The motion of the Solar System with respect to the cosmic rest frame induces a kinematic dipole in the stochastic gravitational-wave background (GWB). Detecting this signal with space-based interferometers would provide an independent measurement of our peculiar velocity and a GW probe of cosmic anisotropies. We present a fully analytic derivation of the response of the \emph{Laser Interferometer Space Antenna} (LISA) to a kinematic dipole, and construct an optimal estimator for its detection. We show that the dipolar response is governed by a single frequency-dependent function fixed by symmetry, and we compute its behaviour across the LISA band. Using Fisher forecasts, we find that for a scale-invariant background detectability requires $h^2Ω_{\rm GW} \gtrsim 5\times 10^{-8}$ for \emph{fiducial} LISA, and $h^2Ω_{\rm GW} \gtrsim 5\times 10^{-10}$ for a detector with characteristic instrumental-noise amplitudes improved by an order of magnitude. Prospects are more favorable for signals with richer frequency profile. We also explore the potential of the kinematic dipole to break degeneracies, particularly in the presence of strong galactic foregrounds or noise features that closely mimic the primordial signal.

Understanding grain-boundary mobility during spark plasma sintering can enable microstructure control in high-entropy carbides, yet quantitative grain-growth kinetics remain scarce. In this work, grain growth kinetics and densification behavior were investigated for single-phase fully dense (Cr,Mo,Ta,V,W)C1-δ high-entropy carbide ceramics. Specimens were densified by spark plasma sintering for a constant dwell time of 10 min at temperatures between 1750 °C and 1950 °C to isolate the role of temperature on microstructural evolution. Increasing sintering temperature produced grain growth and increased lattice parameter, while maintaining a single-phase rock salt structure. Elemental mapping showed a progressive reduction of Ta segregation with increasing sintering temperature, suggesting enhanced chemical homogenization at elevated temperatures. Grain growth kinetics were analyzed using a normal grain growth model with an assumed growth exponent of n=3, physically reasonable for grain-boundary-controlled growth influenced by solute and vacancy pinning. Arrhenius analysis of the growth factor yielded an apparent activation energy of approximately 620 kJ mol-1, comparable to diffusion-controlled processes in refractory transition-metal carbides. Densification curves revealed rapid consolidation prior to reaching the peak temperature followed by temperature-dominated grain coarsening. These results establish quantitative relationships between densification temperature, grain growth, and diffusion kinetics in a carbide system, providing insight into the microstructural stability of high-entropy, ultra-high-temperature carbide ceramics.

Designers often create visualizations to achieve specific high-level analytical or communication goals. These goals require people to extract complex and interconnected data patterns. Prior perceptual studies of visualization effectiveness have focused on low-level tasks, such as estimating statistical quantities, and have recently explored high-level comprehension of visualization. Despite the growing use of Large Language Models (LLMs) as visualization interpreters, how their interpretations relate to human understanding or what reasoning processes underlie their responses remains insufficiently understood. In this work, we explore LLMs' visualization comprehension, examining the alignment between designers' communicative goals and what their audience sees in a visualization. We have conducted a qualitative study to investigate the gap between human interpretative strategies and the reasoning pathways of LLMs across three types of visualizations, line graphs, bar graphs, and scatterplots, to identify the high-level patterns generated by LLMs using three prompt conditions. Our analysis results indicate that LLMs exhibit a consistent interpretative strategy that remains unchanged across prompt constraints. Furthermore, we observe two distinct approaches: humans naturally synthesize data into trend-centric narratives, whereas LLMs persist with a structural enumeration of comparisons and numerical ranges. Lastly, we see LLMs achieve visualization comprehension through mechanisms distinct from human intuition, pointing to critical challenges and new opportunities for visualization design.

