On the relations and differences between Popper dimension, exclusion dimension and VC-Dimension

A high-level relationPopper dimension—( Exclusion dimension—( VC dimension—( between Karl Popper’s ideas on “falsifiability of scientific theories” and the notion of “overfitting”Overfitting in statistical learning theory can be easily traced. However, it was pointed out that at the level of technical details the two concepts are significantly different. One possible explanation that we suggest is that the process of falsification is an active process, whereas statistical learning theory is mainly concerned with supervised learningSupervised learning, which is a passive process of learning from examples arriving from a stationary distribution. We show that concepts that are closer (although still distant) to Karl Popper’s definitions of falsifiability can be found in the domain of learning using membership queries, and derive relations between Popper’s dimension, exclusion dimension, and the VC-dimensionVC dimension.

ORIGO Stepping Stones Grade K Student Journal

A mathematics curriculum for the Common Core Curriculum at the Kindergarten level for the USA

ORIGO stepping stones common core mathematics Grade 5 practice book

ORIGO Stepping Stones is written and developed by a team of experts to provide teachers with a world-class elementary math program. Our expert team of authors and consultants are utilizing all available educational research to create a unique program that has never before been available to teachers. The full color Student Practice Book provides practice pages that support previous and current lessons.

Canards in advection-reaction-diffusion systems in one spatial dimension

This thesis contains a mathematical investigation of the existence of travelling wave solutions to singularly perturbed advection-reaction-diffusion models of biological processes. An enhanced mathematical understanding of these solutions and models is gained via the identification of canards (special solutions of fast/slow dynamical systems) and their role in the existence of the most biologically relevant, shock-like solutions. The analysis focuses on two existing models. A new proof of existence of a whole family of travelling waves is provided for a model describing malignant tumour invasion, while new solutions are identified for a model describing wound healing angiogenesis.