214, and 220.

The increasing occurrence of small-signal instability, particularly sub-synchronous oscillations (SSOs), in power systems with a high penetration of inverter-based resources (IBRs) has made the planning of new IBR connections increasingly important and challenging. The impact of such connections on small-signal stability is not always straightforward, as it strongly depends on the connection location, inverter operating mode, control configuration, parametrisation, and operating conditions. This paper proposes an inverter connection screening tool (ICST) that enables efficient and accurate assessment of the impact of prospective inverter configurations on small-signal system strength. It can identify, among the candidates considered, the most suitable inverter configuration for a given connection location that avoids degrading small-signal system strength and can also enhance it. As a result, higher IBR penetration can be supported while maintaining small-signal stability. The ICST evaluates candidate inverter configurations using their admittances at critical modal frequencies, along with the system's admittance spectrum, thereby avoiding the need for analytical models. The ICST-based planning procedure, which can support system operators, asset owners, and IBR developers in decision-making across different stages of planning studies, is demonstrated using a modified IEEE 57-bus system. Comparisons with model-based studies demonstrate the accuracy of the ICST in predicting the modal impact of inverter connections and its effectiveness in selecting suitable inverter control configurations.

The current study presents a three-dimensional linear stability analysis of particle-laden Couette-Poiseuille flow suspended in a Newtonian fluid between two parallel plates, with the lower plate coated by a porous medium. The influence of suspended particles is examined using a two-domain formulation in which particles are confined to the fluid layer and do not penetrate the porous substrate. The particle-laden suspension is modeled using the dusty-gas framework, while the flow within the porous layer is described by the volume-averaged Navier-Stokes (VANS) equations. In particle-laden flows over impermeable walls, particle inertia may either stabilize or destabilize the flow depending on the governing parameters. In contrast, the presence of a porous layer introduces an additional permeability-dependent destabilizing mechanism that fundamentally modifies these classical trends. Consequently, particle loading can reduce the critical Reynolds number at sufficiently high permeability, even in parameter regimes where particles stabilize the corresponding rigid-wall flow. The coupled formulation also introduces additional disturbance branches associated with fluid-particle coupling near the permeable interface. Although these modes remain stable across the parameter space investigated, they modify the eigenspectrum and influence the dominant instability by altering coupling pathways. Furthermore, unlike impermeable-wall Couette-Poiseuille flow, where increasing the Couette component generally stabilizes the flow, the porous-wall configuration exhibits a monotonic decrease in the critical Reynolds number over the range examined. These results demonstrate that porous boundaries can fundamentally alter established stability behavior in particle-laden shear flows through permeability-dependent coupling between the suspension and the porous substrate.

The interstellar medium (ISM) is a complex, multiphase medium, where disentangling the distribution of gas and magnetic field structure across different phases remains a considerable challenge. Recently, Faraday tomography enabled by broadband polarized radio observations has emerged as a promising probe of 3D ISM gas and magnetic field structures. However, the interpretation of these observations is obscured by our limited understanding of the different ISM components probed by the distinct Faraday depth features. In this work, we present a comprehensive multi-frequency ($\sim$300 MHz - 23 GHz) analysis comparing features in the Faraday-rotated, polarized synchrotron emission and HI structures over the full high-latitude (|b|>30 degrees) diffuse sky. Using measures of HI structure complexity along the line of sight (LOS), we observe enhanced depolarization across synchrotron radio frequencies in regions with high HI complexity characterized by multiple HI velocity components. We also find that the first and second moments of the Faraday depth spectra are linked to the underlying neutral gas structure. These results indicate that regions of the ISM that are dominated by neutral gas could directly contribute a significant portion of the diffuse synchrotron emission and Faraday rotation. These findings establish new observational constraints for Galactic magnetic field models that synthesize multiphase tracers into a single coherent picture.

