In this short note, we prove the non-existence of slow and fast small nontrivial compact solutions for the Euler-Poisson system in $1$D. The proof is based on the virial estimate which provides local in space average decay of bounded small solutions.

Advanced Persistent Threats (APTs) remain difficult to detect due to their stealthy nature and long-term persistence. To tackle this challenge, provenance-based threat hunting has gained traction as a proactive defense mechanism. This technique models audit logs as a whole-system provenance graph and searches for subgraphs that match APT patterns recorded in Cyber Threat Intelligence (CTI) reports. However, several limitations persist: 1) significant memory and time overhead due to the extremely large provenance graphs; 2) imprecise segmentation of APT activities from provenance graphs due to their intricate entanglement with benign operations; and 3) poor alignment of attack representations between CTI-derived query graphs and provenance graphs due to their substantial semantic gaps. To address these limitations, this paper presents ProHunter, an efficient and accurate provenance-based APT hunting system with a platform-independent design. To minimize system overhead, ProHunter creates a compact data structure that efficiently stores long-term provenance graphs using semantic abstraction and bit-level hierarchical encoding strategies. To segment APT behaviors, a heuristic-driven threat graph sampling algorithm is designed, which can extract precise attack patterns from provenance graphs. Furthermore, to bridge the semantic gaps between CTI-derived graphs and provenance graphs, ProHunter proposes adaptive graph representation and feature enhancement methods, enabling the extraction of consistent attack semantics at both localized and globalized levels.Extensive evaluations on real-world APT campaigns from DARPA TC E3, E5 and OpTC datasets demonstrate that ProHunter outperforms state-of-the-art threat hunting systems in terms of efficiency and accuracy. Our code is available at https://github.com/xueboQiu/ProHunter.

An equidistribution is a theoretical quality criteria that measures the uniformity of a linear pseudo-random number generator (PRNG). In this work, we first show that all existing linear cellular automaton (CA) based pseudo-random number generators (PRNGs) are weak in the equidistribution characteristic. Then we propose a list of light-weight combined CA-based PRNGs with time spacing ($2 \leq s \leq 10$) using linear maximal length cellular automata of degree $31 \leq k \leq 128$ (close to computer word size). We show that these PRNGs achieve maximal period as well as satisfy the maximal equidistribution property. Finally, we show that these combined maximal length CA-based PRNGs pass almost all the empirical testbeds, with speed and performance comparable to the Mersenne Twister.

Programmable shaping of femtosecond ultraviolet (UV) pulses is still much less flexible than at visible and near-infrared wavelengths, mainly because direct UV modulators remain limited in bandwidth, throughput and damage threshold. Here we show that dispersive four-wave mixing (DFWM) in a gas-filled hollow-cappillary fibre (HCF) can transfer programmed spectral phase from the near infrared (NIR) to the UV without relying a narrowband pump. A shaped NIR signal at 1032 nm and a chirped 516-nm pump generate a 344-nm idler, which is characterized with transient-grating frequency-resolved optical gating (TG FROG). As a benchmark, second-order dispersion (SOD) applied to the signal is quantitatively reproduced in the idler. We then demonstrate the transfer of two nontrivial phase patterns: a localized nominal π-step and a moderate sinusoidal modulation. In the π-step case, a step imposed on the long-wavelength side of the signal appears on the short-wavelength side of the idler, consistent with the 2*pump - 1*signal mixing relation. In the sinusoidal case, the periodic phase produces a split temporal waveform in both signal and idler. These results show that gas-filled HCF DFWM can act as a practical spectral-phase transducer from the NIR to the UV, while also revealing a trade-off between conversion efficiency and phase-transfer fidelity.

