Quantitation of fetal parameters by prenatal sonography enables the assessment of menstrual age and fetal development. Appropriate fetal growth can be surmised on the basis of sequential measurements, as well as the relative variation of parameters such as biparietal diameter (BPD), femur diaphysis length (FDL), abdominal circumference (AC 1, and head circumference (HC). Accurate determination ...

For every oriented tree T there exists a graph DT (called the dual of T ) such that T 6→ G ⇔ G → DT holds for every G (an arrow denotes the existence of a homomorphism). An explicit construction of DT has been found recently. Although the DT constructed this way may have exponential number of vertices in |V (T )| = n, we will prove that its diameter is linear in n (and therefore DT is ”small” i...

A graph is called integral if all eigenvalues of its adjacency matrix consist entirely of integers. Recently, Csikvári proved the existence of integral trees of any even diameter. In the odd case, integral trees have been constructed with diameter at most 7. In this paper, we show that for every odd integer n > 1, there are infinitely many integral trees of diameter n. AMS Mathematics Subject C...

An automatic method able to recognize a presented section through the biparietal plane of the fetal head and a section through the fetal femur in ultrasound images is developed. Once the correct anatomical section for measurement is identified by the machine, the placement of the measurement calipers is automatically determined by fitting an active contour model to the structure of interest. Th...