Papers

Major geopolitical crises can rapidly reshape online public attention. Yet population-level increases in discussion volume about a new crisis reveal little about how users accommodate this new demand for attention. We study the onset of the Iran-US-Israel conflict, triggered on 28 February 2026, using longitudinal repost activity from Bluesky across four consecutive approximately three-month windows spanning the period before and after its onset; the data comprise 91.0 million unique posts and 645.5 million repost observations. We find that the new conflict reorganized participation through both reallocation among existing conflict participants and substantial activation of previously low-conflict-active users, while some previously active users reduced their conflict-related participation. Attention redistribution differed substantially across pre-existing interests: Iran-US-Israel and Israel-Palestine attention showed strong positive co-movement with little systematic relative replacement, whereas Other Political and Non-Political content more consistently lost attention share, and Russia-Ukraine exhibited weaker, heterogeneous replacement. Finally, disruption of users' broader attention allocation was substantially more prevalent among users with established attention to geopolitical conflicts than in the overall or Non-Political populations. Together, these findings show that a newly emerging conflict reorganizes online attention through turnover in who participates, selective co-attendance or replacement across topics, and disruption of broader attention patterns concentrated among users already engaged with geopolitical conflicts.

Recent findings indicate that Vision Transformers settle into locally similar computational phases, implying a level of depthwise computational redundancy. However, existing methods to exploit this redundancy either fail to reduce inference compute or severely degrade model expressivity. In this work, we formalise a unified view of block redundancy that decouples the geometry from specific surrogate interventions. We then introduce Transformer-Within-Transformer (TWT), a post-hoc method that fuses contiguous groups of redundant layers into a single learned surrogate layer. TWT reduces parameter count and inference compute while remaining competitive with original models using half the depth on natural images, and in several downstream histopathology settings, TWT matches or even improves on the original baseline.

OpenHarmony, an emerging open-source mobile platform, is rapidly gaining attention in the mobile development community. Its fast-evolving Software Development Kit (SDK) introduces numerous Application Programming Interfaces (APIs) to boost developer productivity but inevitably introduces compatibility challenges, an issue well known from platforms like Android. However, existing compatibility analysis tools are ineffective for OpenHarmony due to its newly introduced ArkTS programming language and the lack of a mature behavioral model to capture app execution semantics. To bridge this gap, we present HapCiD, an open-source tool for automatically detecting API-related compatibility issues in OpenHarmony apps. Applied to 4,478 apps, HapCiD successfully detects 2,040 compatibility issues across 163 apps with 100 percent accuracy. Based on these findings, we conduct a comprehensive study of compatibility issues, categorizing their types, examining existing mitigation strategies, and proposing future improvements.

Reliable temporal-difference targets are central to off-policy actor-critic learning. Direct value improvement refines the next-state target with alternative actions, but the reliability of this refinement depends on how candidate actions are ranked, reviewed, and weighted. Noisy rankings may force premature candidate commitment, reusing selection scores may bias target valuation, and fixed enhancement weights may amplify weak evidence. To address these risks, we develop Conservative Adaptive Ranking and Screening (CARS), which retains an ordered candidate prefix within a preset budget and narrows it only when the observed boundary gap exceeds a disagreement-scaled uncertainty radius. Selector-Evaluator Value Assessment (SEVA) uses selector critics to order candidates and a separately parameterized evaluator critic to review the selected value, then caps the reviewed value at the selector reference. Dynamic Adaptive Risk-aware Enhancement (DARE) then regulates each residual correction using candidate reliability, the gap between selector and evaluator signals, and a finite stage factor. Together, CARS, SEVA, and DARE form CARE-VI, an evidence-regulated target construction framework that preserves the backbone interfaces for critic regression and actor updates. The analysis bounds the CARS boundary error, the SEVA selected-value overestimation, and the one-sided deviation of the DARE residual displacement from its population counterpart, and establishes fixed-policy recovery after the finite-stage perturbation ends. Experiments with SAC, TD3, and TD7 on four MuJoCo tasks show that CARE-VI achieves the highest mean return in all twelve settings. Grouped ablations and scalar diagnostics support the roles of the three components in improving target reliability.

We establish interior $C^{1,\alpha}$ regularity estimates, for some $\alpha > 0$, for fractional $p$-caloric functions when $p$ is in the range $p \in (2,2/(1-s))$. As a consequence, we deduce improved regularity in time, which yields interior continuous differentiability in time for $p \in [1/(1-s), 2/(1-s))$.

