We develop an extended Onsager real-cavity framework to describe the Casimir--Polder interaction of small molecules dissolved in dielectric liquids near planar interfaces. By analytically resolving the geometry of the cavity opening, we derive closed-form expressions that capture the modification of the interaction as the molecule approaches a surface and connect smoothly to the asymptotic medium-assisted limit. Using experimentally established dielectric functions for water, propanol, and PTFE together with accurate molecular polarisabilities for O$_2$ and N$_2$, we compute the full distance-dependent potential for representative molecule--liquid--surface combinations. The results reveal how local-field screening, cavity geometry, and material response jointly determine both the magnitude and shape of the interaction, including the characteristic transition between open-cavity ($z\lesssim z_{\rm C}$) and closed-cavity ($z\gtrsim z_{\rm C}$) regimes. Beyond providing quantitative predictions, the framework offers an analytically transparent decomposition of dispersion forces in liquids, enabling a direct identification of the underlying physical contributions and an efficient exploration of parameter dependencies across different systems. The approach thus provides a useful baseline for interpreting dispersion interactions in complex environments within a continuum, local-field corrected description.

We initiate the study of complex rank analogues of parabolic categories $\mathcal{O}$ for general linear Lie algebras defined via Deligne's interpolating categories. We regard these categories as a family varying over an affine parameter space and conjecture that their structure is controlled by a countable locally finite hyperplane arrangement, that is, they are constant along facets. We prove this conjecture on admissible facets using the theory of $\mathfrak{sl}_{\mathbb{Z}}$-categorification. The main technical ingredient is a uniqueness theorem for highest weight categories equipped with a categorical type A action categorifying an ordered tensor product of highest and lowest Fock space representations of $\mathfrak{sl}_{\mathbb{Z}}$. Under some combinatorial conditions on the parameters, this rigidity result allows us to compare complex rank category $\mathcal{O}$ with stable limits of classical parabolic categories $\mathcal{O}$. These equivalences yield character formulas for simple objects in terms of stable limits of parabolic Kazhdan--Lusztig polynomials, answering a problem posed by Etingof. For the case of two Levi blocks of non-integral size, the admissibility assumption is unnecessary, giving a complete description in terms of stable representation theory. As an application, we obtain multiplicities for parabolic analogs of hyperalgebra Verma modules in the large rank and large characteristic limit.

This paper explores the proof by J. Bourgain, H. Furstenberg, Y. Katznelson and D.S. Ornstein of their return times theorem [2] and lights a corner in it regarding the role of auto-correlation. As for pointwise convergence, this was already observed in [5], and here we exploit the opportunity to write down the proof. This yields a more intrinsic characterization of the sequences satisfying the pointwise theorem. Then we proceed and obtain a characterization linked to auto-correlation also to sequences satisfying the mean theorem - by that theorem those were already known to be exactly the sequences with an empty Fourier-Bohr spectrum. Some further investigation is done and examples are provided regarding generic sequences satisfying the pointwise theorem for which the measure on the circle that the auto-correlation function represents (by Fourier transform) is not atomless, and also regarding the existence of sequences that satisfy the mean theorem but not the pointwise one.

We prove a local self-improving property for the gradient of very weak solutions to degenerate parabolic double-phase systems. The result is based on a reverse Hölder inequality with constants that are independent of the solution. Delicate methods are required to avoid a self-referential argument. In particular, we develop a new phase analysis method.

We report on an initiative that seeks to encourage high school girls to develop critical thinking and transferable skills widely used in scientific work, as well as to generate a concrete space of opportunities for girls to experience how real science is done. Our "Niñas Atómicas" workshop combines the teaching of particle physics, electronics, programming and scientific methodology through building and operating a dedicated experiment: a muon counter. Girls from all over Chile can apply to this workshop, where every year they are guided by female scientists for two weeks. We report on the contents and methodology of our workshop and provide details on how to build the muon detector. We report results on muon flux and proper lifetime, two muon properties which can be extracted from the data collected by the girls with the muon detectors they built themselves. Insights into the girl's experiences during the 2024 and 2025 editions of the workshop are also detailed, with the aim to contribute to the wider physics education research and outreach communities.

