Drop impacts are ubiquitous in natural and industrial processes, yet the influence of drop shape on impact force remains a fundamental open question. Combining experiments with theoretical analysis, we show that drop shape plays a critical role, with impact force varying by more than an order of magnitude solely due to changes in shape. By uncovering self-similarity in time and cross-shape similarity across diverse drop profiles, we develop a universal cylinder model that accurately predicts both the magnitude and timing of the impact force. This study establishes a comprehensive framework for understanding impact forces across a wide range of drop shapes. Given the prevalence of drop impacts with varying shapes in real-world scenarios, our findings hold fundamental significance and have broad potential applications across industries such as soil erosion prevention, jet cutting, spray coating, and design of windshields and wind turbines.

We investigate the $Ω(2012)$ resonance in the strangeness $S=-3$ sector within a coupled-channel chiral unitary approach and present the first quantitative predictions for femtoscopic correlation functions directly sensitive to its dynamics. The $Ω(2012)$ is dynamically generated as a quasi-bound $Ξ^{\ast}\bar K$-$Ωη$ molecular state, with its coupling to the $Ξ\bar{K}$ channel driven by $d$-wave transitions. Model parameters are constrained by the measured mass, width, and the Belle determination of the branching fraction $\mathcal R^{Ξ\bar Kπ}_{Ξ\bar K}$, yielding $M_{Ω(2012)}=(2012.53\pm0.73)$ MeV and $Γ_{Ω(2012)}=(4.05\pm0.13)$ MeV. Within this framework, we compute the femtoscopic correlation functions of the $Ξ^{\ast0}K^-$, $Ξ^{\ast-}\bar K^0$, and $Ω^-η$ systems. The $Ξ^{\ast}\bar K$ correlation functions exhibit pronounced near-threshold structures that arise from the proximity of the $Ω(2012)$ pole, demonstrating an exceptional sensitivity to its position and coupled-channel composition. In particular, the $Ξ^{\ast0}K^-$ correlation function is identified as a clean and highly selective probe of the $Ω(2012)$ resonance. These results establish femtoscopic correlation measurements as powerful tools for extracting resonance properties beyond conventional invariant-mass analyses and provide concrete theoretical benchmarks for upcoming experimental studies aimed at elucidating the molecular nature of the $Ω(2012)$.

Historical episodes such as the World War I "live-and-let-live" system and the Christmas Truce of 1914 demonstrate that opposing military units can establish spontaneous, local cooperation even in extreme conflict environments. Such cooperative behavior is typically fragile and temporary, while large-scale wars persist. We develop a hierarchical decision problem in which local units adopt contingent strategies that depend on interactions, accumulated payoffs, and signals from a central command. The command authority can impose enforcement that penalizes non-aggression to prolong hostilities. Our model features a continuous space of parametric strategies and formalizes replicator dynamics over the population. We analytically characterize the conditions under which local cooperation emerges as a stable evolutionary equilibrium and identify critical thresholds of central enforcement that destroy cooperative equilibria. We show that stable peace requires either alignment of command incentives with frontline welfare, external constraints on enforcement, or diminishing political returns to conflict. The framework provides a micro-founded explanation for the persistence of war despite locally beneficial cooperation.

We present a lithographic method for fabricating free-standing microparticles directly from SUEX dry-film epoxy resist. Unlike conventional SU-8 particle fabrication, which requires patterning on solid substrates followed by sacrificial-layer release, our approach eliminates substrate use entirely and produces particles with near 100% yields. The process supports a wide design space of in-plane geometries, including high-aspect-ratio and highly complex shapes. To enable large-scale particle libraries, we integrate the method with the Nazca Python library, allowing programmatic generation of tens of thousands of parametrically defined particle designs. This combination of substrate-free fabrication and automated design provides a scalable route to custom microparticles for materials science, microfluidics, and soft-matter applications.

