Nuclear Star Clusters (NSCs) are dense stellar systems located at the centers of galaxies. Employing Enzo-Abyss, which integrates hydrodynamics with a direct N-body solver, we introduce a simulation capable of resolving the evolution of NSCs within a live galaxy. This includes live dark matter, gaseous dynamics, star formation and feedback, collisional dynamics for star clusters. The evolution of NSCs is typically shaped by two main processes: mergers of star clusters and in-situ star formation. Our simulation enables investigation of the contributions of these mechanisms to the growth of NSCs. This work focuses on the impact of stellar physics and gas content on the growth of NSCs within a dwarf galaxy. To this end, we carry out four simulations, a fiducial simulation, one without supernova feedback, one with low star formation efficiency, and one with higher galactic gas content. This study shows a likelihood that both mergers and in-situ star formation contribute to NSC evolution comparably. In addition, mergers result in disruption of dense gas clumps within star clusters, indicating that in-situ star formation is suppressed when mergers occur. However, the limitations -- such as the lack of individual star physics and limited spatial/particle mass resolution -- hinder drawing a definite conclusion. Nevertheless, with further development, our simulations will serve as a cornerstone that untangles the complex interplay between mergers and in-situ star formation in shaping the structure and mass of NSCs, thereby providing insights into their formation and evolution.

We study the fully mixed formulation of the Biot equations, which is characterized by a symmetric coupling between flow and deformation. This structure enables the use of stable mixed finite elements for each subproblem without a strong compatibility condition across the two subphysics. To exploit this flexibility while preserving the conservation structure of both subproblems, we consider fully mixed finite element methods in which the symmetry of the elastic stress tensor is enforced weakly. The resulting mixed formulation exhibits a saddle-point structure whose stability is determined by suitable inf--sup conditions. Inf--sup stability is established for several families of discrete spaces of arbitrary order, leading to optimal a priori error estimates. Iterative splitting strategies following the classical fixed-stress split with additional tuning are specifically investigated for the fully mixed formulation, with proof of convergence and rates depending on the coupling strength. Contrary to previous analyses on coupled problems with a symmetric structure, we theoretically prove the efficacy of negative stabilization, consistent with Schur-complement ideas. Numerical results based on analytical solutions and the classical Mandel problem support the theory.

This is an extended journal version of the conference paper published in ISIT 2025; submitted to IEEE Transactions on Communications (TCOM). Integrating coded caching (CC) into multiple-input multiple-output (MIMO) communications significantly enhances the achievable degrees of freedom (DoF). This paper investigates a practical cache-aided asymmetric MIMO configuration with cache ratio $γ$, where a server with $L$ transmit antennas communicates with $K$ users. The users are partitioned into $J$ groups, and each user in group $j$ has $G_j$ receive antennas. We propose four content-aware MIMO-CC strategies: \emph{min-$G$} enforces symmetry using the smallest antenna count among users; \emph{Grouping} maximizes intra-subset spatial multiplexing gain at the expense of some global caching gain; \emph{Super-grouping} aggregates users into optimized \emph{min-$G$}-based super-sets with identical effective receive multiplexing gains before applying \emph{Grouping} across them; and \emph{Phantom} redistributes spatial resources assuming ``phantom'' antennas at the users to bridge the performance gains of \emph{min-$G$} and \emph{Grouping}. We develop these asymmetric strategies under three reference symmetric CC placement-delivery policies with guaranteed linear decodability: a DoF-optimal policy achieving the optimal single-shot DoF, and two closed-form policies, namely combinatorial and linear cyclic low-complexity constructions, with the cyclic policy attaining DoF performance close to the others in many operating regimes. Analytical and numerical results demonstrate significant DoF improvements across various system configurations, and that policy-strategy combinations offer flexible trade-offs between DoF and subpacketization complexity.

