The design of a parallel implementation of multilevel recursive spectral bisection (PMRSB) is described. The code is fast enough to enable dynamic repartitioning of adaptive meshes and to partition meshes that are too large for workstations. Two innovations in the implementation are recursive asynchronous task teams and a parallel version of the multilevel accelerator. A performance improvement...

Filter banks, subband/wavelets, and multiresolution decompositions that employ recursive filters have been considered previously and are recognized for their efficiency in partitioning the frequency spectrum. This paper presents an analysis of a new infinite impulse response (IIR) filter bank in which these computationally efficient filters may be changed adaptively in response to the input. Th...

A method of generalized regression that blends tree-structured nonparametric regression and adaptive recursive partitioning with maximum likelihood estimation is studied. The function estimate is a piecewise polynomial, with the pieces determined by the terminal nodes of a binary decision tree. The decision tree is constructed by recursively partitioning the data according to the signs of the r...

We propose a new low-complexity entropy-coding method to be used for coding waveform signals. It is based on the combination of two schemes: (1) an alphabet partitioning method to reduce the complexity of the entropy-coding process; (2) a new recursive set partitioning entropy-coding process that achieves rates smaller than rst order entropy even with fast Hu man adaptive codecs. Numerical resu...

The sparse Cholesky factorization of some large matrices can require a two dimensional partitioning of the matrix. The sparse hypermatrix storage scheme produces a recursive 2D partitioning of a sparse matrix. The subblocks are stored as dense matrices so BLAS3 routines can be used. However, since we are dealing with sparse matrices some zeros may be stored in those dense blocks. The overhead i...

The number of possible methods of generalizing binary classification to multi-class classification increases exponentially with the number of class labels. Often, the best method of doing so will be highly problem dependent. Here we present classification software in which the partitioning of multiclass classification problems into binary classification problems is specified using a recursive c...

We adapt Guth's polynomial partitioning argument for the Fourier restriction problem to context of Kakeya problem. By writing out induction as a recursive algorithm, additional multiscale geometric information is made available. To take advantage this, we prove that direction-separated tubes satisfy version Wolff axioms. Altogether, this yields improved bounds maximal conjecture in~$\Bbb{R}^n$ ...

This paper presents a new object oriented framework DAMPVM/DAC which is implemented on top of DAMPVM and provides automatic partitioning of irregular divide-andconquer (DAC) applications at runtime. The processes are then mapped dynamically to processors taking into account their speeds and even loads by other user processes. The paper presents the programming interface (API) of the framework, ...

Amethod of generalized regression that blends tree-structured nonparametric regression and adaptive recursive partitioning with maximum likelihood estimation is studied. The function estimate is a piecewise polynomial, with the pieces determined by the terminal nodes of a binary decision tree. The decision tree is constructed by recursively partitioning the data according to the signs of the re...

The paper presents a network partitioning strategy for the optimal voltage control of Active Distribution Networks (ADNs) actuated by means of a limited number of Distributed Energy Storage Systems (DESSs). The proposed partitioning uses a linear programming approach by means of the known concept of voltage sensitivities. Then, two decentralized optimal control algorithms are proposed relying, ...