SQL query comprehension is a significant challenge due to complex syntax, diverse join types, and deep nesting. Many queries lack adequate comments, severely hindering code readability, maintainability, and knowledge transfer. Automated SQL comment generation faces two main challenges: limited datasets that inadequately represent complex real-world queries, and Large Language Models' (LLMs) insufficient understanding of SQL-specific semantics. Our empirical analysis shows that even after continual pre-training and supervised fine-tuning, LLMs struggle with complex SQL semantics, yielding inaccurate comments. To address this, we propose SQL-Commenter, an advanced method based on LLaMA-3.1-8B. We first construct a comprehensive dataset of complex SQL queries with expert-verified comments. Next, we perform continual pre-training on a large SQL corpus to enhance the LLM's syntax and semantic understanding, followed by supervised fine-tuning. Finally, we introduce Direct Preference Optimization (DPO) using human feedback. SQL-Commenter utilizes a preference-based loss function to favor preferred outputs, enhancing fine-grained semantic learning and context-dependent quality assessment. Evaluated on the Spider and Bird benchmarks, SQL-Commenter significantly outperforms state-of-the-art baselines. On average, it surpasses the strongest baseline (Qwen3-14B) by 9.29, 4.99, and 13.23 percentage points on BLEU-4, METEOR, and ROUGE-L, respectively. Moreover, human evaluation demonstrates the superior quality of comments generated by SQL-Commenter in terms of correctness, completeness, and naturalness.

We study long-time dynamics of small even perturbations of the soliton in 1D quadratic Klein-Gordon equation. The soliton possesses both an internal mode and the unstable mode. On a codimension-one manifold of fine-tuned initial data the instability is suppressed and the internal mode decays slowly by transferring energy into the continuum. We show that this decay and the associated nonlinear frequency shift are accurately captured by a cubic resonant approximation, with the damping rate determined by a Fermi golde rule-type coefficient. This provides a quantitative description of irreversible energy transfer from the internal mode to dispersive radiation.

Using a sample of 116 wide binary systems as coeval and chemically homogeneous stellar pairs, we investigate the factors governing lithium depletion in main-sequence stars. We recover the well-established morphology of the lithium--effective temperature ($T_{\mathrm{eff}}$) relation, including the Li dip (6200--6600\,K), the Li plateau (6000--6200\,K), and a linear trend for cooler stars ($T_{\mathrm{eff}}$ $<$ 6000\,K), where lithium abundance increases by $\sim$0.15\,dex per 100\,K. We demonstrate that the apparent correlation between projected rotational velocity ($v\sin i$) and lithium abundance is secondary to the underlying $T_{\mathrm{eff}}$ dependence; $v\sin i$ is not an independent driver of lithium depletion in our sample. Notably, we identify an anomalous system within the Li dip where the primary star exhibits a $\sim$1.4\,dex lithium excess compared to its secondary companion at nearly identical $T_{\mathrm{eff}}$. We discuss two plausible origins for this anomaly: external enrichment via planetesimal accretion or planetary engulfment, and binary interactions with an unresolved tertiary companion. Our results confirm $T_{\mathrm{eff}}$ as the dominant parameter controlling lithium depletion, while highlighting that additional, non-standard processes can occasionally produce significant lithium enrichment.

To support future diverse applications, multi-link operation (MLO) has been introduced in the Wi-Fi 7 standard (IEEE 802.11be) to enable concurrent communication over multiple frequency bands. This new capability relies on a two-tier medium access control (MAC) architecture, where the upper MAC (U-MAC) allocates traffic across links and the lower MAC (L-MAC) performs independent channel access. However, MLO optimization is challenging due to the inherent coupling between the U-MAC and L-MAC, as well as the dynamic and complex nature of wireless networks. To address these challenges, we propose a cross-layer framework that jointly optimizes traffic allocation at the U-MAC layer and initial contention window (ICW) sizes at the L-MAC layer to maximize network throughput. Specifically, we extend the single-link Bianchi Markov model to develop an analytical framework that captures the relationship among network throughput, traffic allocation, and ICW sizes. Based on this framework, we formulate a nonconvex, nonlinear cross-layer optimization problem. To solve it efficiently, we design a long short-term memory-based soft actor-critic (LSTM-SAC) algorithm that leverages LSTM to handle the partial observability and non-Markovian dynamics inherent in Wi-Fi networks. Finally, using a well-developed event-based Wi-Fi simulator, we demonstrate that the proposed LSTM-SAC substantially outperforms existing benchmark solutions across a wide range of network settings.

