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This is a survey about finite group actions on CW-complexes and related topics, primarily based on our joint work. The main applications are to finite $G$-CW-complexes which are homotopy equivalent to spheres. We have tried to give a fairly short overview of the extensive literature in this area, and we apologize in advance for our oversights and omissions.

There is an error in our recent preprint ``The EPRL amplitude is supported on flat connections''. The error is in Section 3. Here we leave the original text unchanged, but add a note in Section 3 pointing out exactly what the error is. We apologize for the false alarm. After one month, this preprint will be withdrawn from the arxiv. {\bf Original Abstract:} For the version of the EPRL model based on the original vertex amplitude and the face amplitude selected by its gluing properties, we prove that the EPRL amplitude of any region with the topology of a 4-ball is supported on flat connections. We state immediate consequences of this result, comment on some applications, and discuss physical implications. The results hold in general; they do not rely on a semiclassical analysis.

When encountering a robot in the wild, it is not inherently clear to human users what the robot's capabilities are. When encountering misunderstandings or problems in spoken interaction, robots often just apologize and move on, without additional effort to make sure the user understands what happened. We set out to compare the effect of two speech based capability communication strategies (proactive, reactive) to a robot without such a strategy, in regard to the user's rating of and their behavior during the interaction. For this, we conducted an in-person user study with 120 participants who had three speech-based interactions with a social robot in a restaurant setting. Our results suggest that users preferred the robot communicating its capabilities proactively and adjusted their behavior in those interactions, using a more conversational interaction style while also enjoying the interaction more.

A key part of modern social dynamics is flaking at short notice. However, anxiety in coming up with believable and socially acceptable reasons to do so can instead lead to 'ghosting', awkwardness, or implausible excuses, risking emotional harm and resentment in the other party. The ability to delegate this task to a Large Language Model (LLM) could substantially reduce friction and enhance the flexibility of user's social life while greatly minimising the aforementioned creative burden and moral qualms. We introduce FLAKE-Bench, an evaluation of models' capacity to effectively, kindly, and humanely extract themselves from a diverse set of social, professional and romantic scenarios. We report the efficacy of 10 frontier or recently-frontier LLMs in bailing on prior commitments, because nothing says "I value our friendship" like having AI generate your cancellation texts. We open-source FLAKE-Bench at github.com/Cloakless/flake-bench to support future research.

``When to the sessions of sweet silent thought I summon up re-membranes of things past, I sigh the lack of many a thing I sought''. (Apologies to William Shakespeare)

As chatbots driven by large language models (LLMs) are increasingly deployed in everyday contexts, their ability to recover from errors through effective apologies is critical to maintaining user trust and satisfaction. In a preregistered study with Prolific workers (N=162), we examine user preferences for three types of apologies (rote, explanatory, and empathic) issued in response to three categories of common LLM mistakes (bias, unfounded fabrication, and factual errors). We designed a pairwise experiment in which participants evaluated chatbot responses consisting of an initial error, a subsequent apology, and a resolution. Explanatory apologies were generally preferred, but this varied by context and user. In the bias scenario, empathic apologies were favored for acknowledging emotional impact, while hallucinations, though seen as serious, elicited no clear preference, reflecting user uncertainty. Our findings show the complexity of effective apology in AI systems. We discuss key insights such as personalization and calibration that future systems must navigate to meaningfully repair trust.

Amid accelerated digitalization, not only is the scale of data processing and storage increasing, but so too is the associated infrastructure load on the climate. Current climate models and environmental protocols almost entirely overlook the impact of information and communication technologies on the thermal and energy balance of the biosphere. This paper proposes the theory of information and climate feedback (ICF) as a new nonlinear model describing the loop of digitalization, energy consumption, the thermal footprint, the climatic response, and the vulnerability of digital infrastructure. The system is formalized via differential equations with delays and parameters of sensitivity, greenness, and phase stability. A multiscenario numerical analysis, phase reconstructions, and thermal cartography were conducted. Critical regimes, including digital overheating, fluctuational instability, and infrastructural collapse in the absence of adaptive measures, were identified. The paper concludes with the proposal of an international agreement titled the Green Digital Accord and a set of metrics for sustainable digitalization. This work integrates climatology, information technologies, an