Objectives: This study aims to characterize the dose-performance relationship for opportunistic CT and disentangle the contributions of segmentation failure and dose-dependent HU bias to performance degradation. Methods: Simulated low-dose CT images at 1-75% of full dose were generated from 50 paired full- and low-dose chest CT scans. An independent dataset of 22 paired PCCT acquisitions at lung cancer screening (LCS) and chest x-ray-equivalent (CXR) dose levels provided parallel real-world evaluation. Multiple quantitative disease metrics were obtained using deep learning-based segmentation followed by quantitative metric extraction. Classification performance was evaluated against full-dose reference standards, with additional analyses isolating the contributions of segmentation error and HU bias. Agreement between dose levels was assessed using Bland-Altman and correlation analyses. Results: Mean HU metrics maintained classification accuracy to CXR-equivalent dose (3%); bias correction improved accuracy from 88% to 96% for hepatic steatosis and from 84% to 90% for sarcopenia. Trabecular bone attenuation maintained 98% accuracy at LCS dose. Volume metrics (cardiomegaly) achieved 94% accuracy at CXR-equivalent dose. Threshold-based metrics required LCS dose for reliable classification; bias correction improved accuracy from 58% to 92%. Coronary artery calcification scoring reached 96% accuracy at LCS dose. In both Mayo and PCCT datasets, agreement analyses demonstrated strong correlation for all metrics except coronary artery calcification. Conclusions: Opportunistic CT is feasible at reduced dose levels though it becomes less robust at ultra-low doses. Distinct failure modes are caused by HU bias or segmentation failure and depend on the clinical task. Providers should be aware of these task-specific limitations when designing opportunistic screening programs.

We know that there exist semi-groups for contact type Hamilton-Jacobi equations, which refers to \cite{KLJ2}. Guy Barles and Agnès Tourin give a proof of the commutation properties for normal Hamilton-Jacobi equations at \cite{GA}. In this article, we provide a proof of the commutation property of semi-groups for contact type Hamilton-Jacobi equations.

In implicit time marching of the radiative transfer equation (RTE), the resulting linear systems are commonly solved using source iteration with diffusion synthetic acceleration (SI-DSA). Despite its widespread success, the performance of the DSA preconditioner may deteriorate when the RTE cannot be well approximated by its diffusion limit. Moreover, classical SI-DSA does not exploit low-rank structures of the solution manifold across time steps when the solution evolves smoothly. To address these limitations, we develop an on-the-fly reduced-order-model (ROM)-based acceleration for SI-DSA in implicit time marching of the RTE. Instead of relying on a diffusion approximation, the proposed approach constructs ROMs directly from the underlying kinetic formulation while exploiting low-rank structures in the temporal evolution of the solution. The method is fully offline-free and constructs ROMs to enhance both initial guesses and preconditioners on the fly during time marching. To handle streaming solution data, we design efficient and memory-lean ROM construction and adaptive update strategies based on dynamical mode decomposition, incremental low-rank singular value decomposition, and error indicators. Numerical experiments demonstrate that the proposed method consistently accelerates implicit time marching, delivering $1.4\times$ to $2.0\times$ speedup over classical SI-DSA while incurring only marginal overhead for ROM construction and updates.

Let $G$ be a locally compact abelian group, and let $ω:G \to [1,\infty)$ be a measurable weight, i.e., $ω$ is measurable, and $ω(s+t)\leq ω(s)ω(t)$ for all $s, t \in G$. Let $\mathcal{A}$ be a semisimple commutative Banach algebra with a predual $\mathcal A_\ast$ such that the Gel'fand space $Φ_{\mathcal A}\subset \mathcal{A}_\ast$. If $ω^{-1}$ is vanishing at infinity, then we show that the Banach algebra $L^1(G,ω,\mathcal{A})$ is a BSE- algebra if and only if $\mathcal A$ is a BSE- algebra.

Repeated games are a framework for investigating long-term interdependence of multi-agent systems. In repeated games, zero-determinant (ZD) strategies attract much attention in evolutionary game theory, since they can unilaterally control payoffs. Especially, fair ZD strategies unilaterally equalize the payoff of the focal player and the average payoff of the opponents, and they were found in several games including the social dilemma games. Although the existence condition of ZD strategies in repeated games was specified, its extension to stochastic games is almost unclear. Stochastic games are an extension of repeated games, where a state of an environment exists, and the state changes to another one according to an action profile of players. Because of the transition of an environmental state, the existence condition of ZD strategies in stochastic games is more complicated than that in repeated games. Here, we investigate the existence condition of fair ZD strategies in the periodic prisoner's dilemma game, which is one of the simplest stochastic games. We show that fair ZD strategies do not necessarily exist in the periodic prisoner's dilemma game, in contrast to the repeated prisoner's dilemma game. Furthermore, we also prove that the Tit-for-Tat strategy, which imitates the opponent's action, is not necessarily a fair ZD strategy in the periodic prisoner's dilemma game, whereas the Tit-for-Tat strategy is always a fair ZD strategy in the repeated prisoner's dilemma game. Our results highlight difference between ZD strategies in the periodic prisoner's dilemma game and ones in the standard repeated prisoner's dilemma game.

