We derive expressions for the first and second derivatives of the quintessence potential $V(ϕ)$, in terms of $λ= -V^{\prime}/V$ and $Γ= (V^{\prime \prime}/V)/(V^\prime/V)^2$, as functions of the quintessence density fraction $Ω_ϕ$ and the cosmographic parameters $q$, $j$, and $s$. Our mapping is not explicitly a function of the equation of state parameter $w$. We use these results, along with recent observational data, to derive expansions of $V(ϕ)$ about the present-day value of the scalar field, $ϕ_0$.

Let $B$ be a compact Riemann surface and $B_0\subset B$ a bordered hyperbolic subsurface obtained by removing finitely many disjoint closed disks. Fix a nontrivial loop $α$ in $B_0$. For $s\ge 0$, let $L(α,s)$ denote the supremum, over all finite subsets $S\subset B_0$ with $\#S\le s$, of the minimal Kobayashi length of a loop in $B_0\smallsetminus S$ that is freely homotopic to $α$ in $B_0$. Phung in [7] proved that $L(α,s)$ grows at most linearly and at least as $\sqrt{s}/\log s$. We sharpen the upper bound to $O\left(\sqrt{s\log s}\right)$, which determines $\lim_{s\to\infty}\frac{\log L(α,s)}{\log s}=\frac{1}{2}$, answering a question raised in [7, Question 1.4]. As an application, we improve the counting bound for generalized integral points on abelian varieties over complex function fields: for an abelian variety of dimension $n$ over $\mathbb C(B)$, Phung proved that the number of $(s, B_0)$-generalized integral points modulo the constant trace grows at most as $s^{2nk}$, where $k=\operatorname{rk}(π_1(B_0))$. We sharpen this to $s^{nk+\varepsilon}$ for every $\varepsilon>0$, halving the exponent.

The deformation of heavy nuclei leaves characteristic imprints on the initial conditions of relativistic heavy-ion collisions. However, event-by-event fluctuations make the quantitative extraction of this information challenging. This study examines the identifiability of the quadrupole ($β_2$) and hexadecapole ($β_4$) deformation parameters from nucleon configurations sampled from a deformed Woods-Saxon distribution commonly used in initial-state modeling of heavy-ion collisions. As a baseline, we first establish an upper bound on the "intrinsic identifiability" of deformation information at the most microscopic level by constructing permutation-invariant point-cloud networks under controlled multi-event grouping. We then extend the analysis to the more realistic initial entropy-density profiles generated by the TRENTo model, where both standard regression and simulation-based inference (SBI) with conditional normalizing flows are employed to reconstruct the deformation parameters from ensembles of event images supplemented with global attributes. Multi-event averaging is found to be essential in this setting for suppressing stochastic fluctuations and revealing the underlying deformation information. While standard regression efficiently captures the central trends of deformation through point estimates, SBI provides calibrated posterior distributions, offering a more complete and robust characterization of uncertainty. Collectively, our results demonstrate that deformation information is effectively encoded in the initial state and becomes increasingly identifiable with sufficient ensemble averaging, laying a solid foundation for future extensions toward more complete dynamical modeling and final-state observables.

We study stationary scattering for Schrödinger operators in $\mathbb R^3$ with finitely many concentric $δ$--shell interactions of constant real strengths. Starting from the self--adjoint realization and the boundary resolvent formula for this model, we show that, after partial--wave reduction, the same finite-dimensional boundary matrices that arise in the resolvent formula also determine the channel scattering coefficients. More precisely, for each angular momentum $\ell$, the channel coefficient $S_\ell(k)$ satisfies $S_\ell(k)=\det K_\ell(k^2-i0)/\det K_\ell(k^2+i0)$ for almost every $k>0$, where $K_\ell(z)=I_N+m_\ell(z)Θ$ is the $\ell$--th reduced boundary matrix. Thus, in each channel, the positive--energy scattering problem is reduced to a finite-dimensional matrix problem, and the scattering phase is recovered from $\det K_\ell(k^2+i0)$. We then study the first nontrivial case of two concentric shells in the $s$--wave channel, where the interaction between the shells produces nontrivial threshold effects. We derive an explicit formula for $S_0(k)$ and analyze its behavior as $k\downarrow0$. In the regular threshold regime, we obtain an explicit scattering length. We further identify a threshold--critical configuration characterized by the existence of a nontrivial zero--energy radial solution, regular at the origin, whose exterior constant term vanishes. In the corresponding nondegenerate exceptional case, the usual finite scattering length breaks down, and instead $S_0(k)\to -1$ as $k\downarrow0$.