Large language models (LLMs) can translate and modify source code, and have been shown to do so for codes of different complexity. Whether they can port a complete, production geophysical model to a different language without degrading its physics has not been established. We demonstrate that LLM-assisted code translation can preserve the physics of a complete production ocean model while moving it into a modern performance-portable form. We report our experience using an agentic LLM coding assistant, directed by domain experts, to port the FESOM2 unstructured mesh ocean--sea-ice model (about 74000 lines of core Fortran) first to C and then to C++/Kokkos for performance portability across CPUs and GPUs. We describe the practices that proved necessary, what worked and what did not, and the failure modes that we encountered. Three practices mattered most: translating in two stages that separate reproducing the numerics (Fortran to a clean C reference) from introducing parallelism (C to Kokkos); requiring a strictly literal translation in which the assistant was not permitted to ``improve'' the source; and validating each stage against an acceptance criterion suited to it. The C port reproduces the original Fortran at the level of long-term simulation statistics over five years. The Kokkos port is bit-for-bit identical to the C reference on CPU and statistically close on GPU over multi-year runs. On eddy-rich meshes up to 7.4 million surface vertices a single A100 GPU node runs 1.6--3.7 times faster than a CPU node, reaching the 1-2 simulated-years-per-day required for production integrations. The result is more than a single GPU port: by following a clear validation procedure, an LLM moved a full Fortran ocean model into another language and onto accelerators while preserving its physics in a matter of weeks.

We define and investigate two families of dual polynomials associated with the Gauss--Legendre polynomials, which have recently found interesting applications in computer graphics. Using the presented results, one can derive representations of the Gauss--Legendre polynomials, construct the dual bases for Lagrange bases and solve certain approximation problems arising, for example, in CAGD.

Large Language Model (LLM) offers opportunities to enhance Human-Building Interaction (HBI) by enabling more direct interactions through intuitive interfaces to complex building systems. These systems can be characterized by the vast amounts of data across multiple formats, the lack of nonconfidential and generalizable information, and the requirement of domain expertise for interpretation. Applying LLMs to domain-specific tasks like HBI presents additional challenges. Limited training data makes traditional fine-tuning approaches impractical. Meanwhile, the opacity of LLM training data requires careful integration of domain knowledge to ensure reliability. Additionally, different LLMs exhibit varying alignment characteristics, suggesting that achieving both natural interaction and technical accuracy requires a multi-agent approach. These challenges highlight the need for innovative approaches to adapt LLMs for specialized domains while maintaining accuracy and user engagement. In this paper, we develop a hierarchical multi-agent framework that utilizes semantic routing and programmatic reasoning to decouple natural language understanding from building analytics. Instead of standard RAG approaches, our system employs a "Doorman" mechanism for task decomposition and specialized coding agents that generate executable Python scripts for precise arithmetic. We validate this framework on a dataset from more than 200 commercial buildings. Results demonstrate the effectiveness in providing accurate and contextual responses for diverse users, including stakeholders, from tenants to building managers, across various building system applications.

We study the Threshold Group Testing (TGT) problem in the noiseless and non-adaptive setting, where the objective is to exactly recover a sparse binary vector from pooled tests, using as few tests as possible. In TGT, each test applied to a subset of items returns a positive outcome if the number of 1's (defective items) in that subset meets or exceeds a specified threshold, and has a negative outcome otherwise. We investigate how the complexity of TGT compares to that of Classical Group Testing (CGT), corresponding to the special case of the threshold equal to one, and analyse the impact of increasing the threshold on the required number of tests. Our main contribution is the derivation of a sharp information-theoretic phase transition at $c_{\mathrm{inf}}^{\mathrm{TGT}}k\log(n/k)$ (non-adaptive) tests for TGT within the constant-column test design. The threshold constant $c_{\mathrm{inf}}^{\mathrm{TGT}}$ is expressed as a function of the prevalence of defectives and the threshold value. Our upper bound is derived under an analytic assumption, and we verify that this assumption is satisfied for a threshold value of 2. The value of $c_{\mathrm{inf}}^{\mathrm{TGT}}$ reveals that TGT on the constant-column design has the same information-theoretic behaviour as CGT in the low-prevalence regime. Yet, strikingly, at higher prevalences, the threshold leads to a significant reduction in the number of tests. On the other hand, we provide evidence that when the asymptotic proportion of defective items is positive, TGT actually becomes strictly harder than CGT (excluding trivial reductions).

