The next generation of cellular networks is designed to provide ubiquitous connectivity to a wide range of devices. As Telecommunication Service Providers (TSPs) increasingly collaborate with public cloud providers to deploy 5G and beyond networks, a fundamental shift is underway, from hardware-bound Physical Network Functions (PNFs) to cloud-native, containerized deployments managed through platforms like Kubernetes. While this transition promises greater scalability, flexibility, and cost efficiency, it also introduces a complex set of technical and operational challenges that must be thoroughly understood before large-scale cellular deployments can take place in cloud environments. In this survey, we present a structured taxonomy that categorizes the design space of cloud-based cellular deployments across four dimensions: deployment architecture, resource management and orchestration, multi-tenancy and isolation, and economic and ownership models. Using this taxonomy as a foundation, we critically analyze six key investigation areas, security and privacy, scalability and elasticity, performance and latency, cost optimization, resilience and fault management, and compliance and sovereignty, examining each through a cloud-native lens. To benchmark the state of industry adoption, we examine the deployment strategies of leading Infrastructure-as-a-Service (IaaS) providers, namely Amazon Web Services (AWS), Microsoft Azure, and Google Cloud Platform (GCP). Finally, we identify emerging trends such as AI-driven orchestration, quantum-safe protocols for virtualized network functions, and serverless networking for 6G, while articulating the open challenges that remain in realizing robust, scalable cloud-based cellular networks.

This letter proposes a linear bandit-based beam training framework for near-field communication under multi-path channels. By leveraging Thompson Sampling (TS), the framework adaptively balances exploration and exploitation to maximize cumulative beamforming gain under limited pilot overhead. To ensure data-efficient learning, we incorporate a correlated Gaussian prior in the DFT domain, using a Gaussian kernel to capture spatial correlations and near-field energy leakage. We develop three TS strategies: codebook-constrained search for rapid convergence via structural regularization, continuous-space search to achieve near-optimal performance, and a two-stage hybrid refinement scheme that balances convergence speed and estimation accuracy. Simulation results show that the proposed framework reduces pilot overhead by up to 90\% while achieving more than a 2dB SNR gain over baselines in multipath environments. Furthermore, the continuous-space search is shown to be asymptotically optimal, approaching the full-CSI bound when the pilot overhead is unconstrained.

The second edition of the TREC Retrieval Augmented Generation (RAG) Track advances research on systems that integrate retrieval and generation to address complex, real-world information needs. Building on the foundation of the inaugural 2024 track, this year's challenge introduces long, multi-sentence narrative queries to better reflect the deep search task with the growing demand for reasoning-driven responses. Participants are tasked with designing pipelines that combine retrieval and generation while ensuring transparency and factual grounding. The track leverages the MS MARCO V2.1 corpus and employs a multi-layered evaluation framework encompassing relevance assessment, response completeness, attribution verification, and agreement analysis. By emphasizing multi-faceted narratives and attribution-rich answers from over 150 submissions this year, the TREC 2025 RAG Track aims to foster innovation in creating trustworthy, context-aware systems for retrieval augmented generation.

The main objective of this thesis has been to analyse soliton dynamics in detail, with special attention paid to the role of the internal modes associated with these configurations. Specifically, the thesis has focused on the study of one- and two-dimensional models, with the aim of developing a solid basis that can then be extended to the study in three-dimensional theories. This thesis concentrates on the study of kinks, oscillons, vortices, and sphalerons. Nevertheless, field theories constitute systems with an infinite number of degrees of freedom, which poses challenges both for obtaining analytical results and for predictive modeling. To address these challenges, this thesis employs the construction of effective models that retain the essential degrees of freedom required to capture the phenomenology observed in numerical simulations of the full theory, using the well-known collective coordinate method. In addition, other complementary mathematical tools, such as perturbative techniques, have also been employed. Among the main achievements of this doctoral thesis, it is worth highlighting the introduction, for the first time, of genuine radiation modes within the collective coordinate framework. Furthermore, a generalisation of Samols' moduli space metric for local vortices in the Abelian-Higgs model has been developed through the incorporation of vibrational degrees of freedom. Additionally, a new class of sphalerons that we have coined semi-BPS sphalerons has been identified and analysed. Finally, the role of oscillatory internal modes in the decay process of sphalerons has been studied in detail, leading to the proposal of a dynamic stabilisation mechanism. This mechanism has been further explained and extended to more general models, demonstrating the robustness and potential applicability of this phenomenon to physically relevant theories.

