Next generation wireless networks focus on improving spectral efficiency (SE) while reducing power consumption and hardware cost. Reconfigurable intelligent surfaces (RISs) offer a viable solution to meet these requirements. In order to enhance the SE, index modulation (IM) has been regarded as one of the enabling technologies via the transmission of additional information bits over the transmission media such as subcarriers, antennas and spatial paths. In this work, we explore the usage of spatial paths and introduce spatial path IM (SPIM) for RIS-aided massive multiple-input multiple-output (mMIMO) systems. Thus, the proposed framework improves the network efficiency and the coverage with the use of RIS while SPIM provides SE improvement. In order to perform SPIM, we exploit the spatial diversity of the millimeter wave channel and assign the index bits to the spatial patterns of the channel between the base station and the users through RIS. We introduce a low complexity approach for the design of hybrid beamformers, which are constructed by the steering vectors corresponding to the selected spatial path indices for SPIM-mMIMO. Furthermore, we conduct a theoretical analysis on the SE of the proposed SPIM approach, and derive the SE relationship between the SPIM-based hybrid beamforming and fully digital (FD) beamforming. Via numerical simulations, we validate our theoretical results and show that the proposed SPIM approach presents an improved SE performance, even higher than that of the use of FD beamformers while using a few RF chains.

We study the impact of axial-anomaly effects on the chiral phase structure in a $U(3)$-extended soft-wall holographic QCD model. Including the pseudoscalar singlet sector allows for a dynamical description of the $η$-$η^\prime$ system through a determinant interaction with a holographic-coordinate-dependent strength. Vacuum pseudoscalar observables, particularly the $η^\prime$ mass and the $η$-$η^\prime$ mixing pattern, constrain the overall magnitude of the anomaly contribution but leave its holographic profile largely undetermined. We then examine how different anomaly profiles consistent with vacuum phenomenology affect the finite-temperature chiral transition. Constructing the Columbia plot within this framework, we find that the predicted phase structure depends sensitively on the anomaly implementation: some profiles yield crossover/second-order behavior across the entire quark-mass plane, while others generate a first-order region in the light-quark corner. These results highlight the strong sensitivity of the holographic QCD phase structure to the modeling of axial-anomaly effects.

Tool-augmented LLM agents increasingly rely on multi-step, multi-tool workflows to complete real tasks. This design expands the attack surface, because data produced by one tool can be persisted and later reused as input to another tool, enabling exploitable source-to-sink dataflows that only emerge through tool composition. We study this risk as multi-tool vulnerabilities in LLM agents, and show that existing discovery efforts focused on single-tool or single-hop testing miss these long-horizon behaviors and provide limited debugging value. We present ChainFuzzer, a greybox framework for discovering and reproducing multi-tool vulnerabilities with auditable evidence. ChainFuzzer (i) identifies high-impact operations with strict source-to-sink dataflow evidence and extracts plausible upstream candidate tool chains based on cross-tool dependencies, (ii) uses Trace-guided Prompt Solving (TPS) to synthesize stable prompts that reliably drive the agent to execute target chains, and (iii) performs guardrail-aware fuzzing to reproduce vulnerabilities under LLM guardrails via payload mutation and sink-specific oracles. We evaluate ChainFuzzer on 20 popular open-source LLM agent apps (998 tools). ChainFuzzer extracts 2,388 candidate tool chains and synthesizes 2,213 stable prompts, confirming 365 unique, reproducible vulnerabilities across 19/20 apps (302 require multi-tool execution). Component evaluation shows tool-chain extraction achieves 96.49% edge precision and 91.50% strict chain precision; TPS increases chain reachability from 27.05% to 95.45%; guardrail-aware fuzzing boosts payload-level trigger rate from 18.20% to 88.60%. Overall, ChainFuzzer achieves 3.02 vulnerabilities per 1M tokens, providing a practical foundation for testing and hardening real-world multi-tool agent systems.