Reliable organic ferroelectrics for memory applications require extreme endurance under repeated electrical switching. Here we demonstrate exceptional fatigue resistance in highly crystalline 2-methylbenzimidazole (MBI) films grown by low-temperature deposition followed by restrained crystallization (LDRC) in a simple Pt/MBI/Pt capacitor geometry. Switching kinetics analyzed using the Kolmogorov-Avrami-Ishibashi (KAI) model reveal characteristic millisecond switching times and quasi-one-dimensional domain growth associated with proton transfer along hydrogen-bond chains. Guided by these kinetics, we implemented a stringent fatigue protocol designed to maximize switching stress, involving bipolar switching at approximately 2Ec with 5 ms pulses, well beyond the characteristic switching time, for continuous operation over approximately 2 weeks. The remanent polarization exhibits only a minor wake-up (+10% within the first 10^4 cycles) and ultimately returns to approximately its initial value after 10^8 cycles, with testing limited by experimental duration rather than device failure. This robust endurance is achieved in an unengineered structure and contrasts with polymer ferroelectrics such as P(VDF-TrFE), where comparable performance typically relies on interfacial engineering. The combination of LDRC-enabled high crystallinity and localized proton-transfer switching, which introduces minimal structural perturbation during polarization reversal, enables this outstanding fatigue tolerance and highlights MBI as a simple, fluorine-free platform for durable organic ferroelectric devices.

In this note we consider no-boundary instantons and wine-glass geometries which are of interest in the context of quantum cosmology. While the former usually appears as a dominant saddle in the path-integral, the wineglass geometry can become dominant saddle in some situations. The later has been argued to have a longer inflationary phase of the Universe. Kontsevich-Segal-Witten (KSW)-allowability criterion which classifies geometries on the basis of the requirement of having a meaningful QFT on it, pushes one to analyse the allowability of the various geometries. In this note we do a simple study to seek answer to the allowabilty of no-boundary instantons and wine-glass geometries, where the later is obtained via analytical continuation of Lorentzian deSitter in pure gravity. Our simple analysis which make use of a milder version of KSW allowability criterion shows that no-boundary instanton is KSW allowed while wine-glass geometries obtained via such analytic continuation in pure-gravity are KSW disallowed. This study however doesn't covers wineglass saddles arising in gravity coupled with matter theories.

Quantum simulation of molecular electronic structure is one of the most promising applications of quantum computing. However, achieving chemically accurate predictions for strongly correlated systems requires quantum phase estimation (QPE) on fault-tolerant quantum computing (FTQC) devices. Existing resource estimates for typical FTQC architectures suggest that such calculations demand millions of physical qubits, thereby placing them beyond the reach of near-term devices. Here, we investigate the feasibility of performing QPE for chemically relevant molecular systems in an early-FTQC regime, characterized by partial fault tolerance, constrained qubit budgets, and limited circuit depth. Our framework is based on single-ancilla, Trotter-based QPE implementations combined with partially randomized time evolution. Within this framework, we develop a novel Hamiltonian optimization strategy, termed unitary weight concentration, that reduces algorithmic cost by reshaping linear-combination-of-unitaries representations. Applying this framework to active-space models of iron-sulfur clusters, cytochrome P450 active sites, and CO$_2$-utilization catalysts, we perform end-to-end resource estimation using the latest version of the space-time efficient analog rotation (STAR) architecture. Our results indicate that ground-state energy estimation for active spaces of approximately 20 to 50 spatial orbitals, well beyond the reach of classical full configuration interaction, is achievable using $\sim 10^5$ physical qubits, with runtimes on the order of days to weeks. These findings demonstrate that while full-fledged fault-tolerant quantum computers will be required for even larger molecular simulations, chemically meaningful quantum chemistry problems are already within reach in an experimentally relevant, early-FTQC regime.

