Googling the brain: discovering hierarchical and asymmetric network structures, with applications in neuroscience

Hierarchical organisation is a common feature of many directed networks arising in nature and technology. For example, a well-defined message-passing framework based on managerial status typically exists in a business organisation. However, in many real-world networks such patterns of hierarchy are unlikely to be quite so transparent. Due to the nature in which empirical data is collated the nodes will often be ordered so as to obscure any underlying structure. In addition, the possibility of even a small number of links violating any overall “chain of command” makes the determination of such structures extremely challenging. Here we address the issue of how to reorder a directed network in order to reveal this type of hierarchy. In doing so we also look at the task of quantifying the level of hierarchy, given a particular node ordering. We look at a variety of approaches. Using ideas from the graph Laplacian literature, we show that a relevant discrete optimization problem leads to a natural hierarchical node ranking. We also show that this ranking arises via a maximum likelihood problem associated with a new range-dependent hierarchical random graph model. This random graph insight allows us to compute a likelihood ratio that quantifies the overall tendency for a given network to be hierarchical. We also develop a generalization of this node ordering algorithm based on the combinatorics of directed walks. In passing, we note that Google’s PageRank algorithm tackles a closely related problem, and may also be motivated from a combinatoric, walk-counting viewpoint. We illustrate the performance of the resulting algorithms on synthetic network data, and on a real-world network from neuroscience where results may be validated biologically

A generator of cauchy-distributed time series with specific Hurst index

A generator of artificial Cauchy-distributed time series is presented. This generator transforms any random time series, e.g., standardized fractional Gaussian noise (FGN), into a Cauchy-distributed series with specific location and scale parameters and correlation structure, determined by the Hurst index. The proposed algorithm consists of an inverse cumulative distribution function (ICDF) transformation, a wavelet-analysis synthesis and, finally, a linear transformation. The resulting Cauchy-distributed series has approximately the desired location and scale parameters and exactly the desired Hurst index. The performance of the proposed generator is evaluated by estimating the location, scale and Hurst parameters from artificial time series and by calculating the mean squared error (MSE) of their cumulative distribution function (CDF). The input location, scale and Hurst index used in the simulations are taken from jitter samples of monitored Voice over Internet Protocol (VoIP) calls, which have been proved to be adequately modeled with these processes under some circumstances

Analysis of al-2 Mutations in Neurospora

The orange pigmentation of the fungus Neurospora crassa is due to the accumulation of the xanthophyll neurosporaxanthin and precursor carotenoids. Two key reactions in the synthesis of these pigments, the formation of phytoene from geranylgeranyl pyrophosphate and the introduction of β cycles in desaturated carotenoid products, are catalyzed by two domains of a bifunctional protein, encoded by the gene al-2. We have determined the sequence of nine al-2 mutant alleles and analyzed the carotenoid content in the corresponding strains. One of the mutants is reddish and it is mutated in the cyclase domain of the protein, and the remaining eight mutants are albino and harbor different mutations on the phytoene synthase (PS) domain. Some of the mutations are expected to produce truncated polypeptides. A strain lacking most of the PS domain contained trace amounts of a carotenoid-like pigment, tentatively identified as the squalene desaturation product diapolycopene. In support, trace amounts of this compound were also found in a knock-out mutant for gene al-2, but not in that for gene al-1, coding for the carotene desaturase. The cyclase activity of the AL-2 enzyme from two albino mutants was investigated by heterologous expression in an appropriately engineered E. coli strain. One of the AL-2 enzymes, predictably with only 20% of the PS domain, showed full cyclase activity, suggesting functional independence of both domains. However, the second mutant showed no cyclase activity, indicating that some alterations in the phytoene synthase segment affect the cyclase domain. Expression experiments showed a diminished photoinduction of al-2 transcripts in the al-2 mutants compared to the wild type strain, suggesting a synergic effect between reduced expression and impaired enzymatic activities in the generation of their albino phenotypes

Knowledge, Attitudes, and Practices Associated with Brucellosis in Livestock Owners in Jordan

