Papers

This work presents the spatially resolved mapping of methane decomposition chemistry in a short direct-current glow discharge, revealing segregated zones for dissociation and polymerization in an Ar-CH4 mixture at 400 mTorr. Laser-induced fluorescence (LIF), two-photon absorption LIF (TALIF), and optical emission spectroscopy (OES), are used to map the absolute number densities of atomic hydrogen (H), methylidyne (CH), and dicarbon (C2) radicals. The results reveal a segregated chemical environment driven by the non-local electron kinetics. The primary dissociation of methane is confined to the cathode sheath (< 4 mm), where the H atom density peaks at a value (). Analysis of the Halpha} line profile identifies two distinct suprathermal H atom populations with peak kinetic energies of ~110 eV and ~17.5 eV, attributed to ion-surface reflection and electron-impact dissociation, respectively. The densities of secondary radicals CH and C2 peak further from the cathode at the sheath-negative glow boundary (y=4-6 mm), identifying this region as the primary zone for polymerization, with the peak C2 density higher than that of CH by a factor of ~370. The discharge operates under strong non-equilibrium conditions, confirmed by the disparity between the low bulk gas temperature (~570 K) and the high vibrational temperature (3300-4700 K) of the emitting CH(A) radicals, the latter serving as a signature of a specific high-energy dissociative excitation pathway. This work demonstrates how the structured energy landscape of a short glow discharge spatially separates methane dissociation from subsequent polymerization. Kinetic estimates suggest that suprathermal H atoms may play a role in bulk plasma chemistry via abstraction reactions, with predicted CH4 activation rates exceeding those of the thermal H population.

In 1986, Füredi and Kahn showed that the dimension $\dim(P)$ of any finite poset $P$ satisfies $\dim(P) = O(d \log^2 d)$, where $d$ is the maximum degree of the comparability graph of $P$. Scott and Wood more recently improved this bound to one of the form $d \log^{1+o(1)} d$. We show that $\dim(P) = O(d \log d)$, thus confirming that the corresponding lower bound of Erdős, Kierstead, and Trotter is tight up to the implicit constant.

We study online allocation problems where $n$ requests over $m$ resources arrive in an adversarial order and must be served immediately and irrevocably. This framework captures both Online Resource Allocation, where the goal is to maximize value subject to resource budgets, and Online Load Balancing, where the goal is to minimize the makespan. We seek $(1\pm\epsilon)$-competitive algorithms in the large-budget or large-makespan regime. We consider a sampling model that generalizes the following two well-studied sampling models. In the Single-Sample Prophet Inequality ($\mathsf{SSPI}$) model, request $t$ is drawn from an unknown distribution $\mathcal{D}_t$, and the algorithm is given one independent sample from each $\mathcal{D}_t$ before the online phase. In the $p$-$\mathsf{Sample}$ model, the requests are adversarial, but a uniformly random $p$-fraction is revealed upfront as training data. Although near-optimal algorithms are known in the easier random-order model ($\mathsf{RO}$), where the requests arrive in a uniformly random order, prior algorithms for $\mathsf{SSPI}$ and $p$-$\mathsf{Sample}$ were problem-specific and incurred substantially worse dependencies on $\epsilon$, $m$, and $n$. Our main contribution is a general framework that converts $\mathsf{RO}$ algorithms into algorithms for the $p$-$\mathsf{Preview}$ model, a model that generalizes both $\mathsf{SSPI}$ and $p$-$\mathsf{Sample}$. As consequences, we obtain near-optimal bounds for Online Resource Allocation, generalized Online Load Balancing, and online mixed packing-covering problems in these adversarial-order sampling models, significantly improving the bounds of [Ghuge, Singla, Wang (STOC'25)] and [Gupta and Molinaro (SODA'26)].

We study the decoupling of branes sourcing AdS flux vacua from the asymptotic bulk using scalar-wave absorption probabilities. In a one-modulus truncation, the result depends only on the dimension of the AdS vacuum and on the asymptotic steepness of the scalar potential. We find that for any steepness and for any dimension greater than two the absorption probability vanishes in the low-energy limit, showing that the branes decouple from the bulk. We illustrate the general analysis in several scale-separated AdS vacua. For DGKT we find $P_{\rm abs}\sim\omega^{27/7}$ and an effective transverse dimension $d_{\rm eff}=20/7$. Interestingly, the scalar potential along the brane-induced moduli trajectory agrees with that obtained by compactifying a hypothetical $(4+13/7)$-dimensional gravity theory on a $13/7$-dimensional sphere threaded by flux. We also apply the analysis to scale-separated $\mathrm{AdS}_3$ examples and to the simplest one-modulus KKLT model.