Overcoming the limitations of current nanofabrication techniques to achieve nanoscale feature sizes is essential for achieving new regimes of light-matter interactions at extreme frequencies and length scales. Here, we demonstrate a scalable nanofabrication platform capable of producing in-plane feature sizes down to 1.75 nm, pushing the boundaries of current top-down nanofabrication techniques. Using precise thickness control of atomic layer deposition (ALD) and employing widely spaced oxide nanofins, we transform conventional ALD into a surface structuring method that produces nanolaminates with sub-10 nm periodicities over large areas. The resulting nanostructures can be used as a one-dimensional gate array to control charge carriers in two-dimensional materials. As an initial demonstration, we integrate the platform with graphene and perform electron transport measurements. In the presence of the gate array enabled by the nanolaminate, we observe satellite Dirac peaks consistent with band-structure modulation, suggestive of quantum-confinement effects. Our platform paves the way for exploring previously inaccessible regimes of nanoscale light-matter interactions, holding significant promise for applications in short wavelength optics, electronics, and polaritonics.

Superconducting traveling-wave parametric amplifiers (TWPAs) are essential elements for enhancing the signal-to-noise ratio (SNR) and thus the read-out fidelity of superconducting qubits because of their high gain and near quantum-limited noise. However, the impact of the pump source, e.g., phase noise on these amplifiers, has not yet been studied. In this work, we show that among the two amplification processes in JTWPAs, the three-wave mixing (3WM) process is more sensitive to the pump phase noise than the four-wave mixing (4WM) process. We show that the even-order nonlinearity of 4th order and above in three-wave mixing is responsible for more than 10 dB increase of phase noise at high frequency offsets within the phase noise mask as the power of the pump increases. A polynomial model of the amplifier and cyclo-stationary property of phase noise also corroborate with the simulations. The Harmonic Balance (HB) periodic noise analysis tool and Leeson phase noise model in Keysight Advanced Design System (ADS) simulator were used in this study.

The NA62 experiment at CERN has collected a large sample of $K^+$ and $π^+$ decays in flight during Run 1 in 2016--2018 and the ongoing Run 2 which started in 2021. Searches for the decays $K^+\rightarrowπ^+X$ and $π^+\rightarrow e^+N$ are presented using NA62 data collected in 2016--2022 and 2017--2024, respectively. Results are interpreted to constrain a range of new physics scenarios covering all four portal model scenarios. Upper limits on the $K^+\rightarrowπ^+X$ branching ratio are established at the $10^{-11}$ level, providing constraints on dark photon, scalar and ALP couplings. From the search for heavy neutral lepton production in $π^+\rightarrow e^+N$ decays of beam pions, upper limits of the extended neutrino mixing matrix element $|U_{e4}|^2$ are established at the $10^{-8}$ level over the heavy neutral lepton mass range 95--126~MeV/$c^2$.

We show that implementing a generalized uncertainty principle (GUP) with both minimal length and maximal momentum directly on the reduced phase space of the Schwarzschild black hole (BH) leads to a finite and discrete mass spectrum, a strict upper bound on the BH mass, a bounded entropy, and a fully regulated Hawking temperature. We further construct a GUP-deformed lapse function that preserves the ADM mass and horizon radius while exactly reproducing the GUP temperature through the surface gravity. Using the most massive observed supermassive BHs, we derive the constraint on the GUP parameter, $β\lesssim 10^{-98}$, showing that present astrophysical data already impose robust bounds on minimal length quantum gravity.

A class of solutions in $d$-dimensional Einstein gravity minimally coupled to a massless scalar field is studied, where the spacetime metric is of a generalized Weyl form with $d-2$ commuting Killing vectors. In addition to the procedure to generate scalar multipolar fields, a $SO(2)$ symmetry can be exploited to generate further solutions. A particular result of this procedure is a solution that contains the scalar counterpart of the Schwarzschild--Melvin and the Fisher--Janis--Newman--Winicour solutions as particular limits. Furthermore, a Harrison-type transformation can also be performed to generate solutions with magnetic fields. Using this transformation we obtain a solution with magnetic and scalar fields present and contains both magnetic and scalar counterparts of Schwarzschild--Melvin as limits.