Privacy leakage in LLM agents is often studied through individual storage or execution components, such as memory modules, retrieval pipelines, or tool-mediated artifacts. However, these settings are typically analyzed in isolation, making it difficult to compare how private internal dependence becomes externally recoverable across heterogeneous agent pipelines. In this paper, we present CIPL (Channel Inversion for Privacy Leakage) as a unified channel-oriented measurement interface for evaluating privacy leakage in LLM agent pipelines. Rather than claiming a universally strongest attack recipe, CIPL provides a shared way to represent a target through its sensitive source, selection, assembly, execution, observation, and extraction stages, and to measure how internal exposure is transformed into attacker-recoverable leakage under a common protocol. Using memory-based, retrieval-mediated, and tool-mediated instantiations under this shared interface, we identify a distinct cross-target risk picture. Memory behaves as a near-saturated high-risk special case, while beyond-memory leakage exhibits a different regime: retrieval-mediated targets show frequent but often incomplete leakage, and tool-mediated targets are strongly shaped by the exposed observation surface and provider behavior. We further show that leakage is governed by channel conditions rather than by a universally dominant recipe: cleaned weak controls sharply suppress leakage, and semantic annotation reveals attacker-useful leakage beyond exact-match extraction. Together, these findings suggest that privacy risk in LLM agent pipelines is better understood through \emph{observable channels}, not just storage components. More broadly, our results motivate channel-oriented privacy evaluation as a necessary complement to component-local or exact-only analyses.

Thermal interface materials (TIMs) critically regulate heat dissipation from electronic chips to heat spreaders, yet their thermal conductivity (k), volumetric heat capacity (C), and interfacial thermal resistance (ITR) evolve with mechanical pressure and cannot be determined simultaneously using existing steady-state or transient techniques. As a result, the coupled roles of bulk compaction and interfacial contact in governing heat transport in TIM assemblies remain poorly resolved. Here, we present a square-pulsed source (SPS) thermoreflectance method that enables simultaneous determination of k, C, and ITR in TIM stacks under controlled mechanical loading. By spanning square-wave modulation frequencies from 1 Hz to 10 MHz, SPS probes a broad range of thermal penetration depths, enabling distinction between heat diffusion in the TIM bulk and interfacial heat transfer at the Al/TIM contact. Measurements on a thermally conductive gel, a thermal pad, and a high-vacuum grease during compression-unloading cycles reveal distinct pressure-dependent thermal transport mechanisms. The gel and pad exhibit increases in k and C, reduced ITR, and pronounced hysteresis, indicating coupled bulk densification and persistent interfacial conformity during loading cycles. In contrast, the grease shows nearly pressure-independent bulk properties but a strong pressure dependence of ITR, consistent with an interface-dominated response. These results resolve the long-standing challenge of simultaneously quantifying bulk and interfacial thermal transport in mechanically loaded TIM assemblies, enabling experimentally constrained thermal management and reliability analysis in electronic packaging.

The majority of voice-based conversational agents still rely on pause-and-respond turn-taking, leaving interactions sounding stiff and robotic. We present RESPOND (Responsive Engagement Strategy for Predictive Orchestration and Dialogue), a framework that brings two staples of human conversation to agents: timely backchannels ("mm-hmm," "right") and proactive turn claims that can contribute relevant content before the speaker yields the conversational floor. Built on streaming ASR (Automatic Speech Recognition) and incremental semantics, RESPOND continuously predicts both when and how to interject, enabling fluid, listener-aware dialogue. A defining feature is its designer-facing controllability: two orthogonal dials, Backchannel Intensity (frequency of acknowledgments) and Turn Claim Aggressiveness (depth and assertiveness of early contributions), can be tuned to match the etiquette of contexts ranging from rapid ideation to reflective counseling. By coupling predictive orchestration with explicit control, RESPOND offers a practical path toward conversational agents that adapt their conversational footprint to social expectations, advancing the design of more natural and engaging voice interfaces.