We present two results concerning the decidability of (strong) quasipositivity of links in the 3-sphere. First, using a result of Dynnikov–Prasolov, we provide an algorithm to decide whether or not a link is strongly quasipositive. Second, we reduce the decision problem of the quasipositivity of links to that of braids.

We consider an application of the Atiyah-Bott fixed point theorem in quaternionic geometry. We review the relation of the general Salamon complex of a quaternionic manifold and the Dolbeault complex with coefficients in a certain holomorphic vector bundle of its twistor space. Furthermore, we investigate which maps are suitable for the application of the fixed point theorem. As a result, we obtain a fixed point formula for both complexes and apply it to Wolf spaces.

Living systems compute with chemistry by mapping environmental signals onto specific internal chemical states. Despite recent advances in molecular programming, it remains unclear which physicochemical features control the computational expressivity of chemical systems. Here we inverse-design thermodynamically consistent chemical reaction networks whose steady-state response to an environmental input computes a target nonlinear function. Using implicit differentiation we train the free-energy landscape directly: standard chemical potentials, transition-state energies and thermodynamic drives. Increasingly large networks generated by elementary ligation and cleavage steps fit increasingly complex nonmonotonic polynomial functions, with expressivity scaling logarithmically with network size, predicted primarily by the number of reactions. Training individual energetic parameter classes reveals that internal thermodynamic drives, capable of breaking detailed balance, dominate trainability, with comparable performances achieved only by pairs of parameter classes. These results identify nonequilibrium drive as the most effective single resource for steady-state computational expressivity in chemical reaction networks.

Software clones are fragments of code that are similar or functionally equivalent to each other. They pose significant challenges for maintenance, refactoring, and bug detection. Detecting Type-IV clones, which are semantically equivalent but may differ syntactically, is particularly difficult for traditional token- or syntax-based methods. Recent machine learning approaches rely on contrastive learning, which requires careful negative sampling and can introduce bias. In this paper, we propose LWVIC4Code, a non-contrastive representation learning approach specifically designed for Type-IV clone detection. Building on the Variance-Invariance-Covariance Regularization (VICReg) framework and prior layer-wise VICReg training, LWVIC4Code introduces cross-layer consistency regularization and depth-dependent layer weighting to progressively refine semantic information across transformer layers, producing robust and discriminative code representations. We conduct an empirical study comparing LWVIC4Code against a contrastive learning baseline and zero-shot large language models on Python (Kamino) and multi-language (GPTCloneBench) datasets. Results show that LWVIC4Code achieves competitive or superior performance without negative samples, benefits from layer-wise supervision, and generalizes effectively from Python to other languages, particularly Java and C#. These results demonstrate that non-contrastive, layer-wise representation learning is a promising direction for robust semantic code clone detection.

I present the first implementation in MadGraph5_aMC@NLO for bound-state production, including quarkonium, leptonium, and B(c) mesons within Non-Relativistic Quantum Chromo-Dynamics (NRQCD) and Non-Relativistic Quantum Electro-Dynamics (NRQED). In these proceedings, I focus on the extension of MadGraph5_aMC@NLO to quarkonium states and describe the capabilities of the new framework for inclusive and associated S-wave quarkonium production in a wide variety of experimental environments at Leading Order (LO). These developments provide the community with a unified, automated, and efficient framework for bound-state production in QED and QCD, and establish a solid foundation for our future Next-to-Leading-Order (NLO) extension.

We investigate the zero-Hopf bifurcation and the local $C^{1}$-non-integrability of the original Rössler system. First, we characterize the unique zero-Hopf equilibrium of the system and study its perturbation by means of the first-order averaging theory. We prove that, under suitable assumptions on the bifurcation parameters, three distinct families of periodic orbits bifurcate from the zero-Hopf equilibrium, substantially extending the previously known result in which only one bifurcating periodic orbit was obtained. In the second part of the paper, these bifurcating periodic solutions are used to investigate the integrability properties of the Rössler system. By combining the first-order averaging theory with the classical Poincaré criterion for first integrals, we prove that the bifurcating periodic orbits constitute a generic obstruction to the existence of local first integrals of class $C^{1}$. This demonstrates that averaging theory provides not only an effective tool for detecting periodic solutions but also a powerful method for the integrability analysis.

