Notes on Automating Stem and Leaf Displays

The stem-and-leaf display is a natural semi-graphic technique to include in statistical computing systems. This paper discusses the choices involved in implementing both automated and flexible versions of the display, develops an algorithm for the automated version, examines various implementation considerations, and presents a set of semi-portable FORTRAN subroutines for producing stem-and-leaf displays.

Random Directed Graph Distributions in the Triad Census in Social Networks

This paper uses the concept of the triad census first introduced by Holland and Leinhardt, and describes several distributions on directed graphs. Methods are presented for calculating the mean and the covariance matrix of the triad census for the uniform distribution that conditions on the number of choices made by each individual in the social network. Several complex distributions on digraphs are approximated, and an application of these methods to a sociogram is given.

Percolation theory applied to measures of fragmentation in social networks

We apply percolation theory to a recently proposed measure of fragmentation $F$ for social networks. The measure $F$ is defined as the ratio between the number of pairs of nodes that are not connected in the fragmented network after removing a fraction $q$ of nodes and the total number of pairs in the original fully connected network. We compare $F$ with the traditional measure used in percolation theory, $P_{\infty}$, the fraction of nodes in the largest cluster relative to the total number of nodes. Using both analytical and numerical methods from percolation, we study Erd\H{o}s-R\'{e}nyi (ER) and scale-free (SF) networks under various types of node removal strategies. The removal strategies are: random removal, high degree removal and high betweenness centrality removal. We find that for a network obtained after removal (all strategies) of a fraction $q$ of nodes above percolation threshold, $P_{\infty}\approx (1-F)^{1/2}$. For fixed $P_{\infty}$ and close to percolation threshold ($q=q_c$), we show that $1-F$ better reflects the actual fragmentation. Close to $q_c$, for a given $P_{\infty}$, $1-F$ has a broad distribution and it is thus possible to improve the fragmentation of the network. We also study and compare the fragmentation measure $F$ and the percolation measure $P_{\infty}$ for a real social network of workplaces linked by the households of the employees and find similar results.Comment: submitted to PR

The Web of Human Sexual Contacts

Many ``real-world'' networks are clearly defined while most ``social'' networks are to some extent subjective. Indeed, the accuracy of empirically-determined social networks is a question of some concern because individuals may have distinct perceptions of what constitutes a social link. One unambiguous type of connection is sexual contact. Here we analyze data on the sexual behavior of a random sample of individuals, and find that the cumulative distributions of the number of sexual partners during the twelve months prior to the survey decays as a power law with similar exponents $\alpha \approx 2.4$ for females and males. The scale-free nature of the web of human sexual contacts suggests that strategic interventions aimed at preventing the spread of sexually-transmitted diseases may be the most efficient approach.Comment: 7 pages with 2 eps figures. Latex file. For more details or for downloading the PDF file of the published article see http://polymer.bu.edu/~amaral/WebofContacts.html . For more results on teh structure of complex networks see http://polymer.bu.edu/~amaral/Networks.htm

Small-world networks: Evidence for a crossover picture

Watts and Strogatz [Nature 393, 440 (1998)] have recently introduced a model for disordered networks and reported that, even for very small values of the disorder $p$ in the links, the network behaves as a small-world. Here, we test the hypothesis that the appearance of small-world behavior is not a phase-transition but a crossover phenomenon which depends both on the network size $n$ and on the degree of disorder $p$. We propose that the average distance $\ell$ between any two vertices of the network is a scaling function of $n / n^*$. The crossover size $n^*$ above which the network behaves as a small-world is shown to scale as $n^*(p \ll 1) \sim p^{-\tau}$ with $\tau \approx 2/3$.Comment: 5 pages, 5 postscript figures (1 in color), Latex/Revtex/multicols/epsf. Accepted for publication in Physical Review Letter

Emergence of good conduct, scaling and Zipf laws in human behavioral sequences in an online world

We study behavioral action sequences of players in a massive multiplayer online game. In their virtual life players use eight basic actions which allow them to interact with each other. These actions are communication, trade, establishing or breaking friendships and enmities, attack, and punishment. We measure the probabilities for these actions conditional on previous taken and received actions and find a dramatic increase of negative behavior immediately after receiving negative actions. Similarly, positive behavior is intensified by receiving positive actions. We observe a tendency towards anti-persistence in communication sequences. Classifying actions as positive (good) and negative (bad) allows us to define binary 'world lines' of lives of individuals. Positive and negative actions are persistent and occur in clusters, indicated by large scaling exponents alpha~0.87 of the mean square displacement of the world lines. For all eight action types we find strong signs for high levels of repetitiveness, especially for negative actions. We partition behavioral sequences into segments of length n (behavioral `words' and 'motifs') and study their statistical properties. We find two approximate power laws in the word ranking distribution, one with an exponent of kappa-1 for the ranks up to 100, and another with a lower exponent for higher ranks. The Shannon n-tuple redundancy yields large values and increases in terms of word length, further underscoring the non-trivial statistical properties of behavioral sequences. On the collective, societal level the timeseries of particular actions per day can be understood by a simple mean-reverting log-normal model.Comment: 6 pages, 5 figure