The Pauli exclusion principle (PEP) was tested for nucleons in $\rm{^{12}C}$ nuclei using the Borexino dataset from 2007 to 2021. %the complete Borexino detector data. The approach consists of searching for $γ$-quanta, neutrons, protons, as well as electrons and positrons emitted in non-Paulian transitions of nucleons from the $1P_{3/2}$ shell to the filled $1S_{1/2}$ shell. Due to the uniquely low background level, the large mass, and long measurement time of the Borexino detector, the most stringent experimental constraints to date on the lifetime of the $\rm{^{12}C}$ nucleus with respect to PEP-forbidden transitions were obtained: $τ({^{12}\rm{C}}\rightarrow{^{12}\widetilde{\rm{C}}}+γ) \geq {1.1\times10^{32}}$ y, $τ({^{12}\rm{C}}\rightarrow{^{11}\widetilde{\rm{B}}}+ p) \geq {1.0\times10^{31}}$ y, $τ({^{12}\rm{C}}\rightarrow{^{11}\widetilde{\rm{C}}}+ n) \geq 2.0 \times 10^{31}$ y, $τ({^{12}\rm{C}}\rightarrow{^{12}\widetilde{\rm{N}}}+ e^- + \widetilde{ν_e}) \geq 6.4 \times 10^{30}$ y and $τ({^{12}\rm{C}}\rightarrow{^{12}\widetilde{\rm{B}}}+ e^+ + ν_e) \geq 6.6 \times 10^{30}$ y (90\% C.L.). The upper limits on the relative strengths for the non-Paulian electromagnetic, strong, and weak transitions have been obtained: $δ^2_γ\leq 1.0\times 10^{-57}$, $δ^2_{N}\leq 7.0\times 10^{-61}$ and $δ^2_β\leq 9.6\times 10^{-36}$, all at 90\% C.L..

Whether the 3D compressible Navier-Stokes-Poisson equations admit global classical solutions for general large initial data has long been a challenging open problem. In this paper, we provide an affirmative answer to this question under spherical symmetry on solid balls . Specifically, we consider the initial-boundary value problem for the multi-dimensional compressible equations with density-dependent viscosity coefficients satisfying the BD-type entropy equality, namely, assuming $μ=ρ^α,\ λ=(α-1)ρ^α$ with $N=2, α\in (\frac{1}{2},1]$ and $N=3, α\in (\frac{5}{6},1]$, we establish the global existence of spherically symmetric classical solutions to the compressible Navier-Stokes-Poisson equations for both gaseous stars and plasmas with arbitrarily large initial data on solid balls. Our key observation lies in successfully handling the singularity at the center of the ball. By controlling the growth orders of the density and the gravitational potential at the central singularity, leveraging the structural advantages of the BD entropy and spherical symmetry, and fully exploiting the coupling between the effective velocity and the velocity, we establish $L^\infty$ estimates for the key quantities, which in turn yield upper and lower bound estimates for the density. This can be regarded as the first result on the existence of global classical solutions for arbitrarily large initial data to the compressible Navier-Stokes-Poisson equations in a truly multi-dimensional domain with high-dimensional features.

In this paper, we develop a representation-theoretic formulation of discrete-time linear systems. We show that such systems are naturally viewed as representations of time groups acting on vector spaces, thereby endowing the state space with a canonical algebraic structure. This perspective provides a unified framework for linear systems over different fields, in which familiar structural properties arise from the underlying representation. In particular, invariant decompositions of the state space correspond to invariant subrepresentations, while the distinctions between real, complex, and finite-field systems emerge from the algebraic properties of the base field and the time group. We further show that linear systems over finite fields naturally correspond to representations of finite cyclic time groups, leading to module structures over polynomial quotient rings. This provides a systematic alternative to spectral analysis in settings where eigenvalue-based methods are not the most natural organizing language.