Direct handset-to-satellite (DHTS) communication is emerging as a core capability of 6G non-terrestrial networks, enabling standard devices to directly access low Earth orbit (LEO) satellites. While LEO provides the physical access layer for DHTS, large-scale device connectivity introduces challenges in mobility management, interference control, spectrum efficiency, and constellation-wide coordination. Relay-only LEO architectures are insufficient to manage massive handset access under dynamic traffic and energy constraints. This article introduces a hierarchical architecture in which direct handset-to-LEO access is supported by multi-orbit space-based data centers (SBDCs) spanning LEO, medium Earth orbit (MEO), and geostationary Earth orbit (GEO). In this framework, LEO satellites handle radio access and real-time inference, while higher orbital layers provide regional aggregation, global orchestration, and compute-aware routing. By embedding distributed in-orbit computing, energy-aware scheduling, and AI-driven hierarchical control, the constellation evolves from a passive relay network into an intelligent multi-layer system capable of supporting large-scale DHTS services. We discuss key enabling technologies, envisioned multi-orbit integrated Earth-space compute architecture, and open research challenges in integrating multi-orbit computing, highlighting pathways toward scalable and resilient 6G DHTS networks.

Just as Caesar declared "alea iacta est" (the die is cast) upon crossing the Rubicone river, lane change decisions in autonomous vehicles also represent critical points of no return. RUBICONe addresses this challenge by recognizing that lane change decision-making relying solely on a single vehicle's perception would be as precarious as crossing an unknown river alone. By implementing a distributed consensus framework that extends the RAFT algorithm with wireless connectivity, RUBICONe enables multiple vehicles to collectively process and aggregate their perceptions. Using multiple software-defined radio (SDR) devices as the experimental platform, this study demonstrates how consensus-based decision-making significantly reduces the impact of environmental interference and mitigates the risk of misjudgments by individual vehicles. Just as crossing the Rubicone marked a point of irrevocable action backed by collective intelligence, RUBICONe ensures that lane change decisions are made with comprehensive situational awareness and distributed consensus, showcasing the reliability gain of consensus in wireless communications.

Background stars observed through a circumstellar disk provide valuable benchmarks for investigating the disk's extinction properties. The HD~163296 system is an excellent case study due to its large disk, the clearly visible extinction effects in JWST/NIRCam data, and the presence of numerous background sources within or around its disk. We present the measured contrasts and astrometry of sources surrounding HD~163296 from Cycle~1 JWST/NIRCam coronagraphic observations, which will serve as a useful reference for future studies of the disk's extinction characteristics.

Josephson junctions translate quantum phase coherence into an electrical response and underpin superconducting sensors and quantum circuits. In conventional junctions, the barrier acts primarily as a passive weak link, however, when the barrier is a quantum material with its own internal degrees of freedom like magnetism, strong correlations, or switchable polarization, the Josephson effect becomes a sensitive probe of symmetry and many-body physics in the interlayer. Here we review progress in quantum-material Josephson junctions, (QMJJ) focusing on three rapidly advancing barrier families: 1. magnetic barriers, where exchange, noncollinearity, and spin-active scattering enable 0-π-ϕ ground states, singlet-triplet conversion, and nonreciprocal transport, 2. correlated barriers, where proximity effects acquire many-body character and recent van der Waals Kagome Mott interlayers exhibit field-free Josephson diode behavior, and 3. ferroelectric and multiferroic barriers, where nonvolatile polarization provides an internal control knob and can produce superconducting memory and memristive dynamics.

