This paper introduces the interpolative butterfly factorization for nearly optimal implementation of several transforms in harmonic analysis, when their explicit formulas satisfy certain analytic properties and the matrix representations of these transforms satisfy a complementary low-rank property. A preliminary interpolative butterfly factorization is constructed based on interpolative low-ra...

The Hofstadter butterfly, a quantum fractal made up of integers describing quantum Hall states, is shown to be related to an integral Apollonian gasket with D3 symmetry. This mapping unfolds as the self-similar butterfly landscape is found to describe a close packing of (Ford) circles that represent rational flux values and is characterized in terms of an old ((300BC) problem of mutually tangen...

Children’s ability to interpret color adjective noun phrases (e.g., red butterfly) as contrastive was examined in an eyetracking study with 6-year-old Russian children. Pitch accent placement (on the adjective red, or on the noun butterfly) was compared within a visual context containing two red referents (a butterfly and a fox) when only one of them had a contrast member (a purple butterfly) o...

The Neotropical butterfly Dryas iulia has been collected from several locations in Thailand and Malaysia since 2007, and has been observed breeding in the wild, using introduced Passiflora foetida as a larval host plant. The butterfly is bred by a butterfly house in Phuket, Thailand, for release at weddings and Buddhist ceremonies, and we hypothesized that this butterfly house was the source of...

The flower-visiting behaviors of pollinator species are affected not only by flower traits but also by cues of predators and resident pollinators. There is extensive research into the effects of predator cues and resident pollinators on the flower-visiting behaviors of bee pollinators. However, there is relatively little research into their effects on butterfly pollinators probably because of t...

Van Allen radiation belts consist of relativistic electrons trapped by Earth's magnetic field. Trapped electrons often drift azimuthally around Earth and display a butterfly pitch angle distribution of a minimum at 90° further out than geostationary orbit. This is usually attributed to drift shell splitting resulting from day-night asymmetry in Earth's magnetic field. However, direct observatio...

Introduction: The age of peak freestyle swimming speed was reported to be at ~17 years for women and ~19 years for men. However, the age of peak swimming speed for other strokes such as butterfly is not known. Objectives: We investigated whether the age of peak swimming speed and peak swimming speed changed across years in elite butterfly and freestyle swimmers at national level (Switzerland) b...

Random linear network coding is a feasible encoding tool for network coding, specially for the non-coherent network, and its performance is important in theory and application. In this letter, we study the performance of random linear network coding for the well-known butterfly network by analyzing the failure probabilities. We determine the failure probabilities of random linear network coding...

Few data are available about the regional or local extinction of tropical butterfly species. When confirmed, local extinction was often due to the loss of host-plant species. We used published lists and recent monitoring programs to evaluate changes in butterfly composition on Barro Colorado Island (BCI, Panama) between an old (1923-1943) and a recent (1993-2013) period. Although 601 butterfly ...