We develop a fully relativistic framework to study the rotational response of gravitationally coupled two-fluid neutron stars within the slow-rotation approximation. Treating the two components as independently conserved perfect fluids interacting only through spacetime curvature, we derive the coupled equilibrium and frame-dragging equations and exploit their linear structure to construct a basis decomposition of the rotational response. This formulation leads to a natural definition of the effective total moment of inertia, which generalizes the single-fluid concept and depends solely on the equilibrium background. It further reveals that the coupled system admits two intrinsic collective rotational eigenmodes, characterized by distinct eigen-moments of inertia, even in the absence of relative rotation between the fluids. Applying this framework to neutron stars containing dark matter, we explore how the presence of an additional gravitationally bound component modifies the global rotational response and its relation to tidal deformability. Our results demonstrate that the persistence or breakdown of rotational-tidal universality in two-fluid neutron stars is governed by dark-sector microphysics rather than by the mere presence of an additional component, and establish a unified framework for interpreting rotational observables, intrinsic mode structure, and universal relations in multi-component relativistic stars.

We show that the uniform Littlewood Conjecture (ULC) recently introduced by Bandi, Fregoli and Kleinbock is false. More precisely the counterexamples form a residual set, the method further suggests positive Hausdorff dimension. For a mildly twisted problem, we indeed separately show that the Hausdorff dimension is at least $1$. Moreover, we disprove a uniform version of the $p$-adic Littlewood problem, as well as some twisted weaker version of a more general $S$-arithmetic setting, for any proper subset (possible infinite) of primes $S$. The latter contrasts the classical (non-uniform) case where the answer is known to be affirmative when $S$ has at least two elements. The disproof of ULC, our main new result, is semi-constructive; the non-constructive part involves effective results on Zaremba's famous conjecture by Bourgain and Kontorovich, as well as estimates for the cardinality of product sets over finite fields.

For $2\le k\le t<s$, the Erdős-Rogers function $f^{(k)}_{t,s}(N)$ denotes the largest $m$ such that every $K^{(k)}_s$-free $k$-graph on $N$ vertices contains a $K^{(k)}_t$-free induced subgraph on $m$ vertices. Mubayi and Suk (J. London Math. Soc. 2018) conjectured that $f^{(k)}_{k+1,k+2}(N)=(\log_{(k-2)}N)^{Θ(1)}$ for $k\ge 4$, where $\log_{(i)}$ denotes the $i$-fold iterated logarithm. This is equivalent to the statement that $f^{(k)}_{k+1,s}(N)=(\log_{(k-2)}N)^{Θ(1)}$ for every $s\ge k+2$. In this paper, we introduce multi-color patterns into a random construction of a $2$-graph to build a $4$-graph, and for the first time, combine them with multi-layer extremum structures to prove that $f^{(4)}_{5,s}(N)=(\log \log N)^{Θ(1)}$ for every $s\ge 11$. More generally, using a variant of the Erdős-Hajnal stepping-up lemma, we also establish that $f^{(k)}_{k+1,s}(N)=(\log_{(k-2)}N)^{Θ(1)}$ for every $s\ge k+7$.

Deep research systems powered by LLM agents have transformed complex information seeking by automating the iterative retrieval, filtering, and synthesis of insights from massive-scale web sources. However, existing systems predominantly follow an autonomous "query-to-report" paradigm, limiting users to a passive role and failing to integrate their personal insights, contextual knowledge, and evolving research intents. This paper addresses the lack of human-in-the-loop collaboration in the agentic research process. Through a formative study, we identify that current systems hinder effective human-agent collaboration in terms of process observability, real-time steerability, and context navigation efficiency. Informed by these findings, we propose InterDeepResearch, an interactive deep research system backed by a dedicated research context management framework. The framework organizes research context into a hierarchical architecture with three levels (information, actions, and sessions), enabling dynamic context reduction to prevent LLM context exhaustion and cross-action backtracing for evidence provenance. Built upon this framework, the system interface integrates three coordinated views for visual sensemaking, and dedicated interaction mechanisms for interactive research context navigation. Evaluation on the Xbench-DeepSearch-v1 and Seal-0 benchmarks shows that InterDeepResearch achieves competitive performance compared to state-of-the-art deep research systems, while a formal user study demonstrates its effectiveness in supporting human-agent collaborative information seeking. Project page with system demo: https://github.com/bopan3/InterDeepResearch.

