We consider the problem of gravitational clustering in a D-dimensional expanding universe and derive scaling relations connecting the exact mean two-point correlation function with the linear mean correlation function, in the quasilinear and nonlinear regimes, using the standard paradigms of scale-invariant radial collapse and stable clustering. We show that the existence of scaling laws is a g...

The online unit clustering problem was proposed by Chan and Zarrabi-Zadeh (WAOA2007 and Theory of Computing Systems 45(3), 2009), which is defined as follows: “Points” are given online in the d-dimensional Euclidean space one by one. An algorithm creates a “cluster,” which is a d-dimensional rectangle. The initial length of each edge of a cluster is 0. An algorithm can extend an edge until it r...

The introduction of affordable, consumer-oriented 3-D printers is a milestone in the current "maker movement," which has been heralded as the next industrial revolution. Combined with free and open sharing of detailed design blueprints and accessible development tools, rapid prototypes of complex products can now be assembled in one's own garage--a game-changer reminiscent of the early days of ...

We show that three-dimensional incoherent primary sources can be reconstructed from finite-aperture Fresnel-zone mutual intensity measurements by means of coordinate and Fourier transformation. The spatial bandpass and impulse response for three-dimensional imaging that result from use of this approach are derived. The transverse and longitudinal resolutions are evaluated as functions of apertu...