Continuous-time primal-dual gradient dynamics (PDGD) is an ubiquitous approach for dynamically solving constrained distributed optimization problems. Yet, the distributed nature of the dynamics makes it prone to communication uncertainties, especially time delays. To mitigate this effect, we propose a delay-robust continuous-time PDGD. The dynamics is obtained by augmenting the standard PDGD with an auxiliary state coupled through a gain matrix, while preserving the optimal solution. Then, we present sufficient tuning conditions for this gain matrix in the form of linear matrix inequalities, which ensure uniform asymptotic stability in the presence of bounded, time-varying delays. The criterion is derived via the Lyapunov-Krasovskii method. A numerical example illustrates the improved delay robustness of our approach compared to the standard PDGD under large, time-varying delays.

We study the non-Gaussianity of the large-scale clustering of high-redshift halos, seeking to assess which terms of standard bias expansions are needed to understand these highly biased populations. We find that the clustering can be well modeled with only linear and quadratic bias parameters while assuming a Gaussian underlying matter field. Our analysis focuses on AbacusSummit halos at redshift $z=8$. We work with halos of mass at least $1\times10^{11}h^{-1}M_\odot$ in boxes of side length $2h^{-1}$Gpc. Measurements of bias coefficients are made by fitting bias expansions to the halo power spectrum and bispectrum. Tidal bias is not detected with only a ~$0.1σ$ deviation from $0$, but we see a $17σ$ level detection for a bias term of the form $δ^2$. A bias term of the form $δ^3$ is weakly detected at the $1.3σ$ level. Nonlinear matter is also detected at a $1.3σ$ level. To test how bias evolves, we run one test at $z=5$. We use a mass threshold for halos that gives the same variance in the halo field as our $z=8$ sample. Bias is smaller at $z=5$ and a tidal bias is detected at the $1σ$ level. Bias coefficients at $z=5$ match a linear evolution of the $z=8$ bias coefficients to within $10\%$.

A particularly intriguing subclass of rocky exoplanets are the ultra-short period (USP) worlds that orbit their host stars in less than a day. These planets are particularly rare around M dwarf stars, with so far only ten that have a constrained mass and radius. We present the validation and characterization of the ultra-short period (0.3-days), Earth-sized planet TOI-4552b orbiting a nearby (27.26-pc away) M4.5V dwarf. Complementing the TESS photometry, ground-based transit observations from LCO, ExTrA and SPECULOOS validated the planetary radius and cleared the field of any contaminants. Speckle imaging with Zorro (Gemini-S) rules out false positive scenarios caused by eclipsing binary sources. Spectroscopic observations with NIRPS and HARPS were used to obtain stellar abundances, constrain the planetary mass, and, in conjunction with the transit observations, estimate the orbital parameters. TOI-4552 is a quiet star exhibiting no short-term stellar variations seen in photometric or radial velocity data that can be associated to stellar rotation. TOI-4552b ($M_p=1.83\pm0.47\,M_e$, $R_p=1.11\pm0.04\,R_e$) lies between the Earth-like and iron-rich composition tracks on the Mass-Radius diagram. The EXOPIE interior structure model, without constraints from refractory abundance ratio, yields a core mass fraction (CMF) of 0.54 and a bulk density of 7.74g/cm$^3$. Since the CMF spans a wide range due to the large uncertainty on the mass, the definitive interior composition cannot be determined with the current dataset. TOI-4552b hints as being marginally more iron-rich compared to the Earth but confirmation of its status requires additional, precise radial velocity measurements. Combined with its high emission spectroscopic metric (ESM=19.5), negligible stellar activity and short orbital period, TOI-4552b emerges as a compelling target for atmospheric and surface composition studies with JWST.

