Watermarking is a frequently used tool for digital rights management. An example of this is using watermarks to place ownership information into an object. There are many instances where placing multiple watermarks into the same object is desired. One mechanism that has been proposed for doing this is segmenting the data into a grid and placing watermarks into different regions of the grid. Thi...

INTRODUCTION: It has been shown that high-permittivity dielectric pads can be used to efficiently improve the field homogeneity in the region of interest (ROI) in high-field MRI [1-8]. Recent studies focused on the design of these pads by controlling parameters such as size, position and permittivity, using simple patient specific parameter sweeping to improve the transmit field in a small regi...

We study the asymptotic behavior of a new particle filter approach for estimation of hidden Markov models (HMMs). In particular, we develop an algorithm where the latent-state sequence is segmented into multiple shorter portions, with an estimation technique based upon a separate particle filter in each portion. The partitioning facilitates the use of parallel processing, which reduces the wall...

We study the fixed design segmented regression problem: Given noisy samples from a piecewise linear function f , we want to recover f up to a desired accuracy in mean-squared error. Previous rigorous approaches for this problem rely on dynamic programming (DP) and, while sample efficient, have running time quadratic in the sample size. As our main contribution, we provide new sample near-linear...

The patterning and differentiation of cells in the somitic mesoderm is an important step in the development of axial structures that include the vertebral column and skeletal muscle. Development of the somitic mesoderm is characterized by the progressive segmentation of mesoderm tissue directly flanking the neural tube into two bilateral rows of somites. Somites when they first appear consist o...

A binary matrix is fully nested if its columns form a chain of subsets; that is, any two columns are ordered by the subset relation, where we view each column as a subset of the rows indicated by the 1-entries. A binary matrix is k-nested if its columns can be partitioned into k pairwise disjoint blocks, each of which is fully nested. Such nested patterns are encountered, for example, in presen...

I was intrigued to learn of the study conducted of three preindustrial cultures, without access to electric lighting, by a team of researchers led by Dr. Jerome Siegel in an effort to determine how humans slept “before the modern era.” Titled “Natural Sleep and Its Seasonal Variations in Three Pre-industrial Societies,” it appears in the November issue of Current Biology.1 Having written on the...

We continue the study of partially ordered generalized patterns (POGPs) considered in [9] for permutations and in [10] for words. We deal with segmented POGPs (SPOGPs). We state some general results and treat a number of patterns of length 4. We prove a result from [8] in a much simpler way and also establish a connection between SPOGPs and walks on lattice points starting from the origin and r...