Dilution and magnification effects on image analysis applications in activated sludge characterization

The properties of activated sludge systems can be characterized using image analysis procedures. When these systems operate with high biomass content, accurate sludge characterization requires samples to be diluted. Selection of the best image acquisition magnification is directly related to the amount of biomass screened. The aim of the present study was to survey the effects of dilution and magnification on the assessment of aggregated and filamentous bacterial content and structure using image analysis procedures. Assessments of biomass content and structure were affected by dilutions. Therefore, the correct operating dilution requires careful consideration. Moreover, the acquisition methodology comprising a 100 magnification allowed data on aggregated and filamentous biomass to be determined and smaller aggregates to be identified and characterized, without affecting the accuracy of lower magnifications regarding biomass representativeness.AGERE (Empresa de Águas, Efluentes e Resíduos de Braga – EM) and AGS(Administração e Gestão de Sistemas de Salubridade, S.A.)Fundação para a Ciência e Tecnologia (FCT

A comparison between bright field and phase-contrast image analysis techniques in activated sludge morphological characterization

Different approaches using microscopy image analysis procedures were employed for characterization of activated sludge systems. The approaches varied mainly on the type of visualization and acquisition method used for collection of data. In this context, this study focused on the comparison of the two most common acquisition methods: bright field and phase-contrast microscopy. Images were acquired from seven different wastewater treatment plants for a combined period of two years. Advantages and disadvantages of each acquisition technique and the results are discussed. Bright field microscopy proved to be more simple and inexpensive and provided the best overall results.Fundação para a Ciência e a Tecnologia (FCT) - SFRH/BD/32329/2006, POCI/AMB/57069/200

Evolution of the social network of scientific collaborations

The co-authorship network of scientists represents a prototype of complex evolving networks. By mapping the electronic database containing all relevant journals in mathematics and neuro-science for an eight-year period (1991-98), we infer the dynamic and the structural mechanisms that govern the evolution and topology of this complex system. First, empirical measurements allow us to uncover the topological measures that characterize the network at a given moment, as well as the time evolution of these quantities. The results indicate that the network is scale-free, and that the network evolution is governed by preferential attachment, affecting both internal and external links. However, in contrast with most model predictions the average degree increases in time, and the node separation decreases. Second, we propose a simple model that captures the network's time evolution. Third, numerical simulations are used to uncover the behavior of quantities that could not be predicted analytically.Comment: 14 pages, 15 figure

Heuristic Segmentation of a Nonstationary Time Series

Many phenomena, both natural and human-influenced, give rise to signals whose statistical properties change under time translation, i.e., are nonstationary. For some practical purposes, a nonstationary time series can be seen as a concatenation of stationary segments. Using a segmentation algorithm, it has been reported that for heart beat data and Internet traffic fluctuations--the distribution of durations of these stationary segments decays with a power law tail. A potential technical difficulty that has not been thoroughly investigated is that a nonstationary time series with a (scale-free) power law distribution of stationary segments is harder to segment than other nonstationary time series because of the wider range of possible segment sizes. Here, we investigate the validity of a heuristic segmentation algorithm recently proposed by Bernaola-Galvan et al. by systematically analyzing surrogate time series with different statistical properties. We find that if a given nonstationary time series has stationary periods whose size is distributed as a power law, the algorithm can split the time series into a set of stationary segments with the correct statistical properties. We also find that the estimated power law exponent of the distribution of stationary-segment sizes is affected by (i) the minimum segment size, and (ii) the ratio of the standard deviation of the mean values of the segments, and the standard deviation of the fluctuations within a segment. Furthermore, we determine that the performance of the algorithm is generally not affected by uncorrelated noise spikes or by weak long-range temporal correlations of the fluctuations within segments.Comment: 23 pages, 14 figure

Are randomly grown graphs really random?

We analyze a minimal model of a growing network. At each time step, a new vertex is added; then, with probability delta, two vertices are chosen uniformly at random and joined by an undirected edge. This process is repeated for t time steps. In the limit of large t, the resulting graph displays surprisingly rich characteristics. In particular, a giant component emerges in an infinite-order phase transition at delta = 1/8. At the transition, the average component size jumps discontinuously but remains finite. In contrast, a static random graph with the same degree distribution exhibits a second-order phase transition at delta = 1/4, and the average component size diverges there. These dramatic differences between grown and static random graphs stem from a positive correlation between the degrees of connected vertices in the grown graph--older vertices tend to have higher degree, and to link with other high-degree vertices, merely by virtue of their age. We conclude that grown graphs, however randomly they are constructed, are fundamentally different from their static random graph counterparts.Comment: 8 pages, 5 figure