The odd-red bipartite perfect matching problem asks to find a perfect matching containing an odd number of red edges in a given red-blue edge-colored bipartite graph. While this problem lies in $\mathsf{P}$, its polyhedral structure remains elusive, despite renewed attention to achieving better polyhedral understanding, nurtured by recent advances from two complementary angles. Apart from being a special case of bimodular integer programs, whose polyhedral structure is also badly understood, it is related to one of the most notorious open derandomization questions in theoretical computer science: whether there is a deterministic efficient algorithm for the exact bipartite perfect matching problem, which asks to find a perfect matching with exactly $k$ red edges. Recent progress towards deterministic algorithms for this problem crucially relies on a good polyhedral understanding. Motivated by this, Jia, Svensson, and Yuan show that the extension complexity of the exact bipartite perfect matching polytope is exponential in general. Interestingly, their result is true even for the easier odd-red bipartite perfect matching problem. For this problem, they introduce an exponential-size relaxation and leave open whether it is an exact description. Apart from showing that this description is not exact and even hard to separate over, we show, more importantly, that the red-odd bipartite perfect matching polytope exhibits complex facet structure: any exact description needs constraints with large and diverse coefficients. This rules out classical relaxations based on constraints with all coefficients in $\{0,\pm1\}$, such as the above-mentioned one, and suggests that significant deviations from prior approaches may be needed to obtain an exact description. More generally, we obtain that also polytopes corresponding to bimodular integer programs have complex facet structure.

Fault-tolerant quantum computation demands extremely low logical error rates, yet superconducting qubit arrays are subject to radiation-induced correlated noise arising from cosmic-ray muon-generated quasiparticles. The quasiparticle density is unknown and time-varying, resulting in a mismatch between the true noise statistics and the priors assumed by standard decoders, and consequently, degraded logical performance. We formalize joint noise sensing and decoding using syndrome measurements by modeling the QP density as a latent variable, which governs correlation in physical errors and syndrome measurements. Starting from a variational expectation--maximization approach, we derive an iterative algorithm that alternates between QP density estimation and syndrome-based decoding under the updated noise model. Simulations of surface-code and bivariate bicycle quantum memory under radiation-induced correlated noise demonstrate a measurable reduction in logical error probability relative to baseline decoding with a uniform prior. Beyond improved decoding performance, the inferred QP density provides diagnostic information relevant to device characterization, shielding, and chip design. These results indicate that integrating physical noise estimation into decoding can mitigate correlated noise effects and relax effective error-rate requirements for fault-tolerant quantum computation.

Defects in two-dimensional transition metal dichalcogenides (TMDCs) broadly affect their optical and electronic properties. Directly capturing the ultrafast processes of exciton trapping and defect-bound exciton formation is crucial for understanding and advancing defect-mediated optoelectronics and quantum technologies. However, the weak transient optical absorption of defect-bound excitons has limited their experimental observation to date. Here, we report the direct observation of the ultrafast dynamics of defect-bound excitons in monolayer WS$_2$ crystals with a high density of mono-sulfur vacancies (V$_S$) and W-site defect complexes (S$_W$V$_S$) resulting from synthesis by alkali metal halide-assisted chemical vapor deposition. The dynamics of excitons bound to these defects, along with their coherent interactions with free excitons, are elucidated using ultrafast optical spectroscopy. Using above band-edge photoexcitation, we find that both free and defect-bound excitons simultaneously form within 300 fs from hot carrier relaxation. The defect-bound excitons exhibit shorter lifetimes than free excitons, leading to a population difference of the corresponding excitonic states and free exciton trapping within a 1--100 ps window. Band-edge photoexcitation of free and defect-bound exciton states reveals ultrafast interconversion within ~150 fs (comparable to our temporal resolution), indicating possible coherent coupling between these states. We further demonstrate efficient up-conversion of defect-bound excitons to free excitons with photon energies up to ~300 meV below the free exciton resonance. These findings provide insights into the ultrafast dynamics of defect-bound excitons in TMDCs and their coupling with free excitons, which are relevant to defect-engineered optoelectronic, quantum photonic, and valleytronic applications.

In this work, we have calculated the transport coefficients: shear viscosity and thermal conductivity inside the neutron star core. Our calculation is based on the relativistic kinetic theory approach using a modified BUU equation for quasi-particles whose mass and the chemical-potential and thus in turn the Fermi surface varies with the baryonic density $ρ_{B}$ and the temperature of the medium, and we have used the relaxation time approximation. For the description of the hadronic matter inside the neutron star, we consider the relativistic mean field model with three different kinds of parameterizations. We have found that the shear viscosity is predominantly influenced by neutrons, while thermal conductivity is primarily dominated by electrons.