The advent of high-precision Gaia parallaxes for Milky Way Cepheids enables per cent-level calibration of the local distance ladder and $H_0$. We revisit the Milky Way Cepheid calibration from Gaia EDR3 parallaxes using a fully forward-modelled Bayesian framework that simultaneously infers the period--luminosity relation, the Gaia parallax zero-point offset, and individual stellar distances while explicitly incorporating the disk geometry of the Galaxy through the distance prior and the selection functions specified in two distinct HST SH0ES campaigns. We derive an analytic treatment of the detection probability that accounts for magnitude, parallax, period, and extinction cuts and reduces the selection treatment to a tractable integral over distance and sky position. Posterior predictive checks show that this generative model matches well the observed distributions of parallaxes, magnitudes, and periods. Modelling Galactic structure and survey truncation self-consistently in a Bayesian framework yields period--luminosity parameters that agree with the SH0ES maximum-likelihood values at the ${<}0.5\,σ$ level, a consequence, we show, of the small intrinsic scatter of the Cepheid period--luminosity relation. Adopting, as recently advocated, a uniform-in-volume prior without simultaneously accounting for selection leads to a ${\sim}\,0.05~\mathrm{mag}$ bias in the period--luminosity zero-point and posterior predictive distributions incompatible with the observed data; this shift is mostly driven by the omission of the selection model. A consistent Bayesian treatment of Galactic structure and selection effects reinforces the local distance-ladder determination of $H_0$, and hence the Hubble tension with early-Universe inferences.

A 3 bit Analog to Digital Converter (ADC) is designed using perpendicular Spin Orbit Torque Magnetic Tunnel Junction (SOT MTJ). A sampled analog input signal is transmitted as a spin orbit torque current (Iin) to a perpendicular SOT MTJ, and deterministic switching is supported by the Voltage Controlled Magnetic Anisotropy (VCMA) and Spin Transfer Torque (STT) switching methods. Analog to digital conversion is done by comparing input signal with varied critical current of SOT MTJs. The critical current of each is SOT MTJ governed by varying widths of Heavy Metal (HM). In the 3 bit ADC, there are two sets of 7 SOT MTJs for quantizing input value, a conversion set and dummy set for comparing the change in resistance state. As input signal passed through conversion set SOT MTJs switches from Parallel (P) to AntiParallel (AP) state if the input signal exceeds its critical current. The conversion set change in state is converted to thermometer codes by StrongARM latch comparator by comparing the resistance with dummy set SOT MTJs, where all the in P state or low resistance. A novel architecture is proposed for increasing speed of throughput, by utilizing the dummy set of as a conversion set and conversion set as dummy set, thus eliminating the reset step from analog to digital conversion. And by improving SOT-MTJ and timing blocks a field free spin flash ADC has a power consumption of 476 uW with a conversion rate of 304.1 MHz is produced.

The temporal assumptions underpinning conventional Identity and Access Management collapse under agentic execution regimes. A sixty-second revocation window permits on the order of $6 \times 10^3$ unauthorized API calls at 100 ops/tick; at AWS Lambda scale, the figure approaches $6 \times 10^5$. This is a coherence problem, not merely a latency problem. We define a Capability Coherence System (CCS) and construct a state-mapping $φ: Σ_{\rm MESI} \to Σ_{\rm auth}$ preserving transition structure under bounded-staleness semantics. A safety theorem bounds unauthorized operations for the execution-count Release Consistency-directed Coherence (RCC) strategy at $D_{\rm rcc} \leq n$, independent of agent velocity $v$ -- a qualitative departure from the $O(v \cdot \mathrm{TTL})$ scaling of time-bounded strategies. Tick-based discrete event simulation across three business-contextualised scenarios (four strategies, ten deterministic seeds each) confirms: RCC achieves a $120\times$ reduction versus TTL-based lease in the high-velocity scenario (50 vs. 6,000 unauthorized operations), and $184\times$ under anomaly-triggered revocation. Zero bound violations across all 120 runs confirm the per-capability safety guarantee. Simulation code: https://github.com/hipvlady/prizm