The narrowness of the optical transitions of rare-earth-ion dopants makes them highly sensitive probes of their environment. We measured the optical transitions Er$^{3+}$ dopants to determine the previously unknown magnetic ordering of Gd$_{2}$SiO$_{5}$ -- a promising host for quantum applications of rare-earth dopants. By measuring the transitions' magnetic-field dependence we determined an antiferromagnetic ordering with spins oriented along or slightly canted from the crystal's $a^*$ axis. The optical transitions are narrower than the coupling to gadolinium spins revealing information about the coupling strengths. We further optically measured a Néel temperature of $1.86\pm0.01_\mathrm{stat.}\pm0.07_\mathrm{syst.}$ K, and assembled a phase diagram in applied field and temperature showcasing a triple point where two gadolinium sites order semi-independently from each other. At high applied field the erbium dopants show long optical coherence times up to 0.4 ms at 3 T; at low fields these are probably limited by three low-frequency magnon modes below 10 GHz, observed directly. This study can be used to benchmark a method of magnetic structure determination.

We consider the pricing of derivatives written on accumulated marks, such as weather derivatives or aggregate loss claims, using a self-exciting marked point process. The jump intensity mean-reverts between events and increases at jump times by an amount proportional to the mark. The resulting state process, where the variable $U_t$ accumulates jump magnitudes, is a piecewise deterministic Markov process (PDMP). We derive the discounted pricing equation as a backward partial integro-differential equation (PIDE) in two spatial dimensions. To overcome the dimensionality, we propose an exponential (Laplace/Fourier) transform in the accumulated mark variable, which diagonalizes the translation operator and reduces the pricing problem to a family of one-dimensional PIDEs in the intensity variable along a Bromwich contour. For Gamma-mixture mark laws (under actuarial or Esscher-tilted measures), the nonlocal jump term is efficiently approximated by generalized Gauss--Laguerre quadrature. We solve the reduced PIDEs backward in time using a monotone IMEX finite difference scheme (implicit upwind drift and discounting, explicit jump operator) and recover option prices via numerical inversion. We provide a rigorous, term-by-term global error bound covering time and space discretization, quadrature, interpolation, and boundary effects, supported by numerical experiments and Monte Carlo benchmarks.

Generative artificial intelligence (GenAI) is increasingly embedded in computer-supported collaborative learning (CSCL), yet little empirical research has unpacked how different configurations of AI participation reshape collaborative processes. This study investigates how GenAI configuration shapes collaborative regulation in authentic classroom settings. Two eighth-grade classes engaged in small-group creative problem-solving under two conditions: a shared-AI configuration, in which each group interacted with a single AI mentor, and an individual-AI configuration, in which each student accessed a personal AI instance. Using multi-layer discourse coding combined with lag sequential analysis (LSA) and ordered network analysis (ONA), we examined interaction distribution, AI-student coupling, shared regulation processes, and teacher orchestration. Results reveal distinct regulatory dynamics across configurations. Shared AI access promoted convergence-oriented collaboration, with stronger alignment of shared regulatory states and more coordinated group-level reasoning. In contrast, individual AI access distributed support across learners, producing more exploratory and evaluative cycles but also more fragmented interaction patterns, accompanied by increased teacher intervention to manage divergence. These findings suggest that AI configuration functions as a structural design variable that reorganizes the regulatory ecology of classroom collaboration.