Aggression against Ukraine has drawn widespread international attention, particularly in the wake of the two Russian invasions into Ukrainian territory in 2014 and 2022. Although previous studies have examined social-media dynamics around these events, a comparative longitudinal data-driven view across languages is still missing. This article fills this gap by mapping added attention to "Ukraine" on Twitter in 28 languages from 2008 to 2023, using a deceptively simple DNA microarray-inspired cartography of log over-expression relative to each language's baseline frequency. This macro-scale visualization makes familiar events stand out while uncovering subtler patterns beyond the cognitive reach of any single-language audience. Most strikingly, two nearly non-overlapping language clusters emerge, one peaking around 2014 and the other around 2022 with distinct onset and decay profiles that mirror national readiness (or reluctance) to support Ukraine. By capturing attention at local, meso, and global scales, our approach offers a versatile tool for comparing relative bias across languages, user subgroups, platforms, or even historical print corpora. Ultimately, our cartographic approach reveals a troubling asymmetry: while publicly accessible data allows for an approximation of global attention patterns, the complete and unfiltered view remains largely hidden behind the closed, proprietary algorithms of major social media platforms, granting a far more comprehensive access to understanding global information flows.

On-chip coherent visible and near-infrared (NIR) light generation has broad applications in metrology, bio-sensing, and quantum information. High-Q microresonators are ideal candidates for generating light across such broad wavelength ranges via efficient second- ($χ^{(2)}$) and third-order ($χ^{(3)}$) nonlinear optical processes. However, harnessing these diverse nonlinearities simultaneously in a single microresonator remains elusive yet highly attractive both fundamentally and technologically. Here, we demonstrate coherent light generation from the ultraviolet to NIR in a silicon nitride microresonator pumped by a single continuous-wave telecom laser. This broad frequency generation arises from the interplay of $χ^{(2)}$ and $χ^{(3)}$ nonlinear processes. A cascade of nonlinear processes, including harmonic generation and optical parametric oscillation (OPO), is initiated by the photoinduced second harmonic generation enabled by all-optical poling. The dynamic reconfigurability of this $χ^{(2)}$ nonlinearity enables access to different transverse spatial modes at the second harmonic, enabling highly tunable OPO processes triggered by hybrid modal phase matching conditions and yielding milliwatt-level NIR light. This work sheds new insights into the fundamental physics of cooperative nonlinear multimode interactions in resonant systems and provides a versatile approach for reconfigurable OPOs, highlighting their potential to generate light at wavelengths beyond the reach of photonic integrated lasers.

Adding dynamic bonds in polymer networks enables reprocessing and recycling; however the full impact of reversible bonds on dynamic network mechanics remains unclear. We build model dynamic networks and observe substantial deviations from classic theory. We rationalize these findings by considering that bond exchange enables the networks to rearrange and adopt a topology with a higher entropy. This allows us to accurately predict the gel point and elasticity of the dynamic networks. Further, we show by controlling bond exchange that network rearrangement can dramatically alter the mechanical properties, even without loss of bonds.

Quantum spin liquids (QSLs) are exotic phases of matter characterized by long-range entanglement and the absence of magnetic order even at zero temperature. Here, we present a comprehensive theoretical study of the frustrated magnet Y$_3$Cu$_2$Sb$_3$O$_{14}$ to elucidate its electronic and magnetic properties. We uncover completely opposite crystal-field splittings of the two inequivalent Cu sites owing to their fundamentally distinct oxygen coordination - trigonal distorted octahedral CuO$_6$ and axially compressed CuO$_8$. This inversion places the unpaired hole in the $d_{z^2}$ orbital at the Cu-2 site, while Cu-1 maintains conventional $d_{x^2-y^2}/d_{xy}$ character, which results in a selective band-renormalization of orbitals from the two Cu ions. We further find multiple magnetic instabilities competing with nearly equal strength in this system: the spin susceptibility lacks dominant peaks, and the leading eigenvalues approach unity simultaneously across all wavevectors with increasing interactions. This competitive interplay, originating from the distinct local environments and geometric frustration on the triangular lattice, agrees well with the absence of long-range magnetic order in experiment. Our results support Y$_3$Cu$_2$Sb$_3$O$_{14}$ as a promising QSL candidate where the unique combination of disparate crystal-field environments, strong correlations, and competing exchange interactions conspire to stabilize an exotic quantum ground state.