The induced Ramsey number $r_{\mathrm{ind}}(G,H)$ is defined as the minimum order of a graph $F$ on such that any 2-coloring of its edges with red and blue leads to either a red induced copy of $G$ or a blue induced copy of $H$. Motivated by the Kohayakawa-Prömel-Rödl conjecture, we prove that a quadratic upper bound $\mathrm{r}_{\text {ind}}\left(G, F_n\right) \leq C n^2$ for fixed $G$, where $F_n$ is a graph with one central vertex, $2n$ leaf vertices, and $n$ disjoint edges. In particular, for star graphs $K_{1, \ell}$ $(\ell \leq n)$, constructive coloring and matching arguments yield $2 n+2 \ell-1 \leq \mathrm{r}_{\text {ind}}\left(K_{1, \ell}, F_n\right) \leq(\ell+n-1)(\ell+1)+1$, with the exact value $\mathrm{r}_{\text {ind}}\left(K_{1,2}, F_n\right)=3 n+4$.

Quantum systems promise to revolutionize information processing science and technology [1-3]. The preservation of quantum coherence, the defining property of qubits, fundamentally constrains the performance of quantum information processing with quantum memories [4]. While trapped atomic ions theoretically support million-year coherence based on spontaneous emission [5-7], experimental demonstrations have reached far less, only about an hour [8-13]. Here we combine clock-state qubits with decoherence-free subspace (DFS) encoding to achieve coherence exceeding ten hours. Using correlation-based phase tracking in 171Yb+ ion pairs sympathetically cooled by 138Ba+ ion, we demonstrate this without magnetic shielding or enhanced microwave phase stabilization that previously limited coherence times. DFS encoding references the qubit phase to the inter-ion energy difference to reject microwave phase noise and common-mode magnetic fluctuations, while clock states provide environmental insensitivity. Throughout measurements extended to 1600 seconds, we observe minimal coherence decay, with exponential fits yielding a coherence time of (3.77 +/- 1.09) x 10^4 seconds. Our results establish DFS encoding as a form of passive error correction that eliminates technical noise constraints, unlocking the million-year coherence potential of atomic ions for scalable quantum information processing.

Spin-orbit coupling (SOC) gives rise to complex magnetic states such as spin liquids, skyrmion crystals, and topological spin-wave excitations. We consider exchange interactions in multi-orbital Mott insulators where SOC is strong on ligand ions. SOC on the ligands enables electron hopping accompanied by spin flips and fluctuations in the orbital state of the ligand hole. These processes generate anisotropic exchange interactions and greatly increase the number of possible exchange paths. The number grows further with the inclusion of hopping between ligands, which mediates interactions between more distant spins. We propose an effective method to calculate exchange interactions at arbitrary separations between spins. Applying it to monolayer CrI$_3$, we obtain anisotropic interactions between nearest-neighbor and next-nearest-neighbor Cr spins, as well as single-ion anisotropy induced by long-range hopping. In this material, magnetic anisotropy stabilizes long-range ferromagnetic order and opens a magnon gap at the Dirac points, which defines a nontrivial magnon band topology. Using Hubbard model parameters from first-principles calculations, the resulting spectrum agrees well with the spin-wave dispersion observed experimentally in bulk CrI$_3$, except that the calculated Dirac gap is much smaller.

Asteroseismology of member pulsators provides a robust physical constraint on cluster parameters by linking internal stellar structures to the global properties of the host cluster. However, the parameters of NGC 1647 remains poorly constrained due to limited investigation, a situation that cluster asteroseismology can significantly refine. In this study, we identified 271 high confidential cluster members in NGC 1647, using HDBSCAN clustering with radial-velocity validation. Its initial age is determined in the range of 1250-280 Myr, derived from isochrone fitting based on multi-survey metallicities extinction-corrected Gaia photometry. Among the members, we found 96 periodic variables from TESS and K2 photometry, including nine p-mode pulsators (five δ Sct and four hybrid δ Sct-γ Dor stars). Assuming a common cluster age and initial chemical composition, joint asteroseismic modeling is performed based on measured large frequency separations and individual mode frequencies. This yields a metallicity of [Fe/H] = -0.08+0.04-0.01, well consistent with the spectroscopic determinations, and a seismic age of 178+11-9 Myr, more precise than isochrone-based estimates. This work shows the diagnostic potential of δ Sct asteroseismology in young open clusters and establishes a high-precision benchmark for future studies of NGC 1647 and other open clusters.