We investigate the correspondence between unimodular diffusion cosmology and interacting dark sector models at the background and linear perturbation levels. In the diffusion framework, the effective cosmological constant becomes time dependent, $Λ(t)$, sourced by a diffusion current. We show that at the background level this framework can be mapped onto interacting dark energy models with $w=-1$ and energy transfer $Q$. Using two common parameterizations, $Q = ξH ρ_{\rm de}$ and $Q = ξH ρ_{\rm dm}$, and data from supernovae, DESI BAO, cosmic chronometers, and CMB distance priors, we find $ξ= -0.0197 \pm 0.0076$ for the vacuum-coupled case, while the matter-coupled case gives a best-fit $ξ= 0.0018$ with comparable goodness of fit. At the level of linear perturbations, however, the diffusion framework is consistent only with interacting vacuum models having homogeneous energy transfer ($Q \propto ρ_{\rm de}$ with $δQ=0$), thereby breaking the degeneracy with more general interacting dark energy scenarios. Including redshift-space distortion data, we obtain $ξ= -0.0147 \pm 0.0075$, consistent with $Λ$CDM ($ξ=0$) at $2σ$. The inferred clustering amplitude is $S_8 = 0.782 \pm 0.026$ for the diffusion model, compared to $S_8 = 0.77 \pm 0.025$ for $Λ$CDM under the same dataset, indicating a modest but non-negligible impact on structure growth.

We develop a linear-algebraic framework for dimensional analysis in systems with constraints, particularly when variables are numerous or related by implicit relations so that direct elimination is impractical. By expressing both dimensional relations and constraints in logarithmic variables, the problem is reduced to a linear structure. This formulation yields a simple count of independent dimensionless quantities and, more importantly, a purely algebraic procedure to eliminate redundant ones without trial and error. The method is especially effective for systems with implicit or multiple constraints, and is illustrated with the classical drag force problem.

Let $\mathcal{M}_{2N}(δ_1, δ_2,\dots, δ_N)$ be the moduli space of centrally symmetric convex polyhedral surfaces with $2N$ labeled vertices and prescribed cone-deficits $δ_1$, $δ_2$, $\dots$, $δ_N$. We show that $\mathcal{M}_{2N}(δ_1, δ_2,\dots, δ_N)$ has the structure of a real hyperbolic manifold of dimension $2N-3$. When $N=4$ and $5$, we show that every surface in $\mathcal{M}_{2N}(δ_1, δ_2,\dots, δ_N)$ can be decomposed into at most $2\binom{2N-2}{2}$ parallelograms, and the decomposition is invariant under the antipodal map. Using the edge-lengths of these parallelograms as coordinates, we show that the moduli space of centrally symmetric polyhedral surfaces with $8$ unlabeled vertices and cone-deficits $\fracπ{2}$ is isometric to the quotient of a real hyperbolic regular ideal $5$-simplex by the dihedral group $D_6$.

Spin density waves (SDWs) represent a fundamental paradigm of spatially modulated order in condensed matter systems, yet their electrical and mechanical analogues polarization and strain density waves (PDWs and StDWs) have remained elusive as equilibrium phases. Here, we introduce a general, symmetry-driven strategy to unlock static PDWs and StDWs in perovskites SrTiO3 and SrMnO3. Using first-principles calculations, we uncover a previously overlooked soft antiferrodistortive tilt gradient mode at small-q wavevector in the phonon dispersion of their presumed Ima2 ground state under moderate tensile strain. Group-theory analysis reveals that a hard polaracoustic phonon, which intrinsically carries PDWs and StDWs, is improperly destabilized by a trilinear coupling with this modulated tilt mode and an inherently uniform tilt mode. This interaction drives a structural transition from the Ima2 phase to a novel lower-energy Pmn21 phase that hosts long-range-ordered PDWs and StDWs. Strikingly, the engineered StDWs in SrMnO3 activate an electrically tunable SDW via the flexomagnetic effect. These discoveries fundamentally revise the strain-phase diagrams of prototypical perovskites and establish a unified phonon-engineering framework that links modulated phonon instabilities to targeted density-wave order, offering new pathways for designing advanced electromechanical and magnetoelectric functionalities.