In this paper, we study the existence of nonnegative bound states for the higher-order logarithmic Schrödinger equation $$ -\alpha\Delta u+V(x)u-\beta u\ln|u| = \gamma u(\ln|u|)^m, \qquad u\in H^1(\mathbb R^N), $$ where $\alpha,\beta,\gamma>0$, $m$ is an odd positive integer and $V$ is a positive bounded potential converging to a constant at infinity. The simultaneous presence of the first- and higher-order logarithmic terms leads to a nonsmooth variational structure and additional compactness difficulties. We introduce a family of power-law approximations and derive estimates that are uniform as the approximation exponent tends to the logarithmic limit. Under a structural condition on the autonomous nonlinearity, we obtain uniqueness, up to translations, of the nonnegative autonomous profile with connected positivity set and a corresponding energy gap below the two-profile threshold. The small-amplitude behavior exhibits a maximum-principle/compact-support dichotomy: the case $m=1$ yields positivity, whereas the higher odd orders fall into the compact-support regime for the autonomous profile. We then establish a profile decomposition for constrained Palais-Smale sequences and construct a barycenter-based min-max level below the splitting threshold. This prevents loss of mass through multiple profiles and allows us to pass to the logarithmic limit. Under the stated structural and energy conditions, we obtain a nontrivial nonnegative bound state of the original equation.

The Internet of Agents is expected to enable large numbers of autonomous agents to discover, verify, and collaborate with each other across heterogeneous platforms. However, current agent protocols mainly address tool invocation and inter-agent communication, leaving scalable agent registration, trustworthy identification, and capability-oriented discovery largely unresolved. To address this, this paper proposes a scalable trust discovery architecture for the Internet of Agents. The proposed architecture adopts a hierarchical and distributed design consisting of three layers: Agent Root for trusted registry governance, Agent Registry for agent registration and metadata publication, and Agent Resolver for distributed capability discovery and trust-aware resolution. The architecture further introduces a registry-suffix-anchored composite identity scheme, which binds an agent native identifier to a trusted registry suffix to generate a globally discoverable identity. It also incorporates a dual-certificate and multi-level authentication mechanism to strengthen identity trust among agents. We implement a prototype and evaluate it through large-scale agent registration and resolution experiments. The prototype achieves an average registration latency of 58ms and an average discovery latency of 25ms, and it supports more than 19,000 registration requests per second and more than 29,000 agent discovery requests per second. These results demonstrate the feasibility of the proposed architecture, providing a practical approach toward scalable and identity-trusted agent ecosystems in the Internet of Agents.

We solve a problem posed by Audenaert and Kittaneh in 2012 by proving that the Aujla–Bourin subadditivity inequality can be strengthened to an optimal form. We also answer questions posed by Bourin and the second author: (1) we significantly extend both the reciprocal Lie–Trotter theorem of Audenaert and Hiai and Kato's limit theorem; (2) we determine the best constants in inequalities for sums of contractions and positive block matrices, including the sharp triangle inequality $$ |A+B+C| \leq \frac{3}{4} I + |A|+|B|+|C| $$ for three contractions $A,B,C$; and (3) we prove a remarkable eigenvalue inequality for the symmetric modulus, thereby determining the best dimension-free lower bound in a question studied by Bourin, Lee, and Zhang.

Intrinsic superconductivity in stoichiometric materials with nontrivial electronic topology remains uncommon, limiting opportunities to investigate how these two phenomena coexist within a single electronic system. Here, we report bulk type-I superconductivity below $T_c$ $\sim$ 0.9~K in YbBi$_2$, a layered rare-earth compound with a nonsymmorphic crystal structure and a quasi-two-dimensional Fermi surface. Thermodynamic and transport measurements establish the superconducting ground state, while quantum oscillations reveal exceptionally light carriers, with a cyclotron mass as low as 0.07 $m_e$, and a nonzero Berry phase of approximately 0.82 $\pi$. The latter closely matches the calculated value of the corresponding Wilson phase 0.99 $\pi$ for the corresponding orbit near a symmetry-protected band degeneracy. ARPES measurements show good agreement with key features of the calculated electronic structure, providing complementary experimental constraints on the normal-state band structure. The combination of intrinsic type-I superconductivity, light quasi-two-dimensional carriers, and signatures of nontrivial electronic topology identifies YbBi$_2$ as a distinct stoichiometric platform for investigating superconductivity in a topologically nontrivial electronic environment.