We report the first direct comparisons of multiple alternative social media algorithms on multiple platforms on outcomes of societal interest. We used a browser extension to modify which posts were shown to desktop social media users, randomly assigning 9,386 users to a control group or one of five alternative ranking algorithms which simultaneously altered content across three platforms for six months during the US 2024 presidential election. This reduced our preregistered index of affective polarization by an average of 0.03 standard deviations (p < 0.05), including a 1.5 degree decrease in differences between the 100 point inparty and outparty feeling thermometers. We saw reductions in active use time for Facebook (-0.37 min/day) and Reddit (-0.2 min/day), but an increase of 0.32 min/day (p < 0.01) for X/Twitter. We saw an increase in reports of negative social media experiences but found no effects on well-being, news knowledge, outgroup empathy, perceptions of and support for partisan violence. This implies that bridging content can improve some societal outcomes without necessarily conflicting with the engagement-driven business model of social media.

The Next-Generation Atmospheric Cherenkov Telescope Array (NG-ACTA) is proposed as a prospective infrastructure for very high energy (VHE) gamma-ray astronomy, consisting of a mixed-aperture array of 88 telescopes with a maximum array diameter of 10 km. The array adopts a three-tier configuration of 30 m large-aperture Large Size Telescopes (LSTs), 12 m medium-aperture Medium Size Telescopes (MSTs), and 6 m small-aperture Small Size Telescopes (SSTs), enabling continuous gamma-ray detection across the full energy band from 20 GeV to 100 TeV. With core advantages of an ultra-low detection threshold ($\leq20$ GeV), ultra-high angular resolution ($\leq0.04^\circ$), ultra-large effective area ($\geq1\times10^5$ m$^2$), extreme cosmic ray background rejection (proton rejection efficiency $\geq99.99\%$), and rapid transient response ($\leq100$ ns trigger latency), NG-ACTA targets the most cutting-edge and transformative fundamental scientific topics in modern astrophysics and particle physics, including VHE gamma-ray astronomy, cosmic ray origin, multi-messenger astronomy, and dark matter as well as new physics tests. The array's scientific goals cover five core fields: particle astrophysics, VHE gamma-ray astronomy, cosmic ray physics, multi-messenger astronomy, and new physics exploration, with six hierarchical and mutually supportive scientific objectives from Galactic to extragalactic sources, steady to transient objects, and conventional objects to dark matter. A comprehensive comparison with international under-construction facilities (e.g., CTAO-North, CTAO-South) and Chinese facilities (e.g., LACT) demonstrates that NG-ACTA leads the world in low-energy threshold, baseline length, background suppression, and multi-messenger rapid response capabilities.

The proton-disordered molecular phase of water ice (ice-VII) and its ultrahigh-pressure non-molecular phase (ice-X) share identical macroscopic crystal symmetry (space group $Pn\bar{3}m$). This raises a fundamental thermodynamic question: are they distinct phases separated by a singularity, or are they adiabatically connected via a continuous crossover? To resolve this paradox, we investigate the finite-temperature phase diagram of high-pressure ices VII and X, as well as VIII, the proton-ordered phase that emerges at lower temperatures, using an effective classical spin-$1$ Blume-Capel model on the pyrochlore lattice. Through Monte Carlo simulations, we demonstrate that within this model, the transformation between the states corresponding to ice-VII and ice-X lacks a thermodynamic singularity, as characterized by non-divergent and non-coinciding peaks in the specific heat and susceptibility associated with the $S^z=0$ occupation. We attribute this continuous crossover behavior to the topological fragility of the hydrogen-bond network: the thermal proliferation of point-like monopole excitations (violations of the ice rules) induces Debye-Hückel screening of the emergent gauge field, destroying the topological Coulomb phase at any finite temperature. In contrast, the destruction of the proton-ordered ice-VIII phase involves spontaneous symmetry breaking and remains a first-order phase transition. Our findings provide a microscopic rationale that reconciles the macroscopic crystallographic symmetries of dense ice with its underlying topological properties.

