Diagnosis of suspicious breast lesions using an empirical mathematical model for dynamic contrast-enhanced MRI

The purpose of this study was to test whether an empirical mathematical model (EMM) of dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) can distinguish between benign and malignant breast lesions. A modified clinical protocol was used to improve the sampling of contrast medium uptake and washout. T(1)-weighted DCE magnetic resonance images were acquired at 1.5 T for 22 patients before and after injection of Gd-DTPA. Contrast medium concentration as a function of time was calculated over a small region of interest containing the most rapidly enhancing pixels. Then the curves were fitted with the EMM, which accurately described contrast agent uptake and washout. Results demonstrate that benign lesions had uptake (P<2.0 x 10(-5)) and washout (P<.01) rates of contrast agent significantly slower than those of malignant lesions. In addition, secondary diagnostic parameters, such as time to peak of enhancement, enhancement slope at the peak and curvature at the peak of enhancement, were derived mathematically from the EMM and expressed in terms of primary parameters. These diagnostic parameters also effectively differentiated benign from malignant lesions (P<.03). Conventional analysis of contrast medium dynamics, using a subjective classification of contrast medium kinetics in lesions as "washout," "plateau" or "persistent" (sensitivity=83%, specificity=50% and diagnostic accuracy=72%), was less effective than the EMM (sensitivity=100%, specificity=83% and diagnostic accuracy=94%) for the separation of benign and malignant lesions. In summary, the present research suggests that the EMM is a promising alternative method for evaluating DCE-MRI data with improved diagnostic accuracy.     

The electrical properties of doped silicon,grown by Molecular-Beam-Epitaxy (MBE)

Measurements of the Hall coefficients and of the resistivity of MBE-grown Si, doped with P, As, Sb, B, and Ga in the concentration range 10¹⁴ to 10²⁰ cm^–3, were carried out at 77 K and at 300 K. With the exception of Ga-doped Si, the measured mobilities were close to or higher than those of bulk materials at both temperatures. The Mott metal/non-metal transition has been observed in the present epitaxial materials and the measured values for the critical impurity concentration at which the transition occurs, agree with values reported by other workers for bulk silicon.     

The morphology and electrical properties of heteroepitaxial InAs prepared by MBE

An investigation of the growth of heteroepitaxial InAs by MBE is reported. The surface morphology and electrical properties are shown to be critically dependent on growth parameters and the conditions necessary to obtain good material quality are deduced. Analysis of the thickness dependence of the electrical properties of undoped, and Si- or Te-doped InAs shows that interfacial effects contribute to the measured properties. Material remote from the interfacial region compares favourably with VPE- and bulkgrown InAs.     

On the geometry of the planar 4-bar mechanism

The paper seeks to elucidate the geometry of a simple engineering mechanism, comprising four bars smoothly jointed together to form a movable quadrilateral with one fixed side. The configurations of this mechanism correspond to the points of an elliptic curve, to which is associated interesting geometry and Morse theory. By appropriate projection, this curve yields the 2-parameter family of plane curves described by points rigidly attached to the side of the quadrilateral opposite the fixed side: the geometry of the general projection is related to the configuration of lines on a Segre quartic surface.     

Clifford’s theorem for coherent systems

Let C be an algebraic curve of genus g ≥ 2. We prove an analogue of Clifford’s theorem for coherent systems on C and some refinements using results of Re and Mercat. Received: 27 July 2007     

On coherent systems of type (<Emphasis Type="Italic">n</Emphasis>, <Emphasis Type="Italic">d</Emphasis>, <Emphasis Type="Italic">n</Emphasis> + 1) on Petri curves

We study coherent systems of type (n, d, n + 1) on a Petri curve X of genus g ≥ 2. We describe the geometry of the moduli space of such coherent systems for large values of the parameter α. We determine the top critical value of α and show that the corresponding “flip” has positive codimension. We investigate also the non-emptiness of the moduli space for smaller values of α, proving in many cases that the condition for non-emptiness is the same as for large α. We give some detailed results for g ≤ 5 and applications to higher rank Brill–Noether theory and the stability of kernels of evaluation maps, thus proving Butler’s conjecture in some cases in which it was not previously known. The authors are members of the research group VBAC (Vector Bundles on Algebraic Curves). The first two authors were supported by EPSRC grant GR/T22988/01 for a visit to the University of Liverpool. The second author acknowledges the support of CONACYT grant 48263-F. The third author thanks CIMAT, Guanajuato, México and California State University Channel Islands, where a part of this paper was completed, and acknowledges support from the Academia Mexicana de Ciencias, under its exchange agreement with the Royal Society of London.     

Hodge polynomials and birational types of moduli spaces of coherent systems on elliptic curves

In this paper we consider moduli spaces of coherent systems on an elliptic curve. We compute their Hodge polynomials and determine their birational types in some cases. Moreover we prove that certain moduli spaces of coherent systems are isomorphic. This last result uses the Fourier-Mukai transform of coherent systems introduced by Hernández Ruipérez and Tejero Prieto.     

Bundles computing Clifford indices on trigonal curves

In this paper, we determine bundles which compute the higher Clifford indices for trigonal curves.