For a graph G=(V, E) and a set of vertices S⊆ V, a vertex v∈S is said to be very cost effective if it is adjacent to more vertices in V{set minus}. S than in S. A bipartition π= {S, V{set minus}. S} is called very cost effective if both S and V{set minus}. S are very cost effective sets. Not all graphs have a very cost effective bipartition, for example, the complete graphs of odd order do not. We characterize the cactus graphs having a very cost effective bipartition. Also, we show that if a graph G or H has a very cost effective bipartition, then so does the Cartesian product G□ H.

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A newly discovered activity in human serum protects porcine aortic endothelial cells in culture from injury by very low density lipoproteins (VLDL). This factor, toxicity-preventing activity (TxPA), was measured in 29 relatively young men (43 ± 8 years) who had undergone coronary angiography. The level of TxPA was found to be significantly reduced (P < 0.001) in men who demonstrated more than 15% narrowing of their coronary arteries. Men (n = 18) who had 15% or less narrowing were found to have 104 ± 48 units of TxPA while men (n = 11) with coronary artery disease had 48 ± 24 units of TxPA. A value derived from the product of TxPA and the high density lipoprotein cholesterol (HDL-C) level divided by the non-HDL-C (total cholesterol-HDL-C) accurately separated 97% of the men into 2 groups. TxPA thus appears to be a new protective factor in coronary artery disease, which, when combined with total cholesterol and high density lipoprotein cholesterol values, provides an accurate classification of established coronary artery disease in these subjects.

Lightning strokes create powerful electromagnetic pulses that routinely cause very low frequency (VLF) waves to propagate across hemispheres along geomagnetic field lines. VLF antenna receivers can be used to detect these whistler waves generated by these lightning strokes. The particular time/frequency dependence of the received whistler wave enables the estimation of electron density in the plasmasphere region of the magnetosphere. Therefore the identification and characterisation of whistlers are important tasks to monitor the plasmasphere in real time and to build large databases of events to be used for statistical studies. The current state of the art in detecting whistler is the Automatic Whistler Detection (AWD) method developed by Lichtenberger (2009) [1]. This method is based on image correlation in 2 dimensions and requires significant computing hardware situated at the VLF receiver antennas (e.g. in Antarctica). The aim of this work is to develop a machine learning based model capable of automatically detecting whistlers in the data provided by the VLF receivers. The approach is to use a combination of image classification and localisation on the spectrogram data generated by the VLF receivers to identify and localise each whistler. The data at hand has around 2300 events identified by AWD at SANAE and Marion and will be used as training, validation, and testing data. Three detector designs have been proposed. The first one using a similar method to AWD, the second using image classification on regions of interest extracted from a spectrogram, and the last one using YOLO, the current state of the art in object detection. It has been shown that these detectors can achieve a misdetection and false alarm rate, respectively, of less than 15% on Marion's dataset. It is important to note that the ground truth (initial whistler label) for data used in this study was generated using AWD. Moreover, SANAE IV data was small and did not provide much content in the study.