We present a systematic analytic study of the $p$-Bessel functions $\mathcal{J}_{ω,φ}^{[p]}$, a novel class of generalized Bessel functions arising from Fourier analysis on planar domains bounded by $p$-circles, including astroid-type shapes with $0<p\le2$ satisfying $(2/p)\in\mathbb{N}$. While previous work established Hardy-type oscillatory identities for these domains, expressing lattice point discrepancies via $p$-Bessel functions, the present paper focuses on the intrinsic analytic properties of the functions themselves. In particular, we (i) construct a hierarchical structure of $\{\mathcal{J}_{ω,φ}^{[p]}\}_{ω\ge0}$ using Erdélyi-Kober-type fractional derivatives, (ii) derive explicit real-analytic integral representations suitable for axis-dependent asymptotic estimates, and (iii) extend the functions to the complex domain through Poisson-type integral formulas. These results establish $p$-Bessel functions as genuinely new oscillatory kernels, providing a rigorous framework for studying anisotropic oscillatory phenomena and laying the analytic foundation for applications in $p$-circle lattice point problems.

The analysis of high-dimensional data, common in fields such as genomics, is complicated by the presence of cellwise contamination, where individual cells rather than entire rows are corrupted. This contamination poses a significant challenge to standard variable selection techniques. While recent ensemble methods have introduced deterministic frameworks that partition the predictor space to manage high collinearity, these architectures were not designed to handle cellwise contamination, leaving a critical methodological gap. To bridge this gap, we propose the Fast and Scalable Cellwise-Robust Ensemble (FSCRE) algorithm, a multi-stage framework integrating three key statistical stages. First, the algorithm establishes a robust foundation by deriving a cleaned data matrix and a reliable, cellwise-robust covariance structure. Variable selection then proceeds via a competitive ensemble: a robust, correlation-based formulation of the Least-Angle Regression (LARS) algorithm proposes candidates for multiple sub-models, and a cross-validation criterion arbitrates their final assignment. Despite its architectural complexity, the proposed method enjoys fundamental theoretical guarantees, including invariance properties and local selection stability. Through extensive simulations and a bioinformatics application, we demonstrate FSCRE's superior performance in variable selection precision, recall, and predictive accuracy across various contamination scenarios. This work provides a unified framework connecting cellwise-robust estimation with high-performance ensemble learning, with an implementation available on CRAN.

We present a study probing the Higgs self-coupling with the X-ray free-electron laser Compton $γγ$ Collider (XCC) concept. The analysis is performed considering the $γγ\to HH \to bb\overline{bb}$ channel, and results are then extrapolated to obtain a projection on the Higgs self-coupling sensitivity that ranges between 7% and 12%. An ensemble of boosted decision trees is trained to discriminate between signal and backgrounds, paired with a genetic algorithm optimizer to combine the final classifier outputs. This study suggests that an X-ray FEL-based $γγ$ collider is a powerful tool to probe the mechanism of electroweak symmetry breaking, complementary to $e^+e^-$ Higgs factories and future high-energy hadron colliders.

We present multi-wavelength observations and a comprehensive analysis of the nearby (D$\sim$14 Mpc) Type IIb supernova (SN IIb) 2024iss. Observations of SN2024iss include an early ZTF detection at $\sim$40 minutes after first light and the earliest Hubble Space Telescope UV spectrum for a SN IIb to date at 7 days after first light. With the bolometric light curve and He-star models, we estimate an ejecta mass range of $\sim 1.1-3.3~M_{\odot}$ and a $^{56}\textrm{Ni}$ mass of $0.11 \pm 0.01~M_{\odot}$. We fit shock-cooling emission models to the first peak in the light curve and estimate a progenitor radius of $100-320~R_{\odot}$ and a H-rich envelope mass of $0.07-0.46~M_{\odot}$. We also compared optical/UV spectra to binary progenitor model spectra, which indicate a stripped H-rich envelope mass of $0.19-0.28~M_{\odot}$. We use early-time X-ray detections to calculate CSM densities that are consistent with a progenitor mass-loss rate of $5\times10^{-4}~M_{\odot}$ ($v_w = 100~$km/s), corresponding to a period of significant mass ejection in the final ~2-5 years before core collapse. In the UV spectrum, we observe strong Mg II emission extending to $\sim15,000 ~$km/s as well as weak P-Cygni profiles of iron-group elements (e.g., Fe, Ti, Al, Ni) present in the outer SN ejecta during the end of shock cooling phase. We find that the overall spectroscopic evolution of SN2024iss is comparable to other SNe IIb, but that the increased brightness following the initial light curve peak is likely influenced by SN ejecta-CSM interaction. Finally, optical/NIR nebular spectroscopy of SN2024iss at $\sim 260-412~$ days reveals multi-peaked forbidden line profiles of O I and Mg I] indicative of inner ejecta asymmetry and/or clumping. We demonstrate the utility of a rich, multi-wavelength dataset for constraining the progenitor systems and explosion dynamics of SNe IIb.