Owing to their relevance for spintronics, electronic band splitting and spin-polarization textures in magnets are active areas of research. In non-collinear magnets, alternating spin textures can arise both for isolated bands and for intersecting band pairs with nodal splitting. This raises the question of whether $p,f,...$-wave magnets should be defined by their spin polarization or their band splitting. To resolve this ambiguity, we introduce spin-space symmetries that couple the spin polarization and splitting textures for all bands. Focusing on the nodal $f$-wave magnet, we construct a tight-binding model of itinerant electrons on a honeycomb bilayer coupled to a non-collinear magnetic texture. Analytic expressions for spin polarization and splitting reveal the dependence on hopping and exchange coupling. We predict a canting-induced spin conductivity arising from the nodal structure of the splitting. Furthermore, the $f$-wave magnet in the bulk can induce $p$-wave magnetism on the surface. This surface $p$-wave character leads to a bulk-forbidden Edelstein effect with $f$-wave anisotropy.

We discuss in some details a novel algorithm for performing partial-sky spherical harmonic transforms (SHT), building on the Fourier-sphere method of Reinecke et al (2023) handling efficiently high numbers of arbitrary locations on the sphere. Our main motivations are Cosmic Microwave Background lensing from the South Pole Telescope, and the South Pole Observatory program targeting primordial gravitational waves from inflation, requiring high-resolution, numerically intensive work on small sky fractions. We achieve speed-up factors ranging from 3 to 10 on SPT-3G main field and BICEP3 deep footprint, and much more on smaller patches. More generally, the algorithm eliminates in our case study the usual disadvantages of arbitrary pixelisations in comparison to isolatitude pixelisations or flat-sky approximations, making it ideal for ambitious workflows that require repeated SHTs on limited sky regions.

Quenching quantum order via laser pulses has proven a useful tool to access exotic physical effects in systems that are strongly perturbed out of equilibrium. However, theoretical modelling of experimental measurements is typically done phenomenologically or by assuming translational invariance due to the complexity of the problem. Here, we solve a microscopic real-space model of the time dynamics of a superconductor following an intense laser-pulse. We are able to reproduce recent experimental findings displaying a critical slowing-down of the melting of the order parameter for laser fluences close to the condensation energy. Moreover, we leverage the real-space resolution of our model to predict how phase fluctuations and currents in the system behave both spatially and temporally. We discover an unusual current flow in the superconductor after the pulse has subsided, resembling backward waves that normally require special engineering in metamaterials or wave guides. Our results predict a rich behavior of the superconducting order parameter at a microscopic level which is manifested in current textures that can be probed using radiation detection.

Experimental setups commonly used to study fission properties of nuclei in the exotic neutron-deficient 180Hg region are based on the time-of-flight technique for the fission-product identification. The nuclei of interest are created via fusion reactions at excitation energies of several tens of MeV and identified with limited mass resolution. The deduced final fission-fragment mass distributions are in general structureless, which makes the identification of fission modes, along with their properties, ambiguous and author-dependent. The standard functional-analysis technique applied to the simulated limited-resolution fusion-fission data appears to provide consistent results on the number and parameters of fission modes, even in cases of strong symmetric-mode dominance, i.e. for Gaussian-like fission-fragment mass distribution shapes. The method is shown to work also on data sets with limited statistics (real experimental data with integral of a few tens of thousands of events).