Recent models and simulations of cluster formation within molecular clumps consider multi-scale, hierarchical accretion, which leads to clump mass growth over time. This mode of mass accumulation could have implications regarding the evolution of observable properties such as mass and radius, bringing into question the interpretation of commonly cited thresholds for high-mass star formation. In this paper, we use the conveyor belt model of cluster formation to create synthetic cores/clumps and derive physical and observational properties. We show that while this model successfully predicts many observed trends, modifications are required to match properties of high-mass prestellar clumps. When the model clumps are observationally classified as intermediate- or high-mass star-forming, the threshold delineating these two groups agrees with those found in the literature; however, results show that high-mass clumps at early evolutionary stages can be misclassified using standard surface density thresholds. Our logistic regression analysis reveals the quantity of material to ever enter a star-forming region is the most important factor in differentiating intermediate- and high-mass star-forming regions. This implies observations characterising the environment surrounding star-forming regions are crucial, especially at early evolutionary stages.

Direct laser writing of ferromagnetic microstructures is of great interest for sensing and data storage in compact three-dimensional architectures. However, reliable direct laser writing of metallic and even more so ferromagnetic materials remains a major challenge. Here, we present a novel photoresist suitable to direct laser write ferromagnetic nickel based on sensitized triplet-triplet annihilation upconversion. By combining an in-situ photochemical deoxygenation process with a sensitized triplet-triplet annihilation upconversion process as well as a photoreduction of Ni2+ ions, the deposition of metallic nickel is enabled under ambient conditions. Using this approach, nickel structures are fabricated as a proof of concept. Scanning electron microscopy and EDX analysis confirm the spatially confined deposition of nickel, while magnetic characterization by vibrating sample magnetometry and scanning NV magnetometry demonstrate the ferromagnetic nature of the printed structures. This work presents a major step forward in extending the possibilities of direct laser writing to metallic and ferromagnetic materials.

In recent years, several architectures have been proposed for implementing two-qubit operations on fluxonium superconducting qubits. A particularly promising approach, which was demonstrated experimentally by Refs. [1,2], employs a transmon superconducting qubit as a tunable coupler between the fluxonium qubits. These experiments have shown that the transmon coupler enables fast, high-fidelity two-qubit operations while suppressing unwanted ZZ crosstalk between the fluxonium qubits. In this work, we numerically study the scalability of this architecture. We find that, when trivially scaling this architecture, crosstalk from spectator qubits limits the gate fidelity to below 90%. We show that these spectator errors can be reduced to below $10^{-4}$ by reducing the coupling strength and by dynamically tuning transmons that are not used for a two-qubit operation to an off position. We further investigate the resilience of the operation to direct capacitive coupling between the transmon couplers and to microwave crosstalk.

Quantifying the timescales of star cluster emergence from their natal clouds remains one of the main challenges in our understanding of the star formation process. These timescales are fundamental measurements of the star formation cycle within galaxies, yet they are difficult to constrain due to the complex interplay between stellar feedback and star formation across a vast range of physical scales. Here we present HST and JWST observations of thousands of young star clusters in four nearby galaxies (M51, M83, NGC 628, and NGC 4449). A substantial fraction of these clusters are still embedded within their natal gas and remain invisible at optical wavelengths. We constrain their emergence process by measuring the timescales required to disperse the surrounding material. We find a strong correlation between dispersal timescale and cluster stellar mass, with massive clusters emerging more rapidly than their lower mass counterparts. This is a critical constraint on simulations of star formation and stellar feedback, which struggle to fully reproduce the formation and emergence of star clusters. Our results emphasize the central role of massive clusters in driving the escape of ionizing radiation into the galactic medium. Finally, they impose important limitations to the time available for planet formation in massive cluster environments where disks get exposed to UV irradiation and further gas infall is shut off.