Rotatable antenna (RA) is a promising technology that can exploit new spatial degrees-of-freedom (DoFs) by flexibly adjusting the three-dimensional (3D) boresight direction of antennas. In this letter, we investigate an RA-enhanced cell-free system for downlink transmission, where multiple RA-equipped access points (APs) cooperatively serve multiple single-antenna users over the same time-frequency resource. Specifically, we aim to maximize the sum rate of all users by jointly optimizing the AP-user associations and the RA boresight directions. Accordingly, we propose a two-stage strategy to solve the AP-user association problem, and then employ fractional programming (FP) and successive convex approximation (SCA) techniques to optimize the RA boresight directions. Numerical results demonstrate that the proposed RA-enhanced cell-free system significantly outperforms various benchmark schemes.

Among the fundamental symmetry classes of quantum chaotic systems in Dyson's threefold way, the symplectic class is rarely observed in nature. Characterized by the strongest possible level repulsion in the energy spectrum, the symplectic symmetry class also implies a double (Kramers) degeneracy of levels. Studying the spectral statistics of three quantum particles (identical bosons or mass-imbalanced fermions) in a harmonic trap, we find numerical evidence for strong level repulsion in the regime of weak contact interactions. While the statistical indicators are consistent with quantum chaos in systems with symplectic symmetry, the absence of Kramers degeneracy rules out this symmetry. In the strongly-interacting unitary limit either Poissonian or stick statistics are observed (depending on commensurability of the mass ratio) indicating regular dynamics.

In this work, we derive the renormalized expectation value of the energy--momentum tensor of a quantized charged scalar field in three-dimensional de Sitter spacetime $\mathrm{dS}_{3}$ in the presence of a uniform electric field. Using the adiabatic regularization method, ultraviolet divergences are systematically removed, yielding finite expressions for all components of the induced tensor. We analyze the behavior of the renormalized energy--momentum tensor in both the strong-field and infrared regimes. In the strong-field limit, the induced energy density exhibits a quadratic dependence on the electric field strength; however, this leading contribution is dominated by vacuum polarization effects rather than directly by the Bogoliubov particle-production component. In the infrared regime, the tensor shows a pronounced inverse-mass dependence, indicating strong infrared sensitivity characteristic of light scalar fields in de Sitter spacetime. In the conformally coupled massless limit, the renormalized trace vanishes, as expected from the absence of a genuine Weyl anomaly in odd-dimensional spacetimes. These results provide a precise characterization of vacuum polarization and infrared effects in three-dimensional de Sitter scalar QED.

We present the discovery of EP250827b/SN 2025wkm, an X-ray Flash (XRF) discovered by the Einstein Probe (EP), accompanied by a broad-line Type Ic supernova (SN Ic-BL) at $z = 0.1194$. EP250827b possesses a prompt X-ray luminosity of $\sim 10^{45} \, \rm{erg \, s^{-1}}$, lasts over 1000 seconds, and has a peak energy $E_{\rm{p}} < 1.5$ keV at 90\% confidence. SN 2025wkm possesses a double-peaked optical light curve (LC), though its bolometric luminosity plateaus after its initial peak for $\sim 20$ days, consistent with a central engine injecting additional energy into the explosion. Its spectrum transitions from a blue to red continuum with clear blueshifted broad absorption features consistent with a SN Ic-BL classification. We do not detect any transient radio emission and rule out the existence of an on-axis, energetic jet $\gtrsim 10^{50}~$erg assuming a typical LGRB circumburst constant density ($n \approx 10^{-3}$--$10^{-1}~{\rm cm}^{-3}$) and microphysical parameters ($ε_{\rm e} = 0.1$ and $ε_{\rm B} = 0.01$). In the model we invoke, the collapse gives rise to a long-lived magnetar, potentially surrounded by an accretion disk. Magnetically--driven winds from the magnetar and the disk mix together and break out with a velocity $\sim 0.35c$ and interact with an extended circumstellar medium with radius $\sim 10^{13}$ cm, generating X-ray breakout emission through non-thermal free-free processes. The disk outflows and magnetar winds power blackbody photospheric emission as they cool adiabatically and thermalize, producing the first SN peak. The spin-down luminosity of the magnetar and radioactive decay of $^{56}$Ni powers the late-time emission. We end by discussing the landscape of XRF-SNe within the context of EP's recent discoveries.