Stable and remarkable valley polarization effect is the key to utilizing valley degree of freedom in valleytronic devices. According to first-principles calculations and symmetry analysis, we reveal that valley polarization effect in monolayer V2Se2O altermagnet is correlated with the net magnetic moment between magnetic V atoms under uniaxial strain, thereby proposing two strategies for achieving giant valley polarization effect. Firstly, substituting one V atom in V2Se2O with Cr to construct a ferrimagnetic monolayer VCrSe2O enhances the net magnetic moment between magnetic atoms, thereby realizing a giant valley polarization effect. Applying uniaxial strain along either the a-axis or b-axis significantly increases the value of valley polarization, which exhibits a nearly linear relationship with the net magnetic moments between the magnetic atoms. Secondly, constructing a van der Waals heterostructure composed of V2Se2O and α-SnO monolayers breaks mirror symmetry, thereby inducing a net magnetic moment, which in turn causes a remarkable valley polarization effect. Compressing the interlayer distance of the heterostructure can increase the net magnetic moment between V atoms, then enhancing the value of valley polarization to nearly 400 meV. This work reveals that valley polarization in monolayer altermagnet is correlated with the net magnetic moment between magnetic atoms. Finally, we propose two strategies to achieve giant valley polarization based on monolayer altermagnets, providing theoretical guidance for the potential applications of ferrimagnetic monolayers and altermagnet-based heterostructures in valleytronics.

In high-penetration renewable power systems with complex and highly variable operating scenarios, grid-connected inverters (GCIs) may transition between different control modes to adapt to diverse grid conditions. Among these, the switching between grid-following (GFL) and grid-forming (GFM) control modes is particularly critical. Nevertheless, safe and robust GFL-GFM switching control strategies for GCIs remain largely unexplored. To overcome this challenge, this paper establishes a full-order small-signal state-space model for the GFL-GFM switched system, precisely reflecting all internal circuit and control dynamics. Subsequently, the small-signal security region (SSSR) of the switched system is defined and characterized, followed by an in-depth investigation into the multi-parameter impacts on the SSSRs and internal stability margin distributions (ISMDs). Furthermore, a novel comprehensive stability index (CSI) is proposed by integrating the stability margin, parameter sensitivity, and boundary distance. Based on this CSI, a multi-objective adaptive GFL-GFM switching control strategy is designed to guarantee the dynamic security and robustness of the system. Finally, the proposed SSSR analysis method for the GFL-GFM switched system and the designed CSI-based switching control mechanism are validated through electromagnetic transient (EMT) simulations.

Self-testing is a phenomenon where the use of specific quantum states or measurements can be inferred solely from the correlations they generate. We introduce a universal method for conducting robustness analysis in the self-testing of various quantum resources. Unlike previous numerical approaches, which rely on selecting specific isometries, our method optimizes over equivalence transformations, thereby leading to tighter robustness bounds. This optimization employs the well-established technique of semidefinite programming relaxations for non-commuting polynomial optimization. Our method can be universally applied to diverse self-testing settings, including steerable assemblages in the Bell scenario, constellations of quantum states in the prepare-and-measure scenario, and entangled states in the steering scenario. We demonstrate the method's capability to surpass previously reported robustness bounds across a range of concrete examples.

In this paper, we consider the nonsmooth convex optimization problems over the fixed point constraint sets of firmly nonexpansive operators. To find an optimal solution of the problem, we present an iterative method based on the hybrid steepest descent method and the idea of a delayed subgradient scheme in which allows the use of staled subgradients from the earlier iteration when updating the next iteration. We start the convergence part by deriving an upper bound for the difference of the best-achieved function values and the optimal value. After that, to ensure the convergence in iterations, we prove that there exists a subsequence of the generated sequence by the proposed method which converges to an optimal solution. Moreover, we subsequently show that the whole generated sequence converges to an optimal solution when the strict convexity of the objective function is imposed. We further extend the presented results to the centralized network system consisting of a finite number of workers and a central server. Finally, we apply the proposed method to image inpainting problems. The numerical results describe the effect of delay in many cases of objective functions.