In computational chemistry of molecular materials, strong static correlation effects appear when electronic states, often involving the ground state, become quasi-degenerate, as occurs, for example, in bond-breaking processes. Such situations present significant challenges for accurate theoretical treatment. In these regimes, many-body methods involving a single-determinant description, such as Hartree-Fock theory and its time-dependent extension, fail to reproduce the correct topology of the ground and excited state potential energy surfaces (e.g., near conical intersections). When strongly correlated electronic systems are further strongly coupled to a quantized radiation field within the framework of non-relativistic cavity quantum electrodynamics, an additional photonic degree of freedom introduces both new complexity and new opportunities to control. Excited cavity photons can modify bond-breaking processes and enable tunability of geometrical and spin-phase transitions, for instance, in organometallic complexes. To overcome this bottleneck, in this work, we extend the well-studied spin-flip configuration interaction singles (SF-CIS) approach to explicitly include quantized cavity photons leading to QED-SF-CIS method. We derive the spin-flip Hamiltonian and find that the double excitation subspace of the system (single with respect to electronic excitation) must be included in the configurations to properly describe singlet electronic states interacting with cavity photons. We then illustrate, through representative molecular examples, how cavity coupling can provide additional tunability in bond-breaking processes. We finally generalize this approach to include higher numbers of photonic excitations, which are required in the strong coupling regime.

Kinetically constrained models have been widely studied in the context of glass formers and non-equilibrium statistical mechanics. Although their simple local rules often result in structureless static properties, their dynamics exhibit intricate emergent phenomena. In this work, we investigate monitored quantum circuit models that interpolate between classical stochastic and unitary quantum dynamics. For any finite measurement strength, the measurement records provide an experimentally accessible probe of the emergence of dynamical phases. By interpreting space-time resolved records as microstates of a fictitious 1+1D spin system, we employ thermodynamic concepts that allow us to investigate the dynamical coexistence between an active and inactive phase. We combine insights from classical stochastic dynamics and numerical simulations of monitored quantum dynamics to investigate different signatures of this dynamical phase coexistence as the measurement strength is varied. Our results shed light on the persistence of dynamical phase coexistence in the quantum regime, offering insights into future experimental studies of complex many-body dynamics in quantum simulators.

In the theory of persistent homology, a well known duality relates the barcodes of the absolute homology and relative cohomology of a one-parameter simplicial filtration. Motivated by the problem of computing free presentations of the (co)homology of multiparameter Rips filtrations, we give a multiparameter generalization of this duality. Considering two duality functors on multiparameter persistence modules, the pointwise dual $(-)^*$ and the global dual $(-)^\dagger$, we show that $H_q(C)^* \cong H^{N+q}(C^\dagger)$ for chain complexes $C$ of free $N$-parameter persistence modules with acyclic colimit. We give an elementary and accessible proof based on a long exact sequence argument, and also give an alternate proof that casts the result as a special case of multigraded Grothendieck local duality. As a corollary, we recover a simple correspondence between minimal free resolutions of a persistence module $M$ and those of its pointwise dual $M^*$, a result previously obtained by Miller, 2000. These results form the foundation of a state-of-the-art algorithm for computing free resolutions of the homology of Vietoris--Rips bifiltrations, described in a forthcoming paper.

We study the convergence properties of a payoff-based higher-order version of replicator dynamics, a widely studied model in evolutionary dynamics and game-theoretic learning, in contractive games. Recent work has introduced a control-theoretic perspective for analyzing the convergence of learning dynamics through passivity theory, leading to a classification of learning dynamics based on the passivity notion they satisfy, such as \textdelta-passivity, equilibrium-independent passivity, and incremental passivity. We leverage this framework for the study of higher-order replicator dynamics for contractive games, which form the complement of passive learning dynamics. Standard replicator dynamics can be represented as a cascade interconnection between an integrator and the softmax mapping. Payoff-based higher-order replicator dynamics include a linear time-invariant (LTI) system in parallel with the existing integrator. First, we show that if this added system is strictly passive and asymptotically stable, then the resulting learning dynamics converge locally to the Nash equilibrium in contractive games. Second, we establish global convergence properties using incremental stability analysis for the special case of symmetric matrix contractive games.