Signatures of small-world and scale-free properties in large computer programs

A large computer program is typically divided into many hundreds or even thousands of smaller units, whose logical connections define a network in a natural way. This network reflects the internal structure of the program, and defines the ``information flow'' within the program. We show that, (1) due to its growth in time this network displays a scale-free feature in that the probability of the number of links at a node obeys a power-law distribution, and (2) as a result of performance optimization of the program the network has a small-world structure. We believe that these features are generic for large computer programs. Our work extends the previous studies on growing networks, which have mostly been for physical networks, to the domain of computer software.Comment: 4 pages, 1 figure, to appear in Phys. Rev.

The spread of epidemic disease on networks

The study of social networks, and in particular the spread of disease on networks, has attracted considerable recent attention in the physics community. In this paper, we show that a large class of standard epidemiological models, the so-called susceptible/infective/removed (SIR) models can be solved exactly on a wide variety of networks. In addition to the standard but unrealistic case of fixed infectiveness time and fixed and uncorrelated probability of transmission between all pairs of individuals, we solve cases in which times and probabilities are non-uniform and correlated. We also consider one simple case of an epidemic in a structured population, that of a sexually transmitted disease in a population divided into men and women. We confirm the correctness of our exact solutions with numerical simulations of SIR epidemics on networks.Comment: 12 pages, 3 figure

Subgraphs in random networks

Understanding the subgraph distribution in random networks is important for modelling complex systems. In classic Erdos networks, which exhibit a Poissonian degree distribution, the number of appearances of a subgraph G with n nodes and g edges scales with network size as \mean{G} ~ N^{n-g}. However, many natural networks have a non-Poissonian degree distribution. Here we present approximate equations for the average number of subgraphs in an ensemble of random sparse directed networks, characterized by an arbitrary degree sequence. We find new scaling rules for the commonly occurring case of directed scale-free networks, in which the outgoing degree distribution scales as P(k) ~ k^{-\gamma}. Considering the power exponent of the degree distribution, \gamma, as a control parameter, we show that random networks exhibit transitions between three regimes. In each regime the subgraph number of appearances follows a different scaling law, \mean{G} ~ N^{\alpha}, where \alpha=n-g+s-1 for \gamma<2, \alpha=n-g+s+1-\gamma for 2<\gamma<\gamma_c, and \alpha=n-g for \gamma>\gamma_c, s is the maximal outdegree in the subgraph, and \gamma_c=s+1. We find that certain subgraphs appear much more frequently than in Erdos networks. These results are in very good agreement with numerical simulations. This has implications for detecting network motifs, subgraphs that occur in natural networks significantly more than in their randomized counterparts.Comment: 8 pages, 5 figure

MutSα expression predicts a lower disease-free survival in malignant salivary gland tumors: an immunohistochemical study

Background: Appropriate DNA replication is vital to maintain cell integrity at the genomic level. Malfunction on DNA repair mechanisms can have implications related to tumor behavior. Our aim was to evaluate the expression of key complexes of the DNA mismatch-repair system MutSα (hMSH2-hMSH6) and MutSβ (hMSH2-hMSH3) in a panel comprising the most common benign and malignant salivary gland tumors (SGT), and to determine their association with disease-free survival. Material and Methods: Ten cases of normal salivary gland (NSG) and 92 of SGT (54 benign and 38 malignant) were retrieved. Immunohistochemistry was performed for hMSH2, hMSH3, hMSH6. Scanned slides were digitally analyzed based on the percentage of positive cells with nuclear staining. Cases were further classified in MutSαhigh and MutSβhigh based on hMSH2-hMSH6 and hMSH3-hMSH6 expression, respectively. Results: hMSH3 expression was lower in malignant SGT compared to NSG and benign cases. Adenoid cystic carcinoma (ACC) cases with perineural invasion presented a lower percentage of hMSH3 positive cells. hMSH6 was downregulated in both benign and malignant SGT compared to NSG. Malignant SGT cases with MutSαhigh expression had lower disease-free survival compared to MutSαlow cases. A 10.26-fold increased risk of presenting local recurrence was observed. Conclusions: Our findings suggest that a lack of hMSH3 protein function is associated with a more aggressive phenotype (malignancy and perineural invasion) and that MutSα overexpression predicts a poor clinical outcome in malignant SGT