The Framework for Unified and Robust data Analysis with JAX (Furax) is an open-source Python framework for modeling data acquisition systems and solving inverse problems in astrophysics and cosmology. Built on JAX, Furax provides composable building blocks in the form of general-purpose and domain-specific linear operators, along with preconditioners and solvers for their numerical inversion. Domain-specific tools are provided for astrophysical and cosmic microwave background (CMB) data analysis$-$including map-making, instrument modeling, and astrophysical component separation$-$with a modular architecture designed to extend to other fields.

We introduce a stabilizer formalism for EAQECCs with noise ebits, using special subgroups of product groups of two Pauli groups. This formalism includes the two coding schemes,given by Lai and Brun (C.Y. Lai and T. A. Brun, PHYSICAL REVIEW A 86, 032319 (2012)), for EAQECCs with imperfect ebits as special cases. Then two equivalent formalisms of the formalism are derived in nomenclature of sympletic geometry and additive codes. We apply this theory to construct some EAQECCs with noise ebits, and analyze their performance.

The integration of Large Language Models (LLMs) and Graph Neural Networks (GNNs) promises to unify semantic understanding with structural reasoning, yet existing methods typically rely on static, unidirectional pipelines. These approaches suffer from fundamental limitations: (1) Bidirectional Error Propagation, where semantic hallucinations in LLMs or structural noise in GNNs permanently poison the downstream modality without opportunity for recourse; (2) Semantic-Structural Dissonance, particularly in heterophilous settings where textual similarity contradicts topological reality; (3) a Blind Leading the Blind phenomenon, where indiscriminate alignment forces models to mirror each other's mistakes regardless of uncertainty. To address these challenges, we propose CO-EVOLVE, a dual-view co-evolution framework that treats graph topology and semantic embeddings as dynamic, mutually reinforcing latent variables. By employing a Gauss-Seidel alternating optimization strategy, our framework establishes a cyclic feedback loop: the GNN injects structural context as Soft Prompts to guide the LLM, while the LLM constructs favorable Dynamic Semantic Graphs to rewire the GNN. We introduce three key innovations to stabilize this evolution: (1) a Hard-Structure Conflict-Aware Contrastive Loss that warps the semantic manifold to respect high-order topological boundaries; (2) an Adaptive Node Gating Mechanism that dynamically fuses static and learnable structures to recover missing links; (3) an Uncertainty-Gated Consistency strategy that enables meta-cognitive alignment, ensuring models only learn from the confident view. Finally, an Entropy-Aware Adaptive Fusion integrates predictions during inference. Extensive experiments on public benchmarks demonstrate that CO-EVOLVE significantly outperforms state-of-the-art baselines, achieving average improvements of 9.07% in Accuracy and 7.19% in F1-score.

Nanodiamonds containing nitrogen-vacancy (NV) centers are promising quantum sensors for biological applications thanks to their sub-micron spatial resolution, biocompatibility, and versatile multi-modal responses. However, the optically detected magnetic resonance (ODMR) measurement requires laser irradiation, creating a trade-off between high-throughput and low phototoxicity for applications in live cells. Here to address this challenge we develop a widefield quantum sensing method based on light-sheet microscopy (LSM), in which the sample is illuminated by a vertically movable laser sheet and the fluorescence is collected along the vertical axis that is orthogonal to the light sheet. This LSM-ODMR system is demonstrated to feature high throughput sensing due to the wide-field configuration, fast three-dimensional imaging and sensing due to the vertical mobility of the light sheet, enhanced sensitivity due to suppression of out-of-focus background fluorescence, and low phototoxicity for bio-sensing due to elimination of out-of-focus illumination. This LSM-based widefield nanodiamond sensing provides an approach for biological studies with low phototoxicity, offering three-dimensional and multi-modal sensing capability.

Graph energy has been widely investigated in spectral graph theory. However, the manner in which this energy is distributed among individual vertices has received attention only more recently, following the introduction of energy of a vertex by O. Arizmendi et al. in 2018. Since then, several studies have explored this concept. In the present work, we focus on splitting graphs and shadow graphs and study how the total energy of a graph is distributed among its vertices. We further establish explicit expressions for vertex energies in these derived structures and analyze their behavior in comparison with the underlying graph.