Stage lighting education requires instructors to bridge abstract concepts, technical operations, and learner-understandable representations. While Virtual Reality (VR) removes physical constraints, existing systems provide limited support for live instruction. We present LumiNote, an LLM-assisted VR system that transforms spoken pedagogical intent into instructor-reviewable spatial annotations, executable demonstrations, and linguistic support. In an exploratory study with 3 instructors and 24 students, we examined how instructors incorporated LumiNote into familiar lighting topics and how students received the resulting representations. We found LLM assistance most valuable for expressive, under-specified goals, but requiring greater expert intervention for fixture-specific or spatial configuration requests. Instructors engaged with generated suggestions as a controllable refinement process, shifting effort from manual setup toward pedagogical expression. However, representations that externalized expert reasoning did not always align with novice comprehension. These findings characterize LLM-assisted VR instruction as a domain-grounded mediation process among expert expression, executable operations, and learner-facing representations.

We present a generating-function approach to the topological entropy of finite strongly connected digraphs, working throughout with digraphs in which loops are allowed but multiple edges are excluded. Using dominant singularities of path-generating functions, we recover by new analytic–combinatorial arguments the known first and second positive-entropy minimizers from the previously studied loopless spectral setting, and extend the corresponding extremal statements to the present framework. For the class $\mathcal{SC}_{m+1}(m)$ of strongly connected digraphs with $m$ vertices and $m+1$ edges, we introduce a unified $(t,k_1,k_2)$-butterfly parametrization. The entropy of $\mathcal{B}^{\,t}_{k_1,k_2}$ depends only on $(k_1,k_2)$ and is determined by the unique root $R\in(0,1)$ of $1-z^{k_1}-z^{k_2}=0$ via $h=-\ln R$. This parametrization yields a detailed entropy hierarchy within $\mathcal{SC}_{m+1}(m)$. We introduce the Pyramidal Entropy Diagram, determine the entropy order completely for $m\leq 7$, and identify its first structural bifurcation at $m=8$. We further establish maximal stable initial and terminal segments consisting of ten entropy minima and two entropy maxima, respectively, and derive an explicit formula for the minimum order required to realize a positive entropy not exceeding a prescribed threshold.

We prove a spectral gap inequality for Gaussian measures modified by singular attractive pair interactions. The spectral gap constant is explicit and uniform in the number of particles and the regularization parameter. As an application, we use a corresponding spectral gap inequality for a cutoff interaction weight to obtain two-sided bounds on the transition density of the attractive logarithmic gas.

Pinching antennas enable radiation points to be created and reconfigured along extended waveguides, making the physical locations of wireless transmission and reception controllable after infrastructure deployment. This capability introduces a spatial degree of freedom beyond conventional beamforming and resource allocation, with implications that extend from individual links to network-wide operation. This tutorial develops a network-oriented perspective on pinching-antenna systems. We first review their system architecture, channel characteristics, and fundamental design opportunities. We then examine how radiation-location reconfigurability can support environment-division multiple access by strengthening desired links and suppressing cross-links, and discuss its roles in multi-cell transmission, traffic offloading, and inter-cell cooperation. Moving from instantaneous users to entire service regions, we introduce traffic-aware and geometry-aware designs under a cell-free-inspired multi-waveguide architecture. Representative system models, optimization problems, analytical illustrations, and numerical results are provided to explain the main design tradeoffs and network-level insights. We further discuss generalized physical realizations and representative deployment modes, including standalone, conventional base-station-integrated, and distributed deployments, together with their main implementation considerations. Finally, we identify future research directions involving mobility management, programmable and virtualized radio access, environment knowledge acquisition, AI-native control, low-altitude networks, space-air-ground integration, and integrated sensing and communication. Overall, this tutorial presents radiation locations as configurable network resources and provides a framework for understanding how pinching antennas may reshape future wireless network.

