Low-cost embedded processors such as the ESP32 (Xtensa LX6, 32-bit dual-core, 240 MHz) are increasingly used in edge computing applications that require real-time physical simulation, sensor fusion, and control systems. Although the ESP32 integrates a single-precision IEEE 754 floating-point unit, floating-point operations introduce pipeline overhead and higher energy consumption compared to integer arithmetic, limiting throughput for floating-point intensive workloads. This paper presents the design, formal specification, and empirical evaluation of a Dynamic Precision Math Engine for the ESP32. The system integrates three main components: a Q16.16 fixed-point arithmetic core that maps mathematical operations onto the integer pipeline of the Xtensa LX6, a 16-iteration CORDIC trigonometric module that computes sine and cosine using only additions and bit shifts, and a cache-aware tiled matrix multiplication kernel with deferred correction to reduce rounding operations. The architecture introduces a runtime precision switching mechanism implemented through function pointer dispatch and a synchronization protocol compatible with FreeRTOS. This mechanism allows applications to dynamically transition between a fast fixed-point execution path and a precise IEEE 754 floating-point path without recompilation. Experimental evaluation on ESP32-WROOM-32 hardware using 300 paired measurements shows that the CORDIC trigonometric module achieves median latencies of 293 cycles for both sine and cosine, corresponding to mean speedups of 18.5x and 24.7x compared to the standard math library. The results demonstrate that precision-aware software architecture can significantly improve numerical performance on low-cost microcontrollers.

The QCD Equation of State with $N_f=3$ massless quark flavours is determined non-perturbatively over a broad range of temperatures, extending from the electroweak scale down to 3 GeV, and smoothly connecting to the low-temperature regime. The comparison with perturbative predictions shows that, even at temperatures approaching the electroweak scale, the Equation of State can be accurately described only by adding terms beyond the known perturbative series, including non-perturbative contributions. The strategy that allows this investigation in the previously unexplored high-temperature regime combines shifted boundary conditions with a determination of the lines of constant physics based on the running of a non-perturbatively defined renormalized coupling. This methodology is general and can be applied to QCD with four or five massive quark flavours.

Tor enables anonymous web browsing and access to anonymous onion websites. Prior work has focused on crawling and content analysis rather than on what users actually try to access. Our honeypot approach measures engagement across onion-site categories, revealing behavioral interest rather than inferred popularity. In March--April 2025, we deployed honeypot onion websites and seeded neutral-looking links via three channels -- the Ahmia Tor search engine, Stronghold paste onion "paste" service, and pastebin.com -- to observe discovery and subsequent interaction events (CAPTCHA solves; registration/login attempts). We observe that, almost without exception, human users originate from Ahmia.fi; after removing the honeypot links from the Ahmia.fi search results, visits dropped to nearly zero and no users solved CAPTCHAs. The honeypot landing front pages represent different forums for cybercrime activities -- child sexual abuse, violence, malware, stolen goods, illegal firearms, illegal drugs, and forgery items -- and, as a baseline comparison, an unclear forum. Within that set, the CSAM-themed honeypot drew markedly higher engagement than the other honeypots. When identical sites were offered in multiple languages, interaction events occurred most often on the English-language versions.

Context: Rotating anisotropic convection generates differential rotation in stellar convection zones. Aims: The main aim is to compute the non-diffusive contribution ($Λ$ effect) to angular momentum transport, described by Reynolds stress, from rotating turbulent convection. Methods: Rotating hydrodynamic convection is simulated in Cartesian geometry at different latitudes and rotation rates. Large-scale flows are suppressed such that the Reynolds stress is due to non-diffusive effects. Results: The radial angular momentum flux is downward (outward) for slow (fast) rotation. This is in contrast in prevailing theories in mean-field hydrodynamics where the radial transport is always downward. The outward transport at rapid rotation is due to thermal Rossby waves that manifest as elongated large-scale convection cells near the equator. The horizontal angular momentum flux is always equatorward, with increasing concentration toward the equator as in earlier Cartesian studies. The magnitudes of the $Λ$ effect coefficients are roughly an order of magnitude lower than in the case of anisotropically forced turbulence or in analytic theories. Conclusions: The current results highlight the tension between numerical simulations, widely used mean-field models, and solar observations. The mean-fields models have been remarkably successful in reproducing solar differential rotation but underlying assumptions regarding turbulence in these models seem to be at odds with 3D simulations. The current simulation results for the vertical (radial) angular momentum transport are in accordance with spherical shell simulations, where thermal Rossby waves are responsible for the generation of equatorial acceleration or solar-like differential rotation. Thermal Rossby waves are absent in the turbulence models of current mean-field theories and they have not been unambiguously detected in the Sun.