We address the problem of motivating students in Data Structures and Algorithms courses by presenting two simple problems that each have a series of improvements to a basic algorithm, leading to spectacular decreases in runtimes. Coining a new term, we refer to such sequences as being "thrills of algorithms". Seeing runtimes drop from an estimate of days (or even years) to just a few seconds has a visceral impact which conveys the importance of efficient algorithms in a way unlikely to be forgotten. The demonstrations are particularly compelling because they can be performed live in class on the lecturer's laptop. To assist staff teaching such courses we provide detailed pseudocode descriptions and complexity analyses for the various methods, and can supply implementations on request.

We investigate the extended $t$-$J$ model on honeycomb lattices with next-nearest-neighbor (NNN) electron hopping $t'$ and superexchange coupling $J'=(t'/t)^2 J$ using large-scale density-matrix renormalization group (DMRG) simulations and slave-boson mean-field theory (SBMFT). By systematically varying $t'$ and cylinder geometries, our DMRG results reveal several competing phases with distinct charge and superconducting (SC) properties. On YC4-0 cylinders possessing bonds lying along $\vec{e}_y$ direction, the ground state of doped models exhibits pronounced quasi-long-range $d$-wave SC with coexisting armchair-oriented stripes (a-stripe) across a broad range of $t'$. Notably, the SC Luttinger exponent has a non-monotonic dependence on $t'$, showing an optimal $t'_{op}\sim0.4$ for dominant SC. Conversely, XC cylinders host a competing long-range zigzag stripes phase without SC for $t'>0.5$, highlighting the role of boundary geometry in stabilizing distinct competing phases in DMRG. To elucidate the stability of all these competing phases in 2D limit, we employ SBMFT and identify the a-stripe as the stable configuration across most of phase diagram, with a transition to uniform nematic $d$-wave SC at large $t'$ for $δ=1/8$. The combined results from two complementary approaches suggest a robust $t'$-induced SC phase that might remain stable in doped extended $t$-$J$ model on the honeycomb lattice.

Although sophisticated sequence modeling paradigms have achieved remarkable success in recommender systems, the information capacity of hand-crafted sequential features constrains the performance upper bound. To better enhance user experience by encoding historical interaction patterns, this paper presents a novel two-stage sequence modeling framework termed Instance-As-Token (IAT). The first stage of IAT compresses all features of each historical interaction instance into a unified instance embedding, which encodes the interaction characteristics in a compact yet informative token. Both temporal-order and user-order compression schemes are proposed, with the latter better aligning with the demands of downstream sequence modeling. The second stage involves the downstream task fetching fixed-length compressed instance tokens via timestamps and adopting standard sequence modeling approaches to learn long-range preferences patterns. Extensive experiments demonstrate that IAT significantly outperforms state-of-the-art methods and exhibits superior in-domain and cross-domain transferability. IAT has been successfully deployed in real-world industrial recommender systems, including e-commerce advertising, shopping mall marketing, and live-streaming e-commerce, delivering substantial improvements in key business metrics.

Functional verification has become the most time-consuming phase in IC development, and Assertion-Based Verification (ABV) is key to reducing debugging time. However, existing LLM-based assertion generation methods typically pursue indiscriminate verification, aiming for maximal coverage without considering signal criticality, whereas industrial practice demands maximizing coverage with minimal verification cost. Consequently, identifying signals that have the greatest impact on design functionality and error propagation-enabling a shift from indiscriminate to targeted verification-remains a key challenge. To address this, we propose AgileAssert, a key signal-driven assertion generation framework that constructs RTL semantic graphs and identifies the top-K critical signals via a hybrid scoring and selection mechanism, followed by structure-aware RTL slicing to provide the LLM with precise targets and contextual information, thereby guiding LLMs to generate tightly constrained targeted assertions for efficient verification. Evaluated on block- and CPU-level designs, with an average 66.68% reduction in assertions, our approach outperforms three existing SOTA methods, and significantly improving coverage metrics while reducing input token consumption by 64%. In mutation testing, when our approach surpasses existing methods in error detection rate, the average number of assertions used decreases by 72.74%.

Let $β$ be a non-unit real algebraic integer greater than one and $\{a_{n}\}_{n \geq 0}$ be a sequence satisfying a linear recurrence relation $a_{n+3}=aa_{n+2}+ba_{n+1}+ca_{n}$. Under certain conditions, we prove that the number of $a_{n}$ which are palindromic concatenations of two repdigits in base $β$ is finite.

