Magnetic resonance findings in sarcoidosis of the thorax.

Fifteen patients with sarcoidosis underwent thoracic MRI examinations. The T2 signal intensity of lymphadenopathy varied, with no characteristic pattern noted. Three of four patients with bright lymph nodes on T2 images had stage I sarcoidosis, but low intensity nodes were also seen in stage I patients. Coronal images were complementary to axial images and better depicted subcarinal adenopathy. MRI does not distinguish the lymphadenopathy of sarcoidosis from other entities, but is useful for defining the anatomic extent of disease and differentiating pulmonary artery enlargement from adenopathy.     

Empirical minimization

We investigate the behavior of the empirical minimization algorithm using various methods. We first analyze it by comparing the empirical, random, structure and the original one on the class, either in an additive sense, via the uniform law of large numbers, or in a multiplicative sense, using isomorphic coordinate projections. We then show that a direct analysis of the empirical minimization algorithm yields a significantly better bound, and that the estimates we obtain are essentially sharp. The method of proof we use is based on Talagrand's concentration inequality for empirical processes. Research partially supported by NSF under award DMS-0434393. Research partially supported by the Australian Research Council Discovery Porject DP0343616.     

Rearrangement of epoxynitriles: a convenient homologation of acyclic and cyclic ketones to carboxylic acids

A convenient two-step homologation of both aliphatic and aromatic ketones to the corresponding carboxylic acid has been developed. First ketones were converted to epoxynitriles with the Darzens reaction. Second, a Lewis acid mediated rearrangement of these epoxynitriles with lithium bromide was achieved to give homologated secondary alkanoic acids (as well as aryl-alkanoic) in good yields. The mechanism and the scope of the rearrangement reaction were investigated. This strategy constitutes a two-step homologation of ketones to secondary carboxylic acids.     

Chiral self-propulsion of growing bacterial macrofibers on a solid surface

Supercoiling motions that accompany the growth of bacterial macrofibers (multicellular filamentous structures formed in B. subtilis by cell division without separation) are responsible for rolling, pivoting, and walking of fibers on a surface. Fibers possess a fulcrum about which they pivot and step in a chiral manner; forces and torques associated with cell growth, when blocked by friction, result in self-propulsion. The elastic engine that drives macrofiber motions generates torques estimated as microdyn cm and femtowatts of power; optical trapping studies yield a first direct measurement of the Young's modulus of the bacterial cell wall, the engine's "working fluid," of ca. 0.05 GPa.     

Embedding with a Lipschitz function

We investigate a new notion of embedding of subsets of {?1,1}ⁿ in a given normed space, in a way which preserves the structure of the given set as a class of functions on {1, …, n}. This notion is an extension of the margin parameter often used in Nonparametric Statistics. Our main result is that even when considering “small” subsets of {?1, 1}ⁿ, the vast majority of such sets do not embed in a better way than the entire cube in any normed space that satisfies a minor structural assumption. © 2005 Wiley Periodicals, Inc. Random Struct. Alg., 2005     

Suprema of Chaos Processes and the Restricted Isometry Property

We present a new bound for suprema of a special type of chaos process indexed by a set of matrices, which is based on a chaining method. As applications we show significantly improved estimates for the restricted isometry constants of partial random circulant matrices and time‐frequency structured random matrices. In both cases the required condition on the number m of rows in terms of the sparsity s and the vector length n is m ? s log² s log² n. © 2014 Wiley Periodicals, Inc.     

Entropy and the combinatorial dimension

We solve Talagrand’s entropy problem: the L ₂-covering numbers of every uniformly bounded class of functions are exponential in its shattering dimension. This extends Dudley’s theorem on classes of {0,1}-valued functions, for which the shattering dimension is the Vapnik-Chervonenkis dimension. In convex geometry, the solution means that the entropy of a convex body K is controlled by the maximal dimension of a cube of a fixed side contained in the coordinate projections of K. This has a number of consequences, including the optimal Elton’s Theorem and estimates on the uniform central limit theorem in the real valued case. Oblatum 10-XII-2001 & 4-IX-2002?Published online: 8 November 2002     

Obtaining fast error rates in nonconvex situations

We show that under mild assumptions on the learning problem, one can obtain a fast error rate for every reasonable fixed target function even if the base class is not convex. To that end, we show that in such cases the excess loss class satisfies a Bernstein type condition.     

Comparison of agarose and cross-linked protein gels as magnetic resonance imaging phantoms

Measurements of the magnetic field dependence of spin-lattice relaxation rates and the response of the water-proton signal intensity to off-resonance radio frequency fields show that the commonly used agarose phantom provides a less faithful representation for the magnetic response of tissue than does a cross-linked protein system. The origin of these differences lies in the structure and intramolecular dynamics of the macromolecular system used to make the gel. These distinctions will also cause differences in the magnetic response of the water spin system when paramagnetic relaxation agents or contrast agents are incorporated. Use of a thermally cross-linked bovine serum albumin phantom is suggested.     

Determination of polymer branching with gel-permeation chromatography. II. Experimental results for polyethylene

The recently developed methods of characterizing branching in polymers from gelpermeation chromatography and intrinsic viscosity data are verified experimentally. An iterative computer program was written to calculate the degree of branching in whole polymers. Long-chain branching in several low-density polyethylene samples was determined by both the fraction and whole polymer methods. The two methods gave consistent ranking of the branching in the samples although absolute branching indices differed. Effects of various experimental errors and the particular model used for branching were investigated. For polyethylene, the data show that the effect of branching on intrinsic viscosity is best described by the relation 〈g₃〉_W^1/2 = [η]_br/[η]₁ where 〈g₃〉_w is the weight-average ratio of mean-square molecular radii of gyration of linear and trifunctionally branched polymers of the same weight-average molecular weight.