We present a comprehensive theoretical investigation of dissociative recombination (DR) and resonant ion-pair (RIP) formation in $\mathrm{HeH^+}$ isotopologues using time-dependent wave-packet propagation methods. Nuclear dynamics are treated on a set of 23 coupled electronic states, including $^2Σ$, $^2Π$, and $^2Δ$ symmetries, in both adiabatic and strictly diabatic representations, with rotational couplings explicitly included. Reaction cross sections are computed over collision energies ranging from 0 to 50 eV. The results reveal that inclusion of a large manifold of resonant states and rotational couplings significantly enhances the DR cross section relative to earlier theoretical studies. In the diabatic representation, $^2Σ$ states dominate the recombination dynamics, while in the adiabatic representation, $^2Π$ and $^2Δ$ states contribute significantly at low collision energies. For RIP formation, two different diabatization schemes yield systematically larger cross sections than previous models, highlighting the sensitivity of ion-pair production to electronic coupling structure. Isotopic effects are examined, showing a clear inverse dependence of cross section magnitude on reduced mass. The present results underscore the importance of multi-state coupling and nonadiabatic effects in accurately describing electron-molecule collision processes in primordial and astrophysical plasmas.

In the upcoming 5G Advanced and 6G technologies, joint sensing and communication (JSAC) will play a pivotal role in enabling the simultaneous utilization of hardware and spectrum resources for communication and sensing tasks. While current algorithms primarily focus on designing beampattern invariant covariance matrices for transmitting various symbols for communication, they often overlook the distances among these symbols. While these covariance matrices effectively facilitate ranging operations, they have adverse effects on communication performance. Designing beampattern invariance covariance matrices with maximal distances among themselves poses a challenging non-convex problem. In this paper, we introduce a novel waveform design method based on McCormick relaxation called McCormick-based JSAC (MJSAC). MJSAC sequentially solves an optimization problem to generate a set of covariance matrices by maximizing the distances (Frobenius norm) among themselves while ensuring a consistent beam pattern. Also, MJSAC eliminates the requirement for channel information to generate the covariance matrices. Through simulations, we demonstrate that MJSAC outperforms conventional algorithms, even those utilizing channel information at the transmitter.

We present gas-phase metallicities of star-forming galaxies at $z=1$-10 with deep JWST/NIRSpec spectra from the JADES full data release, Dark Horse, and OASIS programmes. We stack $\sim$1500 medium-resolution spectra, yielding detections of the [OIII]$λ$4363 auroral line down to $12+\log(\mathrm{O/H})=7.0$ to derive stack-based strong-line calibrations over the metallicity range $12+\log(\mathrm{O/H})=7.0$-8.7. At a fixed metallicity, our stacks exhibit [OIII]$λ$5007/H$β$ and [OIII]$λ$5007/[OII]$λλ$3726,3729 values generally lower than calibrations based on high-$z$ individual auroral-line emitters, suggesting an observational bias towards higher excitation introduced when requiring auroral line detections in individual spectra. Based on our new calibrations, we obtain canonical mass-metallicity relations (MZRs) at z$=$1-10, identifying a decrease in metallicities from $z\sim0$ to z$\sim$4-10, without significant change in slope. Moreover, we identify 50 promising candidates of extremely metal-poor galaxies (EMPGs) with $12+\log(\mathrm{O/H})=6.7$-7.3 (1-4\% solar metallicity) at $z=1.2$-9.1. The MZRs of EMPGs are characterised by a large scatter, with those having lower metallicities generally exhibiting lower sSFRs, opposite of what expected from the local Fundamental Metallicity Relation. These results support a stochastic star-formation history involving gas consumption/ejection and metal-poor inflow, strongly affecting metallicities of low-mass galaxies. Furthermore, we identify two Little Red Dots in our EMPG candidates, both exhibiting broad H$α$ and prominent Ly$α$, offering insights into the early black-hole growth in extremely metal-poor environments.

Accretion outbursts have been observed in a variety of young stellar objects, but models of their dynamical evolution have been largely limited to axisymmetric models due to their computational cost. We investigate the azimuthal stability of accretion outbursts and the formation of planetesimals during these events. We performed high-resolution 2D, vertically integrated multifluid radiation-hydrodynamical simulations of the inner 10 au of protoplanetary disks with a dynamically growing dust population, including radiation transport and a realistic dust opacity model. Accretion outbursts are highly unstable to the Rossby-wave instability, with the burst front quickly diffusing into a large number of small-scale vortices that coalesce over time into a single, compact vortex and inducing azimuthal asymmetries. Vortices act as a source of vigorous turbulent diffusion, strongly suppressing planetesimal formation. Our results suggest that azimuthal asymmetries associated with accretion outbursts should be both common and detrimental to planet formation. Nevertheless, planetesimal formation will resume post-burst, as the burst-induced vortices eventually decay and the disk returns to a quiescent state featuring a pressure bump at ~1 au.

