Situations where individuals have to contribute to joint efforts or share scarce resources are ubiquitous. Yet, without proper mechanisms to ensure cooperation, the evolutionary pressure to maximize individual success tends to create a tragedy of the commons (such as over-fishing or the destruction of our environment). This contribution addresses a number of related puzzles of human behavior wi...

This longitudinal study examined how language ability relates to mathematical development in a linguistically and ethnically diverse sample of children from 6 to 9 years of age. Study participants were 75 native English speakers and 92 language minority learners followed from first to fourth grades. Autoregression in a structural equation modeling (SEM) framework was used to evaluate the relati...

Although the field of sparse representations is relatively new, research activities in academic and industrial research labs are already producing encouraging results. The sparse signal or parameter model motivated several researchers and practitioners to explore high complexity/wide bandwidth applications such as Digital TV, MRI processing, and certain defense applications. The potential signa...

All of us have had the experience of asking a class “Remember this...?” and receiving blank stares in response. One demotivator for students to utilise deep learning techniques is a failure to attach value to the concept being learned. In order to encourage students to attach value to concepts, it is suggested that as fundamental, threshold concepts are being taught, they are explicitly linked ...

Links between power law probability distributions and marginal distributions of uniform laws on p-spheres in R show that a mathematical derivation of the Boltzmann-Gibbs distribution necessarily passes through power law ones. Results are also given that link parameters p and n to the value of the nonextensivity parameter q that characterizes these power laws in the context of non-extensive stat...

The mathematical concept of time–changing continuous–time stochastic processes can be regarded as one of the standard tools for building financial models. This article reviews briefly the theory on time–changed stochastic processes and relates them to stochastic volatility models in finance. Popular models, including time–changed Lévy processes, where the time–change process is given by a subor...

Progress in the foundations of mathematics has made it possible to formulate all thinkable mathematical concepts, algorithms and proofs in one language and in an impeccable way. This is not in spite of, but partially based on the famous results of Gödel and Turing. In this way statements are about mathematical objects and algorithms, proofs show the correctness of statements and computations, a...

Proof is a construct of mathematical communities over many generations and is introduced to new generations as they develop cognitively in a social context. Here I present a practical framework for this development in simple terms that nevertheless has deep origins. The framework builds on an analysis of the growth of mathematical ideas based on genetic facilities set-before birth. It unfolds a...

Mathematics and painting are interrelated in many ways. At a technical level mathematics can be used to enhance our appreciation of paintings. This was recently demonstrated beautifully by Taylor, Micolich, and Jones in their analysis of Jackson Pollock’s drip paintings, which led them to the conclusion that Pollock’s paintings are in a way Ž gurative pictures. Relations also exist at a more ba...

Most theories of analogical transfer focus on similarities between the learning and transfer domains, where transfer is more likely between domains that share common surface features, similar elements, or common interpretations of structure. We suggest that characteristics of the learning instantiation alone can give rise to different levels of transfer. We propose that concreteness of the lear...