Suppose that either (i) $N = 2$, $α\in \mathbb{R}$ and $p > 2$ or (ii) $N = 3$, $α< 0$ and $2 < p < 3$. We prove that there exists an explicitly computable $μ_0 = μ_0 (N, α, p) > 0$ such that if $0 < μ< μ_0$, then the following normalized semilinear elliptic problem with a point interaction admits ground states: \[ \begin{cases} - Δ_αu + ωu + u |u|^{p - 2} = 0 &\text{in} ~ \mathbb{R}^N; \\ \|u\|_{\mathscr{L}^2}^2 = μ, \end{cases} \] where $- Δ_α$ denotes the Laplacian of point interaction (centered at the origin) with inverse scattering length $- 2 (N - 1) πα$ and we want to solve for $ω\in \mathbb{R}$, $u \colon \mathbb{R}^N \to \mathbb{R}$. We remark that this kind of solutions does not exist in the framework of the defocusing NLSE without a point interaction.

Apologies serve essential functions for moral agents such as expressing remorse, taking responsibility, and repairing trust. LLM-based chatbots routinely produce output that has the linguistic form of an apology. However, they do this simply because they are echoing the kinds of things that humans say. Moreover, there are reasons to think that chatbots are not the kind of linguistic or moral agents capable of apology. To put the point bluntly: Chatbot apologies are bullshit. This paper explores this concern and develops it beyond the epithet, drawing on the nature of morally serious apologies, the linguistic agency required to perform them, and the moral agency required for them to matter. We conclude by considering some consequences for how chatbots should be designed and how we ought to think about them.

Multi-agent reinforcement learning (MARL) has exploded in popularity in recent years. Many approaches have been developed but they can be divided into three main types: centralized training and execution (CTE), centralized training for decentralized execution (CTDE), and Decentralized training and execution (DTE). CTDE methods are the most common as they can use centralized information during training but execute in a decentralized manner -- using only information available to that agent during execution. CTDE is the only paradigm that requires a separate training phase where any available information (e.g., other agent policies, underlying states) can be used. As a result, they can be more scalable than CTE methods, do not require communication during execution, and can often perform well. CTDE fits most naturally with the cooperative case, but can be potentially applied in competitive or mixed settings depending on what information is assumed to be observed. This text is an introduction to CTDE in cooperative MARL. It is meant to explain the setting, basic concepts, and common methods. It does not cover all work in CTDE MARL as the subarea is quite extensive. I have included work

Apologies are a powerful tool used in human-human interactions to provide affective support, regulate social processes, and exchange information following a trust violation. The emerging field of AI apology investigates the use of apologies by artificially intelligent systems, with recent research suggesting how this tool may provide similar value in human-machine interactions. Until recently, contributions to this area were sparse, and these works have yet to be synthesised into a cohesive body of knowledge. This article provides the first synthesis and critical analysis of the state of AI apology research, focusing on studies published between 2020 and 2023. We derive a framework of attributes to describe five core elements of apology: outcome, interaction, offence, recipient, and offender. With this framework as the basis for our critique, we show how apologies can be used to recover from misalignment in human-AI interactions, and examine trends and inconsistencies within the field. Among the observations, we outline the importance of curating a human-aligned and cross-disciplinary perspective in this research, with consideration for improved system capabilities and long-term ou

Commercial voice assistants are largely feminized and associated with stereotypically feminine traits such as warmth and submissiveness. As these assistants continue to be adopted for everyday uses, it is imperative to understand how the portrayed gender shapes the voice assistant's ability to mitigate errors, which are still common in voice interactions. We report a study (N=40) that examined the effects of voice gender (feminine, ambiguous, masculine), error mitigation strategies (apology, compensation) and participant's gender on people's interaction behavior and perceptions of the assistant. Our results show that AI assistants that apologized appeared warmer than those offered compensation. Moreover, male participants preferred apologetic feminine assistants over apologetic masculine ones. Furthermore, male participants interrupted AI assistants regardless of perceived gender more frequently than female participants when errors occurred. Our results suggest that the perceived gender of a voice assistant biases user behavior, especially for male users, and that an ambiguous voice has the potential to reduce biases associated with gender-specific traits.