Tri-hybrid multiple-input multiple-output (MIMO) architectures have been proposed as a promising solution for enabling energy-efficient communications systems in large-scale antenna arrays by replacing conventional antenna arrays in hybrid beamforming (HBF) systems with low-cost dynamic metasurface antennas (DMAs). In this work, we investigate beamforming design for integrated sensing and communications (ISAC) systems based on tri-HBF architectures, with the objective of jointly enhancing the communications sum rate and sensing sum mutual information. Specifically, we formulate a weighted multi-objective optimization problem that balances communications throughput and sensing mutual information, subject to a total transmit power consumption constraint and the physical limitations inherent to tri-HBF architectures. By exploiting the problem structure, we develop an efficient iterative algorithm with closed-form updates to solve the non-convex optimization problem with low complexity. Numerical results are provided to evaluate the performance of the proposed tri-HBF architecture in various setups. The results demonstrate that the proposed tri-HBF architecture can achieve significant improvement in energy efficiency (EE) compared to the conventional hybrid MIMO and DMA-only configurations, at the cost of minor degradations in sum rate and sensing mutual information.

The Antibandwidth and Cyclic Antibandwidth problems are NP-hard graph labeling problems that aim to maximize the minimum (cyclic) distance between labels assigned to adjacent vertices. Extensive research on these problems has resulted in a variety of mathematical formulations and computational approaches. However, their minimum span perspective, in which a prescribed minimum (cyclic) distance is fixed and the objective is to minimize the label span, has received comparatively little attention. In this paper, we consider this complementary perspective by introducing the Minimum Span Antibandwidth/Cyclic Antibandwidth Labeling (MSABL/MSCABL) problems and developing a unified Boolean Satisfiability (SAT)-based framework for solving them. The SAT-based framework formulates MSABL/MSCABL as a sequence of decision problems and exploits their monotonicity to accelerate the search process. We also consider two SAT solving strategies, parallel and incremental SAT solving: the former examines multiple candidate spans concurrently, while the latter reuses a single SAT instance while progressively restricting the label domain. The proposed approaches are evaluated on benchmark instances from the Harwell-Boeing Sparse Matrix Collection and compared with CPLEXCP, CPLEXMIP, and Gurobi. The results show that SAT-based approaches are highly competitive in solution quality, with the parallel approach performing best overall for MSCABL and the incremental approach for MSABL. With the no-hole constraint, they remain competitive with CPLEXCP and significantly outperform CPLEXMIP and Gurobi, particularly for MSCABL. These results demonstrate the effectiveness of SAT solving as an exact approach for MSABL and MSCABL.

Kramers-Wannier duality of the quantum Ising chain is naturally realized as a noninvertible transformation on a finite periodic chain. Upon incorporating appropriate symmetry-twisted sectors, however, the duality can be promoted to an invertible unitary transformation. In this Letter, we classify when the Kramers-Wannier duality admits an invertible realization on a finite Hilbert space. We show that this is determined by the representation of the Ising bond algebra and establish a necessary and sufficient condition in terms of its two central elements. This representation-theoretic criterion unifies the conventional noninvertible realization with invertible constructions involving symmetry-twisted sectors and applies equally to other models with the same underlying bond algebra. As an explicit example, we find an order-disorder duality in a non-trivial realization of the Ising bond algebra that admits an invertible Kramers-Wannier duality.

Self-evolving methods reduce the need for human-annotated trajectories by allowing tool-using agents to generate their own training data. Yet existing methods typically separate trajectory generation from evaluation, relying on static verifiers that cannot adapt to emerging failure modes or self-consistency signals that may reinforce errors shared across trajectories. Jointly adapting planning, execution, and evaluation offers a promising alternative, but introduces a fundamental coordination challenge: each component continuously changes the data or feedback used to train the others. We address this challenge with UnifiedPlayers, a cooperative framework comprising a Planning Player that generates tasks, an Execution Player that produces multi-turn trajectories with Python tool calls, and an Evaluation Player that constructs executable verifiers. We design role-specific rewards that coordinate the three players toward a shared learning objective under GRPO. Across two model backbones and twelve reasoning benchmarks, UnifiedPlayers outperforms the strongest prior baseline by at least 3.5% on mathematical reasoning and 3.9% on general reasoning tasks. Moreover, the learned verifier achieves 84.2% adversarial detection accuracy, while its reward signal exhibits 2.03$\times$ higher per-question variance than a self-consistency baseline, providing more discriminative verifications. These results highlight cooperation among specialized players as a promising path toward self-enhanced tool-integrated agents.

