We consider the problem of community detection in a network, that is, partitioning the nodes into groups that, in some sense, reveal the structure of the network. Many algorithms have been proposed for fitting network models with communities, but most of them do not scale well to large networks, and often fail on sparse networks. We present a fast pseudo-likelihood method for fitting the stocha...

A linear pseudo-inverse method for unsupervised illuminant recovery from natural scenes is presented. The algorithm, which uses a digital RGB camera, selects the naturally occurring bright areas (not necessarily the white ones) in natural images and converts the RGB digital counts directly into the spectral power distribution of the illuminants using a learning-based spectral procedure. Computa...

We study the interplay between the local geometric properties and the non-blowup of the 3D incompressible Euler equations. We consider the interaction of two perturbed antiparallel vortex tubes using Kerr’s initial condition [14][Phys. Fluids 5 (1993), 1725]. We use a pseudo-spectral method with resolution up to 1536 × 1024 × 3072 to resolve the nearly singular behavior of the Euler equations. ...

We present a multi-domain pseudospectral method for the accurate and efficient time-domain computation of scattering by body-of-revolution (BOR) perfectly electrically conducting objects. In the BOR formulation of the Maxwell equations the azimuthal dependence of the fields is accounted for analytically through a Fourier series. The numerical scheme in the (r, z)-plane is developed in general c...

A class of high-order lowpass filters, the discrete singular convolution (DSC) filters, is utilized to facilitate the Fourier pseudospectral method for the solution of hyperbolic conservation law systems. The DSC filters are implemented directly in the Fourier domain (i.e., windowed Fourier pseudospectral method), while a physical domain algorithm is also given to enable the treatment of some s...

Whether the 3D incompressible Euler and Navier–Stokes equations can develop a finite-time singularity from smooth initial data with finite energy has been one of the most long-standing open questions. We review some recent theoretical and computational studies which show that there is a subtle dynamic depletion of nonlinear vortex stretching due to local geometric regularity of vortex filaments...

In this paper, we study systems of functional equations (FEs) and first-order partial differential equations (PDEs) suggested in [SIAM J. Sci. Statist. Comput., 12 (1991), pp. 607–647 and SIAM J. Numer. Anal., 29 (1992), pp. 1741–1768] as approximations for the computation of invariant tori. The main new ideas of this paper are, first, to investigate these systems in the setting of Hilbert spac...

We present a formalism well adapted to the numerical study of the encounter of an ordinary main sequence star with a massive black hole. Symmetry considerations , the use of a well adapted moving grid and a well adapted moving frame along with integration of the partial differential equations by means of pseudo-spectral methods result in a very powerful and accurate tool. The hydro-dynamical eq...

Spectral methods for the solution of a boundary value problem an ordinary differential equation are reviewed with particular emphasis laid on pseudo-spectral collocation method. The pseudo-collocation method is then used to solve one dimensional bio-heat metabolic heat generation in cylindrical coordinates applied human tissue. It was noticed that increase transfer coefficient (hA), enhanced te...

A class of local spectral wavelet filters, discrete singular convolution (DSC) filters, is utilized to facilitate the Fourier pseudospectral method for the solution of hyperbolic conservation law systems. The DSC lowpass filters are adaptively implemented directly in the Fourier domain (i.e., windowed Fourier pseudospectral method), while a physical domain algorithm is also given to enable the ...