Let $G$ be a reductive algebraic group. A toric principal $G$-bundle is a principal $G$-bundle over a toric variety together with a torus action commuting with the $G$-action. Extending the Klyachko classification of toric vector bundles, Kaveh-Manon classify toric principal bundles by piecewise linear maps to the (extended) Tits building of $G$. In this paper, we use this classification to construct a moduli space of (framed) toric principal bundles with given total equivariant characteristic class, as a locally closed subvariety of a product of partial flag varieties. This extends the construction of moduli of toric vector bundles by Sam Payne.

A convolutional neural network (CNN) is used to construct a new catalog for solar flares based on high resolution (1-s cadence) Geostationary Operational Environmental Satellites (GOES) soft X-ray data. The CNN is trained to identify flare rise episodes. From 1 January 2018 to 22 August 2025, the algorithm detects 111,580 flare candidates, compared with 14,612 events in the corresponding GOES catalog. For each candidate, the probability of being a true positive is quantified by Bayesian inference based on the peak flux, rise time, and temporal coincidence with cataloged events where available. The flare size and waiting-time distributions are studied and compared with the GOES catalog. The CNN catalog shows a steeper power-law index for raw peak fluxes (-2.59 -\+ 0.02) than GOES (-2.25 -\+ 0.04), indicating the CNN's higher sensitivity to small events. After background correction, the indices are -1.97 -\+ 0.02 (CNN) and -2.05 -\+ 0.04 (GOES). The CNN catalog extends the power-law distribution of flare peak fluxes by one order of magnitude at the small-flux end compared with the GOES background-subtracted catalog. A Bayesian blocks analysis of the waiting-time distributions from the GOES and CNN catalogs indicates broad consistency with a piecewise Poisson process. We find that previously reported correlations between flare sizes and waiting times are significantly influenced by obscuration, that is, under-counting weaker or overlapping flares during periods of elevated flux. The new CNN catalog provides a foundation for complete and consistent studies of solar flare statistics.

This paper investigates multi-stream downlink precoding for massive multiple-input multiple-output low-Earthorbit satellite (SAT) communication systems. We adopt a delay and Doppler precompensation approach to achieve coherent transmission. Under this setting, we formulate a signal transmission model that incorporates the near-independent properties of inter-SAT interference and compensation errors. We then demonstrate that moving beyond single-stream transmission requires both multi-SAT cooperation and multi-antenna UTs. Based on this configuration and the established signal transmission model, we derive the first- and second-order statistical channel characteristics and utilize them to design locally optimal precoding algorithms for both total power constraint (TPC) and per-antenna power constraint (PAPC) conditions, which rely only on statistical channel state information (sCSI). In particular, the designed PAPC algorithm achieves linear complexity with respect to the number of antennas on the cooperative SATs. To reduce the computational complexity of the locally optimal precoder under TPC, we propose a low-complexity and robust precoding scheme optimized for both minimum mean squared error and sum-rate maximization objectives. Using majorization theory, we also provide a rigorous theoretical analysis of the optimal precoding structure under TPC. Moreover, the Lanczos algorithm is adopted to further reduce the complexity of the proposed robust designs. Simulation results show that when each SAT is equipped with a sufficiently large number of antennas, the proposed sCSI-based designs achieve performance comparable to that of instantaneous CSI-based designs.

The Lucas sequences are integers defined by a homogeneous recurrence relation. They include the well-known Fibonacci numbers, which appear abundantly in nature. The complementary Lucas numbers, defined by the same recurrence relation, are less well-known. In this work, we show that a special case of such complementary Lucas sequences can be observed on the same physical platform. It consists of a gain-and-loss-modulated non-Hermitian reservoir bridging two mirror-symmetric systems, which manifests the Lucas sequences in linearly localized edge states and a constant-intensity mode, respectively.