We develop a one-class, deep-learning framework to detect the phase transition and recover critical behavior of the 3D Ising model. A 3D convolutional neural network autoencoder (CAE) is trained on ground-state configurations only, without prior knowledge of the critical temperature, the Hamiltonian, or the order parameter. After training, the model is applied to Monte Carlo configurations across a wide temperature range and different lattice sizes. The mean-square reconstruction error is shown to be sensitive to the transition. Finite-size scaling of the peak location for the reconstruction error susceptibility yields the critical temperature $T_c=4.5128(58)$ and the correlation-length critical exponent $ν=0.63(27)$, consistent with results from the literature. Our results show that a one-class CAE, trained on zero-temperature configurations only, can recover nontrivial critical behavior of the 3D Ising model.

This work investigates the universality of cusp formation in the shadows of compact objects. The emergence of cusps is accompanied by three interrelated phenomena: a topological charge transition, an equal-area law governing the self-intersecting structure, and universal critical scaling behavior. We demonstrate that, because these phenomena originate from the global morphology of the shadow, they are fundamentally independent of specific spacetime metric details and apply across diverse models. These features are systematically analyzed for the Kerr black hole endowed with a running Newton coupling. By extending our framework to rotating traversable wormholes, we confirm that the same universal behavior persists in more general compact objects. Our study uncovers the universality underlying cusp formation, offering a model-independent framework for identifying non-Kerr signatures in future black hole observations.

Measurements of Waves instrument onboard the Juno spacecraft suggest that narrowband kilometric radiation (nKOM; 20-141 kHz) and narrowband low-frequency radiation (nLF; 5-70 kHz) are generated within the plasma near the Io plasma torus (IPT) in low-latitude regions. While these emissions are thought to result from the conversion of the natural modes of the plasma into escaping radio waves, at either the fundamental or the first harmonic of the plasma frequency, there is no consensus on the specific mechanism involved. Using the electron density and the magnetic field data from the Jovian Auroral Distribution Experiment (JADE) and the FluxGate Magnetometer (FGM), we determine the range of frequencies accessible to different wave modes during Juno's crossing of the plasma disk environment. We classify the observed nKOM and nLF according to their propagation modes: trapped (Z-mode or Whistler), escaping (X-mode or O-mode), and undetermined (either trapped or escaping). We apply the 3D numerical modeling method that was developed in Boudouma et al. (2024) to the escaping and undetermined nKOM and nLF observations, deriving macroscopic constraints on the generation mechanisms, wave modes, characteristic frequencies, beaming and source locations. Our results support the interpretation in which high-latitude nKOM is consistent with O-mode, while low-latitude is rather X-mode. Both nKOM and nLF appear to be generated near the fundamental of the plasma frequency, but only nLF shows compatibility with emission near the first harmonic, suggesting the possible coexistence of both linear and nonlinear generation mechanisms.

We consider damped driven Maxwell-Bloch equations for a single-mode Maxwell field coupled to a two-level molecule. The equations are used for semiclassical description of the laser action. Our main result is the construction of solutions with single-frequency asymptotics of the Maxwell field in the case of quasiperiodic pumping. The asymptotics hold for solutions with harmonic initial values which are stationary states of averaged reduced equations in the interaction picture. We calculate all harmonic states and analyse their stability. Our calculations rely on the Hopf reduction by the gauge symmetry group U(1). The asymptotics follow by an extension of the averaging theory of Bogolyubov--Eckhaus--Sanchez-Palencia onto dynamical systems on manifolds.The key role in the application of the averaging theory is played by a special a priori estimate.