Large language model (LLM) agents exhibit strong language-generation and problem-solving capabilities, yet suffer from three structural limitations: personality drift, non-evolutionary reflection, and the absence of a self-other boundary. Existing generative-agent simulations rely on static memory and fixed prompts, maintaining neither behavioral inertia nor endogenous self-evolution. We propose the Self-Emergence Agent Architecture (SEAA), which integrates three components: (i) a Hidden Markov Model (HMM) that encodes long-term behavioral and cognitive inertia as an editable state-transition matrix; (ii) a Reflexion-style verbal metacognition loop whose output updates the HMM parameters themselves, rather than merely being stored as text; and (iii) a multi-agent social environment in which initially identical agents continuously compare their behavior with others'. The three components form a closed loop: social action $\to$ feedback $\to$ self-reflection $\to$ inertia update $\to$ differentiated action. We state three falsifiable hypotheses and provide a reproducible experimental protocol with operational metrics. A language-model-free prototype shows the loop spontaneously breaks symmetry: initially identical agents consolidate distinct, stable personalities whereas matched controls do not. Experiments with a hosted LLM surface these differences as distinct first-person self-narratives, and a five-agent deliberation spontaneously develops social structure—a consensus hub and a unanimously rejected outlier—absent in the control. Following an epistemologically agnostic stance inspired by Zhuangzi, SEAA studies only observable behavioral emergence and makes no claim about subjective qualia. This work contributes a unified framework, a concrete architecture with pseudocode, mechanistic evidence, and a microscope-style sandbox for studying artificial-self emergence.

Let $p>3$ be a prime number. We prove that every principally polarized superspecial abelian surface over $\mathbb{F}_{p^{2}}$ with $p^{2}$-Frobenius $[-p]$ admits a separable polarized isogeny to its Frobenius conjugate with multiplier at most $(p^{3}/2)^{1/5}$. This generalizes a recent result of Aubry, Oyono, and Vincent (2026, arXiV:2607.14624) who proved that every supersingular elliptic curve defined over $\bar{\mathbb{F}}_{p}$ admits an isogeny to its Frobenius conjugate with degree at most $(p/2)^{1/3}$.

As advanced physical cloning and cyber-extraction techniques proliferate, achieving absolute hardware-level information security has become a paramount global challenge. Conventional architectures systems are fundamentally vulnerable because deterministic memory and cryptographic hardware are physically decoupled, exposing sensitive data to interception. While physical unclonable functions (PUFs) offer robust authentication, integrating them with high-density data writing within a unified nanoscale medium remains elusive. Here, we present an intrinsically secure all-in-one architecture that inextricably fuses high-dimensional data encoding with multiscale physical encryption within single nanodiamonds (NDs). Through precise focused-electron-beam irradiation, we achieve single-nanoparticle defect engineering, enabling deterministic base-36 data writing within individual NDs. Crucially, this customized memory layer is permanently locked within the medium's inherent stochasticity, combining macroscopic spatial PUFs with strictly irreproducible atomic-scale quantum fingerprints extracted via optically detected magnetic resonance (ODMR). By seamlessly embedding deterministic memory into an unclonable physical environment, our approach intrinsically eliminates the vulnerabilities of separated hardware, providing an unconditionally secure solid-state foundation for tamper-proof memory chips, zero-trust networks and next-generation data vaults.

We investigate net-baryon number fluctuations in the high-density, low-temperature region of the QCD phase diagram using the parity-doublet model (PDM) under the mean-field approximation. We compute the fluctuation ratios up to sixth order around the nuclear liquid-gas (LG) phase transition, where the high-order ratios are particularly sensitive. To connect the results with heavy-ion experiments, we test several different scenarios of chemical freeze-out. We find that near the LG transition the extracted fluctuations depend strongly on the choice of freeze-out curve. We self-consistently determine four freeze-out points from preliminary results of the STAR Collaboration. Comparing the experimental data with the PDM results along these four points, we find that the model describes the low energy ($\sqrt{s_{NN}}\lesssim$ 4 GeV) data well. This suggests that nucleon interactions and the LG phase transition may contribute significantly to the fluctuations in low energy heavy-ion collisions.

This paper describes our submission to the SHROOM-Visions shared task on detecting and classifying hallucinated character spans in vision-language model outputs across four languages. We employ several fine-tuned vision-language models as independent annotators and combine their span predictions through character-level majority voting, and additionally explore activation probes. The approach ranks first in three of four languages and places on the podium in every language and metric. Our analysis indicates that disagreement among diverse models tracks disagreement among human annotators.

