This study proposes a homological approach to mathematically define three-dimensional texture feature of emphysema and fibrosis on chest computed tomography using persistent homology. The proposed definition enabled accurate segmentation with comparable quality deep learning while offering higher interpretability than learning-based methods.

Students learn mathematics through practical applications without applying it. Consequently, the concept images and definitions that students offer do not match. This study examines gap in mathematical ability between of professionals education students' content, including quadrilaterals. employed a qualitative approach with hermeneutic phenomenology method. Sixty-two seventh-grade were involve...

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...

Starting from the continuum definition of helicity, we derive from first principles its different contributions for superfluid vortices. Our analysis shows that an internal twist contribution emerges naturally from the mathematical derivation. This reveals that the spanwise vector that is used to characterize the twist contribution must point in the direction of a surface of constant velocity p...

We present a content-independent formulation of higher cognitive pedagogy, by identifying higher cognitive pedagogy with executive function which in turn we equate with continual multi-dimensional processing of drivers of outcomes. The key focus in this definition is on multiple dimensions. We apply our definition to four diverse disciplines: a) mathematical modeling of verbal problems is prese...

We bring together two apparently disconnected lines of research (of mathematical and of physical nature, respectively) which aim at the definition, through the corresponding zeta function, of the determinant of a differential operator possessing, in general, a complex spectrum. It is shown explicitly how the two lines have in fact converged to a meeting point at which the precise mathematical c...

mathematical models have the potential to provide a cost-effective, objective, and flexible approach to assessing management decisions, particularly when these decisions are strategic alternatives. in some instances, mathematical model is the only means available for evaluating and testing alternatives.  however, in order for this potential to be realized, models must be valid for the applicati...

We propose a new decision procedure for dependency quantified Boolean formulas (DQBFs) that uses interpolation-based definition extraction to compute Skolem functions in counter-example guided inductive synthesis (CEGIS) loop. In each iteration, family of candidate is tested correctness using SAT solver, which either determines model has been found, or returns an assignment the universal variab...