Traditionally categorical data analysis (e.g. generalized linear models) works with simple, flat datasets akin to a single table in a database with no notion of missing data or conflicting versions. In contrast, modern data analysis must deal with distributed databases with many partial local tables that need not always agree. The computational agents tabulating these tables are spatially separ...

We study the relationship between assumptions of state separability and both preparation measurement contextuality, these to frame problem, problem predicting what does not change in consequence an action. a quantum analog latter prove its undecidability. show how contextuality is generically induced by basis choice, thermodynamic exchange, imposition priori causal models, fine-tuning appear ub...

There are contextual sets of multiple qubits whose commutation is parametrized thanks to the coset geometry G of a subgroup H of the two-generator free group G = 〈x, y〉. One defines geometric contextuality from the discrepancy between the commutativity of cosets on G and that of quantum observables. It is shown in this paper that Kleinian subgroups K = 〈f, g〉 that are non-compact, arithmetic, a...

Presheaf models [7, 27, etc.] provide a formulation of labelled transition systems that is useful for, among other things, modelling concurrent computation. This paper aims to extend such models further to represent stochastic dynamics such as shown in quantum systems. After reviewing what presheaf models represent and what certain operations on them mean in terms of notions such as internal an...

The notion of (non)contextuality pertains to sets of properties measured one subset (context) at a time. We extend this notion to include so-called inconsistently connected systems, in which the measurements of a given property in different contexts may have different distributions, due to contextual biases in experimental design or physical interactions (signaling): a system of measurements ha...

We describe a mathematical language for determining all possible patterns of contextuality in the dependence of stochastic outputs of a system on its deterministic inputs. The central principle (contextualityby-default) is that the outputs indexed by mutually incompatible values of inputs are stochastically unrelated; but they can be coupled (imposed a joint distribution on) in a variety of way...

In this Letter, we demonstrate that the property of monogamy of Bell violations seen for no-signaling correlations in composite systems can be generalized to the monogamy of contextuality in single systems obeying the Gleason property of no disturbance. We show how one can construct monogamies for contextual inequalities by using the graph-theoretic technique of vertex decomposition of a graph ...