Medical image segmentation supports quantitative clinical analysis and computer-aided diagnosis. Recent methods for medical image segmentation have improved both local feature representation and volumetric context modeling. However, existing methods still strug- gle to efficiently model cross-slice relations in anisotropic volumet- ric images, limiting segmentation consistency and accuracy. This pa- per proposes G^2RA-Net, a medical image segmentation framework that combines graph-based cross-slice relation modeling with atten- tion gating. Graph-Based Slice Relationship Modeling (GSRM) cap- tures anatomical dependencies across consecutive slices by repre- senting each slice as a graph node and propagating semantic con- text through graph message passing. The Cross-Slice Attention Gate (CSAG) then selects relevant neighboring context and emphasizes target anatomical regions through attention-guided feature modula- tion. Experiments on brain MRI and abdominal CT datasets demon- strate that G^2RA-Net outperforms representative methods in seg- mentation accuracy and boundary quality. Ablation studies further validate the proposed design.

Effective manipulation across diverse objects is critical for applications ranging from agricultural harvesting to laboratory and domestic automation. While the inherent compliance of soft robotics is well suited to this challenge, designing grippers that generalize across tasks remains difficult due to the vast design space of continuum mechanics and the risk of overfitting to specific scenarios. We propose a graph-based design space for representing soft structures and mechanisms, coupled with a multi-objective, diversity-driven genetic optimization framework that explicitly promotes solution variety throughout the design process. Using multiple grasping scenarios during optimization, we study how task diversity influences the emergence of generalization to unseen objects and contact conditions. Our results show that optimization over a sufficiently diverse set of grasping cases leads to designs with emergent generalization, exhibiting improved robustness compared to task-specific solutions on novel scenarios. These findings suggest that diversity-driven optimization offers a principled pathway toward general-purpose soft grippers, aligned with the adaptable nature of soft robotics.

Long-term multivariate time series plays a significant role in many application areas such as power systems, trading, etc. However, their accurate prediction is quite difficult for conventional forecasting methods as they often exhibit high dimensionality and complex relationships. Recent works show that transformer-based approaches are quite effective for long-term forecasting thanks to their attention mechanism. However, in the presence of complex high-dimensional inputs, they show evidence of oversmoothing, limited capacity, and opacity. To this end, this paper introduces SETTer, a transformer-based model that addresses these challenges by incorporating novel techniques for decoupled self-attention and hybrid masking. The proposed techniques enable SETTer to effectively capture the dominant short- and long-term patterns across the temporal and channel dimensions. In addition, we enrich the model layers with simple explainable structures that indicate the discriminative pattern of SETTer. We show that with a single-layer transformer architecture, SETTer can effectively model long-term dependencies in the presence of varying data complexities. Extensive experiments on real-word benchmark datasets for long-term multivariate time series forecasting demonstrate that SETTer outperforms state-of-the-art models in 88% of the scenarios.

High-harmonic generation (HHG) from solids has emerged as a powerful probe of electronic structure and ultrafast dynamics in condensed matter systems. In this chapter, we review recent advances in solid-state HHG spectroscopy and control, with a focus on semiconductors and correlated materials. We discuss the theoretical foundations of HHG and summarize experimental approaches for extracting information from harmonic emission. HHG has been shown to be sensitive to a wide range of microscopic properties, including band structure, transition dipole moments, Berry phases, crystal symmetry, carrier populations, dephasing processes, and lattice dynamics. This sensitivity enables access to electronic and structural dynamics on femtosecond and attosecond timescales and has established HHG as a versatile spectroscopic tool. At the same time, the strong dependence of HHG on many coupled material and excitation parameters makes the emitted harmonics intrinsically difficult to associate with a single microscopic quantity. Rather than representing a limitation alone, this sensitivity also provides numerous pathways for control. We review how photoexcitation, multicolor driving fields, waveform engineering, and transient modification of material properties can be used to enhance, suppress, and shape harmonic emission. These developments position solid-state HHG not only as a spectroscopic technique, but also as a platform for programmable nonlinear optics with applications ranging from compact extreme-ultraviolet sources to super-resolution microscopy and ultrafast photonic devices.

