Problem statement: The need for wireless communication has driven the communication systems to high performance. However, the main bottleneck that affects the communication capability is the Fast Fourier Transform (FFT), which is the core of most modulators. Approach: This study presented on-chip implementation of pipeline digit-slicing multiplier-less butterfly for FFT structure. The approach ...

A "butterfly" vertebra is a rare congenital anomaly, presenting as a sagittal cleft in the vertebral body. In the literature it has been described as an isolated finding, but it can also be associated with various syndromes, such as Alagille, Jarcho-Levin, Crouzon and Pfeiffer syndrome. We present a case of a 35-year old man with chronic low back pain. The diagnosis of a butterfly vertebra of S...

The contribution of this paper is a framework for relating butterfly-shaped hysteresis maps to simple (single-loop) hysteresis maps, which are typically easier to model and more amenable to control design. In particular, a unimodal mapping is used to transform simple loops to butterfly loops. For the practically important class of piecewise monotone hysteresis maps, we provide conditions for pr...

A scheme for generating a fractal butterfly Floquet spectrum, first proposed by Wang and Gong [Phys. Rev. A 77, 031405(R) (2008)], is extended to driven SU(2) systems such as a driven two-mode Bose-Einstein condensate. A class of driven systems without a link with the Harper-model context is shown to have an intriguing butterfly Floquet spectrum. The found butterfly spectrum shows remarkable de...

The colors of butterfly wings are determined by the structural as well as pigmentary properties of the wing scales. Reflectance spectra of the wings of a number of pierid butterfly species, specifically the small white, Pieris rapae, show that the long-wavelength reflectance of the scales in situ, on the wing, is distinctly higher than that of single, isolated scales. An optical model explains ...

Segmentation defects are often seen with congenital atlantoaxial dislocation (AAD) though an associated absence of posterior arch of C2 and butterfly C3 is rare. Apart from rarity, the combination of formation and segmentation defects adds to the management dilemma. We report a case of AAD with assimilated atlas, absent C2 posterior arch, C3 butterfly vertebra with floating posterior elements, ...

Surveys of butterfly and moth diversity in tropical forest fragments suggest that nocturnality confers a dispersal, and possibly a survival, advantage. The butterfly faunas of smaller fragments were depauperate; in contrast, the species richness of nocturnal moths was similar in all fragments and even in pasture. The lack of correlation between butterfly and moth species richness among fragment...

Stochastic gradient descent is a widely used method to find locally-optimal models in machine learning and data mining. However, it is naturally a sequential algorithm, and parallelization involves severe compromises because the cost of synchronizing across a cluster is much larger than the time required to compute an optimal-sized gradient step. Here we explore butterfly mixing, where gradient...

We are interested in the experimental characterization of the Hofstadter butterfly by means of acoustical waves. The transmission of an acoustic pulse through an array of 60 variable and resonant scatterers periodically distribued along a waveguide is studied. An arbitrary scattering arrangement is realized by using the variable length of each resonator cavity. For a periodic modulation, the st...

Mapping an algorithm to an architecture with faults is an important problem in parallel processing. This paper deals with wrapped butterfly architectures with edge faults. We investigate the effect of automorphisms of a wrapped butterfly on its edges. Given a fault set, one can then choose an appropriate automorphism to map the algorithm to use only fault-free edges. By using an algebraic model...