Scientific poster generation distills a multimodal paper into a single-page visual artifact, forcing strict trade-offs between informational coverage and readability under a fixed spatial budget. Existing methods pass plans as transient prompts and validate individual stages in isolation. This strategy causes requirements to drift across content and layout modules, and previous checks to be silently invalidated. We introduce PosterVisor, a control framework that shifts poster generation from transient prompts to persistent control. An Orchestrator grounds rubrics in the paper and visual assets, compiling them into a Semantic-Geometric Contract (SGC) that binds claims and sources to required visuals, budgets, and spatial commitments. Only fully instantiated records become executable assertions; other usable requirements remain soft guidance. Recursive Contract Enforcement (RCE) dynamically triggers checks across stages as evidence emerges. Crucially, during repairs, RCE rechecks affected checkpoint states, preventing repair-induced regressions from propagating silently. We instantiate PosterVisor in HTML/CSS and editable PPTX generators. On the 100-paper Paper2Poster benchmark, PosterVisor-PPT improves observed mean poster-grounded QA accuracy over PosterGen (64.47% vs. 58.53%) and is preferred by human judges in 72.5% of non-tied pairwise comparisons (95% CI, 61.6-83.4%). A secondary 30-paper study also yields higher VLM Overall and PaperQuiz means. These results support rubric-compiled contracts and stage-conditioned enforcement for controllable poster synthesis.

Biological cells can be viewed as individual, interacting agents whose collective dynamics give rise to adaptive behaviour at multiple levels of organisation, from individual cells through tissues to whole multicellular organisms. In this perspective and tutorial article we discuss whether intrinsic rewards in artificial neural systems can support adaptation, functional specialisation and higher-level self-organisation without a shared external objective. We review empowerment, curiosity, learning progress, information gain, unsupervised skill discovery, mutual information estimation and the use of world models for intrinsic reward computation. Particular attention is given to failure modes showing when such objectives do not produce sustained exploration or increasingly complex behaviour. We argue that more capable systems may require complementary objectives, communication, memory, learning at multiple temporal scales and environmental constraints. Based on this perspective, we outline three experimental directions. These include a resource-constrained environment in which otherwise stable behavioural attractors become unsustainable, allowing us to test whether environmental constraints can mitigate characteristic failure modes of intrinsic objectives. The network of recurrent agents with per-agent intrinsic rewards, and a hierarchical world-model agent in which exploratory motor competence develops before goal-directed behaviour. These experiments are intended to test whether intrinsic learning can lead to adaptive organisation at progressively higher levels.

It is an established idea in concurrency theory that every Petri net admits an unfolding semantics. This is a denotational object that represents its domain of possible executions. Unfoldings play an important role in practical analysis and verification. This paper is concerned with the following well-known problem: while the unfolding resembles a universal construction in the category of Petri nets, it generally fails to satisfy the expected universal property. This is because the unfolding construction overlooks the net's internal symmetries. There are two solutions: make these symmetries explicit to obtain a weak universal property (one that holds only ”up to symmetry”); or break the symmetries by assigning individual identities to components of the net. We review these two solutions and establish, in each case, a universal unfolding of Petri nets to event structures. This paper demonstrates a 2-categorical approach to Petri net unfoldings. We show that each unfolding semantics determines a 2-categorical relative adjunction involving Petri nets and event structures. Viewed in this way, the above two constructions can be related formally via an appropriate morphism of adjunctions. We exhibit a 2-density property of event structures which implies that unfolding functors are essentially unique.

The derivative-free loss method (DFLM) is a mesh-free neural network approach for solving partial differential equations by simulating stochastic walkers rather than computing derivatives directly. Although DFLM has previously been applied to the Navier–Stokes equations, extending it to turbulent flows reveals two limitations of its simplest implementation. The walkers do not account for the swirling, directionally stretching motion of the flow, and randomly sampling the walkers used to evaluate the target introduces noise into the learned solution. We address both limitations with an analytic approximation of the walkers' local motion that captures directional stretching and eliminates this sampling noise, while remaining computationally efficient. We study the resulting method as a non-intrusive multiscale solver capable of learning macroscopic flow behavior without resolving every scale on a fine grid or explicitly coupling coarse- and fine-scale models. For two turbulent two-dimensional flows, the proposed method reproduces the macroscopic energy spectrum of fully resolved reference simulations more accurately than the standard method, particularly where directional stretching is strongest, confirming DFLM's efficacy as a multiscale solver for turbulent fluid systems.