Radial migration and dynamical heating redistribute stars within galactic discs and thereby modify the chemo-kinematic structure of their host galaxies. Usually, these secular processes are studied in N-body and hydrodynamical simulations of Milky Way analogues with stellar-dominated discs. In contrast, discs at high redshift are gas-rich, which may qualitatively change how secular evolution proceeds. We use the Nexus framework to construct and evolve a suite of isolated galaxies with fixed halo and disc mass but varying initial disc gas fraction, from 0% to 100%. We show that in gas-rich models, the root-mean-square change in stellar angular momentum is up to a factor of two larger than in gas-poor analogues and is accompanied by stronger radial and vertical heating, leading to enhanced radial mixing. We further dissect the role of gas in specific migration channels. For bar-driven migration, corotation resonance dragging dominates in gas-poor discs, whereas in gas-rich discs, stars more readily reach and accumulate at the outer Lindblad resonance, which acts as a barrier. The high radial mixing efficiency in gas-rich phases can flatten the stellar metallicity gradient relative to that of the initial gaseous disc within only a few orbital timescales. Together, these results imply that radial mixing in early, gas-rich discs is substantially more vigorous than in late-time, gas-poor discs, naturally producing distinct evolutionary tracks for chemically bimodal discs such as that of the Milky Way.

In this paper we examine the topology of manifolds equipped with a local quaternionic toric action modeled on the regular representation of the quaternionic torus $Q^n=(S^3)^n$. Building on our previous work, where the toric, differential and tetraplectic foundations were established, we show that the global topology of such manifolds is determined by the orbit space and its characteristic data. We construct Leray--Serre and Atiyah--Hirzebruch spectral sequences for the orbit projection, yielding explicit descriptions of the cohomology and $K$-theory of manifolds equipped with local quaternionic toric actions. In dimension four, we develop a quaternionic analogue of the Meyer signature formula and we briefly outline an $L$-theoretic interpretation of the resulting signature invariants. These results extend the methods of the classical (complex) toric topology to the quaternionic setting.

The main objective of this paper is to propose a new approach for estimating the entire collection of Sobol' indices simultaneously. Our approach exploits the fact that Sobol' indices can be rewritten as solutions to an optimisation problem over the simplex of $\R^d$, to construct an online sequence of estimators using a stochastic mirror descent algorithm. We prove that our estimation procedure is consistent and provide a non-asymptotic upper bound for its rate of convergence. Furthermore, we demonstrate the numerical accuracy of our method and compare it with other classical estimation procedures.

We present a new approach for extracting information about cosmic magnetic fields using cross-correlations between extragalactic Faraday rotation measure (RM) catalogs and galaxy surveys. Specifically, we propose measuring the two-point cross-correlation between RM squared, ${\rm RM}^2$, towards background sources and the projected density field of foreground galaxies, $\langle {\rm RM}^2 \times {\rm g} \rangle$, as a function of transverse separation. This statistic is analogous to the ''projected fields'' estimator used for the kinetic Sunyaev-Zel'dovich (kSZ) effect, $\langle {\rm kSZ}^2 \times {\rm g} \rangle$. Our estimator avoids contamination, and is also free from the noise bias that arises when correlating the absolute value of the RMs with galaxies. Moreover, by binning in foreground galaxy redshifts, $\langle {\rm RM}^2 \times {\rm g} \rangle$ enables a tomographic reconstruction of the redshift evolution of large-scale cosmic magnetic fields. We model this statistic using the Illustris-TNG cosmological magnetohydrodynamic simulations and compare with approximate analytic predictions. We show that $\langle {\rm RM}^2 \times {\rm g} \rangle$ can be related to a bispectrum involving two copies of the electron-density--weighted magnetic field strength and one of the galaxy overdensity. In Illustris-TNG, the effective field strength is primarily set by the magnetic field amplitudes within the inner regions of galaxy-hosting dark matter halos. It increases towards low redshift, driven by dynamo amplification and magnetized outflows. Our forecasts suggest that $\langle {\rm RM}^2 \times {\rm g} \rangle$ is detectable at high significance with current galaxy surveys and future RM catalogs from the SKA, offering a tomographic probe of large-scale magnetic fields across cosmic time.

