Abstract
The Hanson-Wright inequality establishes exponential concentration for quadratic forms $X^T M X$, where $X$ is a vector with independent sub-Gaussian entries and with parameters depending on the Frobenius and operator norms of $M$. The most elementary proof to date is due to Rudelson & Vershinyn, who still rely on a convex decoupling argument due to Bourgain, followed by Gaussian comparison to arrive at the result. In this note we sidestep this decoupling and provide an arguably simpler proof reliant only on elementary properties of sub-Gaussian variables and Gaussian rotational invariance. As a consequence we also obtain improved constants.

Abstract
The partial transpose map is a linear map widely used quantum information theory. We study the equality condition for a matrix inequality generated by partial transpose, namely $\rank(\sum^K_{j=1} A_j^T \otimes B_j)\le K \cdot \rank(\sum^K_{j=1} A_j \otimes B_j)$, where $A_j$'s and $B_j$'s are respectively the matrices of the same size, and $K$ is the Schmidt rank. We explicitly construct the condition when $A_i$'s are column or row vectors, or $2\times 2$ matrices. For the case where the Schmidt rank equals the dimension of $A_j$, we extend the results from $2\times 2$ matrices to square matrices, and further to rectangular matrices. In detail, we show that $\sum^K_{j=1} A_j \otimes B_j$ is locally equivalent to an elegant block-diagonal form consisting solely of identity and zero matrices. We also study the general case for $K=2$, and it turns out that the key is to characterize the expression of matrices $A_j$'s and $B_j$'s.

Abstract
We study a dynamic reputation model with a fixed posted price where only purchases are public. A long-lived seller chooses costly quality; each buyer observes the purchase history and a private signal. Under a Markov selection, beliefs split into two cascades - where actions are unresponsive and investment is zero - and an interior region where the seller invests. The policy is inverse-U in reputation and produces two patterns: Early Resolution (rapid absorption at the optimistic cascade) and Double Hump (two investment episodes). Higher signal precision at fixed prices enlarges cascades and can reduce investment. We compare welfare and analyze two design levers: flexible pricing, which can keep actions informative and remove cascades for patient sellers, and public outcome disclosure, which makes purchases more informative and expands investment.

Abstract
This paper introduces a novel approach to tackle the challenges of preserving and transferring tacit knowledge--deep, experience-based insights that are hard to articulate but vital for decision-making, innovation, and problem-solving. Traditional methods rely heavily on human facilitators, which, while effective, are resource-intensive and lack scalability. A promising alternative is the use of Socially Interactive Agents (SIAs) as AI-driven knowledge transfer facilitators. These agents interact autonomously and socially intelligently with users through multimodal behaviors (verbal, paraverbal, nonverbal), simulating expert roles in various organizational contexts. SIAs engage employees in empathic, natural-language dialogues, helping them externalize insights that might otherwise remain unspoken. Their success hinges on building trust, as employees are often hesitant to share tacit knowledge without assurance of confidentiality and appreciation. Key technologies include Large Language Models (LLMs) for generating context-relevant dialogue, Retrieval-Augmented Generation (RAG) to integrate organizational knowledge, and Chain-of-Thought (CoT) prompting to guide structured reflection. These enable SIAs to actively elicit knowledge, uncover implicit assumptions, and connect insights to broader organizational contexts. Potential applications span onboarding, where SIAs support personalized guidance and introductions, and knowledge retention, where they conduct structured interviews with retiring experts to capture heuristics behind decisions. Success depends on addressing ethical and operational challenges such as data privacy, algorithmic bias, and resistance to AI. Transparency, robust validation, and a culture of trust are essential to mitigate these risks.

Abstract
Humans intuitively navigate social interactions by simulating unspoken dynamics and reasoning about others' perspectives, even with limited information. In contrast, AI systems struggle to automatically structure and reason about these implicit social contexts. In this paper, we introduce a novel structured social world representation formalism (S3AP), designed to help AI systems reason more effectively about social dynamics. Following a POMDP-driven design, S3AP represents social interactions as structured tuples, such as state, observation, agent actions, and mental states, which can be automatically induced from free-form narratives or other inputs. We first show S3AP can help LLMs better understand social narratives across 5 social reasoning tasks (e.g., +51% improvement on FANToM's theory-of-mind reasoning with OpenAI's o1), reaching new state-of-the-art (SOTA) performance. We then induce social world models from these structured representations, demonstrating their ability to predict future social dynamics and improve agent decision-making, yielding up to +18% improvement on the SOTOPIA social interaction benchmark. Our findings highlight the promise of S3AP as a powerful, general-purpose representation for social world states, enabling the development of more socially-aware systems that better navigate social interactions.

Abstract
A fundamental question in cognitive science concerns how social norms are acquired and represented. While humans typically learn norms through embodied social experience, we investigated whether large language models can achieve sophisticated norm understanding through statistical learning alone. Across two studies, we systematically evaluated multiple AI systems' ability to predict human social appropriateness judgments for 555 everyday scenarios by examining how closely they predicted the average judgment compared to each human participant. In Study 1, GPT-4.5's accuracy in predicting the collective judgment on a continuous scale exceeded that of every human participant (100th percentile). Study 2 replicated this, with Gemini 2.5 Pro outperforming 98.7% of humans, GPT-5 97.8%, and Claude Sonnet 4 96.0%. Despite this predictive power, all models showed systematic, correlated errors. These findings demonstrate that sophisticated models of social cognition can emerge from statistical learning over linguistic data alone, challenging strong versions of theories emphasizing the exclusive necessity of embodied experience for cultural competence. The systematic nature of AI limitations across different architectures indicates potential boundaries of pattern-based social understanding, while the models' ability to outperform nearly all individual humans in this predictive task suggests that language serves as a remarkably rich repository for cultural knowledge transmission.

Abstract
This paper introduces and overviews a multidisciplinary project aimed at developing responsible and adaptive multi-human multi-robot (MHMR) systems for complex, dynamic settings. The project integrates co-design, ethical frameworks, and multimodal sensing to create AI-driven robots that are emotionally responsive, context-aware, and aligned with the needs of diverse users. We outline the project's vision, methodology, and early outcomes, demonstrating how embodied AI can support sustainable, ethical, and human-centred futures.

Abstract
The potential of social media to create open, collaborative and participatory spaces allows young women to engage and empower themselves in political and social activism. In this context, the objective of this research is to analyze the polarization in the debate at the intersection between the defense of feminism and transsexuality, preferably among the young population, symbolized in the use of the term 'TERF'. To do this, the existing communities on this subject on Twitter and TikTok have been analyzed with Social Network Analysis techniques, in addition to the presence of young people in them. The results indicate that the debates between both networks are not very cohesive, with a highly modularized structure that suggests isolation of each community. For this reason, it may be considered that the debate on sexual identity has resulted in a strong polarization of feminist activism in social media. Likewise, the positions of transinclusive feminism are very much in the majority among young people; this reinforces the idea of an ideological debate that can also be understood from a generational perspective. Finally, differential use between both social networks has been identified, where TikTok is a less partisan and more dialogue-based network than Twitter, which leads to discussions and participation in a more neutral tone.