Nonlinear pulse propagation in multimode fibers (MMFs) offers a compact, low-cost route to broadband, tunable femtosecond light, but most control schemes act by changing the spatial mode composition, typically resulting in irregular or speckled beams in exchange for maximal spectral tunability. Here we introduce a complementary mechanism: bending-induced local dispersion modification of a high-order mode (HOM) to steer the spectrum while keeping the spatial mode fixed. We launch an LP0,7 mode into a step-index MMF and apply programmable macrobends near the input. With a standard Yb pump at 1030 nm, this yields spatially clean, continuous spectral tuning across 700-1350 nm, while the output profile remains Bessel-like and robust to reconfiguration of controlled bends. A perturbative model explains the observed spatial-spectral decorrelation, showing that moderate curvature produces first- and second-order shifts in group delay and group-velocity dispersion of the HOM with minimal change in its modal composition; these dispersion shifts control soliton fission, dispersive-wave emission, and the soliton self-frequency shift. We further validate application utility by driving multicolor, extended-depth-of-focus multiphoton microscopy directly from this all-fiber source. To our knowledge, this is the first demonstration of bending-induced dispersion modification, rather than mode mixing, used to tune MMF supercontinuum spectra without sacrificing beam quality, laying the foundation for an alternative pathway to tunable femtosecond illumination for imaging and spectroscopy.

There is a series of scalar models possessing reflectionless kinks whose linear perturbations are described by a Pöschl-Teller potential at integer level $σ$. The cases $σ=1$ and $2$ are the well-known Sine-Gordon and $ϕ^4$ double-well models. The $σ=3$ kink has received relatively little attention because it exhibits a $ϕ^{8/3}$ potential, whose third derivative diverges in the vacuum. In old-fashioned perturbation theory this yields a cubic interaction that diverges far from a kink. We nonetheless use this interaction to calculate the amplitudes and probabilities for incoming radiation to excite or de-excite one of the kink's two shape modes. As each shape mode is localized about the kink, the leading order amplitudes are nonetheless finite. This suggests that the $σ=3$ model is not pathological, but rather its mesons are quantum field theoretic extensions of Znojil's bound states.

Strong magnetic fields modify the force that confines quarks inside hadrons and make it direction-dependent. Using quark-antiquark potentials obtained from lattice simulations as inputs to a quark potential model, we investigate how the anisotropic confinement affects the mass spectrum of quarkonium. In the strong-field regime, we find downward mass shifts induced by a softening of the confining potential along the field direction. In particular, the mass shifts of radially excited states are more significant than that of the ground state. For the longitudinal spin eigenstates, the excited-state spectrum strongly depends on the magnetic-field strength, in contrast to the spectrum with conventional isotropic confinement, which is insensitive to the field strength. This provides a clean probe of magnetically induced confinement anisotropy that can be confirmed in future lattice simulations.

For scalar maximum distance separable (MDS) codes, the conventional repair schemes that achieve the cut-set bound with equality for the single-node repair have been proven to require a super-exponential sub-packetization level.As is well known, such an extremely high level severely limits the practical deployment of MDS codes.To address this challenge, we introduce a partial-exclusion (PE) repair scheme for scalar linear codes.In the proposed PE repair framework, each node is associated with an exclusion set.The cardinality of the exclusion set is called the flexibility of the node.The maximum value of flexibility over all nodes defines the \textit{flexibility} of the PE repair scheme. Notably, the conventional repair scheme is the special case of PE repair scheme where the flexibility is 1. Under the PE repair framework, for any valid flexibility, we establish a lower bound on the sub-packetization level of MDS codes that meet the cut-set bound with equality for single-node repair. To realize MDS codes attaining the cut-set bound under the PE repair framework, we propose two generic constructions of Reed-Solomon (RS) codes. Moreover, we demonstrate that for a sufficiently large flexibility, the sub-packetization level of our constructions is strictly lower than the known lower bound established for the conventional repair schemes.This implies that, from the perspective of sub-packetization level, our constructions outperform all existing and potential constructions designed for conventional repair schemes. Finally, we implement the repair process for these codes as executable Magma programs, thereby exhibiting the practical efficiency of our constructions.

