Detection and characterization of breast tumours by time-domain scanning optical mammography

The paper gives a short overview of various methods of optical mammography, emphasizing scanning time-domain mammography. The results of a clinical study on time-domain optical mammography are reviewed, comprising 154 patients carrying a total of 102 carcinomas validated by histology. A visibility score attributed to each carcinoma as qualitative measure of tumour detectability indicates acceptable sensitivity but poor specificity for discrimination between malignant and benign lesions. Likewise, a multi-variate statistical analysis yields sensitivity and specificity between 80% and 85% for tumour detection and discrimination with respect to normal (healthy) breast tissue, but values less than 70% for discrimination between malignant and benign breast lesions, being too low to be of clinical relevance. For 87 of the 88 tumours detected retrospectively in both projection optical mammograms, optical properties and tissue parameters were derived based on the diffraction of photon density waves by a spherical inhomogeneity as forward model. Following injection of a bolus of indocyanine green as non-targeted absorbing contrast agent, dynamic contrast-enhanced time-domain optical mammography was carried out on a small number of patients, but no differences in wash-out kinetics of indocyanine green between tumours and healthy breast tissue were observed.     

Dissociation kinetics of peptide ions

The dissociation of peptide ions has been found to have ultrafast components that in many ways are uniquely different from typical unimolecular kinetics. As such, some peptide reactions provide new channels, which do not conform to statistical models of reaction kinetics. When the dissociation rates are in the 100 fs range, they are in a time scale where statistical methods do not yet apply, although molecules that have not yet dissociated will later in time undergo statistical redistribution of their excess energy, which, however, may not lead to noticeable reactivity within the experimental time frames for large peptides and hence are simply dissipative. This work is meant to reconcile the long time statistical results of Lifshitz et al. (2003) with the work of Schlag et al. (1995/6) that suggests an alternate parallel and much faster time scale for dissociation. It is argued that the two sets of results and interpretations augment one another and in fact open up a most interesting new field of peptide kinetics in addition to the unimolecular behavior, which becomes de facto arrested by the shear size of the molecule being unable to find a transition state on any reasonable time scale.     

Anderson Localization for Schrödinger Operators on ℤ with Potentials Given by the Skew–Shift

In this paper we study one-dimensional Schr?dinger operators on the lattice with a potential given by the skew shift. We show that Anderson localization takes place for most phases and frequencies and sufficiently large disorders. Received: 19 September 2000 / Accepted: 15 February 2001     

On continuum incidence problems related to harmonic analysis

We consider averaging operators over curves and surfaces satisfying the rotational curvature condition of Phong and Stein. Using combinatorial arguments restricted weak-type versions of the standard estimates are obtained under weaker assumptions on the regularity of these surfaces. We also consider maximal functions over circles in the plane and obtain a simpler proof of Wolff's endpoint result.     

Interaction of Adjacent Amino Acids

Ramachandran plots display the dihedral angles of a single protein residue. We propose a crossed torsion angle plot called SSY‐plot between two neighboring amino acids and demonstrate that a special coherence motion can exist between some very special amino acid pairs leading to spontaneous unusual structures. A 6mer was extracted from a BBA polypeptide chain which in this plot shows two diagonal domains for the Ser‐Arg pair after some induction time. Other amino acid pairs in general do not show this kind of split domain. This shows that a special pair is required for stabilizing two distinct native structures in protein folding. We suggest that the existence of these two domains corresponds to a bifurcation between two different protein structures and that the special pair is the key to producing these two structures. These two different structures are produced spontaneously without an external agent.     

A remark on Littlewood-Paley theory for the distorted Fourier transform

We consider the classical theorems of Mikhlin and Littlewood-Paley from Fourier analysis in the context of the distorted Fourier transform. The latter is defined as the analogue of the usual Fourier transform as that transformation which diagonalizes a Schrödinger operator . We show that for such operators which display a zero energy resonance the full range in the Mikhlin theorem cannot be obtained: in the radial, three-dimensional case it shrinks to .