Altermagnets are a novel class of magnets that exhibit a large spin splitting but the total magnetic moment is vanishing. This unconventional spin splitting gives rise to various characteristic phenomena, such as spin current generation. In this paper, we study the orbital-Zeeman (OZ) cross term in altermagnets. Specifically, we consider the Rashba metal and the surface Dirac cones of three-dimensional topological insulators (TIs) in the presence of the altermagnetic order parameters. For the Rashba metals, the $p$-wave order parameter exerts only a limited influence on the OZ term, whereas the $d$-wave one causes the sign change of it when the order parameter becomes sufficiently large. For the TI surface, the $p$-wave order parameter retains the step-function-type dependence of the OZ term as a function of the chemical potential ($μ$) associated with the jump at $μ=0$, observed in the TI surface without magnetism, but its magnitude is reduced. For the $d$-wave case, the magnitude of jump at $μ=0$ is preserved but the OZ term decreases as increasing $|μ|$.

We develop an analytically tractable model featuring heterogeneous workers and firms, where labor markets clear through a one-to-many sorting mechanism. Firms determine both the number and composition of their employees, shaping (1) the income distribution among workers and (2) the productivity distribution across firms. We study business cycles driven by market efficiency shocks that disproportionately benefit more productive firms. The model's implications are consistent with empirical regularities on the cyclical behavior of wage and productivity distributions.

The detection of life on rocky exoplanets in the habitable zones of nearby stars would be a paradigm-shifting advance, and it is one of the greatest scientific challenges of our time. There is no single spectral feature that is an unambiguous sign of life on a given exoplanet. Instead, the current state-of-the-art approach involves detecting multiple molecular atmospheric features that should not exist together in equilibrium, e.g. simultaneous detection of O$_2$ and CH$_4$. Spectra across a wide wavelength (0.3-1.7 $μ$m) range are necessary to cover multiple spectral features per molecule of interest and to contextualise the suite of molecular features detected. While the US will lead the optical arm of the Habitable Worlds Observatory (HWO) coronagraph, a UK-led contribution of a near-infrared Integral Field Spectrograph (IFS) for the infrared arm will ensure UK leadership in the flagship scientific goal of HWO - to search for signatures of life on potentially habitable exoplanets.

Anomaly detection methods are widely used but often rely on ad hoc rules or strong assumptions, and they often focus on tail events, missing ``inlier'' anomalies that occur in low-density gaps between modes. We propose a unified framework that defines an anomaly as an observation with unusually low probability under a (possibly misspecified) model. For each observation we compute its surprisal (the negative log generalized density) and define an anomaly score as the probability of a surprisal at least as large as that observed. This reduces anomaly detection for complex univariate or multivariate data to estimating the upper tail of a univariate surprisal distribution. We develop two model-robust estimators of these tail probabilities: an empirical estimator based on the observed surprisal distribution and an extreme-value estimator that fits a Generalized Pareto Distribution above a high threshold. For the empirical method we give conditions under which tail ordering is preserved and derive finite-sample confidence guarantees via the Dvoretzky--Kiefer--Wolfowitz inequality. For the GPD method we establish broad tail conditions ensuring classical extreme-value behavior. Simulations and applications to French mortality and Test-cricket data show the approach remains effective under substantial model misspecification.

The spherical version of the Hopfield model for pattern recognition is considered in the static limit. Structures inside the patterns are modeled by Gaussian random variables that reward correlation between pairs of spins in a given pattern. The free energy is derived analytically with the replica method. The overlap distribution obeys a self-consistent equation. Coming from high temperatures, a spin glass phase is entered, in which patterns and correlations appear at lower temperatures. For small enough loading capacity, also a glass phase with patterns and correlations appears.