Bell statistical-strength analyses and complexity-based model selection are usually treated separately. Here we relate them by showing that a witness obtained from a coarse-graining of full Bell trials yields, through data processing, a lower bound on the Kullback-Leibler (KL) distance to a competitor class in terms of the induced witness distribution. For binary Bell-game witnesses this reduces to a Bernoulli bound, and in the CHSH scenario the local image collapses to a single threshold, giving the closed-form expression D_KL(Bern(omega) || Bern(3/4)) under uniform inputs, with a corresponding extension to known nonuniform designs. A finite-sample Hoeffding argument gives a lower confidence bound under independent trials. We also include a non-CHSH example based on the three-party Mermin-GHZ game. Because the bound is measured in bits per trial, it can be compared directly with an MDL/BIC-type complexity penalty and thereby yields a conservative crossover criterion for when a more expressive competitor becomes worthwhile. For the reproducible four-photon data of Wang et al., the witness certifies a positive information gap against locality, while a full-table comparison across local, no-signaling, saturated, and two compact nonlocal families favors low-dimensional nonlocal descriptions once complexity is charged. A four-parameter unbiased-correlator control shows that the data support compact nonlocality over locality, while only weakly distinguishing the specific cosine structure of the two-parameter model; an AIC comparison instead favors broader nonlocal controls. We also report witness-based benchmarks from additional published CHSH experiments and discuss the interpretational scope of BIC for constrained or non-regular model classes.

In this paper, we propose an unfitted finite element method to solve PDE-constrained shape optimization problems via shape gradient flow. The shape gradient flow system consists of the state equation, the adjoint equation, the velocity equation, as well as the flow map that generates the evolution of the boundary driven by the velocity field, which can be viewed as a limit system of the classical shape gradient descent algorithm. In \cite{GongLiRao} the authors proposed an evolving finite element method to solve the shape gradient flow system. Instead, in this paper, we propose an unfitted finite element method in which the evolution of the boundary is realized by cubic splines and the equations are solved by cut finite element methods with ghost penalization. Under reasonable assumptions, we are able to prove some optimal convergence rates that are further validated by numerical experiments.

This paper introduces Nemo-Nemo, a practical crash-fault tolerant (CFT) consensus protocol designed to outperform existing protocols in wide-area networks by bridging design principles from the CFT and Byzantine-fault tolerant (BFT) worlds. By structuring command propagation through a causally ordered DAG, Nemo-Nemo allows all consensus replicas to propose commands with a naturally self-regulating communication regime. By exploiting multi-leader architecture, Nemo-Nemo avoids the performance bottleneck inherent to single-leader protocols. By separating command dissemination from consensus logic, Nemo-Nemo handles challenging network conditions even when consensus commits are stalled. Moreover, leader proposals that miss a deadline are never dropped, but deterministically deferred and executed later, preserving throughput under transient network delays. And by enabling Nemo-Nemo to commit on a DAG in just two network hops, it matches the latency of existing CFT systems, while achieving significantly higher throughput. The result is a robust, deployable system: the first DAG-based CFT consensus protocol proven to exceed state-of-the-art wide-area network performance in both speed and resilience.

Determinantal point processes (DPPs) are probability models over subsets of a ground set that favor diverse selections while suppressing redundancy. That is, they tend to assign higher likelihood to collections whose elements complement one another instead of repeating the same information. For example, in recommendation systems, a DPP prefers showing users several relevant items that differ in content or style, rather than many near-duplicates of essentially the same item. Although DPPs have been studied extensively in machine learning, random matrix theory, and popularized through components of YouTube's search recommendation system, they have not been considered in the context of dynamic systems; time domain analysis is not a feature of DPPs. This paper establishes interesting connections between DPPs and control theory. By showing that the observability (controllability) Gramian parameterized by sensor (control) node subsets is a DPP, we provide a probabilistic and spectral perspective on sensor (actuator) selection for linear dynamic systems. This notion of probability here does not represent stochastic uncertainty in the system dynamics; it instead represents a likelihood measure over sensor (actuator) configurations induced by the Gramian. To that end, we derive an effective observable rank condition, characterize the balance between individual node contributions and diversity, and establish node inclusion monotonicity and negative dependence properties. Finally, we show that this formulation recovers classical greedy optimization guarantees and admits a maximum a posteriori interpretation of the sensor/actuator node selection problem. Numerical case studies on three network topologies corroborate the theoretical results.