JWST can pierce through dusty molecular clouds to study the early stages of star formation, where young star clusters are actively driving stellar feedback and still emerging from their natal cloud. We present a first look of the JWST/NIRSpec multiplex spectroscopy observations acquired by the Feedback in Emerging extrAgalactic Star clusTers (FEAST) program for the nearby spiral galaxy NGC628. We showcase JWST's ability to resolve the spectral properties of emerging young star clusters (eYSCs) and their immediate interstellar medium (ISM) by focusing on a bright star-forming complex ($0.5\times0.5~\mathrm{kpc}^2$) in the northern spiral arm as a science proof-of-concept. The eYSC spectra are rich in ionized gas (from HII regions), as well as warm H$_2$ and polycyclic aromatic hydrocarbon (PAH) emission from photodissociation regions (PDRs), consistent with young star formation. $\mathrm{Pa}α$ equivalent widths and H/He ionizing photon fluxes both indicate the presence of hot, young massive stars (O8.5V-O8V), consistent with photometry SED estimates. The ionized gas is highly correlated with H$_2$ and PAH emission, suggesting that the PDR morphology evolves as clusters emerge from their natal cloud. We find a photoionization-dominated regime from independent line diagnostics, with little contribution from Supernovae-driven shocks, highlighting the importance of pre-Supernovae feedback when massive stars are present. This pilot study showcases how JWST's multiplex spectroscopy mode can disentangle the mechanisms present in the youngest stages of star formation for the first time outside the Local Group.

We consider optimization problems containing nonconvex quadratic functions for which semidefinite programming (SDP) relaxations often yield strong bounds. We investigate linear inequalities that outer approximate the positive semidefinite cone and are sparse in the sense that they are supported only on the variables corresponding to products of variables present in quadratic functions. We show that these sparse linear inequalities yield an LP relaxation that gives the same bound as the SDP relaxation. We demonstrate how to identify these inequalities via a separation procedure that involves solving a structured ``projection'' SDP. In a computational study, we find that the sparse LP relaxations defined by these inequalities can accelerate branch-and-bound methods for globally solving nonconvex optimization problems.

The realization of spin based devices is one of the most aspiring goals of spintronics research. Single molecule magnets are an important class of nanoscale magnetic systems with potential to realize different spintronic devices where each molecule can be used as a fundamental building block for devices. In this work, we have systematically investigated metallocenes, a class of single molecule magnets, with 4d and 3d transition metal elements for their electronic and magnetic anisotropic properties, using first-principles density functional theory. Among the seven 4d elements studied in this work, the largest anisotropy of about 20 Kelvin is obtained for Mo and Rh with uniaxial anisotropy. We found that the anisotropy does not increase with an increasing number of $d$ electrons; rather, it depends strongly on the orbital ordering of the $d$ states of the transition metal. Our calculations also show that the anisotropy of Mo-metallocene increases for cationic charge states to 60 Kelvin but with an easy-plane anisotropy. For 3d elements, the anisotropy of the molecules is calculated to be less than 10 Kelvin. We also have studied the role of ligands on the structural stability of these molecules and have provided a clear guideline to construct an appropriate model of molecules for theoretical studies.

The Variational Quantum Eigensolver (VQE) is a key algorithm for near-term quantum computers, yet its performance is often limited by the classical optimization of circuit parameters. We propose using the velocity Verlet algorithm, inspired by classical molecular dynamics, to address this challenge. By introducing an inertial "velocity" term, our method efficiently explores complex energy landscapes. We compare its performance against standard optimizers on H$_2$ and LiH molecules. For H$_2$, our method achieves chemical accuracy with fewer quantum circuit evaluations than L-BFGS-B. For LiH, it attains the lowest final energy, demonstrating its potential for high-accuracy VQE simulations.

Protein function is executed at the molecular surface, where shape and chemistry act together to govern interaction. Yet most comparison methods treat these aspects separately, privileging either global fold or local descriptors and missing their coupled organization. Here we introduce IFACE (Intrinsic Field-Aligned Coupled Embedding), a correspondence-based framework that aligns protein surfaces through probabilistic coupling of intrinsic geometry with spatially distributed chemical fields. From this alignment, we derive a joint geometric--chemical distance that integrates structural and physicochemical discrepancies within a single formulation. Across diverse proteins, this distance separates conformational variability from true structural divergence more effectively than fold-based similarity measures. Applied to the cytochrome P450 family, it reveals coherent family-level organization and identifies conserved buried catalytic pockets despite the complex topology. By linking interpretable surface correspondences with a unified distance, IFACE establishes a principled basis for comparing protein interfaces and detecting functionally related interaction patches across proteins.