Multiparameter quantum estimation faces two fundamental obstacles: sloppiness, i.e., anisotropy of the quantum Fisher information matrix (QFIM) that renders some parameter directions insensitive, and incompatibility, the non-commutativity of optimal measurements for different parameters. The trade-off bound $C_T$ captures their joint impact on precision, but it has remained unclear how the distribution of incompatibility across parameter planes affects its overall cost. Here we separate the total amount of incompatibility from its location. We introduce a dimensionless quantity $G_n^{(F)}$ that measures the alignment between the incompatibility distribution and the eigenvalues of the QFIM, and show how the Frobenius scale of the incompatibility contribution factorizes. We obtain a bound and prove the incompatibility cost lies between this bound and a rank-dependent multiple thereof. We also prove that at fixed sloppiness, or equivalently fixed Fisher volume, concentrating incompatibility into a single parameter plane reduces the optimized trade-off cost because the Fisher geometry can then be reshaped to allocate more Fisher area to that plane. A qutrit $SU(2)$ encoding numerically confirms that states with larger incompatibility strength can nevertheless incur a smaller cost if the matching factor $G$ is sufficiently small. Our results establish that the distribution of incompatibility relative to the Fisher eigenbasis is a central diagnostic for multiparameter estimation, beyond the total incompatibility strength.

A single-radio-frequency (RF) movable array is investigated, in which all movable elements are driven by a single RF chain with equal amplitude and equal phase. The achievable beamforming gain enabled by antenna placement is analyzed. Linear beamforming gain scaling with the number of antennas is shown to be achievable in single-path channels, while coherent-combining conditions and aperture requirements are established for multipath channels. For multiuser transmission, the optimal max-min power allocation is derived in closed form, based on which an element-wise coordinate-search algorithm is developed for antenna placement design. Numerical results validate the analysis and reveal a fundamental tradeoff: beamforming gains can be achieved through antenna placement alone, but only at the expense of increased aperture resources.

As distributed quantum computing (DQC) offers a leading path towards scalable quantum computation, the ability to benchmark distributed algorithms under realistic conditions becomes critical for system co-design. However, without access to physical systems, researchers lack tools to evaluate distribution protocols. We introduce Q-DICE (Quantum Distributed Interconnect Compiler and Emulator), a hardware-aware emulation environment for benchmarking distributed quantum circuits on classical simulators and on NISQ-era monolithic hardware. This work provides three core contributions: (1) a programmatic scheme to construct distributed QPU backends, utilizing two novel techniques - QPU slicing and stitching - to facilitate distributed circuit mapping, (2) a methodology for modeling nonlocal link noise using physically motivated Kraus operators and stochastic error channels, and (3) a boundary-aware circuit mapping algorithm enforcing distributed QPU topology constraints during transpilation. Together, these components constitute a distribution-aware compiler and noise-modeling engine that faithfully enforces the physical limitations of distributed quantum hardware within existing execution environments. We validate Q-DICE against a multitude of experimentally demonstrated quantum circuits, including a distributed Grover's search on optically linked trapped-ion hardware, achieving a worst-case fidelity deviation of 4% between simulated and experimental results. These findings demonstrate Q-DICE's capacity to accurately reproduce real distributed quantum system behavior across platforms, streamlining experimentation with distributed quantum algorithms and architectures.

Ideal Bose-Einstein condensation (BEC) remains a paradigmatic example of a continuous phase transition and a cornerstone for understanding quantum degenerate bosonic matter. We demonstrate that critical behavior of the ideal Bose gas near the BEC phase transition falls into three distinct classes, determined exclusively by the low-energy scaling of the density of states. Depending on its scaling exponent, which is controlled by dimensionality and confinement, the transition displays either the usual algebraic divergences of thermodynamic susceptibilities, divergent behavior with marginal logarithmic corrections, or a more subtle form of criticality, where only the correlation length diverges. Our work provides a unified framework for criticality in noninteracting bosonic systems. This classification applies broadly to atomic, photonic, polaritonic, and magnonic condensates, where dimensionality, confinement, and spectral engineering can strongly reshape the density of states.