We demonstrate that $k$-Markov sequences of unitary gates provide low-cost handles to manipulate the rate and structure of information spreading compared to traditional random, 0-Markov, circuits. For SWAP gates and brickwork circuits, we use graph cover time to demonstrate how $k$-Markov processes can be used to control operator transport. With SWAP gates and the set of Clifford gates that can change operator weight, we show how $k$-Markov sequences can be used to manipulate scrambling time and generate novel structures of spatial-temporal correlations across a qubit network. We show that $k$-Markov circuits constructed from PSWAP gates at fixed angle are equivalent to standard brickwork circuits with PSWAP angle drawn from non-uniform distributions generated by the $k$-Markov process. In those circuits, the time evolution of the average Hamming weight and the space-time correlation structure after equilibrium again vary significantly from the 0-Markov case, depending on the transition probabilities of the process.

Sparsity is a fundamental modeling principle in statistics, signal processing, and data science. However, optimization with sparsity constraints is notoriously difficult. We introduce a new convex relaxation framework for {sparse quadratically constrained quadratic programs} (QCQPs), a class that subsumes sparse regression, sparse principal component analysis (PCA), and related problems. Our approach is based on a novel convex cone, the spartrahedron, which exactly characterizes sparsity at the matrix level. This leads to a semidefinite programming (SDP) relaxation that is tight whenever its solution is rank-one, providing a simple certificate of global optimality. We establish theoretical guarantees, including approximation bounds and exactness regions for sparse PCA and sparse ridge regression, as well as a general stability result under perturbations. Numerical experiments on sparse PCA, sparse regression, RIP constant estimation, and sparse canonical correlation analysis (CCA) demonstrate the practical success of our methods.

The TeV neutrino signal observed by IceCube from the active galactic nucleus (AGN) NGC 1068 can probe its innermost coronal regions. If these neutrinos originate from hadrons accelerated within a magnetized turbulent corona, their intensity and spectrum depend on the turbulent magnetic field strength and turbulence coherence scale. The gamma rays accompanying neutrino production are absorbed in this optically thick environment, in a way that depends sensitively on the size of the corona. By a joint fit of the IceCube and Fermi-LAT observations, we translate the multimessenger signal from NGC 1068 and the tentative signal from NGC 7469 into quantitative constraints on coronal properties. NGC 1068, with a significant TeV neutrino excess, favors a compact, strongly magnetized corona with a large turbulence coherence length relative to the coronal size. NGC 7469, with two $\sim 100$ TeV neutrino events, points instead to a somewhat larger corona with much smaller coherence length and high magnetization, but a very small fraction of energy in non-thermal protons. We obtain the diffuse flux from a population of Seyfert galaxies identical to either NGC 1068 or NGC 7469. Finally, we consider a third scenario, motivated by the spectral break observed in the diffuse neutrino flux at tens of TeV, with coronal properties intermediate between the two point-source-inspired models. To enable detailed comparisons with the IceCube and electromagnetic observations, we release our model predictions in a GitHub repository.

It is known that preprocessing noise may boost quantum key distribution by expanding the range of values of tolerated noise. For BB84, adding trusted noise may allow the generation of secret keys even for qubit error rate (QBER) beyond the 11% threshold in the asymptotic regime. Here we study the effect of preprocessing noise in the finite-size regime where only a limited number of signals are exchanged between Alice and Bob. We compute tight numerical lower bounds in terms of the sandwiched Rényi entropy of order alpha, optimized via a two-step Frank-Wolfe algorithm, in the presence of a trusted flipping probability q. We find that trusted noise improves the key rate only for a finite interval of alpha, from the alpha -> 1 limit up to alpha approx 1.4. By optimizing on the value of alpha, we determine finite-size key rates for different values of the QBER, observing enhancement due to trusted noise both in asymptotic and finite-size regimes. Finally, we determine the maximum tolerable QBER as a function of the block size.