In the category of modules, injective and projective objects are characterized by the splitting of short exact sequences. Motivated by this principle, we investigate analogous phenomena in the category of finite-dimensional Lie algebras over a field of characteristic zero. Since this category is not abelian, extensions admit two distinct notions of splitting, which we call \emph{trivial} and \emph{semi-trivial}. The first main result establishes the converse of Jacobson's classical theorem: a Lie algebra $\A$ trivially splits every extension by it if and only if $\A$ is complete. This identifies completeness as the ``injective-type'' property in this category -- although, seemingly weaker than category-specific injectivity. By contrast, no nontrivial Lie algebra has the dual property: the second main result asserts that, for every nontrivial Lie algebra $\Cc$, some extension of $\Cc$ fails to split trivially, so no ``projective-type'' analogue exists. Restricting to central extensions restores a workable dual notion: a Lie algebra $\Cc$ is called cocomplete if every central extension of it splits trivially, and we prove that this holds if and only if $H^2(\Cc, \K) = 0$; in particular, semisimple Lie algebras are both complete and cocomplete. Each of these results admits an equivalent homomorphism-lifting reformulation, paralleling the lifting properties of injective and projective modules. For almost abelian Lie algebras, cocompleteness reduces to an explicit spectral condition on the defining derivation. These characterizations underlie three corresponding algorithms, which yield tabulations of the complete, the cocomplete, and the almost abelian cocomplete Lie algebras of dimension at most 4.

Large Language Models (LLMs) are increasingly used to query knowledge graphs (KGs) due to their strong semantic understanding and extrapolation capabilities compared to traditional approaches. However, when KGs contain sensitive information and users lack local access to generative models, privacy becomes a critical concern. To address this issue, we propose a privacy-aware query generation approach for KGs. Our method identifies sensitive information in the graph based on its structure and omits such values before requesting the LLM to translate natural language questions into Cypher queries. Experimental results show that our approach effectively prevents sensitive data from being transmitted to third-party services, while maintaining a high level of query accuracy.

In comparisons of precision measurements at colliders to the most accurate predictions available in perturbative quantum chromodynamics (QCD), it is required to correct for nonperturbative effects. By means of Monte Carlo event generators this article investigates the impact of such nonperturbative effects on two processes relevant for precision determinations of the strong coupling constant and the proton structure: triple-differential dijet and Z+jet production. We observe significant differences between the two processes. Whether this non-universal behaviour is realized in nature remains an open question. We therefore propose a triple-differential measurement of the underlying event in Z+jet production.

We establish the existence of weak solutions of coupled systems of elliptic partial differential equations with quasimonotone nonlinearities in the differential equation and on the boundary.

Double Machine Learning is widely used to estimate treatment effects from non-experimental data. The "residuals-on-residuals" regression (RORR) is especially popular for its simplicity and computational tractability. However, with heterogeneous treatment effects, the proper interpretation of RORR may not be well understood. We show that, for non-binary treatments with continuous dose-response functions, RORR estimates a conditional variance-weighted average of derivatives evaluated at treatment values not in the observed dataset. This estimand does not equal the Average Causal Derivative (ACD) in general. Hence, even if all units share the same dose-response function, RORR does not estimate an average treatment effect in the population represented by the sample. We propose an alternative estimator for the ACD that is well suited to the large datasets found in applied data science settings. We demonstrate the pitfalls of RORR and the favorable properties of the proposed estimator through an illustrative numerical example and with real-world data from Netflix. Our methodology is used by default in Netflix's observational causal inference platform, where it regularly powers causal research and decision-making at scale.

Optimizing modern wireless networks is exceptionally challenging due to their high dynamism and complexity. While the AI agent powered by reinforcement learning (RL) offers a promising solution, its practical application is limited by prohibitive exploration costs and potential risks in the real world. The emerging digital twin (DT) technology provides a safe and controlled virtual environment for agent training, but its effectiveness critically depends on the DT's reliability. Policies trained in an unreliable DT that does not accurately represent the physical network may experience severe performance degradation upon real-world deployment. In this article, we introduce a new DT evaluation framework to ensure trustworthy DTs in AI agent-based network optimization. This framework shifts from model-level accuracy, such as wireless channel and user trajectory similarities, to a more holistic, task-centric DT assessment, which relies on the Markov decision process that the agent actually perceives. We demonstrate it as an effective guideline for design, selection, and lifecycle management of wireless network DTs. A comprehensive case study on a real-world wireless network testbed shows how this evaluation framework is used to pre-filter candidate DTs, leading to a significant reduction in training and testing costs without sacrificing deployment performance. Finally, potential research opportunities are discussed.