This paper investigates properties concerning transposed triple products in rings. Motivated by Cline's formula, we characterize symmetric rings by means of group invertible elements and EP elements. We prove that a unital ring $R$ is symmetric if and only if $abc\in R^{\sharp}$ implies $acb\in R^{\sharp}$ for all $a,b,c\in R$. In particular, we give an answer to the problem posed in \cite[Problem 2.9]{MW1}. An example is provided to illustrate that for a symmetric ring $R$, $abc=e$ does not generally yield $acb=e$. For $\ast$-rings, we introduce the notion of pro-symmetric rings: a ring $R$ is pro-symmetric if $abc\in P(R)$ implies $acb\in P(R)$ for all $a,b,c\in R$. We show that every pro-symmetric ring is symmetric. Several counterexamples are constructed to distinguish these classes of rings, and their mutual inclusion relations are also discussed.

Artificial neural networks (ANNs), as core components of modern deep learning (DL) systems, lack the adaptive flexibility and long-term stability exhibited by biological systems. This limitation largely stems from the fact that conventional ANNs rely on uniform, local, and gradient-based parameter updates, while neglecting internal learning principles that are biological mechanisms such as neurotransmitters signalling or neuroplasticity. Consequently, many existing approaches focus on architectural expansion or mathematical fine-tuning techniques such as regularisation or parameter isolation. Inspired by the superior adaptability and plasticity of mammalian brains, we posit that neuromodulation with neurotransmitters constitutes a third axis of learning, complementary to neural activity and synaptic plasticity, and should be explicitly modelled in artificial neural networks. In this positional paper, we argue that incorporating neuromodulatory principles into ANN design represents a promising and underexplored research direction, and we advocate for greater attention to this perspective in the development of adaptive and continual learning systems.

Tool learning enables large language models (LLMs) to use external tools for tasks beyond parametric knowledge. Reinforcement learning can optimize tool-call behavior from feedback, but current methods still face two problems: fixed-threshold curricula can become misaligned with the policy's evolving capability boundary, and additive rewards can leak argument-level credit when the predicted tool is wrong. To address these problems, we propose MATCH, a closed-loop framework for model-aware tool learning with curriculum scheduling and hierarchically gated rewards. Model-Aware Curriculum Learning (MACL) maintains reward-derived sample difficulty that co-evolves with the policy, and each epoch selects samples near the current capability boundary together with a top-k pool of harder cases. Hierarchical Tool-call Gated Reward (HTGR) scores tool name, argument key, and argument value as a gated chain, granting credit at each level only when prerequisites hold. The same HTGR rewards drive both GRPO updates and MACL's difficulty refresh, closing the loop between policy optimization and sample scheduling. On API-Bank and BFCL V3, MATCH reaches 72.19% and 62.87% overall accuracy, outperforming the main supervised and RL-based baselines. Backbone experiments further show consistent improvements across four backbones from two model families.

SpeechLLMs can recognise emotion by generating a label token, but this approach relies on the LLM's existing output representations. We compare this generative approach with a discriminative alternative that uses a linear classification head on top of the LLM's hidden states. Because most multimodal emotion recognition studies evaluate with ground-truth transcripts, whereas deployed systems receive ASR output, we run every comparison with both, using a compact speechLLM (frozen Whisper-medium encoder, 3B LLM) on IEMOCAP and MELD. The classification head improves Macro F1 in 10 of 14 configurations. On IEMOCAP, it improves every configuration using ASR transcripts, reaching 76.97% Macro F1, with a significant gain when using speech alone. On MELD, where ASR transcripts have a 32.38% word error rate, it helps with speech alone but not with ASR transcripts. The benefit thus depends on both the dataset and the transcript source: in 4 of the 6 configurations that use text, the head's effect changes sign between ground-truth and ASR transcripts. Conclusions drawn with ground-truth transcripts therefore need not hold with ASR transcripts. Finally, comparing the learned class vectors with the LLM's vocabulary shows that, on IEMOCAP and MELD, their nearest tokens are mostly emotion-related words rather than explicit emotion labels.