High-dimensional photonic entanglement holds significant promise for advancing quantum communication, computation, and metrology. For example, large-alphabet quantum communication protocols are known to benefit from enhanced noise resilience and information capacity via multi-bit time-bin encoding. Yet, characterizing high-dimensional entangled states is challenging, as full state tomography becomes prohibitively costly and often requires unrealizable measurements. Here, we demonstrate a scan-free method to characterize high-dimensional entanglement in the time-frequency domain. Our reconstruction achieves a record $5.70\pm0.07$ ebits and a fidelity of $65.4\pm0.4\%$ with the maximally entangled state of local dimension $1021$, certifying the presence of $668$-dimensional entanglement. We further prove the attainability of a secure key rate of $15.6$ kB/s in a composable finite-size, entanglement-based protocol, and show that in continuous operation, the setup can quickly approach asymptotic key rates. Using commercial telecom components and state-of-the-art low-jitter single-photon detectors, our scalable architecture offers a practical path towards high-rate, noise-resilient quantum communication testbeds.

Quantum kernels offer a valid procedure for learning quantum phase transitions on quantum processing devices, yet issues on the scalability of the learning strategy in connection with the symmetry of the critical model have not been clarified. We derive a link between model symmetry and fidelity-kernel resource scaling. We quantify the measurement resources required to estimate fidelity-based quantum kernels for many-body ground states while preserving the structure of the resulting Gram matrix under finite-shot sampling. Crucially, we show that increasing symmetry in the underlying spin model systematically amplifies these shot requirements. Moving from the $\mathbb{Z}_2$-symmetric Ising/XY regimes to the $U(1)$-symmetric XX (and XXZ) regimes leads to stronger kernel concentration and therefore substantially larger shot costs under the same bounds. We consider a tunable one-dimensional spin-$\tfrac{1}{2}$ Hamiltonian spanning the transverse-field Ising, XY, XX, and XXZ limits, and define the kernel as the ground-state fidelity. Kernel entries are estimated using a SWAP-test estimator with $S$ shots, and we adapt the ensemble spread and concentration-avoidance shot bounds to obtain practical shot requirements in terms of the interquartile range of kernel values and a representative kernel magnitude. For the free-fermion XY/XX family, we use the closed-form Bogoliubov-angle fidelity, while for the interacting XXZ chain we compute fidelities by exact diagonalization and benchmark shot-noise effects. Our symmetry-aware bounds provide a pragmatic procedure for physics-informed quantum machine learning.

The interplay between quantum orientation entanglement and Wigner rotation plays a fundamental role in understanding the behavior of spin angular momentum in quantum states. To analyze the quantum orientation entanglement of the relativistic helicity states interpolating between the Jacob-Wick helicity and the light-front helicity, we examine the relative angle between the particle's momentum direction and the spin orientation for the interpolating helicity states. For this analysis, we introduce a novel method for expanding the interpolating helicity states in terms of the Jacob-Wick helicity. The corresponding probabilistic coefficients follow the structure of the Wigner d-matrix elements, which we use for the interpretation of the quantum orientation entanglement manifested in the angular distributions of the interpolating scattering helicity amplitudes. As an explicit demonstration, we compute the interpolating helicity amplitudes for the pair production of spin-1 (vector) particles in the annihilation of two spin-0 (scalar) particles, focusing primarily on their contact interaction. In particular, we identify the critical interpolation angle that bifurcates the dynamical branches between the instant-form dynamics and the light-front dynamics and discuss the underlying orientation entanglement in the interpolating helicity amplitudes.

We consider the soliton solutions of a recently proposed coupled Sasa-Satsuma-mKdV equation using the Kadomtsev-Petviashvili reduction method. The system consists of a complex-valued component coupled with a real-valued one. Under zero or nonzero boundary conditions, we derive four distinct classes of soliton solutions: bright-bright, dark-dark, bright-dark, and dark-bright. These solutions are derived from the vector Hirota equation, for which the bright, dark, and bright-dark soliton solutions are provided in the Appendix. We perform asymptotic analysis of soliton collisions for each class of solutions, in which inelastic collisions are observed between bright-bright solitons. In the dark-dark case, we identify soliton profiles similar to the Sasa-Satsuma equation, including double-hole, Mexican hat, and anti-Mexican hat solutions; this study further explores the collisions between these structures and hyperbolic tangent shaped kink solitons. Regarding the bright-dark case, beyond the expected soliton-kink interactions, we report and analyze a notable collision occurring between kink solitons.