We study grey-body factors for a massless scalar field in the spacetime of regular black holes arising in four-dimensional non-polynomial quasi-topological gravity. We consider two representative metrics that capture the typical features of regular geometries. Using the WKB method, we compute the transmission probabilities and analyze their dependence on the regularization parameter. The grey-body factors are found to deviate only slightly from the Schwarzschild case, indicating that the scattering properties are largely insensitive to near-horizon regularization of the geometry. The correspondence between quasinormal modes and grey-body factors is shown to be sufficiently accurate for higher multipole numbers.

Let $G$ be a graph with vertex set $V=V(G)$. A double Roman dominating function on a graph $G$ is a function $f : V \to \{0,1,2,3\}$ satisfying the conditions that if $f(v) = 0$, then vertex $v$ must have at least two neighbors in $V_2$ or one neighbor in $V_3$, if $f(v) = 1$, then vertex $v$ must have at least one neighbor in $V_2 \cup V_3$. The weight of a double Roman dominating function $f$ is the sum $f(V) = \sum_{v \in V} f(v)$, and the double Roman domination number $γ_{dR}(G)$ is the minimum weight of a double Roman dominating function on $G$. A double Italian dominating function on a graph $G$ is a function $f : V \to \{0,1,2,3\}$ satisfying the condition that for every vertex $u \in V$, if $f(u) \in \{0,1\}$, then $\sum_{v \in N[u]} f(v) \ge 3$. The double Roman domination number $γ_{dI}(G)$ is the minimum weight of a double Italian dominating function on $G$. Mojdeh and Volkmann [D.A. Mojdeh and L. Volkmann, Roman {3}-domination (double Italian domination), Discrete Appl. Math. 283 (2020), 555--564] proved that $γ_{dI}(T) = γ_{dR}(T)$ for any tree $T$. However, we find that there is a minor issue in the proof. In this paper, we first prove that $γ_{dI}(T) \neq γ_{dR}(T)$. Subsequently, we present a sharp bound on the double Italian domination number of any non-trivial tree $T$, and characterize the trees attaining this bound.

Square-lattice J-Q models provide a sign-problem-free setting for probing the quantum phase transition between Néel antiferromagnet and columnar valence-bond solid. We analyze this transition through the scaling of Lee-Yang zeros, computed within stochastic series expansion quantum Monte Carlo by reweighting configurations sampled near criticality in the presence of complex source fields. Benchmark studies of the dimerized Heisenberg model and the checkerboard J-Q model validate the method, yielding stable O(3) critical scaling in the former and clear spacetime-volume scaling in the latter, as expected for a first-order transition. Applying the same analysis to the J-Q models, we find a pronounced and systematic drift of the leading-zero scaling with increasing system size, consistent with an extended pseudocritical regime. The Lee-Yang scaling implies an effective scaling dimension of the SO(5) order-parameter field that decreases with size and is consistent with vanishing in the thermodynamic limit. Such behavior lies below the scalar unitarity bound of any unitary relativistic conformal field theory in 2+1 dimensions and enforces inverse spacetime-volume scaling of the zeros, the hallmark of a first-order transition. These results support a weakly first-order interpretation of the Néel-VBS transition and establish finite-size Lee-Yang zeros as a sensitive, symmetry-resolved diagnostic of pseudocriticality and transition order in the J-Q family.

The simplest genuinely multidimensional monopolist's problem involves minimizing a linearly perturbed Dirichlet energy among nonnegative convex functions $u$ on an open domain $X \subset [0, \infty)^2$. The geometry of the region of strict convexity $Ω\subset X$ for the unique minimizer $u$ is of central interest. A relatively closed portion $X_1^0 \subset X$ of the domain is comprised of line segments starting and ending on $\partial X$ along which $u$ is affine. For convex polygons and potentially all domains $X \subset \mathbf{R}^2$, we build on results with Zhang to show that outside $X_1^0 \cup \{u=0\}$, the free boundary of $Ω$ is a continuous curve of Hausdorff dimension one, and that $Ω$ has density $1/2$ along it (and is $C^α_{\mathrm{loc}}$ for all $0<α<1$), except perhaps at a discrete set of singular points. We do this by showing that much of the free boundary solves an obstacle problem whose endogenous obstacle is $C^2$. From a slightly stronger conclusion, we deduce the free boundary becomes locally $C^\infty$ outside a closed set whose relative interior is empty. In response to the circulation of the present manuscript, we received a concurrent but independent work of Chen, Figalli and Zhang who verify a strengthening sufficient for this partial regularity result; (they show in particular that $α=1$ and the discrete set mentioned above is empty).