Bars in disk galaxies slow down as they transfer their angular momentum to their dark matter halo via dynamical friction from near-resonant orbits. This bar-halo dynamical friction can become ineffective once phase mixing erases the phase-space gradient around the main resonances. We present fully self-consistent $N$-body simulations of a Milky Way-like disk galaxy with a single dwarf-galaxy fly-by in prograde and retrograde orbits before, during, and after bar formation. In our models, the fly-bys do not trigger a long-lived tidal bar; the bar forms on essentially the same time as in the isolated model. After the encounter, however, all perturbed models develop bars that are stronger and slower than in the isolated one. The final pattern speed depends little on the encounter time, but it does depend on the encounter direction relative to the disk rotation: prograde encounters slow the bar more than retrograde ones. The angular-momentum evolution shows that the disk loses its angular momentum and the halo gains it, consistent with bar-halo friction. By probing the particle distribution of the halo in angle-action space, we demonstrate that the isolated bar enters a metastable, saturated state with a flattened distribution in the phase space around the bar's corotation resonance, whereas a dwarf passage excites long-lived fluctuations in the halo that restore the phase-space gradients near the corotation and thereby sustain the bar-halo friction. This mechanism explains the continued slowdown and growth of bars after fly-bys. It may be relevant to the Milky Way, whose bar formed near the epoch of a major ancient accretion event, suggesting that an early encounter could have influenced the subsequent secular evolution of the bar.

Gravitational waves constitute a powerful probe of the underlying theory of gravity. In extensions of general relativity, additional degrees of freedom, such as scalar fields in the gravitational sector, can modify their propagation through changes in the effective friction term and propagation speed. These modifications may potentially induce resonant phenomena leading to distinctive signatures in the gravitational wave spectrum. One important aspect to be investigated is whether the resonances can be strong enough to enhance the underlying background of primordial tensor modes to levels detectable by upcoming gravitational wave detectors, such as LISA or the Einstein telescope. The characteristic peaks in the SBGW spectrum depend on the parameters of the resonant model as well as on the parameters of the primordial tensor spectrum, such as $r$ and $n_{t}$. Thus these resonance effects open a powerful pathway to explore physics of the very early Universe by amplifying otherwise feeble signals to experimentally detectable levels. Here we analyze how the signals of the primordial Universe can resonate in these scenarios, bringing the early universe physics into the realm of experimental access.

Click-through rate (CTR) prediction tasks typically estimate the probability of a user clicking on a candidate item by modeling both user behavior sequence features and the item's contextual features, where the user behavior sequence is particularly critical as it dynamically reflects real-time shifts in user interest. Traditional CTR models often aggregate this dynamic sequence into a single vector before interacting it with contextual features. This approach, however, not only leads to behavior information loss during aggregation but also severely limits the model's capacity to capture interactions between contextual features and specific user behaviors, ultimately impairing its ability to capture fine-grained behavioral details and hindering models' prediction accuracy. Conversely, a naive approach of directly interacting with each user action with contextual features is computationally expensive and introduces significant noise from behaviors irrelevant to the candidate item. This noise tends to overwhelm the valuable signals arising from interactions involving more behaviors relevant to the candidate item. Therefore, to resolve the above issue, we propose a Core-Behaviors and Distributional-Compensation Dual-View Interaction Network (CDNet), which bridges the gap between sequential and contextual feature interactions from two complementary angles: a fine-grained interaction involving the most relevant behaviors and contextual features, and a coarse-grained interaction that models the user's overall interest distribution against the contextual features. By simultaneously capturing important behavioral details without forgoing the holistic user interest, CDNet effectively models the interplay between sequential and contextual features without imposing a significant computational burden. Ultimately, extensive experiments validate the effectiveness of CDNet.

