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Monoid Structures on Indexed Containers
(2025) De Pascalis, Michele; Uustalu, Tarmo; Veltrì, Niccolò; Department of Computer Science
Containers represent a wide class of type constructions that are relevant for functional programming and (co)inductive reasoning. Indexed containers generalize this notion to better fit the scope of dependently typed programming. When interpreting types to be sets, a container describes an endo functoron the category of sets while an I-indexed container describes an endo functor on the category SetI of I-indexed families of sets. We consider the monoidal structure on the category of I-indexed containers whose tensor product of containers describes the composition of the respective induced endofunctors. We then give a combinatorial characterization of monoids in this monoidal category, and we show how these monoids correspond precisely to monads on the induced endofunctors on SetI. Lastly, we conclude by presenting some examples of monads on SetI that fall under our characterization, including the product of two monads, indexed variants of the state and the writer monads and an example of a free monad. The technical results of this work are accompanied by a formalization in the proof assistant Cubical Agda.
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Introduction to Inclusive and Responsible Entrepreneurship in a Turbulent Era
(Edward Elgar Publishing Ltd., 2025-01-01) Durst, Susanne; Department of Business and Economics
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Inclusive and Responsible Entrepreneurship in a Turbulent Era
(Edward Elgar Publishing Ltd., 2025-01-01) Durst, Susanne; Mbena, Jacques Yana; Viala, Céline; Department of Business and Economics
This incisive book uses real-world examples and historical insights to shed light on how inclusive and responsible entrepreneurship can lead to stronger economies and communities. Combining inclusivity, responsibility, crisis management and other related concepts, authors Susanne Durst, Jacques Yana Mbena and Céline Viala adopt a holistic approach to examining the practical benefits of inclusive and responsible entrepreneurship. The book highlights the crucial role that entrepreneurship plays in developing and implementing sustainable solutions in turbulent times and emphasises that contemporary entrepreneurship is more than just making money, but is about inclusion and equity in all entrepreneurial activities. The authors provide a variety of historical insights and examples to demonstrate the ways in which inclusive and responsible entrepreneurship can be a tool for social justice, economic equality and societal sustainability. Inclusive and Responsible Entrepreneurship in a Turbulent Era identifies barriers to incorporating inclusive and responsible entrepreneurship and presents practical and effective solutions to address them. Inclusive and Responsible Entrepreneurship in a Turbulent Era is an essential resource for scholars of entrepreneurship and business, as well as students of sustainable business development, business ethics and other related subjects in the social sciences. Entrepreneurs, policymakers and organisations wishing to support this form of entrepreneurship will also benefit from the book’‘s insights.
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New Distributed Interactive Proofs for Planarity : A Matter of Left and Right
(Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing, 2025) Gil, Yuval; Parter, Merav; Kowalski, Dariusz R.
We provide new distributed interactive proofs (DIP) for planarity and related graph families. The notion of a distributed interactive proof (DIP) was introduced by Kol, Oshman, and Saxena (PODC 2018). In this setting, the verifier consists of n nodes connected by a communication graph G. The prover is a single entity that communicates with all nodes by short messages. The goal is to verify that the graph G satisfies a certain property (e.g., planarity) in a small number of rounds, and with a small communication bound, denoted as the proof size. Prior work by Naor, Parter and Yogev (SODA 2020) presented a DIP for planarity that uses three interaction rounds and a proof size of O(log n). Feuilloley et al. (PODC 2020) showed that the same can be achieved with a single interaction round and without randomization, by providing a proof labeling scheme with a proof size of O(log n). In a subsequent work, Bousquet, Feuilloley, and Pierron (OPODIS 2021) achieved the same bound for related graph families such as outerplanarity, series-parallel graphs, and graphs of treewidth at most 2. In this work, we design new DIPs that use exponentially shorter proofs compared to the state-of-the-art bounds. Our main results are: There is a 5-round protocol with O(log log n) proof size for outerplanarity. There is a 5-round protocol with O(log log n) proof size for verifying embedded planarity and O(log log n + log ∆) proof size for general planar graphs, where ∆ is the maximum degree in the graph. In the former setting, it is assumed that an embedding of the graph is given (e.g., each node holds a clockwise orientation of its neighbors) and the goal is to verify that it is a valid planar embedding. The latter result should be compared with the non-interactive setting for which there is lower bound of Ω(log n) bits for graphs with ∆ = O(1) by Feuilloley et al. (PODC 2020). The non-interactive deterministic lower bound of Ω(log n) bits by Feuilloley et al. (PODC 2020) can be extended to hold even if the verifier is randomized. Moreover, the lower bound holds even with the assumption that the verifier’s randomness comes in the form of an unbounded random string shared among the nodes. We also show that our DIPs can be extended to protocols with similar bounds for verifying series-parallel graphs and graphs with tree-width at most 2. Perhaps surprisingly, our results demonstrate that the key technical barrier for obtaining o(log log n) labels for all our problems is a basic sorting verification task in which all nodes are embedded on an oriented path P ⊆ G and it is desired for each node to distinguish between its left and right G-neighbors.
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Generative artificial intelligence (GenAI) use and dependence : an approach from behavioral economics
(2025) Robayo-Pinzon, Oscar; Rojas-Berrio, Sandra; Camargo, Jorge E.; Foxall, Gordon R.; Department of Business and Economics
Objective: This study aims to explore the perceived dependence on Generative Artificial Intelligence (GenAI) tools among young adults and examine the relative reinforcing value of AI chatbots use compared to monetary rewards, applying a behavioral economics approach. Participants/methods: A total of 420 university students from Bogotá, Colombia, participated in an online survey. The study employed a Multiple Choice Procedure (MCP) to assess the relative reinforcement between different durations of GenAI use (1, 2, and 4 weeks) and monetary rewards, which varied in amount and delay. Additionally, an adapted AI Dependence Scale evaluated levels of dependence on AI tools. Data analysis included repeated measures ANOVA to examine the effects of reward magnitude and delay on choices, and correlations to assess the relationship between perceived dependence and reinforcement values. Results: Participants reported low average dependence on AI tools (mean AI Dependence Scale score = 65.6), with no significant gender differences. MCP findings indicated significant differences in crossover points across varying durations or delays for AI chatbots use, suggesting a higher relative value of use for the option to use AI chatbots immediately. The average reinforcement value for AI use versus monetary rewards did significantly vary with reward magnitude. On the other hand, significant differences were found in the levels of perceived dependence on AI, according to the average daily time of AI tool use. Conclusion: The results suggest that young adults exhibit low perceived dependence on GenAI tools but show differential reinforcement values based on usage duration or delay conditions. This behavioral economics approach provides novel insights into decision-making patterns related to AI chatbots use, emphasizing the need for further research to understand the psychological and social factors influencing dependence on AI technologies.

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