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.

Abstract Cartesian reverse differential categories (CRDCs) are a recently defined structure which categorically model the reverse differentiation operations used in supervised learning. Here, we define a related structure called a monoidal reverse differential category, prove important results about its relationship to CRDCs, and provide examples of both structures, including examples coming from models of quantum computation.

The reverse derivative is a fundamental operation in machine learning and automatic differentiation. This paper gives a direct axiomatization of a category with a reverse derivative operation, in a similar style to that given by Cartesian differential categories for a forward derivative. Intriguingly, a category with a reverse derivative also has a forward derivative, but the converse is not true. In fact, we show explicitly what a forward derivative is missing: a reverse derivative is equivalent to a forward derivative with a dagger structure on its subcategory of linear maps. Furthermore, we show that these linear maps form an additively enriched category with dagger biproducts.

Abstract The paper shows how the Scott–Koymans theorem for the untyped λ-calculus can be extended to the differential λ-calculus. The main result is that every model of the untyped differential λ-calculus may be viewed as a differential reflexive object in a Cartesian-closed differential category. This extension of the Scott–Koymans theorem depends critically on unraveling the somewhat subtle issue of which idempotents can be split so that differential structure lifts to the idempotent splitting. The paper uses (total) Turing categories with “canonical codes” as the basic categorical semantics for the λ-calculus. It develops the main result in a modular fashion by showing how to add left-additive structure to a Turing category, and then – on top of that – differential structure. For both levels of structure, it is necessary to identify how “canonical codes” must behave with respect to the added structure and, furthermore, how “universal objects” must behave. The latter is closely tied to the question – which is the crux of the paper – of which idempotents can be split while preserving the differential structure of the setting. This paper is the full version of a conference paper and includes the proofs which were omitted from that version due to page-length restrictions.