The growing complexity of multi-domain operational environments (land, aerospace, naval, cyber, and electromagnetic spectrum) has increased the volume and velocity of data reaching command-and-control (C2) centers, straining the observe-orient-decide-act (OODA) decision cycle. Artificial Intelligence (AI) systems currently employed in defense are, in general, reactive and isolated tools that still rely heavily on human operators to integrate information, assess scenarios, and formulate courses of action. This paper proposes a conceptual Agentic AI architecture for AI systems that can plan, access data sources, execute tools, and act autonomously and audibly, aimed at supporting decision-making across the three Brazilian Armed Forces (Navy, Army, and Air Force). Four application fronts are discussed (decision support, situational analysis, feasibility studies, and countermeasure suggestion), as well as the data and sensor access requirements and the security and permission safeguards necessary for responsible employment across administrative, strategic, operational, and tactical contexts.

Giant Star-forming Clumps (GSFCs) are kpc-scale regions of enhanced star-formation with stellar masses of $10^6$ to $10^{10}\,M_\odot$ that are commonly observed in high-redshift ($z \gtrsim 1$) galaxies but their formation and role in galaxy evolution remain unclear. We applied a Faster R-CNN object detection framework (FRCNN) to identify star-forming clumps in astrophysical imaging data from a mass-complete sample of $\sim$210,000 low-redshift galaxies ($z\lesssim0.32$), located in the HSC-SSP Wide and Deep fields observed by the Hyper Suprime-Cam Subaru Strategic Survey (HSC-SSP) and CFHT Large Area U-band Deep Survey (CLAUDS). We present a population of $\sim$710,000 detected clumps for which we measured the (u)grizy-photometry and derived the physical properties (stellar mass, age, dust extinction and star-formation rate) for each clump by fitting the photometric data to stellar population models. We estimate that the clump Stellar Mass Function (cSMF) for young clumps ($<100\,\mathrm{Myr}$) follows a power law with an exponent of $\alpha=1.98\pm0.02$ down to a completeness limit of $\sim10^{8}\,M_\odot$ which is consistent with an in situ formation through violent disk instabilities (VDI). The clumps show elevated star-formation rates and negative gradients in their ages and stellar masses as a function of galactocentric distance. These gradients are steeper than those measured for the intra-clump regions of the host galaxies and are robust against uncertainties introduced by different modelling assumptions. For nearby galaxies we argue that the observed low-redshift clumps are likely analogues of high-redshift GSFCs and that the inward migration of star-forming clumps directly contributes to the central bulge formation of the host galaxy.

Active visual exploration of tabletop objects often requires reorienting an unknown resting object onto a different stable support face to expose occluded surfaces. To identify such placements without exhaustive physical search, we learn a probabilistic placement prior from a single-view point cloud. Stable placement prediction is inherently multimodal, and conventional 6-DoF regression introduces further ambiguity by modeling translation and in-plane yaw. We therefore propose FlipToSee, a probabilistic framework that removes this representational ambiguity by parameterizing placements as unit support normals on $S^2$ while modeling their multimodal conditional distribution via a von Mises–Fisher mixture density network. To decouple mode diversity from physical robustness, FlipToSee deterministically extracts a compact candidate set from the mixture components and applies robustness-aware reranking using an auxiliary head trained with candidate-aligned supervision. In simulation, FlipToSee achieves $98.4\%$ first-proposal success on in-distribution objects, $95.3\%$ on out-of-distribution shapes, and $90.0\%$ under zero-shot transfer to household YCB objects. We further demonstrate the learned placement prior on a physical robot by integrating it with grasp and motion planning for exploratory regrasping.

Interest in developing personalised language models is rapidly growing. While personalisation is often viewed as a mechanism to better serve diverse user needs, the effects of sustained interactions with personalised models on people's perception of and behaviour toward AI remain poorly understood. Most critically, downstream consequences outside the immediate human–AI interaction loop, such as effects on users' self-perceptions and interpersonal relationships, remain largely unexamined. In this study, we recruited 992 participants to complete daily advice-seeking interactions with language models over the course of five days, comparing outcomes from a non-personalised baseline against two personalisation approaches: memory-based (conditioned on prior conversational history) and survey-based (conditioned on information collected through a pre-study intake survey). We find that several changes in human-AI interaction over time are driven primarily by repeated exposure rather than personalisation itself. However, participants interacting with personalised models experienced differences in advice-seeking and information-sharing attitudes and behaviours. We conclude by highlighting the nuanced effects of different personalisation approaches on interaction outcomes, and discussing the implications of these findings for the responsible design and deployment of personalised AI systems.

