We present exact learning algorithms that learn several classes of (discrete) boxes in f0; : : : ; ` 1gn. In particular we learn: (1) The class of unions of O(log n) boxes in time poly(n; log `) (solving an open problem of [16, 12]; in [3] this class is shown to be learnable in time poly(n; `)). (2) The class of unions of disjoint boxes in time poly(n; t; log `), where t is the number of boxes....

We prove dispersive estimates at high frequency in dimension two for both the wave and the Schrödinger groups for a very large class of real-valued potentials.

The deterministic reaction rate equations are not an accurate description of many systems in molecular biology where the number of molecules of each species often is small. The master equation of chemical reactions is a more accurate stochastic description suitable for small molecular numbers. A computational difficulty is the high dimensionality of the equation. We describe how it can be solve...

To cope with the increasing design complexity and size, significant efforts are being made in high level synthesis methodologies, design languages and verification methodologies to leverage the expressive power of high-level models and reduce the design cycle time and cost. High level synthesis is a process of generating a concrete structure to the high level design meeting, three main design c...

When the dimensionality of dataset increases slightly, the number of skyline points increases dramatically as it is usually unlikely for a point to perform equally good in all dimensions. When the dimensionality is very high, almost all points are skyline points. Extract interesting skyline points in high dimensional space automatically is therefore necessary. From our experiences, in order to ...

We propose a new nonparametric test for equality of two or more multivariate distributions based on Euclidean distance between sample elements. Several consistent tests for comparing multivariate distributions can be developed from the underlying theoretical results. The test procedure for the multisample problem is developed and applied for testing the composite hypothesis of equal distributio...

Probability in High Dimension Report Title Lecture notes from course ORF 570 Probability in High Dimension (educational material made freely available on my website) Ramon van Handel Probability in High Dimension ORF 570 Lecture Notes Princeton University This version: June 30, 2014 Preface These lecture notes were written for the course ORF 570: Probability in High Dimension that I taught at P...

A fundamental process in data mining is to approximate the joint distribution of a multivari-ate data set. A typical approach is to use histograms. However, conventional histograms (with dimension-normal data partitions) create an exponential number of partitions as the number of dimensions increases. In previous work, we presented the DataSphere method for data space partitioning and used it f...