Safety, Immunogenicity, and Transmissibility of Single-Dose Live Oral Cholera Vaccine Strain CVD l03-HgR in 24- to 59-Month-Old Indonesian Children

Recombinant A-B+ Vibrio cholerae O1 strain CVD 103-HgR is a safe, highly immunogenic, single-dose live oral vaccine in adults in industrialized countries, Safety, excretion, immunogenicity, vaccine transmissibility, and environmental introduction ofCVD 103-HgR were investigated among 24- to 59-month-old children in Jakarta. In 81 households, 1 child was randomly allocated a single dose of vaccine (5 x 109 cfu) and another, placebo. Additionally, 139 unpaired children were randomly allocated vaccine or placebo. During 9 days of follow-up, diarrhea or vomiting did not occur more often among vaccinees than controls. Vaccine was minimally excreted and was isolated from no controls and from 1 (0.6%) of 177 unvaccinated family contacts. A 4-fold or higher rise in serum vibriocidal antibody was observed in 75% of vaccinees (10-fold rise in geometric mean titer over baseline). Of 135 paired placebo recipients or household contacts, 5 had vibriocidal seroconversions. Moore swabs placed in sewers and latrines near 97 households failed to detect vaccine. These observations pave the way for a large-scale field trial of efficac

Safety and Immunogenicity of Different Immunization Regimens of CVD 103-HgR Live Oral Cholera Vaccine in Soldiers and Civilians in Thailand

Attenuated Vibrio cholerae oral vaccineCVD 103-HgR was well tolerated by 324 Thai soldiers and civilians. Most receiveda single 5 × 108 cfu dose, while 40 each receivedone or two 5 × 109 cfu doses. Vibriocidal antibody (the best correlate of immunity) seroconversion was lower in soldiers than civilians (P < .001). Increasing the vaccinedose to 5 × 109 cfu raised the geometric mean titer (P < .001).Asecond 5 × 109 cfu dose one weeklater did not notably increase seroconversions. Likelihood of seroconversionwas inverselycorrelated with baseline vibriocidal titer (P < .001). CVD 103-HgR caused seroconversion in most subjects with baseline titers ⩽1:40, including 100% of civilians after one 5 × 108 cfu dose, 79% of soldiers after one 5 × 109 cfu dose, and 45% of soldiers after one 5 × 108 cfu dose. In persons with elevatedbaseline titers, vibriocidal antibody seroconversion is not a sensitive measure of whether vaccine has boosted intestinal immunity; for such subjects,other measurements must be used. Study regimens in endemic areas should use a single 5 × 109 cfu dos

Scale-free models for the structure of business firm networks

We study firm collaborations in the life sciences and the information and communication technology sectors. We propose an approach to characterize industrial leadership using k-shell decomposition, with top-ranking firms in terms of market value in higher k-shell layers. We find that the life sciences industry network consists of three distinct components: a “nucleus,” which is a small well-connected subgraph, “tendrils,” which are small subgraphs consisting of small degree nodes connected exclusively to the nucleus, and a “bulk body,” which consists of the majority of nodes. Industrial leaders, i.e., the largest companies in terms of market value, are in the highest k-shells of both networks. The nucleus of the life sciences sector is very stable: once a firm enters the nucleus, it is likely to stay there for a long time. At the same time we do not observe the above three components in the information and communication technology sector. We also conduct a systematic study of these three components in random scale-free networks. Our results suggest that the sizes of the nucleus and the tendrils in scale-free networks decrease as the exponent of the power-law degree distribution λ increases, and disappear for λ≥3. We compare the k-shell structure of random scale-free model networks with two real-world business firm networks in the life sciences and in the information and communication technology sectors. We argue that the observed behavior of the k-shell structure in the two industries is consistent with the coexistence of both preferential and random agreements in the evolution of industrial networks

Bad news travels fast! | Notícia ruim corre depressa!

Many proverbs are created through everyday experience. Although many of them are readily understood by ordinary people, the more detailed view generates many questions and doubts related to their credibility. Motivated by one of these proverbs, in the present paper, we analyse propagation of news in the network of electronic contacts (e-mails). More specifically, we propose transmission protocols intended to reproduce properties of real systems. These protocols are simulated in a real e-mail network and in the random network proposed by p. Erdos and a. Rényi prize. The results suggest that news spreads faster in the random network. The hubs in the real network tend to attract the news, in prejudice to the less connected nodes