Functional magnetic resonance imaging (fMRI) data were collected while students worked with a tutoring system that taught an algebra isomorph. A cognitive model predicted the distribution of solution times from measures of problem complexity. Separately, a linear discriminant analysis used fMRI data to predict whether or not students were engaged in problem solving. A hidden Markov algorithm me...

In this paper we consider cooperative transferable utility games with limited communication structure, called graph games. Agents are able to cooperate with each other only if they can communicate directly or indirectly with each other. For the class of acyclic graph games recently the average tree solution has been proposed. It was proven that the average tree solution is a core element if the...

The newfound importance of “entanglement as a resource” in quantum computation and quantum communication behooves us to quantify it in as many distinct ways as possible. Here we explore a new quantification of entanglement of a general (mixed) quantum state for a bipartite system, which we name entanglement of assistance. We show it to be the maximum of the average entanglement over all ensembl...

Finally, here is a modern, self-contained text on quantum information theory suitable for graduate-level courses. Developing the subject “from the ground up,” it covers classical results as well as major advances of the past decade. Beginning with an extensive overview of classical information theory suitable for the non-expert, the author then turns his attention to quantum mechanics for quant...

A model for a Choquet integral for arbitrary finite set systems is presented. The model includes in particular the classical model on the system of all subsets of a finite set. The general model associates canonical nonnegative and positively homogeneous superadditive functionals with generalized belief functions relative to an ordered system, which are then extended to arbitrary valuations on ...

The paper aims at generalizing the notion of restricted game on a communication graph, introduced by Myerson. We consider communication graphs with weighted edges, and we define arbitrary ways of partitioning any subset of a graph, which we call correspondences. A particularly useful way to partition a graph is obtained by computing the strength of the graph. The strength of a graph is a measur...

In this note we make a comparison between the class of monotonic TU cooperative games and the class of superadditive TU cooperative games. We first provide the equivalence between a weakening of the class of superadditive TU games and zero-monotonic TU games. Then, we show that zero-monotonic TU games and monotonic TU games are different classes. Finally, we show under which restrictions the cl...

We give a deterministic polynomial-time 2O(r)-approximation algorithm for the number of bases given matroid rank r and common any two matroids r. To best our knowledge, this is first nontrivial approximation that works arbitrary matroids. Based on lower bound Azar, Broder, Frieze, almost possible result assuming oracle access to independent sets matroid. There are main ingredients in result. Fo...