Suppose $\{\widehatθ_n\colon n\ge1\}$ is a strongly consistent sequence of estimators for a parameter $θ$, where $\widehatθ_n$ is based on the first $n$ observations. Consider $Q_\varepsilon$, the number of times $|\widehatθ_n-θ|\ge\varepsilon$. In another paper (Hjort and Fenstad, 1992) we have shown that $\varepsilon^2 Q_\varepsilon$ has a limit distribution as $\varepsilon\rightarrow0$, depending only on $σ$, the standard deviation of the limit distribution for $\sqrt{n}(\widehatθ_n-θ)$, under natural regularity conditions. The present paper investigates some second order asymptotics for differences between $Q_\varepsilon$ variables. The limit of ${\rm E}(Q_{1,\varepsilon}-Q_{2,\varepsilon})$ is calculated in cases where ${\rm E} Q_{1,\varepsilon}/{\rm E} Q_{2,\varepsilon}$ goes to 1, leading to a notion of `asymptotic relative deficiency' in cases where the asymptotic relative efficiency is 1. This is used to distinguish between competing estimators with identical limit distributions. Thus using denominator $n-{1\over3}$ in the familiar formula for estimating a normal variance is better than both $n$ and $n-1$ and indeed all other choices, for example, in the sense of leading to the smallest possible expected number of $\varepsilon$ errors. Results of this type are found in a selection of familiar estimation problems, using limit results for expected differences, and are compared to corresponding asymptotic relative deficiency analysis in the sense of Hodges and Lehmann. Some second order distributional results are reached as well. It is shown how $\varepsilon$ times a $Q_\varepsilon$-difference tends to a variable which is related to some exponential distributions associated with Brownian motion, and that have recently been investigated by Hjort and Khasminskii (1993).

Dark matter comprises ~85% of the entire mass of the Universe, but the fundamental nature of its constituent particles remains elusive. In this thesis, I test for two competitive dark matter models: the conventional heavy particle paradigm, and dark matter being ultralight bosons of mass $\sim 10^{-22}$eV ($ψ$DM). More specifically, I test for the faint-end turnover induced by $ψ$DM models, exploiting the strong lensing power by massive galaxy clusters to probe intrinsically fainter magnitudes. A key challenge for such an analysis would be contamination by low-z galaxies sharing similar observed SEDs as high-z galaxies. As I will demonstrate, such a contamination issue is generally severe and may wash out the faint-end turnover signatures. I also show that $\sim 50\%$ of the purported $3.5\leq z\leq 5.5$ galaxies within existing photometric redshift catalogs constructed for Hubble Frontier Fields (HFF) are in fact low-z interlopers. Luckily, individual mitigation of interlopers can be achieved with the combination of deep HST and JWST observations. For fields without supplementary data, machine learning methods will be shown useful in preserving the mitigating power. Cleaner $3.5\leq z\leq 5.5$ and $6\leq z\leq 10$ samples are derived for a more reliable test in strong lensing field of MACS J0416, with which I found no evidence for faint-end turnovers, leading to a constraint on the $ψ$DM mass of $>2.97\times10^{-22}$eV at 95\% confidence. This constraint will also be interpreted in an scheme where dark matter is composed of multiple particle copies, where I argue the derived mass bound is likely on an effective de Broglie scale governing the collective behavior of the entire $ψ$DM budget under gravitational equilibrium established.

Unnormalized (or energy-based) models provide a flexible framework for capturing the characteristics of data with complex dependency structures. However, the application of standard Bayesian inference methods has been severely limited because the parameter-dependent normalizing constant is either analytically intractable or computationally prohibitive to evaluate. A promising approach is score-based generalized Bayesian inference, which avoids evaluating the normalizing constant by replacing the likelihood with a scoring rule. However, this approach requires careful tuning of the likelihood information, and it may fail to yield valid inference without appropriate control. To overcome this difficulty, we propose a fully Bayesian framework for inference on unnormalized models that does not require such tuning. We build on noise contrastive estimation, which recasts inference as a binary classification problem between observed and noise samples, and treat the normalizing constant as an additional unknown parameter within the resulting likelihood. For exponential families, the classification likelihood becomes conditionally Gaussian via Pólya-Gamma data augmentation, leading to a simple Gibbs sampler. We demonstrate the proposed approach through two models: time-varying density models for temporal point process data and sparse torus graph models for multivariate circular data. Through simulation studies and real-data analyses, the proposed method provides accurate point estimation and enables principled uncertainty quantification.

