Interactions within human teams are highly complex, dynamic, and multidimensional. Understanding these dynamics can help improve team efficacy and predict future outcomes. However, machine learning approaches to model these dynamics require a significant amount of data to make meaningful predictions. This paper describes the design and implementation of the Complex Dynamics of Online Professional Squads (CDOPS) dataset, developed for exploring human team dynamics. CDOPS comprises a collection of over 1 million rounds of CounterStrike: Global Offensive (CS:GO) games played in professional tournaments under regulated Counter-Strike servers, providing a foundational dataset for exploring squad dynamics in the context of E-sports. We here provide the context of CS:GO followed by a description of the CDOPS dataset, how it was collected, and how we believe it may be best used.

The goal of this paper is to report on a formalization of the p -adic numbers in the setting of the second author's univalent foundations program. This formalization, which has been verified in the Coq proof assistant, provides an approach to the p -adic numbers in constructive algebra and analysis.

We present a new coherence theorem for comprehension categories, providing strict models of dependent type theory with all standard constructors, including dependent products, dependent sums, identity types, and other inductive types. Precisely, we take as input a “weak model”: a comprehension category, equipped with structure corresponding to the desired logical constructions. We assume throughout that the base category is close to locally Cartesian closed: specifically, that products and certain exponentials exist. Beyond this, we require only that the logical structure should be weakly stable —a pure existence statement, not involving any specific choice of structure, weaker than standard categorical Beck--Chevalley conditions, and holding in the now standard homotopy-theoretic models of type theory. Given such a comprehension category, we construct an equivalent split one whose logical structure is strictly stable under reindexing. This yields an interpretation of type theory with the chosen constructors. The model is adapted from Voevodsky's use of universes for coherence, and at the level of fibrations is a classical construction of Giraud. It may be viewed in terms of local universes or delayed substitutions.

Abstract We present a solution to the problem of denning a counterpart in Algebraic Set Theory of the construction of internal sheaves in Topos Theory. Our approach is general in that we consider sheaves as determined by Lawvere-Tierney coverages, rather than by Grothendieck coverages, and assume only a weakening of the axioms for small maps originally introduced by Joyal and Moerdijk, thus subsuming the existing topos-theoretic results.