When free/libre and open source software (FLOSS) stewards centralize project development, they potentially undermine project sustainability and impact how contributors talk to each other. To study the relationship between steward-centralized development and contributor discussion, we compared the development of three Wikimedia platform features that the Wikimedia Foundation (WMF) built in MediaWiki. In a mixed-methods multi-case comparison, we used repository mining, linguistic style features, and principal component analysis to track MediaWiki feature development and issue discussions. Contrary to both our intuition and prior work, there were no identifiable differences in the linguistic style of WMF-affiliates and external contributors, even when feature development was guided by WMF contributions. From these results, we offer two provocations to the study of collaborative FLOSS development: (1) stewards dominate development according to their own use of specific project functionality; (2) centralized project development does not entail hierarchical language within project discussions.

Two-dimensional superconductivity has become a major frontier in condensed matter physics. It holds the key to the mechanism of high-temperature superconductors and offers an exceptional arena to stabilize emergent quantum states enabled by enhanced electron correlations in reduced dimensionality. These states are frequently characterized by spatial modulations and intertwined with competing orders, calling for studies that combine real-space imaging with local spectroscopy. Scanning tunneling microscopy and spectroscopy meets this need by directly accessing local density of states with lattice-scale resolution. In this review, we summarize recent advances of the study on several representative unconventional superconductors using this technique, focusing on direct characterization of high-temperature superconducting planes, pair-density waves, and topological superconductivity in both artificial heterostructures and intrinsic materials. We conclude by outlining current challenges and future directions motivated by the microscopic insights.

For a stable real bundle $E$ of rank $2$ and degree $1$ on a real genus $2$ curve, we describe the action of the real structure of the curve on the set of $4$ maximal line subbundles of degree $0$ of $E$. This describes the Galois action on the set of lines through a real point in the moduli space of such bundles, and is a real algebraic extension of classical work of Newstead. Our proof is an application of techniques of Atiyah from the 1950's. We prove also results on real line subbundles in higher genus using work of Lange-Narasimhan.

A handful of planetary systems hosting a Hot Jupiter have been subsequently found to also host long-period giant planets. These ``cold Jupiters,'' giant planets residing beyond the snow line ($\sim$3\,au), play an important role in the dynamical evolution of the system as a whole. In this work, we investigate the detectability of cold Jupiters around a sample of 28 well-studied Hot Jupiter host stars to estimate the occurrence rate of this distinctive system architecture. We perform extensive simulations using the combination of all publicly available radial velocity (RV) data for those stars with synthetic RV data. The synthetic data test observing strategies along three axes: cadence, duration, and measurement precision. For each scenario, we determine detection limits based on the semi-major axis at which a 1 Jupiter mass planet would be recovered 50\% of the time. We find the following: 1) the existing RV data are remarkably insensitive to these Hot Jupiter/Cold Jupiter pairs; 2) the total baseline over which an observational campaign is carried out is the dominant factor in our ability to detect cold Jupiters; and 3) the results are relatively insensitive to the individual RV measurement precision. We conclude that metre-class telescopes with lower RV precision are ideally suited to surveying Hot Jupiter-cold Jupiter systems.

Financial platforms and enterprise systems frequently provide transaction export capabilities to support reporting, reconciliation, auditing, and regulatory compliance workflows. In many environments, these exports involve very large datasets containing hundreds of thousands or even millions of transaction records. Traditional REST API implementations often construct the entire export payload in application memory before transmitting the response to the client, which can lead to high memory consumption and delayed response initiation when processing large datasets. This paper presents a streaming-based REST API architecture that retrieves transaction records incrementally from relational databases and writes them directly to the HTTP response output stream. By integrating database cursor retrieval with progressive HTTP transmission, the proposed design allows export data to be delivered continuously as records are processed rather than after the full dataset has been assembled. The architecture is implemented using a Java-based JAX-RS framework with the StreamingOutput interface and supports multiple financial export formats including CSV, OFX, QFX, and QBO. In practice, the streaming approach significantly reduces memory buffering requirements and allows large export downloads to begin immediately, improving responsiveness and scalability for high-volume export operations.