Sustained driving automation systems are envisioned to be used as the foundation for driverless mobility services. However, both researchers and practitioners acknowledge that current driving automation systems are not yet able to handle all traffic situations that a human driver can handle. To bridge this gap and enable mobility services without an in-vehicle human driver or fallback, remote operation (or teleoperation) is increasingly discussed. Recently, first legal actions have been taken to enable some forms of remote operation on public roads. Remote operation encompasses a broad spectrum of methods to support a driving automation system, ranging from remote assistance, which includes providing information or releasing a maneuver, to remote driving, which includes driving the vehicle from a remote location. As such, safe implementation of remote operation in public road traffic challenges the collaboration of multiple academic disciplines (e.g. engineering, psychology, informatics, law, etc.) and stakeholders (e.g. remote operation service providers, remote operators, vehicle manufacturers, regulatory authorities, etc.). At the same time, the interdisciplinary discourse is often challenging due to differing expectations and language. To build a common ground, this article traces terminology back to the original differences in information processing both on human and vehicle side. This framework aims to help further discourse by directly specifying what is needed to engage a diverse audience including researchers and stakeholders of different backgrounds and interests. Recently discussed forms of teleoperation are integrated into this framework.

This paper studies a lattice structure for almost perfect matchings on certain planar, bipartite (plabic) graphs embedded in a disk. Postnikov's boundary measurement map, and subsequent related work, yielded that plabic graphs parameterize positroid cells within the totally nonnegative Grassmannian with the map itself given in terms of almost perfect matchings with fixed boundary condition. For finite planar bipartite graphs, Propp introduced a distributive lattice structure on their set of perfect matchings. Subsequently Muller--Speyer, provided this distributive lattice structure on the aforementioned almost perfect matchings with fixed boundary condition. Their work also identified the extremal matchings of this lattice for boundary conditions that coincide with face labels of the plabic graph given by the positroid structure. We extend this by giving an explicit construction of extremal matchings in terms of height functions and show that all possible boundary conditions of an almost perfect matching can be obtained within this construction.

Finite-dimensional operator algebras can be viewed as $\mathrm{C}^*$, $\mathrm{W}^*$, or $\mathrm{H}^*$-algebras, leading to different notions for their categories of modules and correspondence 2-categories. In this article, we show how these differences can be understood systematically using the notion of $G$-dagger category from arXiv:2403.01651 for different subgroups $G\leq O(2)$. To do so, we first introduce $G$-Hermitian $2$-vector spaces using fixed points of a certain $O(2)$-action on $2\mathsf{Vect}$. We then propose criteria for when such pairings are `positive', generalizing the passage from Hermitian vector spaces to Hilbert spaces. Finally, we outline an inductive approach to defining higher Hilbert spaces in arbitrary dimension, suggesting an extension of these ideas beyond the 2-categorical setting.

Non-Hermitian quantum systems exhibit qualitatively distinct physical behavior compared to Hermitian systems, a prime example being spectral singularities known as exceptional points. Their relevance in, e.g., quantum sensing, unidirectional transport, and robust lasing makes it important to be able to identify exceptional points through observable features of a many-body system. Here, using as an example a one-dimensional complex XY spin chain realizing both rotation-time RT- and parity-time PT-symmetric regimes, we develop a framework for detecting exceptional points based on the distinction between left and right eigenvectors of the Hamiltonian, which in a non-Hermitian system are no longer the adjoint of each other. We first show that a global measure constructed from the difference between the Hamiltonian and its adjoint locates exceptional points via distinct non-analytic behavior. At the level of observables, differences in local spin correlations evaluated on the right and left eigenstates provide a reliable static detection scheme. In contrast, static bipartite entanglement measures fail to capture this distinction, urging us to study the quantum dynamics of the model. Following a sudden quench, we demonstrate that the time-averaged right-left entanglement entropy difference directly encodes signatures of the exceptional point. In the RT-symmetric regime, it exhibits a pronounced peak at the exceptional point, whereas in the PT-symmetric regime it behaves as an order-parameter-like quantity, remaining finite in one phase and vanishing at the transition. Our results establish a direct link between the structure of non-Hermitian eigenstates and observable signatures of exceptional points, providing a practical route to identify them in existing quantum simulators.