A theoretical framework based on the Spin Density Matrix (SDM) formalism is developed to describe polarization transfer in the decay chain $e^+e^- \rightarrow ψ^\prime \rightarrow ψππ$. Explicit relations connecting the SDMs of $ψ^\prime$ and $ψ$ are derived, generalizing Cahn's analysis into a complete SDM treatment. For the dominant $S$-wave $ππ$ emission, the SDM is shown to be perfectly preserved, $ρ_ψ= ρ_{ψ^\prime}$, rendering the $ψ$ an ideal probe of the initial polarization state. Deviations arising from $D$-wave contributions are quantified, and a self-consistency experimental test is proposed that simultaneously validates the framework and constrains partial wave amplitudes. This formalism provides a consistent basis for extracting $ψ$ polarization and for amplitude analyses of subsequent $ψ$ decays in a continuum-background-free environment. The framework extends to other hadronic transitions, including $ψ' \to h_cπ^0$ in charmonium and $Υ(nS) \to Υ(mS)ππ$ in bottomonium, as well as to electroweak processes such as $e^+e^- \to Z^\ast \to ZH$, where the same angular-momentum structure governs polarization transfer -- offering a unified probe of dynamics from charmonium to the Higgs sector.

This paper investigates sloshing problems defined by $-Δu=0$ in $Ω$, with mixed boundary conditions: $\partial_νu=λu$ on $S$, and either $\partial_νu=0$ or $u=0$ on $W$. Here, $Ω$ represents a smooth bounded domain in $\mathbb{R}^n$ with boundary $\partialΩ=S \cup W$. We demonstrate that under small domain perturbations, all resulting eigenvalues are simple.

We investigate the equilibrium partition function of non-relativistic conformal field theories in harmonic quantization. We first analyze the hydrodynamic regime and show that, at leading order, the partition function exhibits a universal structure determined by the equation of state: the logarithm of the partition function develops simple poles in $ω^2-Ω_a^2$, where $ω$ is the harmonic trapping frequency and $Ω_a$ are angular velocities acting as chemical potentials for angular momentum. The corresponding residue is determined by a single-variable function of $μ/T$, with $μ$ the particle-number chemical potential and $T$ the temperature. We then study the large-angular-momentum limit $Ω_a\toω$. In this regime centrifugal effects nearly cancel the trapping potential, and the logarithm of the partition function again exhibits simple poles in $ω^2-Ω_a^2$, but with a less universal residue depending separately on $μ/T$ and $ω/T$. As explicit examples we analyze superfluid systems realizable in cold-atom experiments, in particular fermions at unitarity confined in a harmonic trap.

Assessing the resilience of the economy requires accounting for its intrinsic multi-layer nature, by assessing for instance how disruptions at the firm level spread through the production network and propagate to the banking sector. Methods exist to measure the reverberation of shocks over the multilayer network of supply-customer relations among firms, corporate loans of banks and their interbank market exposures. However, empirical network data are often privacy protected and thus inaccessible to researchers and regulators. In this work we develop an unified framework, combining state-of-the art techniques to reconstruct the whole multilayer structure of the economy from balance sheet information of banks and firms, as well as dynamics of shock propagation from the inter-firm to the interbank layers. We showcase application of our methodology using data of the Italian economy. We identify the most systemically important firms and industries, as well as the most vulnerable banks, further assessing the determinants of systemic risk -- obtaining results coherent with the empirical literature on network contagion. Overall, our framework allows performing detailed network-based stress tests on a digital twin of the economy, without requiring detailed network information that is difficult to acquire.

We consider variational energies of the form \[E_H(u)=\frac12\int_ΩH^2(\nabla u)\,dx\] defined on the Sobolev space $H^1_0(Ω)$, where $H$ is a general seminorm. Our primary objective is to investigate optimization problems associated with the first eigenvalue $λ_H(Ω)$ and the torsional rigidity $T_H(Ω)$ induced by the seminorm $H$. In particular, we focus on functionals of the type \[F_{q,Ω}(H)=λ_H(Ω)\,T_H^q(Ω),\] where $q>0$ is a fixed real parameter. The optimization is performed with respect to the control $H$; we analyze both minimization and maximization problems for $F_{q,Ω}(H)$, as $H$ ranges over a suitable class of seminorms.