These notes are a transcript of Carlo Rovelli's lectures on Loop Quantum Gravity, given in Marseille in 2018, which (at present) can be entirely found on YouTube. I transcribed them in LaTeX in early 2020 as an exercise to get ready for my Ph.D. in LQG at Western University. This transcript is meant to be a (hopefully helpful) integration for the video version. I reported the order of the topics and the chronological structure exactly as presented by Rovelli throughout the course, primarily to facilitate the comparison. Each Section corresponds to a different Lecture. The parts written in textit are my additions. Sometimes in the text, I report references, which specify precisely the minute and the second of the corresponding video on YouTube, to very short historical digressions or excursus made during the lectures by Rovelli that I have not explicitly transcribed in these notes. Where appropriate, I took some figures from the book "Covariant Loop Quantum Gravity - An elementary introduction to Quantum Gravity and Spinfoam Theory" by Carlo Rovelli and Francesca Vidotto, to which I always refer by the term "the book" in the following. For what concerns the equations, where possible

The purpose of this survey is to serve both as a gentle introduction and a coherent overview of state-of-the-art Frank--Wolfe algorithms, also called conditional gradient algorithms, for function minimization. These algorithms are especially useful in convex optimization when linear optimization is cheaper than projections. The selection of the material has been guided by the principle of highlighting crucial ideas as well as presenting new approaches that we believe might become important in the future, with ample citations even of old works imperative in the development of newer methods. Yet, our selection is sometimes biased, and need not reflect consensus of the research community, and we have certainly missed recent important contributions. After all the research area of Frank--Wolfe is very active, making it a moving target. We apologize sincerely in advance for any such distortions and we fully acknowledge: We stand on the shoulder of giants.

In this chapter we present an overview of the main ideas and methods in the fractional integration and cointegration literature. We do not attempt to give a complete survey of this enormous literature, but rather a more introductory treatment suitable for a researcher or graduate student wishing to learn about this exciting field of research. With this aim, we have surely overlooked many relevant references for which we apologize in advance. Knowledge of standard time series methods, and in particular methods related to nonstationary time series, at the level of a standard graduate course or advanced undergraduate course is assumed.

Recent advances in technology have allowed an automation system to recognize its errors and repair trust more actively than ever. While previous research has called for further studies of different human factors and design features, their effect on human-automation trust repair scenarios remains unknown, especially concerning emotions. This paper seeks to fill such gaps by investigating the impact of anthropomorphism, users' individual differences, and emotional responses on human-automation trust repair. Our experiment manipulated various types of trust violations and apology messages with different emotionally expressive anthropomorphic cues. While no significant effect from the different apology representations was found, our participants displayed polarizing attitudes toward the anthropomorphic cues. We also found that (1). some personality traits, such as openness and conscientiousness, negatively correlate with the effectiveness of the apology messages, and (2). a person's emotional response toward a trust violation positively correlates with the effectiveness of the apology messages.

Certain forms of linguistic annotation, like part of speech and semantic tagging, can be automated with high accuracy. However, manual annotation is still necessary for complex pragmatic and discursive features that lack a direct mapping to lexical forms. This manual process is time-consuming and error-prone, limiting the scalability of function-to-form approaches in corpus linguistics. To address this, our study explores the possibility of using large language models (LLMs) to automate pragma-discursive corpus annotation. We compare GPT-3.5 (the model behind the free-to-use version of ChatGPT), GPT-4 (the model underpinning the precise mode of Bing chatbot), and a human coder in annotating apology components in English based on the local grammar framework. We find that GPT-4 outperformed GPT-3.5, with accuracy approaching that of a human coder. These results suggest that LLMs can be successfully deployed to aid pragma-discursive corpus annotation, making the process more efficient, scalable and accessible.

This paper is originally designed as a part of revision of the author's preprint math.AG/9908174 "P-adic Schwarzian triangle groups of Mumford type". Recently, Yves Andr'e pointed out a flaw in that preprint; more precisely, Proposition II there was not correct, and consequently, as he pointed out, some triangle groups are missing (but only in p=2,3,5). I apologize to the readers, and will release the other part soon by the original title. In this paper, we concentrate on the constructive part, but more systematically and in more general situation. More precisely, this paper presents a complete criterion for an abstract tree of groups to be realized in the context of p-adic uniformization. This criterion provides a practical way of constructing finitely generated discrete subgroups in PGL(2,K) over a p-adic field K. In the end of this paper, we will exhibit concrete examples of such construction, which in particular shows that there exist infinitely many triangle groups.