Many-particle quantum systems often give rise to exotic behaviors in their nonequilibrium dynamics that are rather challenging to reveal with analytical methods or with classical computation. Here, we consider the case of a system of many quantum emitters coupled through a radiation bath. By adopting an efficient mapping of the bosonic modes onto a set of quantum bits, we implement quantum circuits, compatible with NISQ (Noisy Intermediate-Scale Quantum) era systems, that allow us to investigate the dynamics of the ensemble as a function of various parameters, including the number of emitters, the spectral inhomogeneity in the system, the emission lifetime of independent emitters, and the spatial separation between emitters. The quantum algorithms afford us the capacity to precisely track the emergence of cooperative dynamics, manifested through superradiant emission, as the system is tuned towards optimal coupling with respect to various parameters. We are particularly able to characterize superradiant emission in an inhomogeneous ensemble as a function of the linewidth of the individual emitters. These quantum algorithms avoid approximations performed in conventional studies of many-emitter systems and provide a robust and intuitive characterization. Despite being limited to a small number of qubits, the present calculations are found to provide a reliable characterization validated by comparison with analytical solutions and classical computation results in their respective regimes of validity. These findings indicate that the approach can be employed to effectively simulate a broad variety of many-emitter systems.

This paper investigates change-point of variance in panel data models with time series of $α$-mixing. Based on the cumulative sum (CUSUM) method and the individual differences, we construct a CUSUM test for panel data models to detect variance changes. Under the null hypothesis, we derive the limit distribution of this test, which can be used to detect the change-point of variance. Under the alternative hypothesis, the limit behavior of the CUSUM test is also derived. To validate the performance of the test, we conducted simulation analyses on with Gaussian and Gamma errors. The results demonstrate that this testing method significantly outperforms existing approaches, particularly in detecting sparse variance changes. Finally, we conducted a practical case study using panel data from the Shanghai Shenzhen CSI 300 Index Components. Not only did we successfully identify the change-points of variance, but we also delved deeper into the underlying economic drivers behind these changes.

The utilization of Large Language Models (LLMs) to power human-like agents has shown remarkable potential in simulating individual mobility pattern. However, a significant gap remains in modeling cohorts of agents in dynamic and interactive systems where they must take strategic routing decisions to response mobility-specific task. To bridge this gap, we introduce LLM-DR, a novel agent framework designed to simulate the heterogeneous decision-making of riders in the on-demand instant delivery task scenario. Our framework is founded on two principles: 1) Empirically-grounded personas, where we use unsupervised clustering on a large-scale, real-world trajectory dataset to identify four distinct rider work strategies; and 2) Reasoning-based routing process, where each persona is instantiated as an LLM agent that employs a structured Chain-of-Thought (CoT) process to make human-like routing choices. This framework enables the construction of high-fidelity simulations to investigate how the strategic composition of a rider workforce influences system-level outcomes regarding their mobility pattern. We validate our framework on an real-world instant deliver order datasets, demonstrating its capacity to model complex rider behavior in an interactive market scenario. This work provides pioneering findings in agentic mobility system empowered by LLM.