We establish the first observational bounds on causal nonlocal extensions of gravity characterized by retarded Stieltjes-type kernels with positive spectral density rho(mu) >= 0, using two complementary gravitational-wave channels. From a Bayesian ringdown analysis of 17 binary black hole events in the LIGO-Virgo GWTC-3 catalogue, we set an observational ceiling on universal fractional quasi-normal mode deformations of |epsilon_Omega| < 0.05 (90% C.L.), with a cumulative log Bayes factor ln B = -0.46 +/- 0.77. By mapping published GWTC-3 modified dispersion relation bounds together with the GW170817 propagation speed constraint onto the Stieltjes spectral parameter space (mu_char, M0), we exclude a broad class of infrared-extended spectral densities with mu <= 10^{-6} m^{-2}, thereby ruling out non-trivial regions of the nonlocal kernel parameter space for the first time. The theoretically motivated fiducial range mu_char ~ M_*^2 ~ 10^8-10^10 m^{-2} satisfies all current bounds. We further show that sub-millimetre gravity experiments, which already operate at the predicted causal scale l_* ~ 10^{-4} m, provide the most promising path toward a direct test. These results define quantitative benchmarks against which future observations across the gravitational-wave, short-range gravity, and cosmological sectors can be compared.

A recent result of the first author with Li and Pipher has established the extrapolation of solvability of the $L^p$ parabolic Neumann problem on unbounded graph domains of the form $Ω=\{(x',x_n):\,x_n>φ(x')\}\times\mathbb R$, where $φ:\mathbb R^{n-1}\to\mathbb R$ is a Lipschitz function. The result shows that under the assumptions that the $L^p$ parabolic Neumann problem for the equation $Lu=-\partial_t u+\mbox{div}(A\nabla u)=0$ in $Ω$ and also the $L^{p'}$ parabolic Dirichlet problem for the adjoint equation $L^*u=\partial_t u+\mbox{div}(A\nabla u)=0$ in $Ω$ are solvable, then also the $L^q$ parabolic Neumann problem for the equation $Lu=0$ in $Ω$ is solvable for all $1<q<p$. However the mentioned paper does not answer the question whether the same claim is also true for domains of the form $\mathcal O\times\mathbb R$, where $\mathcal O$ is a bounded Lipschitz domain (in spatial variables) since this case does not follow from our argument for the unbounded case. Indeed, the bounded Lipschitz cylinder case requires a significantly different approach which we present in this article and establish an analogous result when $\mathcal O$ is a bounded Lipschitz domain.

Very low-luminosity objects in nearby star-forming regions have been identified as promising proto-brown dwarf candidates. The study of their multiplicity can shed light on the dominant formation mechanism of these substellar objects. We aim at studying the multiplicity of the very low luminosity object IRAM 04191+1522. To do so, we have obtained 0.89mm ALMA observations with a very extended configuration, achieving an angular resolution of ~0.04 arcsec (6 au at 140 pc). We have complemented our data with new VLA observations, and ALMA archival data at 1.3mm. As a result, we resolve IRAM04191+1522 into a close binary candidate for the first time. The binary is detected in the ALMA continuum data with a projected separation of ~80 mas, or 11 au at a distance of 140 pc. The two sources are oriented in the East-West direction, with the eastern component being brighter and more extended than the western one, which is marginally resolved. The analysis of C18O(2-1) archival data reveals gaseous material in rotation around the binary, presumably from a circumbinary disk with ~27 au of radius centered on the faintest ALMA component. A fit of the position-velocity diagram allows us to estimate a total dynamical mass for the system of 50+-40 MJup. Therefore, we classify IRAM04191 as a tight proto-brown dwarf binary candidate. The VLA data reveals the detection of a single object closer to the western ALMA source, and with a spectral index consistent with a radio jet.

