The complexity of irredundant sets parameterized by size

An irredundant set of vertices V′V in a graph G=(V,E) has the property that for every vertex uV′, N[V′−{u}] is a proper subset of N[V′]. We investigate the parameterized complexity of determining whether a graph has an irredundant set of size k, where k is the parameter. The interest of this problem is that while most “k-element vertex set” problems are NP-complete, several are known to be fixed-parameter tractable, and others are hard for various levels of the parameterized complexity hierarchy. Complexity classification of vertex set problems in this framework has proved to be both more interesting and more difficult. We prove that the k-element irredundant set problem is complete for W[1], and thus has the same parameterized complexity as the problem of determining whether a graph has a k-clique. We also show that the “parametric dual” problem of determining whether a graph has an irredundant set of size n−k is fixed-parameter tractable.     

Reduction of spectral interferences in inductively-coupled plasma emission spectrometry by selective spectral-line modulation

Spectral interferences in inductively-coupled plasma (i.c.p.) emission spectrometry can be significantly reduced through the use of selective spectral-line modulation. In this method, a mirrored, rotating chopper directs the emission from an i.e.p. alternately through and past a flame; selective modulation is achieved when the flame contains absorbing atoms identical to emitting atoms in the i.c.p. The ability of selective spectral-line modulation to minimize broadband, narrow line, and scattered light spectral interferences is demonstrated. Signal-to-background ratios for detection with spectral-line modulation are shown to be higher than those obtained by conventional detection. The effect of modulating conditions on working curve slope and linearity is discussed and the limitations of the proposed method are critically evaluated.     

Three-dimensional ultrasound imaging and its use in quantifying organ and pathology volumes

Although ultrasonography is an important cost-effective imaging modality, technical improvements are needed before its full potential is realized for accurate and reproducible monitoring of disease progression or regression. Two-dimensional viewing of three-dimensional anatomy, using conventional ultrasonography, limits our ability to quantify and visualize pathology and is partly responsible for the reported variability in diagnosis and monitoring of disease progression. Efforts of investigators have focused on overcoming these deficiencies by developing 3D ultrasound imaging techniques that are capable of acquiring B-mode images using existing conventional ultrasound systems, reconstructing the information into 3D images, and then allowing interactive viewing of the 3D images on inexpensive desktop computers. In addition, the availability of 3D ultrasound images has allowed the development of manual and semi-automated techniques to quantify normal and abnormal anatomical volumes. In this paper we review our semi-automated 3D segmentation approaches for segmenting the surface of the carotid arteries and plaques, and segmenting the prostate. These techniques demonstrate that efficient segmentation techniques can be used with 3D ultrasound images to quantify anatomical organ volumes and morphology.     

Ni(II) bis(oxazoline)-catalyzed enantioselective syn aldol reactions of N-propionylthiazolidinethiones in the presence of silyl triflates

An enantioselective aldol reaction of N-propionylthiazolidinethione and representative aldehydes is disclosed. The reaction is catalyzed by [Ni(S,S)-t-BuBox](Otf)2. Enolization is effected by 2,6-lutidine, and TMSOTf facilitates catalyst turnover. Syn diastereoselectivities range from 88:12 to 97:3, and enantioselectivities are 90% or greater. Both aromatic and enolizable aliphatic aldehydes are included within the scope of this aldol addition process.     

On Schnorr and computable randomness,martingales, and machines

We examine the randomness and triviality of reals using notions arising from martingales and prefix‐free machines. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)