The last decades have seen tremendous growth and transformation in the Internet's commercial landscape. Underneath this success, however, the underlying network architecture has shown a marked resistance to change; it is now described as stagnant and ossified. Numerous design proposals have been developed by researchers, implemented in code, and…

We discuss the boundary in the Poincare phase plane for boundedness of solutions to spring model equations of the form [second derivative of]x + x + epsilonx[superscript 2] = Fcoswt and the [second derivative of]x + x + epsilonx[superscript 3] = Fcoswt and report the results of a systematic numerical investigation on the global stability of…

Virtual worlds provide useful platforms for social behavioral research, but impose stringent limitations on the rules of engagement, responsiveness, and data collection, along with other resource restrictions. The major challenge from a computer science standpoint in developing group behavior applications for such environments is accommodating the…

Say that a subset S of the plane is a "circle-center set" if S is not a subset of a line, and whenever we choose three non-collinear points from S, the center of the circle through those three points is also an element of S. A problem appearing on the Macalester College Problem of the Week website stated that a finite set of points in the plane,…

This tricentennial tribute commemorates Euler's major contributions to mathematical and physical sciences. A brief biographical sketch is presented with his major contributions to certain selected areas of number theory, differential and integral calculus, differential equations, solid and fluid mechanics, topology and graph theory, infinite…

Two experiments investigated how 3-year-old children select a tool to perform a manual task, with a focus on their perseverative parameter choices for the various relationships involved in handling a tool: the actor-to-tool relation and the tool-to-target relation (topology). The first study concerned the parameter value for the tool-to-target…

Many scholars have proposed concepts relevant to spatial reference. Herskovits (1982) proposed that the topological concepts support, contiguity and containment are basic in English, while Levinson et al.'s (2003) examination of nine unrelated languages revealed that the concept attachment is primary. Neither of these proposals is confirmed in…

Starting in the late eighties, with a growing discontent with analytical methods in science and the growing power of computers, researchers began to study complex systems such as living organisms, evolution of genes, biological systems, brain neural networks, epidemics, ecology, economy, social networks, etc. In the early nineties, the research…

Cognitive processes require a functional interaction between specialized multiple, local and remote brain regions. Although these interactions can be strongly altered by an acquired brain injury, brain plasticity allows network reorganization to be principally responsible for recovery. The present work evaluates the impact of brain injury on…

People are especially efficient in processing certain visual stimuli such as human faces or good configurations. It has been suggested that topology and geometry play important roles in configural perception. Visual search is one area in which configurality seems to matter. When either of 2 target features leads to a correct response and the…

In our prior study the negative correlation between Topology, a behavioral measure of fluid reasoning, and adult age diminished with the increase in the level of expertise in a cognitively-demanding domain of expertise in the game of GO. The present fMRI study was designed to investigate neural substrates of Topology. The modified topology…

We explore how curvature and torsion determine the shape of a curve via the Frenet-Serret formulas. The connection is made explicit using the existence of solutions to ordinary differential equations. We use a paperclip as a concrete, visual example and generate its graph in 3-space using a CAS. We also show how certain physical deformations to…

Brian Griffiths (1927-2008) was a British mathematician and educator who served as a member of the founding editorial board of "Educational Studies in Mathematics". As a mathematician, Griffiths is remembered through his work on what continue to be known as "Griffiths-type" topological spaces. As a mathematics educator, his…

In this note, it is shown that in a symmetric topological space, the pairs of sets separated by the topology determine the topology itself. It is then shown that when the codomain is symmetric, functions which separate only those pairs of sets that are already separated are continuous, generalizing a result found by M. Lynch.

This article reports on the e-Framework Reference Model for Assessment (FREMA) project that aimed at creating a reference model for the assessment domain: a guide to what resources (standards, projects, people, organisations, software, services and use cases) exist for the domain, aimed at helping strategists understand the state of e-learning…