Recent analyses of Fermi-LAT data have identified a nearly spherical, halo-like excess of gamma rays peaking at E_gamma ~ 20 GeV. If interpreted as dark matter annihilation, the excess directly probes the thermal freeze-out epoch and therefore any non-standard corrections to the early-Universe expansion rate. In this work we examine the implications of this tentative signal for CET Omega, an informational and modular extension of relativistic quantum field theory and cosmology. CET Omega predicts a universal state-dependent modification to the radiation energy density of the early Universe, characterized by a doubly logarithmic correction originating from renormalized modular fluctuations in the spectral triple of the theory. The correction is negligible during Big Bang nucleosynthesis and recombination but becomes relevant during thermal WIMP freeze-out. We derive the correction from the modular two-point function, justify the onset scale associated with the informational sector, and compute its quantitative impact on freeze-out through numerical solutions. We also analyze the evolution of the informational field Phi_Omega(x) and show that it freezes in before the freeze-out epoch and survives to the present time under gravitational advection. The resulting modification induces percent-level shifts in the relic abundance and sub-percent morphological corrections to the annihilation gamma-ray flux. We compare the scenario with Early Dark Energy, kination, and varying N_eff models, and show that the parameter range 10^{-4} < alpha_log < 10^{-2} remains consistent with Planck, BBN, and BAO constraints while predicting potentially observable deviations in the gamma-ray morphology accessible to next-generation MeV-GeV missions.

This work presents a highly optimized implementation of PAC-DB, a recent and promising database privacy model. We prove that our SIMD-PAC-DB can compute the same privatized answer with just a single query, instead of the 128 stochastic executions against different 50% database sub-samples needed by the original PAC-DB. Our key insight is that every bit of a hashed primary key can be seen to represent membership of such a sub-sample. We present new algorithms for approximate computation of stochastic aggregates based on these hashes, which, thanks to their SIMD-friendliness, run up to 40x faster than scalar equivalents. We release an open-source DuckDB community extension which includes a rewriter that PAC-privatizes arbitrary SQL queries. Our experiments on TPC-H, Clickbench, and SQLStorm evaluate thousands of queries in terms of performance and utility, significantly advancing the ease of use and functionality of privacy-aware data systems in practice.

Answering Select-Join-Aggregate queries with DP is a fundamental problem with important applications in various domains. The current SOTA methods ensure user-level DP (i.e., the adversary cannot infer the presence or absence of any given individual user with high confidence) and achieve instance-optimal accuracy on the query results. However, these solutions involve solving expensive optimization programs, which may incur prohibitive computational overhead for large databases. One promising direction to achieve scalability is through sampling, which provides a tunable trade-off between result utility and computational costs. However, applying sampling to differentially private SJA processing is a challenge for two reasons. First, it is unclear what to sample, in order to achieve the best accuracy within a given computational budget. Second, prior solutions were not designed with sampling in mind, and their mathematical tool chains are not sampling-friendly. To our knowledge, the only known solution that applies sampling to private SJA processing is S&E, a recent proposal that (i) samples users and (ii) combines sampling directly with existing solutions to enforce DP. We show that both are suboptimal designs; consequently, even with a relatively high sample rate, the error incurred by S&E can be 10x higher than the underlying DP mechanism without sampling. Motivated by this, we propose Differentially Private Sampling for Scale (DP-S4S), a novel mechanism that addresses the above challenges by (i) sampling aggregation units instead of users, and (ii) laying the mathematical foundation for SJA processing under RDP, which composes more easily with sampling. Further, DP-S4S can answer both scalar and vector SJA queries. Extensive experiments on real data demonstrate that DP-S4S enables scalable SJA processing on large datasets under user-level DP, while maintaining high result utility.

Spontaneous parametric downconversion (SPDC) has been considered as a reliable source of high- dimensional entangled states in orbital angular momentum (OAM) basis. In real-world experiments, the spatial walk-off of the pump often degrades the fidelity of the generated quantum state. Since the walk-off effect breaks the rotational symmetry of the system, the conservation of total OAM is violated. Although the compensation of walk-off effects has become a well-established experimental technique, a systematic modal analysis of the spatial walk-off effect is still incomplete for SPDC. Here, we quantitatively analyze the violation of OAM conservation due to the pump walk-off effect in SPDC processes. We have derived a scaling law of the total OAM distribution with respect to the pump walk-off angle. We have also explored the feasibility of using the spatial walk-off as a mechanism to engineer the generated quantum state. Our study has provided guidelines for the generation of OAM-entangled state under realistic experimental conditions.