In arXiv:2603.18175, the authors argue, based on numerical studies of particular cases, that the quantum damping of cosmological shear in a modified loop quantum cosmological model (mLQC-I) that was recently found in arXiv:2510.14021 is not generic and that the universe never becomes truly classical. In this brief Note, we revisit these claims by carefully examining the underlying assumptions and the class of initial conditions considered. We show that the examples analyzed in arXiv:2603.18175 correspond to configurations that do not represent physically admissible collapsing Bianchi I universes, as they involve mixed expanding-contracting directions and lead to effectively lower-dimensional post-bounce geometries. Restricting to physically relevant initial conditions corresponding to genuine three-dimensional contraction, we find that the quantum damping of cosmological shear is a robust dynamical feature. This conclusion is supported by both numerical and perturbative analyses, which demonstrate that the post-bounce evolution admits an isotropic attractor, with anisotropies decaying exponentially and independently of the matter content, provided that the weak energy condition is satisfied. We further outline a plausible post-bounce mechanism for the onset of classicalization.

We study the Wasserstein projection of a compactly supported probability measure onto the class of measures whose density ratio is bounded, and we place this projection in a broader program connecting generative modeling, optimal transport, and nonlinear diffusion. The paper proves existence and uniqueness of the sampleability projection, uniqueness of the Brenier map at the minimizer, path independence of the quadratic Wasserstein generation loss, and the diffusion-threshold picture for the heat semigroup. The porous medium equation is then analyzed as a candidate forward regularizer. We prove the two rigorous properties that make the equation attractive for this purpose, namely finite propagation of compact support and an explicit Wasserstein cost bound obtained from dissipation of the Rényi entropy. We then identify a structural obstruction inherent to any porous-medium version of the sampleability theory. Every nontrivial compactly supported whole-space porous-medium profile has vanishing essential infimum on any compact set containing its support, hence infinite density ratio in the original sense, and the assertion that the porous medium flow reaches the same density-ratio sampleable class while preserving compact support is false. To isolate the mathematically valid content of the nonlinear-diffusion program, we also prove an endpoint-constrained Benamou-Brenier principle for the sampleability projection and derive the corrected spectral picture near a strictly positive equilibrium on a fixed compact domain. In that regime the leading-order damping is exponential, with quadratic mode coupling in the first nonlinear correction. The Hele-Shaw and mesa-limit interpretation is therefore presented here as a conjectural variational extension rather than as a proved theorem.

Wearable Human Activity Recognition (WHAR) is a prominent research area within ubiquitous computing, whose core lies in effectively modeling intra- and inter-sensor spatio-temporal relationships from multi-modal time series data. Existing methods either suffer from high computational complexity due to attention-based fusion or lack robustness to data variations during feature extraction. To address these issues, we propose a lightweight and generalizable framework that retains the core "decomposition-extraction-fusion" paradigm while introducing two key innovations. First, we replace the computationally expensive Attention and Cross-Variable Fusion (CVF) modules with a Cascaded Fusion Block (CFB), which achieves efficient feature interaction without explicit attention weights through the operational process of "compression-recursion-concatenation-fusion". Second, we integrate a MixStyle-based data augmentation module before the Local Temporal Feature Extraction (LTFE) and Global Temporal Aggregation (GTA) stages. By mixing the mean and variance of different samples within a batch and introducing random coefficients to perturb the data distribution, the model's generalization ability is enhanced without altering the core information of the data. The proposed framework maintains sensor-level, variable-level, and channel-level independence during the decomposition phase, and achieves efficient feature fusion and robust feature extraction in subsequent processes. Experiments on two benchmark datasets (Realdisp, Skoda) demonstrate that our model outperforms state-of-the-art methods in both accuracy and macro-F1 score, while reducing computational overhead by more than 30\% compared to attention-based baselines. This work provides a practical solution for WHAR applications on resource-constrained wearable devices.