The Highly Adaptive Lasso (HAL) delivers unprecedented guarantees in nonparametric minimum loss estimation under minimal smoothness assumptions, such as dimension-free minimax optimal rates. However, the practical use of HAL has been severely limited by its exponentially growing computationally prohibitive indicator basis expansion in moderate to high dimensions. Existing screening strategies drastically reduce this dimension but lack any theoretical justification. We introduce the Principal Component Highly Adaptive (PC-HA) family of estimators, which for the first time provide a principled and theoretically valid dimension reduction. We establish formal results on the score equations solved by these PC-HA estimators, allowing to transfer plug-in efficiency and pointwise asymptotic normality results from HAL to these PC-HA estimators, under comparable complexity control.

Electrified propulsion is expected to play an important role in the sustainable development of Advanced Air Mobility (AAM). However, the limited energy density of batteries motivates the need to minimize energy consumption during flight. This paper studies the minimum total energy problem for an all-electric aircraft in steady cruise flight. The problem is formulated as an optimal control problem in which the cruise airspeed and final cruise time are optimization variables. The battery supply voltage is modeled as an affine function of the battery charge. Pontryagin's Minimum Principle is used to derive the necessary and sufficient conditions for optimality, from which closed-form expressions for the optimal cruise airspeed and optimal final cruise time are obtained. Additional analytical conditions are derived that determine when all-electric operation is feasible, one of which is that sufficient electric charge must be available. Numerical simulations based on the BETA Technologies CX300 all-electric aircraft and a representative AAM scenario illustrate how the aircraft weight, cruising altitude, electrical system efficiency, and initial battery charge influence the optimal airspeed and the feasibility of all-electric cruise.

Experimentally relevant signatures of superconductivity require access to real-frequency quantities, such as the spectral functions, optical response, and transport properties, yet Migdal-Eliashberg calculations are commonly performed on the imaginary axis and then analytically continued, a step that is numerically delicate and can obscure physically relevant spectral features. Here we present a practical route to solving the finite-temperature Migdal-Eliashberg equations directly on the real-frequency axis, while retaining the effects from the full-bandwidth electronic structure. Our formulation accounts for particle-hole asymmetry through an energy-dependent electronic density of states, avoiding the constant density of states approximation often used in real-axis calculations, and includes a static screened Coulomb contribution. We introduce an efficient numerical technique to solve the Migdal-Eliashberg integrals whose computational cost scales linearly with the real-frequency grid, making high-resolution, full-bandwidth real-axis calculations feasible and providing direct access to the interacting Green's function and derived observables without analytic continuation. As an illustration, we apply the method to H$_{3}$S, where a van-Hove singularity near the Fermi level produces strong particle-hole asymmetry. The full-bandwidth solution yields noticeably different spectra than the constant density of states approximation and brings the superconducting gap and lineshapes into closer agreement with experiment, highlighting when band-structure details are essential. Furthermore, the methods presented here open the door to time-dependent, nonequilibrium simulations within Eliashberg theory.

We present a local unitary theory of a Bell-EPR measurement, starting with the premeasurement filtering of the individual photon polarizations and extending through the detection process involving four photodetectors, two at each receiving station. The essential feature is that decoherence occurs locally and independently with each detector upon its absorption of a photon. Communication between observers after they read their local outcomes confirms the known Bell-EPR correlations. This theory is manifestly local, but there exist other formulations, and interpretations, that are non-local.