Involution, a phenomenon of excessive competition with diminishing returns, has become a pressing socio-economic concern in contemporary China, prompting both academic inquiry and policy interventions. This paper proposes an evolutionary game model of involution that incorporates agent migration and spatial heterogeneity in resource distribution. The model captures realistic features such as effort-based resource allocation, local interactions on a lattice, and mobility driven by payoff comparisons. We explore how varying conditions of migration and resource allocation influence the dynamics of involution. The key findings from our simulations are as follows: when total resources are held constant, similar resource levels across different regions tend to suppress involution; conversely, an increase in total resources exacerbates it. In addition, the probability of migration does not significantly affect the final evolutionary outcome. We further identify threshold effects in the effort ratio and utility multiplier, revealing critical conditions under which involution emerges or subsides. To further elucidate these simulation results, we conduct a theoretical analysis using mean-field theory, which provides analytical expressions for the equilibria and stability conditions. The theoretical predictions are in excellent qualitative agreement with simulation outcomes. Finally, we discuss real-world counterparts of the model, including competition among food delivery riders and between stores offering similar services.

In this paper we utilize a convex integration scheme to construct non-trivial solutions to the stationary KdV equation which lie in $L^p(\mathbb{T})$, $p < 2$. In addition, we demonstrate this result is sharp in the sense that if $u \in L^2(\mathbb{T})$ is a weak solution then $u \in C^\infty(\mathbb{T})$.

This study proposes an acceleration technique for the computational challenges in extending the variational deterministic-particle-based scheme (VDS) [Bao et al., Journal of Computational Physics 522 (2025) 113589] to 3D complex fluid simulations with multi-bead polymers. While the original VDS effectively captures configuration space dynamics for 2D dumbbell polymers, its direct extensions reveal critical scalability limitations. The growing configuration space dimensionality necessitates prohibitively large particle ensembles to maintain distributional accuracy, so its quadratic computational cost scaling impedes practical applications. In this paper, we develop a model reduction framework integrating proper orthogonal decomposition (POD) to speed up the computation of the VDS for microscopic Fokker-Planck equations. Numerical validation using bead-spring chain models in simple shear flow demonstrates that the computational efficiency of the reduced model increases systematically with molecular complexity. The reduced-order model introduces about $6\%$ relative error in predicting the dynamics while requiring only about $6\%$ of the original computational time for $4$-bead chain polymers, where the relative numerical error of the reference dynamics is about $5\% \sim 10\%$, and the degrees of freedom can be reduced significantly to about $0.1\%$ of the original model, which means the low-dimensional structure is found by POD. This establishes a practical pathway for multiscale and complex fluid simulations.

A priori estimates for the mean curvature evolution of Killing graphs in Cartan-Hadamard manifolds with asymptotic Dirichlet conditions are established. As an application, the existence of the corresponding parabolic flow is proved, ensuring regularity of the obtained solutions through the construction of suitable barriers at points of the asymptotic boundary. Such a construction is made possible under an appropriate notion of convexity at infinity.

Non-terrestrial networks (NTNs) increasingly rely on non-geostationary (NGSO) constellations that combine radio frequency (RF) feeder links (FLs) with free space optical (FSO) inter-satellite links (ISLs). Downlink performance in such systems is often constrained by uneven satellite-gateway visibility, data traffic congestion, and rain-induced FL attenuation, leaving the downlink capacity of some satellites underutilized while others become bottlenecks. To prevent such non-uniform load distribution, this paper presents a fairness-driven load balancing strategy that treats the satellite constellation in space as an anycast multi-commodity flow problem. Then, by solving an equivalent linear programming optimization problem, the proposed algorithm dynamically selects the most convenient ground station (GS) to serve each satellite and, when needed, offloads data traffic to adjacent satellites through FSO ISLs. Using a realistic MEO satellite constellation with 1550 nm FSO ISLs and Ka-band feeder links, the method stabilizes the reverse link data service, maintaining the average data rate but notably improving the worst-case throughput. Our proposed algorithm enhances the minimum downlink data rate by more than 25% in the presence of rain and by over 10% under no-rain conditions. These results demonstrate that the use of an ISL-assisted load-balancing scheme mitigates FL bottlenecks and enhances fairness across the satellite constellation, offering a scalable basis for resource allocation in future NTN systems.