The Mori-Zwanzig formalism is a powerful theoretical framework for deriving equations of motion for coarse-grained observables in the form of generalized Langevin equations (GLEs) involving evolution and projection operators. Using a time-dependent many-body Hamiltonian and a multi-dimensional Mori projection operator, we derive a non-equilibrium Mori GLE for a multi-dimensional observable of interest $\vec{A}$ that consists of a Markovian force, a running integral over time of a non-Markovian friction force, and an orthogonal force that is often interpreted as a random force. We study the structure of the derived GLE in three limiting cases: when the components of $\vec{A}$ are uncorrelated, when the Hamiltonian is time-independent and thus the system is at equilibrium, and when both conditions are simultaneously satisfied. We highlight the presence of a contribution to the Markovian force that takes the form of an instantaneous friction force which only vanishes when the components of $\vec{A}$ are uncorrelated. Our non-Markovian framework is an important step towards the systematic modeling of the coupled kinetics of coarse-grained reaction coordinates in biological complex systems, exemplified for the coupled intra- and inter-protein folding during fibril formation of the human islet amyloid polypeptide (IAPP).

Acoustic control and coupling of quantum systems via phonons can enable miniaturized quantum technology devices for on-chip integration. Optically active quantum dots (QDs) are essential for such platforms, yet they have long lacked direct acoustic transitions between charge states. The recently proposed hybrid acousto-optical swing-up scheme introduces such high-fidelity transitions but has been proposed for sub-THz phonon frequencies, limiting practical implementations. Here, we overcome this limitation by exploiting higher-harmonic-assisted processes arising from strain-induced modulation of the optical transition energy. This parametric modulation of the optically dressed splitting produces multi-phonon-like resonances when a harmonic of the mechanical modulation matches the generalized Rabi frequency. We predict faithful state preparation with an acoustic frequency that is only a fraction of this splitting, specifically 42 GHz for a 0.341 THz splitting, thereby bridging control at accessible acoustic frequencies with the THz energy scales. In doing so, we establish control principles that separate optical energy delivery from coherent acoustic control. We complement numerical simulations with an effective model and a geometric interpretation. Evaluation of phonon-induced decoherence within a non-Markovian framework indicates high state-preparation fidelities, comparable to one-phonon and all-optical schemes. Potential applications extend beyond QD charge state preparation. Since the same interaction structure arises for a quantized acoustic field, our results provide a foundation for multi-phonon processes in QDs coupled to phononic resonators, including QD-phonon entanglement, state transfer, and the optical preparation of nonclassical multi-phonon states in quantized acoustic modes, all essential for future on-chip quantum technologies.

Transition waves in mechanical metamaterials manifest themselves as propagating interfaces between different stable states in lattices composed of arrays of coupled, intrinsically bistable elements. Here, we show experimentally and numerically that arrays of elastic unit cells that are individually monostable, yet whose energy landscapes can be programmed through interactions with neighboring units, provide a rich and largely unexplored platform for transition wave propagation. We implement this concept by designing a unit cell comprising a von Mises truss supported by two vertical elastic beams. In one-dimensional arrays of such units, we demonstrate that each cell's energy landscape can change from monostable to bistable depending on the state of its neighbors. This neighbor-programmable energy landscape enables the controlled initiation and propagation of transition waves, giving rise to highly discrete, directionally unbiased, domino-like wave propagation. Experiments and numerical simulations show that the existence and speed of the waves are governed by geometric design and mass distribution. Our results establish neighboring effects as a distinct mechanism for transition wave propagation, expanding the design space of mechanical metamaterials beyond architectures that rely on intrinsically multistable building blocks.

We experimentally demonstrate how spatiotemporal optical vortices (STOVs) control long-range atmospheric filamentation of intense laser pulses. High-power pulses long enough to overlap with the delayed rotational nonlinearity of air molecules undergo periodic collapse arrest events, each of which generates toroidal STOV pairs with +/- topological charge that separate and accumulate into increasingly squeezed arrays of +1 charges at the front of the pulse and -1 charges at the back. These dynamics manifest as periodic energy deposition peaks along the propagation path and a pulse envelope modulated into a temporal intensity comb. Filamentation in this regime can be understood in terms of self-organized, topologically constrained defect dynamics embedded within nonlinear wave propagation.

The $k$-median and $k$-means clustering objectives are classic objectives for modeling clustering in a metric space. Given a set of points in a metric space, the goal of the $k$-median (resp. $k$-means) problem is to find $k$ representative points so as to minimize the sum of the distances (resp. sum of squared distances) from each point to its closest representative. Cohen-Addad, Feldmann, and Saulpic [JACM'21] showed how to obtain a $(1+\varepsilon)$-factor approximation in low-dimensional Euclidean metric for both the $k$-median and $k$-means problems in near-linear time $2^{(1/\varepsilon)^{O(d^2)}} n \cdot \text{polylog}(n)$ (where $d$ is the dimension and $n$ is the number of input points). We improve this running time to $2^{\tilde{O}(1/\varepsilon)^{d-1}} \cdot n \cdot \text{polylog}(n)$, and show an almost matching lower bound: under the Gap Exponential Time Hypothesis for 3-SAT, there is no $2^{{o}(1/\varepsilon^{d-1})} n^{O(1)}$ algorithm achieving a $(1+\varepsilon)$-approximation for $k$-means.