Previous studies using p-H$_2$CO $J=3$--$2$ transitions at 218 GHz suggested widespread high-temperature gas exceeding 60 K and even 100 K in the CMZ, with heating mechanisms possibly related to cosmic rays or turbulent dissipation. However, at temperatures above 100 K, p-H$_2$CO $J=3$--$2$ line emission may lead to significant overestimates of kinetic temperature. This study combines o-H$_2$CO $J=5$--$4$ data from JCMT with p-H$_2$CO $J=3$--$2$ data from APEX to analyze three molecular clouds (The Brick, Sgr A1, and Sgr A2) with high temperatures. We used the non-LTE radiative transfer code RADEX to model spectral lines and constrain physical parameters with multiple line ratios, obtaining more reliable kinetic temperatures. Our results show that the previously reported extreme temperatures ($>100$ K) based on p-H$_2$CO $J=3$--$2$ line ratios are revised downward, with the average kinetic temperatures now constrained to 84--95 K using o-H$_2$CO $J=5$--$4$ line ratios, indicating systematic overestimation in the earlier studies. Further analysis reveals that the relationship between temperature and gas line width aligns more closely with predictions from models incorporating both high cosmic ray ionization rate and turbulent heating, suggesting that these molecular clouds are likely heated by a combination of cosmic-ray and turbulent dissipation mechanisms.

Beamforming design for extremely large-scale multiple-input multiple-output (XL-MIMO) systems is challenging due to prohibitive computational complexity and complex near-field propagation effects. To address this, this paper introduces a holographic beamforming paradigm that reformulates the design from optimizing variables at spatially discrete antenna locations to shaping a continuous electromagnetic wave function over the array aperture, effectively mitigating the growth of algorithmic complexity as the array scale increases. We apply this paradigm to the challenging dual near-field (DNF) scenario, where strong transceiver coupling severely degrades conventional iterative algorithms. In this case, we propose a novel Virtual Point Source (VPS) method, which approximates the ideal wave function with a single and analytically tractable spherical-wave. A rigorous geometric-optical analysis is provided to show that the optimal VPS location can be determined in a fully non-iterative manner, thus decoupling the coupled DNF problem. The proposed method is demonstrated in an intelligent reflecting surfaces (IRS)-assisted system, where simulation results show that our non-iterative approach achieves performance comparable to converged alternating-optimization (AO) algorithms, while incurring significantly lower complexity and avoiding convergence uncertainty. This work offers a new theoretical framework for holographic beamforming design in XL-MIMO systems.

Based on first-principles calculations combined with theoretical analysis, we identify a family of monolayer chromium-based group-IV chalcogenides as a new class of two-dimensional (2D) magnetic higher-order topological insulators (HOTIs). Specifically, the CrC$X_3$ ($X=$ S, Se, Te) and CrSiS$_3$ monolayers are found to host conventional antiferromagnetic ground states with $\mathcal{PT}$ symmetry, whereas the Janus compounds Cr$_2$C$_2$S$_3$Se$_3$ and Cr$_2$Si$_2$S$_3$Se$_3$ exhibit altermagnetic ground states. We demonstrate that all these monolayer magnetic materials realize 2D HOTI phases, in which the nontrivial topology is protected by lattice $C_3$ rotational symmetry and manifests as zero-dimensional corner states carrying quantized fractional charges. Moreover, upon inclusion of spin-orbit coupling, these systems remain in the HOTI phase and continue to host robust corner-localized states, confirming the stability of their higher-order topological nature. Our results reveal an intrinsic connection between higher-order topology and magnetic order in 2D antiferromagnetic and altermagnetic systems, identifying chromium-based group-IV chalcogenide monolayers as promising platforms for exploring higher-order topological phases and their potential relevance for future topological and spintronic applications.