The generation of white noise on large scales is a generic property of the dynamics of physical systems described by local non-linear partial differential equations. Non-linearities prevent the small scale dynamics from being erased by smoothing. Unresolved small scale dynamics act as an uncorrelated (white or Poissonian) noise (seemingly stochastic but actually deterministic) contribution to large scale dynamics. This white noise exists even when the dynamics is very nearly linear. In cases where the power spectrum is sub-Poissonian on large scales, this noise will dominate on the largest scale power no matter the amplitude of the inhomogeneities. Such is the case in the standard model of cosmology, where the primordial density power spectrum is expected to have an almost Harrison-Zel'dovich, $P[k]\sim k$, spectrum on a much broader range of scales than can be observed. Even though linear gravitational evolution dominates non-linear corrections by a factor $\sim10^5$, the non-observation of white noise on the Hubble scale precludes the extrapolation of this power law below the comoving $1\,$pc scale. More generally, observation or non-observation of large scale white noise provides a powerful probe of the universe on very small scales in the early early universe. Gravitational radiation, phase transitions, vorticity, and running of the spectral index are all phenomena that can be probed with large scale white noise. Large scale white noise is a non-optional feature of all cosmological models but one which has not heretofore been appreciated.

Caffarelli's contraction theorem bounds the derivative of the optimal transport map between a log-convex measure and a strongly log-concave measure. We show that an analogous phenomenon holds on the level of the trace: The trace of the derivative of the optimal transport map between a log-subharmonic measure and a strongly log-concave measure is bounded. We show that this trace bound has a number of consequences pertaining to volume-contracting transport maps, majorization and its monotonicity along Wasserstein geodesics, growth estimates of log-subharmonic functions, the Wehrl conjecture for Glauber states, and two-dimensional Coulomb gases. We also discuss volume-contraction properties for the Kim-Milman transport map

The interplay between external gauge fields and lattice geometry can induce extreme localization dynamics through complete destructive interference. We show that combining this flux-induced localization with engineered dissipation leads to robust spin synchronization in rotationally symmetric spin geometries, referred to as Aharonov-Bohm motifs, with cyclic symmetries of any order. The synchronized dynamics is independent of initial conditions and features entanglement among spins within each motif. We further demonstrate that multiple motifs can fully synchronize when coupled, which is achieved by applying additional collective dissipation acting on all intra-motif spins. These results reveal a direct connection between flux-induced localization, dissipative engineering, and collective quantum synchronization.

Quantum approaches to combinatorial optimization problems (COPs) are often limited by the resource demands of Quadratic Unconstrained Binary Optimization (QUBO) encodings, which enlarge circuits through penalty terms and increase qubit and gate counts. We show that Higher-Order Unconstrained Binary Optimization (HUBO) enables a more resource-efficient formulation. Our method systematically constructs HUBO Hamiltonians and, compared to a QUBO formulation in benchmarks on Gate Assignment (GAP), Maximum k-Colorable Subgraph (MkCS), and Integer Programming (IP) problems, significantly reduces qubit requirements and decreases total CNOT gate counts by at least 89.6% for all tested instances. These results highlight HUBO as a practical alternative for quantum optimization on near-term devices. To promote adoption, we release an open-source Python library that automates HUBO model construction, extends beyond the examples presented in this work, and broadens access to resource-efficient quantum optimization.

The internal structure of exotic hadrons remains one of the most compelling puzzles in strong interaction physics. In this work, we provide crucial insights into the nature of doubly-charmed pentaquarks by investigating their electromagnetic properties. Using QCD light-cone sum rules, we present the first comprehensive calculation of the magnetic dipole moments of $DΛ_c$, $D^*Λ_c$, and $DΛ_c^*$ molecular pentaquarks with $J^P = \frac{1}{2}^-$, $\frac{3}{2}^-$, and $\frac{3}{2}^-$, respectively. Our analysis reveals a striking hierarchy of magnetic moments: $μ_{DΛ_c^*} > μ_{D^*Λ_c} > μ_{DΛ_c}$, driven by distinct quark-level mechanisms. While light quarks dominate the overall response, we find that charm quark contributions become strategically important when light quark contributions partially cancel. Beyond dipole moments, we predict higher multipoles--electric quadrupole and magnetic octupole moments--for the spin-$3/2$ $D^*Λ_c$ and $DΛ_c^*$ states, which fingerprint the spatial deformation of these configurations, revealing prolate versus oblate charge distributions. These results provide the first systematic predictions for electromagnetic moments of molecular pentaquark configurations, establishing essential benchmarks for future theoretical and experimental studies. By systematically comparing our predictions with both compact doubly-charmed and hidden-charm pentaquark configurations, we establish robust benchmarks that discriminate between competing structural models, ultimately resolving the nature of doubly-charmed exotic hadrons.