We present a derivation of the classical log soft graviton theorem within the asymptotic framework of Compère, Gralla, and Wei. The proof relies solely on Einstein equations near timelike, spatial, and null infinity, together with matching properties across these regions. The approach is fully covariant under time reversal and incorporates contributions from incoming soft radiation. In the absence of incoming memory one recovers the standard log soft factor, which features an asymmetry between future and past hard components. From an asymptotic perspective, the origin of this asymmetry lies in a long-known discontinuity of the gravitational field at spatial infinity.

Large Language Models (LLMs) have revolutionized recommendation agents by providing superior reasoning and flexible decision-making capabilities. However, existing methods mainly follow a passive information acquisition paradigm, where agents either rely on static pre-defined workflows or perform reasoning with constrained information. It limits the agent's ability to identify information sufficiency, often leading to suboptimal recommendations when faced with fragmented user profiles or sparse item metadata. To address these limitations, we propose RecThinker, an agentic framework for tool-augmented reasoning in recommendation, which shifts recommendation from passive processing to autonomous investigation by dynamically planning reasoning paths and proactively acquiring essential information via autonomous tool-use. Specifically, RecThinker adopts an Analyze-Plan-Act paradigm, which first analyzes the sufficiency of user-item information and autonomously invokes tool-calling sequences to bridge information gaps between available knowledge and reasoning requirements. We develop a suite of specialized tools for RecThinker, enabling the model to acquire user-side, item-side, and collaborative information for better reasoning and user-item matching. Furthermore, we introduce a self-augmented training pipeline, comprising a Supervised Fine-Tuning (SFT) stage to internalize high-quality reasoning trajectories and a Reinforcement Learning (RL) stage to optimize for decision accuracy and tool-use efficiency. Extensive experiments on multiple benchmark datasets demonstrate that RecThinker consistently outperforms strong baselines in the recommendation scenario.

Diffusion-influenced reactions in the presence of gates which randomly open and close have been studied for decades in a variety of biophysical and biochemical scenarios. The diffusive flux from a large bulk reservoir to the end of a narrow tube with a stochastically gated entrance has been previously estimated. In this paper, we extend this gated flux estimate to be valid if (i) the tube is not necessarily narrow and/or (ii) the diffusivity differs in the tube versus the bulk. Extension (i) is challenging because it entails a nontrivial three-dimensional geometry. Extension (ii) is challenging because it introduces multiplicative noise. We derive an explicit flux estimate formula and prove that it is exact in certain parameter regimes. We further use stochastic simulations to show that the estimate remains accurate across a very broad range of parameters. Our results differ from prior work on extensions (i) and (ii).

Aims. We investigated the transport of solar energetic particles (SEPs) during the relativistic widespread event of 28 October 2021, quantifying the role of parallel and perpendicular diffusion and constraining the spatial extent of the injection region. Methods. We employed inverse modeling of particle focused transport and 2D numerical simulations including cross-field diffusion. Multi-spacecraft observations from STEREO-A, Solar Orbiter, and near-Earth spacecraft are used to reproduce particle intensity profiles and anisotropies across a wide range of electron and proton energies. Simulated flux profiles are compared across different heliolongitudes to derive consistent transport parameters. Results. The analysis yields parallel mean free paths within or slightly above the Palmer consensus range, and perpendicular mean free paths that correspond to $\sim 1$--$3\%$ of parallel for electrons and $\sim 5$--$10\%$ for protons. The injection region is found to be relatively narrow ($\leq 20^\circ$), and decreasing with particle rigidity. Multipoint simulations indicate that the observed flux and anisotropy profiles can only be reproduced by a narrow injection region and significant cross-field diffusion. Electron and proton release times align well with the parent X1.0 flare and associated coronal mass injection (CME) onset, indicating that a compact acceleration region coupled with efficient interplanetary diffusion governed the event's broad spatial extent.