Abel Jansma
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View article: Möbius transforms and Shapley values for vector-valued functions on weighted directed acyclic multigraphs
Möbius transforms and Shapley values for vector-valued functions on weighted directed acyclic multigraphs Open
We generalize the concept of Möbius inversion and Shapley values to directed acyclic multigraphs and weighted versions thereof. We further allow value functions (games) and thus their Möbius transforms (synergy function) and Shapley values…
View article: Fast Möbius transform: An algebraic approach to information decomposition
Fast Möbius transform: An algebraic approach to information decomposition Open
The partial information decomposition (PID) and its extension integrated information decomposition (ΦID) are promising frameworks to investigate information phenomena involving multiple variables. An important limitation of these approache…
View article: Mereological approach to higher-order structure in complex systems: From macro to micro with Möbius
Mereological approach to higher-order structure in complex systems: From macro to micro with Möbius Open
Relating macroscopic observables to microscopic interactions is a central challenge in the study of complex systems. While current approaches often focus on pairwise interactions, a complete understanding requires going beyond these to cap…
View article: Superdense Coding and Stabiliser Codes with Ising-coupled Entanglement
Superdense Coding and Stabiliser Codes with Ising-coupled Entanglement Open
A new class of quantum states is introduced by demanding that the computational measurement statistics approach the Boltzmann distribution of higher-order strongly coupled Ising models. The states, referred to as $n$-coupled states, are su…
View article: High order expression dependencies finely resolve cryptic states and subtypes in single cell data
High order expression dependencies finely resolve cryptic states and subtypes in single cell data Open
A bstract Single cells are typically typed by clustering in reduced dimensional transcriptome space. Here we introduce Stator, a novel method, workflow and app that reveals cell types, subtypes and states without relying on local proximity…
View article: Higher-Order Interactions and Their Duals Reveal Synergy and Logical Dependence beyond Shannon-Information
Higher-Order Interactions and Their Duals Reveal Synergy and Logical Dependence beyond Shannon-Information Open
Information-theoretic quantities reveal dependencies among variables in the structure of joint, marginal, and conditional entropies while leaving certain fundamentally different systems indistinguishable. Furthermore, there is no consensus…
View article: A compositional game to fairly divide homogeneous cake
A compositional game to fairly divide homogeneous cake Open
The central question in the game theory of cake-cutting is how to fairly distribute a finite resource among multiple players. Most research has focused on how to do this for a heterogeneous cake in a situation where the players do not have…
View article: Higher-Order Interactions and Their Duals Reveal Synergy and Logical Dependence beyond Shannon-Information
Higher-Order Interactions and Their Duals Reveal Synergy and Logical Dependence beyond Shannon-Information Open
Information-theoretic quantities reveal dependencies among variables in the structure of joint, marginal, and conditional entropies, but leave some fundamentally different systems indistinguishable. Furthermore, there is no consensus on ho…