This paper presents a refined analysis of the block error rate (BLER) of polar codes over symmetric binary-input discrete memoryless channels under successive cancellation (SC) and successive cancellation list (SCL) decoding. A novel expression for the BLER under SC decoding is derived directly in terms of the decoder's LLRs. Building on this formulation, we propose a polar code construction algorithm optimized for SC decoding and evaluate its performance under SC and dynamic SC flip (DSCF) decoding against established SC-optimized constructions, including Gaussian approximation (GA)-based and Tal-Vardy polar codes. Furthermore, by decomposing the BLER into path loss and path selection components, we derive a novel LLR-based expression for the path loss probability, which enables an SCL-optimized polar code construction method. The proposed constructions are evaluated under SCL decoding with list sizes 2, 4, and 8, and are compared with 5G standard polar codes, GA-based designs, and Reed-Muller polar codes. Simulation results show that the proposed SC-optimized polar codes achieve up to a 0.2 dB performance gain under DSCF decoding over the AWGN channel compared to benchmark constructions, and exhibit superior performance over binary symmetric channels. For SCL-optimized polar codes, the proposed method achieves comparable or improved performance across all considered list sizes, with gains of up to 0.4 dB relative to benchmark designs.

Let k be an algebraically closed field of characteristic zero and let B be a finitely generated k-domain. We study semisimple derivations on B, with special emphasis on those whose eigenvalues are integers. For such derivations, after passing to the field of fractions and choosing a rational slice s with D(s) = s, we describe the kernel of D explicitly in terms of semi-invariant generators. We also obtain descriptions of the kernel on suitable localizations of B and on B itself by intersection. Several basic properties of semisimple derivations and their behavior under conjugation are also discussed

In this paper, building on previous work, we extend the thermodynamic formalism for random open dynamical systems generated by piecewise monotone interval maps with countably many branches. Under summable and contracting assumptions on the potential, we establish the Ruelle-Perron-Frobenius type theorem for the associated random open operator and prove exponential decay of correlations. In addition, we investigate the escape rate for the hole and conditionally invariant measure for the open system.

Multi-Task Fusion plays a pivotal role in industrial short-video search systems by aggregating heterogeneous prediction signals into a unified ranking score. However, existing approaches predominantly optimize for immediate engagement metrics, which often fail to align with long-term user satisfaction. While Reinforcement Learning (RL) offers a promising avenue for user satisfaction optimization, its direct application to search scenarios is non-trivial due to the inherent data sparsity and intent constraints compared to recommendation feeds. To this end, we propose SaFRO, a novel framework designed to optimize user satisfaction in short-video search. We first construct a satisfaction-aware reward model that utilizes query-level behavioral proxies to capture holistic user satisfaction beyond item-level interactions. Then we introduce Dual-Relative Policy Optimization (DRPO), an efficient policy learning method that updates the fusion policy through relative preference comparisons within groups and across batches. Furthermore, we design a Task-Relation-Aware Fusion module to explicitly model the interdependencies among different objectives, enabling context-sensitive weight adaptation. Extensive offline evaluations and large-scale online A/B tests on Kuaishou short-video search platform demonstrate that SaFRO significantly outperforms state-of-the-art baselines, delivering substantial gains in both short-term ranking quality and long-term user retention.

Since its discovery, global polarization of the $Λ$ hyperon in heavy-ion collisions has been firmly established and is widely attributed to the large vorticity generated in the rotating quark-gluon plasma. In contrast, nearly fifty years after the first observation of unexpectedly large transverse $Λ$ polarization in unpolarized hadron collisions, its underlying mechanism remains an open and long-standing puzzle, despite being observed across a broad range of collision systems. Although these two phenomena exhibit notable similarities, they are generally regarded as arising from distinct physical origins. In this work, we propose a direct connection between $Λ$ global polarization in heavy-ion collisions and the long-standing transverse polarization observed in unpolarized collision systems. We demonstrate that the alignment between the $Λ$ production plane and the reaction plane, driven by directed flow, can transfer transverse polarization into the measured global polarization signal. Realistic Monte Carlo simulations of Au+Au collisions at $\sqrt{s_{\rm NN}} = 3$ GeV indicate that this mechanism can generate a sizable global polarization, accounting for approximately $23\%\pm6\%$ of the magnitude reported by the STAR Collaboration. Our results establish, for the first time, a quantitative link between these two well-known phenomena and have important implications for the interpretation of $Λ$ global polarization measurements in low-energy heavy-ion collisions.