Avalanche-size distribution of Cayley tree.

Attacks on networks is a very important issue in developing strategies of eradicating spreads of malicious phenomena in networks, such as epidemics and fake information. This field of research is referred to as networks immunization. The traditional approach to evaluating the effectiveness of attacks on networks focuses on measuring macro parameters related to the entire attack, such as the critical probability of a percolation occurrence in the network [Formula: see text] and the relative size of the largest component in the network, known as the giant component, but not considering the attack on a micro perspective, which is the analysis of node removals, during an attack, themselves, their characteristics and results. In this paper we present and apply the last method of focusing on the micro scale of an attack. Based on the theory of percolation in networks, we analyze the phenomenon of an avalanche which results due to a single node removal from a network. An avalanche is a state in which a removal of a single node from the giant component of a network leads to the disconnection of additional nodes. This process significantly contributes to the fragmentation (immunization) of the network, comparing to the impact of the initial node removal alone. Specifically, we focus on the size parameter of an avalanche, which is the number of nodes that are disconnected from the giant component due to a single node removal. Relating to a random attack on a network of the type of Cayley tree, we derive analytically the distribution of the sizes of avalanches that occur during the entire attack on it, until the network is dismantled (immunized) and the attack is terminated.

Optimal cost for strengthening or destroying a given network.

Strengthening or destroying a network is a very important issue in designing resilient networks or in planning attacks against networks, including planning strategies to immunize a network against diseases, viruses, etc. Here we develop a method for strengthening or destroying a random network with a minimum cost. We assume a correlation between the cost required to strengthen or destroy a node and the degree of the node. Accordingly, we define a cost function c(k), which is the cost of strengthening or destroying a node with degree k. Using the degrees k in a network and the cost function c(k), we develop a method for defining a list of priorities of degrees and for choosing the right group of degrees to be strengthened or destroyed that minimizes the total price of strengthening or destroying the entire network. We find that the list of priorities of degrees is universal and independent of the network's degree distribution, for all kinds of random networks. The list of priorities is the same for both strengthening a network and for destroying a network with minimum cost. However, in spite of this similarity, there is a difference between their p_{c}, the critical fraction of nodes that has to be functional to guarantee the existence of a giant component in the network.

Automatic noninvasive measurement of systolic blood pressure using photoplethysmography.

BACKGROUND: Automatic measurement of arterial blood pressure is important, but the available commercial automatic blood pressure meters, mostly based on oscillometry, are of low accuracy. METHODS: In this study, we present a cuff-based technique for automatic measurement of systolic blood pressure, based on photoplethysmographic signals measured simultaneously in fingers of both hands. After inflating the pressure cuff to a level above systolic blood pressure in a relatively slow rate, it is slowly deflated. The cuff pressure for which the photoplethysmographic signal reappeared during the deflation of the pressure-cuff was taken as the systolic blood pressure. The algorithm for the detection of the photoplethysmographic signal involves: (1) determination of the time-segments in which the photoplethysmographic signal distal to the cuff is expected to appear, utilizing the photoplethysmographic signal in the free hand, and (2) discrimination between random fluctuations and photoplethysmographic pattern. The detected pulses in the time-segments were identified as photoplethysmographic pulses if they met two criteria, based on the pulse waveform and on the correlation between the signal in each segment and the signal in the two neighboring segments. RESULTS: Comparison of the photoplethysmographic-based automatic technique to sphygmomanometry, the reference standard, shows that the standard deviation of their differences was 3.7 mmHg. For subjects with systolic blood pressure above 130 mmHg the standard deviation was even lower, 2.9 mmHg. These values are much lower than the 8 mmHg value imposed by AAMI standard for automatic blood pressure meters. CONCLUSION: The photoplethysmographic-based technique for automatic measurement of systolic blood pressure, and the algorithm which was presented in this study, seems to be accurate.

Effects of external pressure on arteries distal to the cuff during sphygmomanometry.

The aim of this study was to examine the effect on distal arteries of external pressure, applied by upper arm sphygmomanometer cuff. Photoplethysmographic (PPG) signals were measured on the index fingers of 44 healthy male subjects, during the slow decrease of cuff air pressure. For each pulse the ratio of PPG amplitude to its baseline (AM/BL) and its time delay (deltaTD) relative to the contralateral hand were determined as a function of cuff pressure. At cuff pressures equal to systolic blood pressure, pulses reappeared with the pulse time delay in the cuffed arm significantly greater than in the noncuffed arm, with (deltaTD) (mean +/- SD) 150 +/- 31 ms (p < 0.001). At cuff pressures equal to diastolic blood pressure (81 +/- 12 mmHg), deltaTD was 42 +/- 19 ms (p < 0.001), and at 50 mmHg, which is below diastolic blood pressure, (deltaTD) was still significantly positive at 6 +/- 9 ms (p < 0.001). AM/BL relative to its initial value rose at cuff pressures between systolic and diastolic blood pressure, then deceased to 0.6 +/- 0.41 (p < 0.001) at diastolic blood pressure and 0.54 +/- 0.24 (p < 0.001) at 50 mmHg. The changes in (deltaTD) and AM/BL can be interpreted as originating from changes in the compliance of conduit arteries and small arteries with cuff inflation and deflation.