This paper investigates the perturbation dynamics of massless scalar and electromagnetic fields on magnetically charged de Sitter (dS) black holes within the framework of string-inspired Euler-Heisenberg (EH) gravity. We calculate the quasinormal frequencies (QNFs) and discuss the influences of black hole magnetic charge $Q_{\mathrm{m}}$, the cosmological constant $Λ$, coupling parameter $ε$ and multipole number $l$ on QNFs, emphasizing the relationships between these parameters and quasinormal modes (QNMs) behavior. We find that the results obtained through the asymptotic iteration method (AIM) are in good agreement with those obtained by the WKB method. Importantly, the Bernstein spectral method is employed as a rigorous cross-check for QNFs in the $l=0$ scalar perturbation sector, where the WKB approximation is often unreliable. The greybody factor (GFs) is calculated using WKB method. The effects of the parameters $Q_{\mathrm{m}}$ and $ε$ on the greybody factor are also studied.

In this paper, we consider the classical robust adaptive beamforming (RAB) problem. Conventionally, this problem is solved either with an off-the-shelf solver like MOSEK or through the well-known RMVB algorithm based on Lagrange multiplier approaches. The solver MOSEK is implemented with the general interior point method and RMVB is only limited to the full-rank covariance scenario. In order to improve the existing benchmarks, we develop a novel closed-form solution scheme containing three consecutive stages: Diagonalization Transform, Phase Alignment, and KKT Solution. The proposed scheme is specifically intended for the RAB problem and thus more efficient than MOSEK. Moreover, the derivation process is simpler than RMVB and the output solution can cover the rank-deficient covariance scenario in extra. Aside from a new solution, we manage to unveil the existence and uniqueness conditions, which have never been studied before. The simulation results show that the proposed solution improves the existing benchmarks in terms of computational time while maintaining optimality.

This paper studies a sequential decision-making problem in a two-stage queueing system modeled after operations in CVS MinuteClinics, where nurse practitioners (NPs) oversee patient care throughout the entire visit. All services are non-preemptive, and NPs cannot begin treating a new patient until the current patient has completed both stages of care. Following an initial diagnosis in the upstream phase, NPs must decide for low-acuity patients whether to proceed with treatment independently through immediate service, or to collaborate with a dedicated general physician (GP) via telemedicine. While collaboration typically improves service quality and is preferred by individual patients, it may introduce delays as the NP-patient pair waits for a GP to become available. This work explores the structural properties of optimal policies under different system parameters, with a focus on large initial upstream queues, revealing unconventional and complex policy behaviors. Leveraging these structural insights and supporting theoretical results, we design simple and effective heuristics that are computable in linear time and suitable for practical implementation. These heuristics are robust across the entire parameter space of interest, and offer clear, actionable guidance for NPs as system parameters vary. They also achieve near-optimal performance, averaging within 0.1% of the optimal, while commonly used benchmark policies are highly sensitive to parameter shifts and can incur costs more than 100% higher than optimal. The work provides applicable insights for decision-makers on improving policy robustness and effectiveness, as well as recommendations for stakeholders on the value of investing in telemedicine infrastructure. For instance, we identify scenarios where such investments may be either unnecessary or essential based on specific system parameters.

Marginally twisted bilayer graphene having small twist angles is predicted to exhibit unique structural and electronic properties, though experimental characterization remains limited. Using scanning tunneling microscopy, we investigate such systems with twist angles of 0.06^{\circ}-0.35^{\circ}. AA-stacked regions reveal a pronounced tunneling spectral peak signifying highly localized electronic states. Conversely, AB domains display uniform multiple spectral peaks, indicative of strong lattice reconstruction and enhanced electronic homogeneity. We identify two distinct strain-induced domain walls: one exhibits a sharp -120 meV spectral peak (shear type), while the other shows distinct spectral characteristics (mixed shear-tensile type). Tight-binding calculations verify strain-driven transformations of both domain wall types and confirm direct observation of strain-mediated domain wall transitions. These results elucidate the electronic structure of marginally twisted bilayer graphene and establish strain as a control parameter for domain wall states.

Networked virtual reality (NVR) whiteboards are increasingly important for enabling geographically dispersed users to engage in real-time idea sharing, collaborative design, and discussion. However, latency caused by network limitations, rendering delays, or synchronization issues can significantly degrade the Quality of Experience (QoE) in whiteboard collaboration. To systematically investigate the impact of latency, this study classified QoE into pragmatic and hedonic aspects, each comprising multiple sub-dimensions. Controlled experiments were conducted to identify the sub-dimensions most affected by latency, which were then adopted as the primary QoE indicators, with the aim of uncovering the processes and mechanisms through which latency shapes QoE. Building on this, we further examined how these impacts vary across different collaboration modes, namely sequential collaboration (SC) for structured design workflows and free collaboration (FC) for open discussion. We also compared two VR whiteboard types, one with avatars (VR+) and the other without avatars (VR), and included a traditional PC-based whiteboard as a baseline. This multi-dimensional design enables a comprehensive evaluation of latency's impact on QoE across collaboration modes and platforms, providing practical guidance for optimizing NVR whiteboard systems under real-world network and system constraints.