This paper pays tribute to Professor Giovanni Andrea Cornia's lifelong contributions to the measurement of global inequality. We review twelve world and regional databases of the Gini coefficient, illustrate their coverage, overlapping, and data gaps, and analyse the major sources of discrepancy among published Ginis. Merging all databases into a unified collection of over 122,000 observations spanning 222 countries from 1867 to 2024, we document how differences in welfare metrics, reference units, sub-metric definitions, post-survey adjustments, and survey design produce Gini estimates that diverge considerably -- sometimes by as much as 50 percentage points -- for the same country and year. We quantify pairwise cross-database discordance, document the income-consumption Gini gap by region and income group, and discuss the contributions of welfare metric and equivalence scale choices to cross-database dispersion. We extend the analysis with a dedicated discussion of comparability across time and across measurement dimensions, showing how multiple layers of methodological choice interact to make any single Gini figure a product of a complex chain of decisions that are rarely fully disclosed. Our analysis confirms that the choice of welfare metric remains the single most important source of cross-country non-comparability, while sub-metric definitions and equivalence scales introduce further systematic differences that are routinely overlooked in comparative work.

We analytically study the orbital response of alternating-twist graphene systems with four and five layers to an in-plane magnetic field, using the unitary transformation introduced by Khalaf et al. (Phys. Rev. B 100, 085109 (2019)). This transformation maps an alternating-twist N-layer system onto N/2 decoupled twisted bilayer graphene (TBG) systems with distinct effective twist angles, together with a single decoupled layer for odd N, thereby generating a hierarchy of N/2 magic angles. For five layers, we find that the orbital in-plane magnetic response is negligibly small, and we expect this property to hold for all systems with an odd number of layers. For a tetralayer system, we approximately express the in-plane orbital susceptibility in terms of the corresponding TBG responses, which are large compared to the spin susceptibility and even diverge in the clean limit at charge neutrality near the magic angle. Remarkably, the in-plane magnetic response is strongly angle dependent: compared with TBG, it is about 0.01 times smaller at the first magic angle, whereas at the second it reaches about 3.6 times the value of magic angle TBG. We finally introduce the in-plane Maki parameter as the ratio between the difference in orbital susceptibility of the normal and superconducting states and the paramagnetic Pauli susceptibility. For TBG, we find values up to 2 near the magic angle. Our analysis can be extended to other response functions and suggests that the different effective magic angles in alternating-twist multilayers may host distinct superconducting phases.

Optical beam steering is a key technology for free-space optical communication, sensing, and imaging. Mechanical beam steering systems suffer from limited scanning speed and bulky form factors, while existing solid-state solutions rely on pixelated synthetic aperture that requires complex fabrication and control architectures. Integrated acousto-optic beam steering (AOBS) is an emerging technology that enables continuous one-dimensional beam steering using integrated acoustic transducers and fixed-wavelength laser sources. Here, we integrate AOBS with an optical ring resonator on the same thin-film lithium niobate (TFLN) platform to significantly enhance beam steering efficiency and system functionality. The resulting device achieves a resonance-enhanced beam steering efficiency of up to 20% over a 18 degrees field of view. Moreover, by leveraging integrated electro-optic control, we dynamically lock the ring-resonator's resonance to a chirped laser frequency, enabling frequency-modulated continuous-wave (FMCW) LiDAR operation. By combining lithium niobate's piezoelectric and electro-optic properties, this work establishes a compact, efficient, and scalable beam-steering platform with co-integrated acousto-optic modulation and electro-optic control for multifunctional applications.

We investigate dissipative phase transitions (DPTs) in a parametrically amplified open quantum Rabi model (QRM) with both single- and two-photon decay. In the classical oscillator limit, four composite phases emerge, arising from the possible normal or superradiant regimes across the upper and lower spin branches. A mean-field analysis reveals an ``inverted" regime where superradiance emerges only at sufficiently low spin-boson coupling. This regime features first- and second-order DPTs separated by a tricritical point, while two-photon dissipation preserves the stability of the superradiant phase. Utilizing an adiabatic approach and the semi-classical Langevin formalism, we further study the steady-state structure beyond the mean-field level. We show that the tricriticality stems from the intrinsic nonlinearity of QRM, unveiled by the interplay of coherent and dissipative two-photon processes. The universality classes of the DPTs are identified, with the corresponding critical and finite-size scaling exponents derived and a scaling ansatz proposed to describe the critical behavior.