Two-level system (TLS) defects in dielectrics are a major source of decoherence in superconducting circuits, yet their microscopic origin and distribution remain poorly understood. Existing circuit-QED probes access limited frequency ranges and mode volumes, restricting studies of isolated materials and interfaces. Here, we present Broadband Cryogenic Transient Dielectric Spectroscopy (BCTDS), a technique for probing TLS-hosting materials over a broad frequency range at cryogenic temperatures. Under strong finite-duration microwave excitation, the transient homodyne I-Q response exhibits coherent phase dynamics after the drive is turned off. Fourier analysis of the transient phase reveals characteristic V-shaped structures that move between cooldowns, consistent with thermocycling-induced changes in the local TLS defect environment that shift defect resonance frequencies. The transient response of BCTDS further enables estimation of susceptibility and two-time correlation functions of the TLS defect ensemble. The observed phase dynamics are qualitatively captured by a driven standard tunneling model containing only a few representative TLS defects. Despite its simplicity relative to the full experimental ensemble, the model reproduces the essential Floquet-dressed dynamics during the drive and generates post-pulse V-shaped structures and interference fringes consistent with the experimental data. The observed BCTDS response may reflect a crossover from localized TLS defect dynamics to a delocalized regime under strong driving, before being quenched into a transient regime that reflects the TLS defect resonance frequencies. Overall, BCTDS represents a potentially useful broadband, time-resolved wafer-level approach for probing TLS defects relevant to quantum technologies.

Small solar system bodies (SSSB), which in this study are defined primarily as asteroids and comets, are becoming increasingly important as more data have become available for their study. Their significance is also highlighted by missions like NASA's OSIRIS-REx or ESA's Rosetta. However, the study of the characteristics and behavior of these objects on Earth is a challenge as the simulation of their environmental conditions are difficult. We present in this paper an approach to enable the gravity simulation of SSSBs such as comets or asteroids in a drop tower facility on Earth, which is being addressed as part of the AKUS ("Activity of Comets under Partial Gravity") project. This especially concerns gravity levels between 10$^{-2}$~\textit{g} and 10$^{-4}$~\textit{g}, where the duration of the adjusted acceleration ranges from 2.5 to 3.2 seconds. In order to simulate the conditions of SSSB as accurately as possible, an acceleration system based on servo motors and spindle axes has been developed. The accelerations are transferred from the motors to the spindle axes containing a comet-like sample. The current dimensions of the total load (including sample, sample holder, data- and communication box) are 315~mm x 160~mm x 331~mm (w x d x h), with a total weight of approximately 15~kg. These are together placed inside a vacuum chamber providing a vacuum quality of 10$^{-6}$~mbar. The whole setup is installed inside the Einstein-Elevator. Our results show that, with the current setup, we are able to generate conditions from 10$^{-2}$~\textit{g} down to 10$^{-3}$~\textit{g}. The maximum deviations under these conditions are $\pm5$$\cdot 10^{-4}$~\textit{g}.

Uncrewed Aerial Vehicles (UAVs) serving as Aerial Base Stations (ABSs) are expected to extend 6G millimeter-Wave (mmWave) coverage and improve link reliability in urban areas. However, UAV-based Air-to-Ground (A2G) channels are highly dependent on height and urban geometry. This paper proposes an ABS height-dependent mmWave channel model and investigates whether urban geometry, beyond the standard built-up parameters, significantly affects LoS probability (PLoS) and Large-Scale Fading (LSF). Using MATLAB ray tracing at 26 GHz, we simulate approximately 10K city realizations for four urban layouts that share identical built-up parameters but differ in their spatial organization. We extract elevation-based PLoS using a sigmoid model and derive height-dependent Path-Loss Exponents (PLEs) and shadow-fading trends using exponential fits. Results show that PLE for Non-Line-of-Sight (NLoS) decreases toward 2.5-3 at high altitudes, Line-of-Sight (LoS) PLE remains near 2, and shadow fading reduces with height. We also find that geometric layout introduces a modest but consistent change in PLE (+/- 0.2), even when built-up parameters are fixed. The proposed unified model aligns well with ray-tracing statistics and offers a practical, height-dependent LSF model suitable for ABS planning in complex urban scenarios.