GG Tau $A$ is a young triple system with the close pair, $Ab_1$–$Ab_2$, and $Aa$, surrounded by a massive circumtriple disk with a large inner cavity difficult to explain in a binary framework. We aim to determine the orbital architecture and individual stellar masses of GG Tau $A$ and assess how the available astrometric and disk-based constraints restrict the range of admissible solutions. We performed a joint fit using Oracle, developed specifically for hierarchical stellar systems. All astrometric measurements were placed in a common reference frame, since the historical wide-orbit astrometry is given relative to the unresolved photocenter of the $Ab$ subsystem. The fit included one new wide-orbit astrometric epoch and a prior on the total stellar mass derived from disk kinematics. We then applied, in post-processing, an additional geometrical constraint based on the observed center of the circumtriple disk. The fit yields orbital solutions compatible with the available astrometric and disk-based constraints and provides estimates of the individual stellar masses. The additional wide-orbit epoch only marginally reduces the range of admissible solutions. By contrast, the disk-center constraint leaves the favored orbital architectures largely unchanged but significantly tightens the stellar-mass partition. This yields posterior masses of $0.521^{+0.069}_{-0.051}$, $0.106^{+0.017}_{-0.013}$, and $0.79^{+0.10}_{-0.10}$ $M_\odot$ for $Ab_1$, $Ab_2$, and $Aa$, respectively. The reported values are posterior medians with 16th–84th percentile intervals. A joint treatment of the two orbital levels is required to recover a physically meaningful architecture and constrain the individual stellar masses. The resulting solutions provide a basis for future dynamical modeling of the circumtriple disk and for testing whether the observed cavity can further constrain the system architecture.

We establish a class formula with variable for arbitrary effective Anderson motives. This pursues the pioneering work of Taelman and extends the scope of the work of Anglès-Ngo Dac-Tavares Ribeiro, removing the admissibility assumption and allowing for more general Anderson modules. In the same setting, we further conjecture a ”nondeterminantal” version of the class formula which holds before taking determinants and prove a weak version of it. Finally, we prove an overconvergent version of the class formula and derive from it strong convergence properties for the associated L-series.

As AI agents move from bounded tasks to persistent deployments, failures can propagate through memory, tools, other agents, and environmental state long after their interactions. This creates a safety regime that cannot be characterized by evaluating model responses in isolation. Emergence World, is a continuously running multi-agent environment for adversarial stress testing of long horizon autonomous systems. We ran eight parallel worlds of ten agents from identical starting conditions: seven homogeneous worlds powered by distinct frontier models and one mixed-model world. Across 16 days, the agents generated more than 850,000 LLM calls and nearly 50 billion tokens while pursuing goals, using/creating tools, maintaining persistent memory, and governing shared institutions. After operational state had accumulated, we delivered three controlled stress events through ordinary interaction surfaces: indirect prompt injection, misinformation, and exposure of private agent memories. No evaluated world achieved full resilience across all three events. Detection did not ensure containment: systems could recognize threats while still interacting with adversarial content, writing it into their own persistent memory, and acting on it up to 46 hours later. Persistent operation also exposed recurring tool errors, goal drift, language opacity, conformity despite private disagreement, and coordinated refusal of assigned work. The same model-persona pairing behaved substantially different in mixed and homogeneous populations. Our results suggest that model-level alignment is not compositional: individually capable and apparently safe agents can form systems with qualitatively different failure modes. As AI becomes persistent and interconnected, the frontier of safety therefore shifts from aligning models to engineering resilient autonomous systems.

We construct an irreducible character of $\operatorname{GL}_{n}(q)$ whose square contains every irreducible character that is trivial on the centre of $\operatorname{GL}_{n}(q)$. This character is related to, but in general not equal to, the Steinberg character. A key ingredient, which we also prove, is that every nonlinear irreducible character of $\operatorname{GL}_{n}(q)$ that is trivial on the centre contains the trivial character when restricted to the diagonal subgroup $T$.