We introduce an updated, time-dependent treatment to the split-tail ("croissant-like") heliosphere model with data-driven solar wind conditions at 1 au, to study the evolution of the heliosphere with solar-cycle variations in plasma speed, plasma density, and magnetic field intensity. The model produces a sub-Alfvénic and low beta region, not observed by the Voyagers, ~15 au ahead of the heliopause. The simulated magnetic field and radial flow depart from Voyager observations in this region, indicating that time-dependent effects alone are not sufficient to understand this regime of the heliosheath. We decompose fast and slow magnetosonic wave modes from time-dependent plasma pulse structures in the heliosheath, using a linear Riemann variable analysis, for the first time. Fast mode waves can both reflect at the heliopause and transmit into the interstellar medium, and their speeds are unaffected by the low beta plasma regime in front of the heliopause. The model reproduces the pf2 jump in the magnetic field at ~2020 in the interstellar medium and we attribute the source of pressure fronts observed by Voyager 1 in the interstellar medium, and pressure pulses observed by Voyager 2 in the heliosheath, to fast mode waves that are commonly recurring solar-cycle features. The presence of fast mode waves drive a highly variable termination shock, with average radial speeds of 6.05 au yr$^{-1}$ $\pm$ 5.37 au yr$^{-1}$ in the New Horizons direction. We find that the termination shock has a sinusoidal-like oscillatory motion in the rising phase of the solar cycle, and broad inward motions during the declining phase.

This paper investigates testing for deviation of a high-dimensional mean vector $\boldsymbolμ$. In contrast to the standard one-sample significance test of the form: $H_0^\texttt{e} : \boldsymbolμ = \boldsymbolμ_0$ versus $H_1^\texttt{e} : \boldsymbolμ \neq \boldsymbolμ_0$, we focus on testing the deviation $H_0 : \|\boldsymbolμ - \boldsymbolμ_0\|_2 \ge d_0$ versus $H_1 : \|\boldsymbolμ - \boldsymbolμ_0\|_2 < d_0$ for a prespecified length $d_0 > 0$. Constructing a valid test statistic for this problem is technically nontrivial. By applying the concept of positive and negative feedback processes from control theory, we propose a test statistic based on a two-armed bandit (TAB) process. The deviation test is also extended to the two-sample setting. Simulation experiments confirm a good performance of the tests in finite samples. Finally, a real data analysis demonstrates the practical significance of the proposed deviation tests.

We present CETOmega, a unified framework that completes gravity through a causal-informational principle. The theory reconciles general relativity and quantum mechanics within a strictly four-dimensional, nonlocal, and causal formulation. At its core lies an analytic and retarded kernel K^-1(Box_R), derived from a discrete causal network, which governs the propagation of the gravitational and scalar sectors. A scalar field, the texon, emerges as the effective excitation of causal connectivity and accounts simultaneously for dark matter and dark energy without introducing extra degrees of freedom or breaking locality. The formalism ensures analyticity, spectral positivity, and holographic completeness. The kernel admits a Stieltjes representation with positive spectral density rho(mu) greater than or equal to zero, guaranteeing unitarity and causal propagation. At cosmological scales, CETOmega predicts stable inflationary dynamics consistent with Planck observations. Black hole ringdown frequencies acquire perturbative corrections controlled by the causal scale and remain subleading for astrophysical black holes within the fiducial window l* between 10^-5 and 10^-4 meters, where l* defines the mean causal correlation length of the texonic field. CETOmega thus provides a complete, causal, and informational foundation for spacetime dynamics, recovering Einstein gravity in the infrared while extending its validity to the quantum and cosmological domains.