We describe a new interconnection network called the Enhanced Butterfly (EBn). It is a Cayley graph with n2 nodes, each incident with five edges. This new network has a diameter n which compares favorably to the wrap-around butterfly (Bn) with the same number of nodes and a diameter of b3n/2c. Bn is a subgraph of EBn. The simple and optimal routing algorithms for this network are presented.

This paper describes in detail the design of a CMOS custom fast Fourier transform (FFT) processor for computing a 256-point complex FFT. The FFT is well-suited for realtime spectrum analysis in instrumentation and measurement applications. The FFT butterfly processor reported here consists of one parallel–parallel multiplier and two adders. It is capable of computing one butterfly computation e...

This paper presents a robust method for the automated segmentation and quantitative measurement of reflections from single ommatidia in the butterfly compound eye. Digital pictures of the butterfly eye shine recorded with a digital camera are processed to yield binary images from which single facet centers can be extracted using a morphological image analysis procedure. The location of the face...

The FFT performs butterfly computations on pairs of data elements that differ in a single bit. The computations start from the most significant bit in the index space and proceeds monotonically to the least significant bit. In a binary cube, adjacent nodes differ in a single bit in their addresses. Thus, mapping data to nodes by a binary encoding of the indices is suitable for the FFT. We assum...

Long term studies of Vietnamese Rhopalocera suggest that by using a taxonomic composition analysis of the modern fauna, with ecological and biogeographical characteristics and comparative data with butterfly faunas of adjacent regions, it is possible to offer a plausible account of the history and derivation of the Vietnamese fauna. In former works on the butterfly fauna of Vietnam and of the O...

Butterflies were inventorised in nine sites of three different habitat types of the Emilia-Romagna rural landscape (Northern Italy). Sites were situated in three different landscape contexts, from high to low landscape complexity. A total of 39 butterflies species were collected, including some rare species for the region. Diversity indices and correspondence analysis showed that the butterfly ...

The problems posed by mission-critical legacy systems brittleness, inflexibility, isolation, non-extensibility, lack of openness etc. are well known, but practical solutions have been slow to emerge. Most approaches are “ad hoc” and tailored to peculiarities of individual systems. This paper presents an approach to mission-critical legacy system migration : the Butterfly Methodology, its data m...

We are studying a juggler’s skill called the “butterfly.” Startingwith a ball resting on the palm of his/her open hand, a skilled juggler can accelerate and shape his/her hand so that the ball rolls up the fingers, over the top, and back down to the back of the hand. This paper describes a robotic implementationof the butterfly. The hand’sshape and motion combine to effect the rolling motion of...

Given a connected graph G, a spanning subgraph G' of G is called a t-spanner if every pair of two adjacent vertices in G has a distance of at most t in G! A t-spanner of a graph G is minimum if it contains minimum number of edges among all t-spanners of G. Finding minimum spanners for general graphs is rather difzcult. Most of previous results were obtained for some particular graphs, e.g., but...

This paper presents an efficient multiscale butterfly algorithm for computing Fourier integral operators (FIOs) of the form (Lf)(x) = ∫ Rd a(x, ξ)e f̂(ξ)dξ, where Φ(x, ξ) is a phase function, a(x, ξ) is an amplitude function, and f(x) is a given input. The frequency domain is hierarchically decomposed into a union of Cartesian coronas. The integral kernel a(x, ξ)e in each corona satisfies a spec...