In the sealed-off cesium vapor cell studied in this work, a residual rubidium fraction of approximately $\sim$1\% was observed. We investigate the optical response of these trace Rb atoms in a sealed 1~cm long Cs-filled vapor cell. Despite the low concentration, laser excitation at 795~nm allows the observation of saturated absorption and electromagnetically induced transparency (EIT) resonances. The surrounding Cs vapor effectively acts as a buffer medium, reducing the Rb atomic velocity and increasing the interaction time with the laser field, which improves the EIT signal. The experiments are performed in an all-sapphire cell that can be heated up to 500$^{\circ}$C without window blackening, unlike conventional glass cells. From the measured spectra, Cs--Rb collisional cross sections are estimated. These results show that residual atomic species in high-temperature vapor cells can be exploited for spectroscopic and nonlinear-optical studies.

A two-stage hybrid transceiver is designed by considering a partially connected architecture at the base station (BS) for a low-resolution multi-user (MU) THz massive multiple input multiple output (MIMO) system. Due to its high bandwidth coupled with a high number of antennas, the THz band suffers from the deleterious spatial-wideband and frequency-wideband effects jointly termed as the dual-wideband effect. To address this undesired phenomenon, we rigorously model the THz MIMO channel at each subarray corresponding to each user by incorporating the absorption, reflection, and free-space losses. Subsequently, a novel beamforming technique is proposed that employs only a few true time delay (TTD) lines for eliminating the beam-split effect, which is the manifestation of the spatial-wideband effect in the frequency domain. Our simulation results demonstrate a performance improvement of around 13% in terms of spectral efficiency over the existing state-of-the-art techniques.

We establish the following quantitative form of the Green--Tao theorem: if a set $\mathcal{A}$ of relative density $δ$ within the primes up to $N$ contains no nontrivial arithmetic progressions of length $k\geq 4$, then $δ\ll \exp(-(\log \log \log N)^{c_k})$ for some $c_k>0$. This improves on previous work of Rimanić and Wolf. The main new ingredients in the proof are a version of the Leng--Sah--Sawhney quasipolynomial inverse theorem for unbounded functions and a dense model theorem with quasipolynomial dependencies, which may be of independent interest.

We study intergenerational transfers of income. In our stylized model, each generation in an infinite (but countable) stream is endowed with some income. An allocation rule associates with each infinite stream another stream, thus involving intergenerational transfers of income. We single out a family of geometric rules as a consequence of imposing axioms formalizing the principles of consistency, continuity and independence (as well as the basic requirements of feasibility and scale invariance).

Symmetry-broken plasmonic nanocavities provide a simple route to engineer reflective optical response in continuous-metal metasurfaces. Here, we report an experimental study of trifolium-shaped nanocavity arrays milled into single-crystal Au(111) microplates and characterized by white-light reflection spectroscopy in the visible--near-infrared. The structured Au surfaces exhibit broad but well-defined reflection bands and pronounced low-reflectance regions that differ strongly from flat gold. We show that the optical response is highly sensitive to groove depth: increasing the cavity depth from $300$ nm to $350$ nm induces a clear redshift ($\sim 63$ nm) of the dominant long-wavelength minimum band ($λ= 700-800$ nm) and reshapes the intermediate spectral profile. In addition, the trifolium geometry shows a measurable azimuth-dependent response under sample rotation, unlike the azimuthally invariant behaviour often associated with circular groove cavities. These experimentally demonstrated properties directly support application directions in reflective structural colour, compact colour filtering, frequency-selective reflective surfaces, and optical-variable anti-counterfeiting features.