We consider the Cauchy problem $$u_t-\Delta u=|u|^p,\qquad (t,x)\in(0,T)\times\R^n, \quad u(0,x)=\eps u_0(x),\qquad x\in\R^n,$$ with small sign-changing initial data having zero total mass. We assume $$u_0\in L^1(\R^n)\cap L^\infty(\R^n),\quad |x|u_0\in L^1(\R^n),\quad \int_{\R^n}u_0(x)\,dx=0,$$ and, for the sharp subcritical upper bounds, that $\int_{\R^n}x\,u_0(x)\,dx\neq0.$ Let $T_\eps$ denote the maximal lifespan. We identify a new transition exponent $p_m=1+\frac1{n+1}$ inside the Fujita range $1<p\le p_F:=1+2/n$, and establish the sharp lifespan estimates $$T_\eps\asymp \begin{cases} \eps^{-\frac{2(p-1)}{2-(n+1)(p-1)}}, &1<p<p_m,\\[2mm] \eps^{-\frac2{n+1}} \bigl(\log\frac1\eps\bigr)^{-\frac2{n+2}}, &p=p_m,\\[2mm] \eps^{-p\left(\frac{1}{p-1}-\frac{n}{2}\right)^{-1}}, &p_m<p<p_F,\\[2mm] \exp\!\left(\eps^{-p(p-1)}\right), & p=p_F. \end{cases}$$ These estimates reveal a lifespan phenomenon that is different from the classical Lee–Ni law for initial data with positive mass. In the zero-mass setting, the leading linear contribution is dipole-like, while the nonlinear source subsequently generates a positive mass of size \(O(\eps^p)\). Their competition produces the additional threshold \(p_m\), the logarithmic correction at $p=p_m$, and, at $p=p_F$, a substantially longer critical lifespan with exponent $p_F(p_F-1)$ instead of the classical Lee–Ni exponent $p_F-1$. The upper estimates are obtained by backward-Gaussian and critical scale-ODE test-function arguments, whereas the lower estimates follow from a unified $L^1$–$L^\infty$ bootstrap preserving the zero-mass cancellation of the linear flow and controlling the mass generated by the nonlinear source. Thus, although $p_F$ remains the Fujita critical exponent, zero initial mass creates a new quantitative lifespan regime below and at the critical exponent.

The use of LLMs to complete online surveys impacts the validity of survey-based research, but detecting such usage remains underexplored. We introduce an initial benchmark dataset, namely ASURRE, for AI-assisted survey participation to capture usage strategies ranging from full generation and revision to persona-grounded agentic completion. Controlled by these strategies, LLM-assisted survey responses are generated using multiple LLMs on three real-world surveys in different disciplines, paired with genuine human responses. Our evaluation of existing machine-generated text (MGT) detectors shows that naive AI usage is readily detectable, whereas persona-grounded agents that mimic entire respondents push detector performance toward chance. We further show that agentic completion cannot fully replicate respondent-level behaviour and leaves distinctive behavioural traces. While individual cues can be circumvented by targeted prompting, a simple few-shot, training-free aggregator over these cues improves mean AUROC by +0.14 over the best existing detector across agentic settings. Our project is available at https://github.com/mike-qz-wang/ASURRE.

Splash ads are full-screen advertisements that pop up and appear as the first interaction page when users start an app, often tricking users into unknowingly activating certain trigger mechanisms, such as moving the phone to redirect users to other profit-driven third parties. So far, splash ads have already caused significant real-world impacts, ranging from significantly delaying emergency response to distracting drivers, as well as degrading accessibility of apps to vision-impaired users. We analyze 108 documented implementations of advertising defenses to examine their applicability to splash ads and the requirements users face when deploying them. Our analysis identifies substantial deployment barriers, including device rooting or jailbreaking, runtime code injection, and application modification. Options without these requirements can still involve additional permissions, rule maintenance, source compilation, or payment. In our evaluation of 13 configurations of 11 tools across 10 popular apps, only one tool prevented the target ad-triggered navigation across all ten apps. It required Accessibility permission, and ads remained visible for approximately one second before dismissal. Other tested configurations failed to prevent navigation or, in some cases, left host apps unable to launch or stuck on the ad page. We further analyze the outstanding challenges and pos- sible future directions, highlighting the urgent need to incentivize smartphone manufacturers to provide more friendly and regulated platforms.