In the course of the growth of the Internet and due to increasing availability of data, over the last two decades, the field of network science has established itself as an own area of research. With quantitative scientists from computer science, mathematics, and physics working on datasets from biology, economics, sociology, political sciences, and many others, network science serves as a para...

When users interact with one another on social media sites, the volume and frequency of their communication can shift over time, as their interaction strengthens or weakens. We study the interplay of several competing factors in the maintainance of such links, developing a methodology that can begin to separate out the effects of several distinct social forces. In particular, if two users devel...

Recently, cutting planes derived from maximal lattice-free convex sets have been studied intensively by the integer programming community. An important question in this research area has been to decide whether the closures associated with certain families of lattice-free sets are polyhedra. For a long time, the only result known was the celebrated theorem of Cook, Kannan and Schrijver who showe...

This paper uses a social network approach to examine gender clustering in a complete network of teenagers and their friends. It demonstrates the advantages of using increasingly sophisticated social network techniques, including clustering coefficients and their visualization, and social selection models within the ERGM framework, to visualize and explain the process of clustering which takes p...

There are actually many different zigzag theorems. We will discuss two different zigzag theorems. We will begin with Isbell’s zigzag theorem, which is a an algebraic result involving semigroups and dominions. Then we will also discuss zigzags between two circles, an ergodic result, which is a closure theorem, similar to Poncelet’s porism and Steiner’s porism. We will then mention a general theo...

To study the e ect of cancelations within long-range interactions on local isotropy at the small scales (Wale e, Phys. Fluids A, 4, 1992), we calculate explicitly the degree of cancelation in distant triadic interactions in the simulations of Yeung & Brasseur (Phys. Fluids A, 3, 1991) and Yeung, Brasseur & Wang (to appear, J. Fluid Mech.) using the single scale disparity parameter \s" developed...

An analysis is made of the perception of musical intervals. Two kinds of stimuli were used; intervals consisting of two simultaneous simple tones (sinusoids) and intervals consisting of two simultaneous complex tones (fundamental plus harmonics). Subjects judged the stimuli by the method of triadic comparisons in an incomplete balanced design. Multidimensional analysis was performed according t...