Long-standing optical quasi-periodic oscillations (QPOs) with periodicity of hundreds to thousands of days have been accepted as indicators for central sub-pc binary black hole systems (BBHs) in broad line active galactic nuclei (BLAGN). However, there are so far no direct reports on whether such reported optical QPOs have their periodicities constant in different periods. Here, based on different methods applied to light curves of 4C 50.43 in different periods, optical QPOs with periodicity of 1124days was detected in the CSS V-band light curve, while a shorter periodicity of 513days was detected in the ZTF g/r band light curves. Despite the two periodicities near-harmonic 2:1 ratio, their absence of simultaneous detection in the lomb-scargle periodograms of the ZTF light curves suggests that they are unlikely to be harmonically related. Potential factors were considered to explain these two distinct periodicities, especially different temporal coverage, signal-to-noise ratio and time steps between the CSS and ZTF light curves, as well as the effects of red noises related to intrinsic AGN variability. Our analysis shows that red noises have strong influence on the different periodicities in 4C 50.43 supporting our previous simulations. The results in this manuscript strongly indicate that it should be cautioned for applications of determined optical QPOs in BLAGN having strong intrinsic AGN variability.

Mycorrhizal networks -- often called nature's ``wood-wide web'' -- are vast underground mycelial systems that connect individual plants through countless hyphae of mycorrhizal fungi joining with plant roots. Through these hyphal webs, resources and signals -- carbohydrates, minerals, and biochemical cues -- are mutualistically exchanged and redistributed across plants, sustaining forests as relational symbiotic ecologies rather than isolated individuals. What is it like to be a plant within the wood-wide web? We present \emph{FungiSync}, a multi-person, co-located mixed reality (MR) experience that translates mycorrhizal interdependence into a felt, somaesthetic participatory ritual. Participants embody different forest plants by holding masquerade-style MR headset masks with wood-branch-like handles decorated with mushrooms. In MR, each participant perceives a distinct, audio-reactive psychedelic augmented reality overlay -- composed of resource-representing visual elements -- layered atop a shared physical terrain, symbolizing an individualized digital \emph{umwelt} (perceptual world). FungiSync reprograms human hand touch into a metaphorical mycorrhizal exchange. When participants touch hands, their digital \emph{umwelten} begin to entangle: visual elements leak, mix, and merge across perspectives, as if hyphae were forging new connections and carrying resources between hosts within a larger mycelial network. By making mycorrhizal interdependence perceptible through embodied contact, FungiSync invites participants to feel with \emph{fungal epistemics} -- a more-than-human alternative way of knowing grounded in symbiotic relationality as both an aesthetic experience and an ethical orientation -- offering a critique of the accelerated individualism characterizing our technology-mediated posthuman era.

Using multi-wavelength observations from the Solar Dynamics Observatory (SDO), we investigated the six-month decay process of the solar active region NOAA AR 12738 from April to October 2019. We systematically analyzed the region's evolution by examining extreme ultraviolet (EUV) intensity variations, quantifying magnetic flux diffusion, and investigating thermodynamic changes via Differential Emission Measure (DEM) analysis. This study presents the first long-term tracking of a peripheral dimming region (dark moat), revealing its continuous areal decrease over time. DEM results reveal cooling plasma signatures and thermal restructuring, with the dimming region exhibiting a distinct temperature deficit in range 10$^{5.5}$ -- 10$^{5.9}$~K. Potential field extrapolation identifies two dominant magnetic configurations: low-lying loops with cool plasma ($<$10$^{5.5}$ K), and high-arching structures connecting to the AR core, contributing to localized emission reduction. We found that the dimming is dominated by high-lying loops extending from the AR core, which are heated to temperatures above the main response of the 171~Å passband ($>$ 10$^{5.8}$ K), consequently lacking plasma at the typical 10$^{5.8}$~K formation temperature. The thermal deficit, not just the absence of material, is the key driver of the reduced emission. Our results demonstrate that long-duration dimming provides a valuable diagnostic for understanding active region decay, thermal evolution, and coronal magnetic restructuring.

We assess dataset agreement and late-time predictive adequacy in $Λ$CDM and its sign-switching extension, $Λ_{\rm s}$CDM, using a suite of Gaussian and exact non-Gaussian consistency diagnostics. Both models are constrained with cosmic microwave background measurements from Planck, ACT, and SPT, baryon acoustic oscillation data from DESI DR2, and low-redshift Type Ia supernova data from PantheonPlus+SH0ES. We find that commonly used Gaussian tension metrics can significantly overstate inconsistencies when broad, non-Gaussian posteriors are combined with tightly constrained datasets. In contrast, the exact non-Gaussian parameter shift indicates excellent consistency between CMB and BAO observations in both models. The $Λ_{\rm s}$CDM extension modestly improves geometric compatibility at intermediate redshifts, although reductions in parameter-level tension do not necessarily imply improved predictive consistency. These results highlight the importance of exact, non-Gaussian, and predictive diagnostics for robust assessments of cosmological model consistency.

