By viewing the operations of the Richardson purification algorithm as a discrete time dynamical process, we propose a method to overcome the instability of the algorithm by controlling chaos. We present theoretical analysis and numerical results on the behavior and performance of the stabilized algorithm. Typeset using REVTEX

Confocal laser scanning microscopy is a powerful and popular technique for 3D imaging of biological specimens. Although confocal microscopy images are much sharper than standard epifluorescence ones, they are still degraded by residual out-of-focus light and by Poisson noise due to photon-limited detection. Several deconvolution methods have been proposed to reduce these degradations, including...

We develop the Littlewood-Richardson homotopy algorithm, which uses numerical continuation to compute solutions Schubert problems on Grassmannians and is based geometric rule. One key ingredient of this algorithm our new optimal formulation in local Stiefel coordinates as systems equations. Our implementation can solve problem instances with tens thousands solutions.

We present a quantum algorithm to solve systems of linear equations the form Ax = b , where A is tridiagonal Toeplitz matrix and results from discretizing an analytic function, with circuit complexity O (1/??, poly (log ?, log N )), denotes number equations, ? accuracy, ? condition number. The repeat-until-success has be run (?/(1-?)) times succeed, leveraging amplitude amplification, needs sam...

The Lucy-Richardson Algorithm is a well-known iterative method for the deconvolution of images convolved with a known point spread function. It is derived from a statistical point of view as it converges to the maximum-likelihood solution under the condition that the data follow a Poisson distribution. This assumption holds true for images detected by a digital camera. However, there are images...

Littlewood-Richardson coefficients are the multiplicities in the tensor product decomposition of two irreducible representations of the general linear group GL(n,C). They have a wide variety of interpretations in combinatorics, representation theory and geometry. Mulmuley and Sohoni pointed out that it is possible to decide the positivity of Littlewood-Richardson coefficients in polynomial time...