We compute the holographic Euclidean two-point function of scalar operators in a thermal state. We work directly using the Fourier series on the thermal circle. The Fourier series does not converge as a function, but instead converges as a distribution, consistent with QFT expectations. The result is manifestly periodic and consistent with analyticity in the strip $0<\mathfrak{Re}(τ)<β$. Expanding in $τ$ we obtain all OPE coefficients, including the double-trace sector. Thus our approach has an advantage compared to recent work where double-traces were bootstrapped from stress-tensor data. Bouncing singularities appear as non-perturbative sectors in the transseries for Fourier coefficients, but their transseries parameters are all zero in the case of the Euclidean correlator.

It was proposed in \cite{Chu:2024qil} that a quantum black hole can be described by a quantum space configuration of a fuzzy sphere together with a half-filled Fermi sea. In this paper we propose that the tunneling of the fuzzy sphere system to a small one describes the quantum decay of black hole by Hawking radiation. Since the Fermi sea shrinks and the quantum mechanical Hamiltonian conserves fermion number, the amplitude of transition naively vanishes unless the tunneling path provides exact number of zero modes to soak up the excess fermi states. We show that a monopole on fuzzy sphere does exactly that. This fixes the tunneling path. The resulting tunneling rate reproduces Page's result for the semi-classical decay rate of black hole. The quantum states released by the monopole corresponds to gravitational Hawking radiation. At the level of probability, the Hawking radiation is found to be given by a Boltzmann distribution at the Hawking temperature. One can go beyond the probabilistic description by determining the full wave function of the multi-partite Hawking quanta. This is possible with a real time formulation of the tunneling process. Unitarity is manifest in our quantum mechanics.

Sixth-generation (6G) communication systems are expected to support direct-to-device (D2D) connectivity, enabling standard user equipment (UE) to seamlessly transition to non-terrestrial network (NTN), particularly satellite communication mode, when operating beyond terrestrial network (TN) coverage. This D2D concept does not require hardware modifications to conventional UEs and eliminates the need for dedicated satellite ground terminals. D2D-capable UEs can be mounted on both manned and unmanned aircraft, however, they are especially well-suited for low-altitude unmanned aircraft due to their compact form factor, lightweight design, energy efficiency, and TN-NTN roaming capabilities. D2D can also enable beyond-visual-line-of-sight operation by providing NTN support for Communications, Navigation, and Surveillance (CNS) services during TN outages or congestion. This paper investigates the capabilities and limitations of D2D connectivity for low-altitude unmanned aircraft operating in urban environments. We analyze the variation in line-of-sight probability for both TN and NTN links as a function of aircraft altitude. We further compute path loss and received signal strength while accounting for a representative TN deployment with down-tilted antennas. The results show that the TN and NTN links complement each other, significantly improving the availability of the CNS service at low altitudes. These findings provide insights to support the design and optimization of future 6G-enabled integrated CNS services.

We present near-term quantum algorithms for auxiliary-field quantum Monte Carlo (AFQMC), viewed as imaginary-time projection for ground-state calculation as an ensemble of one-body propagators driven by stochastic fields $Ω$. Starting from the Feynman-Kac formula, we convert each trajectory into a sequence of piecewise-constant one-body generators using stochastic Magnus expansions up to second order, and embed the resulting nonunitary slices into unitaries with a small ancilla overhead. This lifts the projector dynamics to a unitary evolution, enabling coherent circuit execution in the regime $\|Ω\| τ=O(1)$ and reducing the need for frequent mid-circuit measurement. We further derive an equivalent linear-combination-of-unitaries (LCU) form that yields system-only, shallower circuits by trading ancilla cost for additional trajectory sampling. Benchmarks on the Hubbard model verify the accuracy of the dilation and Magnus expansions classically and demonstrate multi-step executions on IBM quantum hardware.