This paper introduces a generalized descent algorithm (DEAL) for minimizing smooth nonconvex functions. If the objective function is nonsmooth, a smoothing technique (e.g., forward-backward and high-order Moreau envelopes) is applied to generate a smooth counterpart. The proposed framework unifies several methods, such as gradient-based methods with constant step-sizes and Armijo line search, and several proximal splitting methods. The method is built around a generalized descent inequality that adapts the amount of decrease to the geometry of the objective function. Under the Kurdyka-Łojasiewicz (KL) property, we establish global convergence of the generated sequence to critical points and provide a unified convergence rate analysis. In particular, we show that the convergence behavior depends jointly on the KL exponent and the descent order, and we identify a precise condition under which generalized descent methods achieve linear convergence. By choosing the order of high-order proximal regularization according to the KL exponent, our boosted high-order proximal-point method achieves linear convergence for arbitrary KL exponents. If the objective function satisfies a global KL inequality, we further strengthen the results by proving convergence to global minimizers and deriving explicit iteration-complexity bounds. Numerical experiments validate our theoretical foundation.

The integration of diamond with $β$-Ga$_2$O$_3$ presents a promising pathway to enhance thermal management in high-power electronic devices, where the inherently low thermal conductivity of $β$-Ga$_2$O$_3$ can lead to localized self-heating and elevated junction temperatures. In this work, we demonstrate a scalable, low-damage approach for integrating polycrystalline diamond films on (010) $β$-Ga$_2$O$_3$ substrates via microwave plasma chemical vapor deposition (MPCVD), employing dielectric interlayers and polymer-assisted electrostatic nanodiamond seeding to systematically evaluate the impact of growth conditions on film morphology, grain evolution, phase purity, and optical characteristics. At a growth temperature of 800$^\circ$C, progressive grain coarsening is observed with extended deposition, with the lateral grain size increasing from 37.6 nm (53 nm thickness) to 192.5 nm for an 886 nm-thick film. This microstructural evolution is accompanied by narrowing of the diamond Raman peak and a monotonic increase in the sp$^3$ phase fraction from 95.9\% to as high as 98.9\%, indicating continued suppression of non-diamond carbon with prolonged growth. Comparison of SiO$_2$ and SiN$_x$ interlayers under identical growth conditions shows only marginal differences in grain size and phase purity, indicating limited interlayer influence once a high nucleation density is established. Importantly, diamond films exhibiting greater than 96\% sp$^3$ phase content were achieved at substrate temperatures as low as 480$^\circ$C, highlighting the viability of diamond-on-Ga$_2$O$_3$ integration under reduced thermal budgets. These findings establish a robust and scalable platform for integrating diamond on $β$-Ga$_2$O$_3$, supporting the development of next-generation power and RF devices with improved thermal management.

We present the first study of jet substructure modifications during the bottom-up evolution that describes the early stages of heavy-ion collisions. To this end, we study the bremsstrahlung radiation rate of soft gluons from a hard parton propagating through out-of-equilibrium QCD matter. The gluon spectrum is computed within the Improved Opacity Expansion, which accounts for both multiple soft and single hard momentum exchanges between the hard probe and the medium. The background evolution is obtained from effective kinetic theory simulations that determine the jet quenching parameter, which in turn controls the radiation rate. We compute the radiation rate for initially under- and over-occupied systems, as well as for an expanding system undergoing hydrodynamization, which typically represents the initial stages of heavy-ion collisions. The results for these dynamical backgrounds are compared to static and thermally matched scenarios, allowing to gauge the importance of bulk expansion in the evolution of the jet cascade. Our findings show that the early stages of the bulk matter evolution in heavy-ion collisions leave a sizable imprint on the radiation pattern inside jets. These results establish a basis for incorporating pre-equilibrium dynamics into realistic descriptions of jet quenching and hard-probe evolution.