Droplet impact on rough surfaces is of critical importance to various applications, yet remains incompletely understood. The present work aims to uncover droplet impact dynamics on random hydrophobic surfaces using volume of fluid simulations. Random fractal surfaces with RMS roughness ranging from 2 to 50 micrometers were generated using the Weierstrass-Mandelbrot function. Three identifiable impact outcomes including no bouncing, complete bouncing, and bouncing with breakup have been identified as Weber number varies between 5.7 and 12.9 and RMS roughness varies between 0 and 50 micrometers. We examine the spreading, retraction, re-spreading, and breakup stages of the impact events under different velocity and surface morphologies conditions. Numerical simulations show that the maximum spreading factor decreases linearly as surface roughness increases. Two scaling laws have been proposed for droplet impact on surfaces with small and large roughness values, respectively. A key finding is that the droplet contact time remains constant, independent of both Weber number and surface roughness. The joint effect of Weber number and surface roughness governs the wetting-bouncing transition, with larger roughness delaying the transition. This work elucidates the mechanisms governing droplet impact dynamics on random rough surfaces, thereby providing new insights directly relevant to droplet-based applications.

Remote Collaborative Augmented Reality (RCAR) enables geographically distributed users to collaborate by integrating virtual and physical environments. However, because RCAR relies on real-time transmission, it is susceptible to delay and stalling impairments under constrained network conditions. Perceptual interaction fluency (PIF), defined as the perceived pace and responsiveness of collaboration, is influenced not only by physical network impairments but also by intrinsic task characteristics. These characteristics can be interpreted as the task-specific just-noticeable difference (JND), i.e., the maximal tolerable temporal responsiveness before PIF degrades. When the average response time (ART), measured as the mean time per operation from receiving collaborator feedback to initiating the next action, falls within the JND, PIF is generally sustained, whereas values exceeding it indicate disruption. Tasks differ in their JNDs, reflecting distinct temporal responsiveness demands and sensitivities to impairments. From the perspective of the Free Energy Principle (FEP), tasks with lower JNDs impose stricter temporal prediction demands, making PIF more vulnerable to impairments, whereas higher JNDs allow greater tolerance. On this basis, we classify RCAR tasks by JND and evaluate their PIF through controlled subjective experiments under delay, stalling, and hybrid conditions. Building on these findings, we propose the Task-Aware Perceptual Interaction Fluency Model (TPIFM). Experimental results show that TPIFM accurately assesses PIF under network impairments, providing guidance for adaptive RCAR design and user experience optimization under network constraints.

The KdV-Burgers equation is a canonical model describing the interplay between nonlinearity, viscosity and dispersion, and it admits viscous-dispersive shocks as traveling wave solutions. In this paper, we establish an $L^2$-contraction property for viscous-dispersive shocks under arbitrarily large perturbations, up to a time-dependent shift. This yields time-asymptotic stability and uniform estimates with respect to the strengths of viscosity and dispersion. We present the proof for the monotone shocks, and introduce the companion work in [6] on the stability and structural properties of oscillatory shocks.

We introduce and study the weighted version of an online matching problem in the Euclidean plane with non-crossing constraints: points with non-negative weights arrive online, and an algorithm can match an arriving point to one of the unmatched previously arrived points. In the classic model, the decision on how to match (if at all) a newly arriving point is irrevocable. The goal is to maximize the total weight of matched points under the constraint that straight-line segments corresponding to the edges of the matching do not intersect. The unweighted version of the problem was introduced in the offline setting by Atallah in 1985, and this problem became a subject of study in the online setting with and without advice in several recent papers. We observe that deterministic online algorithms cannot guarantee a non-trivial competitive ratio for the weighted problem, but we give upper and lower bounds on the problem with bounded weights. In contrast to the deterministic case, we show that using randomization, a constant competitive ratio is possible for arbitrary weights. We also study other variants of the problem, including revocability and collinear points, both of which permit non-trivial online algorithms, and we give upper and lower bounds for the attainable competitive ratios. Finally, we prove an advice complexity bound for obtaining optimality, improving the best known bound.