Let $R$ be a $\ast$-ring with $a,b\in R$. A ring $R$ is said to be $\ast$-reversible if $ab=0$ implies $b^{\ast}a=0$. In this paper, we first establish several new characterizations of $\ast$-reversible rings and reversible rings. In particular, we prove that $\ast$-reversible rings coincide with $\ast$-symmetric rings. Using these characterizations, we introduce two new classes of generalized $\ast$-reversible rings: pro-$\ast$-reversible rings and nil-$\ast$-reversible rings. A ring $R$ is called pro-$\ast$-reversible if $ab\in P(R)$ implies $b^{\ast}a\in P(R)$, and $R$ is nil-$\ast$-reversible if for every $c\in N(R)$, $cb=0$ yields both $b^{\ast}c=0$ and $cb^{\ast}=0$. The basic properties and characterizations of pro-$\ast$-reversible and nil-$\ast$-reversible rings are investigated. The interrelationships among all these ring classes are considered. The related examples to distinguish these rings are constructed.

An instance of Pinwheel Packing is a list of positive integers $a_1,\ldots,a_k$. A feasible schedule assigns one task to every integer time so that every interval of $a_i$ consecutive times contains task $i$. The instance is dense when $\sum_i1/a_i=1$. We prove that Dense Pinwheel Packing is NP-complete even when every period is encoded in unary and equal periods are listed as distinct tasks. Consequently, the usual binary-encoded problem is strongly NP-complete. Kleinberg and Mishra also prove NP-completeness \cite[Corollary~5.1]{KleinbergMishra2026}, but their reduction uses periods of exponential numerical size and therefore yields only weak NP-hardness. Our proof uses a direct reduction from triangle partition in a sparse tripartite graph. If each of the three parts of the source graph has $n$ vertices, the reduction produces $O(n^4\log^3 n)$ explicitly listed tasks, each with period $O(n^4\log^3 n)$; consequently, its full unary encoding has length $O(n^8\log^6 n)$.

We give a computer-assisted proof that the universal real Grothendieck constant satisfies $K_G^{\mathbb R}\le 1.7813$. The construction combines an explicit odd Hermite threshold of degree $11$ with a signed correlation polynomial of degree $51$. A sufficient inverse-majorant inequality is certified by enclosing the scalar coefficient head through degree $301$ and bounding the entire remaining tail using a weighted Gaussian trace estimate. The finite integral is bounded on a complete interval partition; its spatial exterior is controlled analytically. Exact parameters and source code that regenerate all accepted numerical inputs accompany the paper. The bound improves both the explicit bound $1.7818666069360661$ in the recent literature and the subsequently reported, system-tested value $1.7813319810625639$.

Let $S$ be a set of vertices in a connected graph $G$. A vertex outside $S$ is represented by the multiset of its distances to the vertices of $S$. The outer multiset dimension $\operatorname{odim}(G)$ is the minimum cardinality of an $S$ for which these representations distinguish all vertices outside $S$. We determine $\operatorname{odim}(C_s \square C_t)$ for all $s,t\geq 3$, answering a problem of Klavžar, Kuziak, and Yero. The values range from $3$ to $8$. The proof combines a half-turn argument giving a universal four-landmark lower bound when both factors have length at least four, explicit three- and four-landmark constructions for the infinite families, and exact finite enumeration on the remaining strip. The collision classification behind the infinite four-landmark construction is certified by exact quantifier elimination in linear integer arithmetic; source code and all finite upper certificates accompany the paper.

So conjectured that, for a fixed positive integer n, the ordinary adjacency spectrum of an integral circulant graph of order n determines its divisor set. We prove this for graphs of order p to the power a times q, where p and q are primes with p less than q and a is at least one. To handle coincident eigenvalues arising from distinct greatest-common-divisor classes, we use a spectral counting measure. For connected graphs, an exact identity recovers the part of the divisor set consisting of one and q, when present, together with the counting measure for a graph of order p to the power a minus one times q. Strong induction and decomposition into connected components then recover the full divisor set, including the case p equals two and disconnected graphs.