We evaluated livestock owners' knowledge, attitudes, and practices regarding brucellosis in Jordan. A questionnaire was administered and biological samples were examined to verify the serological status of animals. Seroprevalence estimates indicated that 18.1% (95% CI: 11–25.3) of cattle herds and 34.3% (95% CI: 28.4–40.4) of small ruminant flocks were seropositive. The results showed that 100% of the interviewed livestock keepers were aware of brucellosis: 87% indicated a high risk of infection if unpasteurized milk is consumed and 75% indicated a high risk if unpasteurized dairy products are consumed. Awareness of the risk of infection through direct contact with fetal membranes or via physical contact with infected livestock is considerably lower, 19% and 13%, respectively. These knowledge gaps manifest in a high frequency of high-risk practices such as assisting in animal parturition (62%), disposing aborted fetuses without protective gloves (71.2%) or masks (65%), and not boiling milk before preparation of dairy products (60%). When brucellosis is suspected, basic hygiene practices are often disregarded and suspect animals are freely traded. Public health education should be enhanced as the disease is likely to remain endemic in the ruminant reservoir as long as a suitable compensation program is not established and trust on available vaccines is regained

Double gaussianization of graph spectra

The graph spectrum is the set of eigenvalues of a simple graph with n vertices. Here we fold this graph spectrum at a given pair of reference eigenvalues and then exponentiate the resulting folded graph spectrum. This process produces double Gaussianized functions of the graph adjacency matrix which give more importance to the reference eigenvalues than to the rest of the spectrum. Based on evidences from mathematical chemistry we focus here our attention on the reference eigenvalues ±1. In the examples that we have examined, they enclose most of the HOMO (highest occupied molecular orbital) and LUMO (lowest unoccupied molecular orbital) of organic molecular graphs. We prove here several results for the trace of the double Gaussianized adjacency matrix of simple graphs–the double Gaussianized Estrada index. Finally we apply this index to the classification of polycyclic aromatic hydrocarbons (PAHs) as carcinogenic or inactive ones. We discover that local indices based on the previously developed matrix function allow to classify correctly 100% of the PAHs analyzed. Such indices reflect the electron population of the HOMO/LUMO and eigenvalues close to them, in the so-called K and L regions of PAHs

The oxygenase CAO-1 of Neurospora crassa is a resveratrol cleavage enzyme.

The genome of the ascomycete Neurospora crassa encodes CAO-1 and CAO-2, two members of the carotenoid cleavage oxygenase family that target double bonds in different substrates. Previous studies demonstrated the role of CAO-2 in cleaving the C40 carotene torulene, a key step in the synthesis of the C35 apocarotenoid pigment neurosporaxanthin. In this work, we investigated the activity of CAO-1, assuming that it may provide retinal, the chromophore of the NOP-1 rhodopsin, by cleaving β-carotene. For this purpose, we tested CAO-1 activity with carotenoid substrates that were, however, not converted. In contrast and consistent with its sequence similarity to family members that act on stilbenes, CAO-1 cleaved the interphenyl Cα-Cβ double bond of resveratrol and its derivative piceatannol. CAO-1 did not convert five other similar stilbenes, indicating a requirement for a minimal number of unmodified hydroxyl groups in the stilbene background. Confirming its biological function in converting stilbenes, adding resveratrol led to a pronounced increase in cao-1 mRNA levels, while light, a key regulator of carotenoid metabolism, did not alter them. Targeted Δcao-1 mutants were not impaired by the presence of resveratrol, a phytoalexin active against different fungi, which did not significantly affect the growth and development of wild-type Neurospora. However, under partial sorbose toxicity, the Δcao-1 colonies exhibited faster radial growth than control strains in the presence of resveratrol, suggesting a moderate toxic effect of resveratrol cleavage products

Molecular characterization of a fungal gene paralogue of the penicillin penDE gene of Penicillium chrysogenum

<p>Abstract</p> <p>Background</p> <p><it>Penicillium chrysogenum </it>converts isopenicillin N (IPN) into hydrophobic penicillins by means of the peroxisomal IPN acyltransferase (IAT), which is encoded by the <it>penDE </it>gene. <it>In silico </it>analysis of the <it>P. chrysogenum </it>genome revealed the presence of a gene, Pc13g09140, initially described as paralogue of the IAT-encoding <it>penDE </it>gene. We have termed this gene <it>ial </it>because it encodes a protein with high similarity to IAT (IAL for IAT-Like). We have conducted an investigation to characterize the <it>ial </it>gene and to determine the role of the IAL protein in the penicillin biosynthetic pathway.</p> <p>Results</p> <p>The IAL contains motifs characteristic of the IAT such as the processing site, but lacks the peroxisomal targeting sequence ARL. Null <it>ial </it>mutants and overexpressing strains indicated that IAL lacks acyltransferase (penicillin biosynthetic) and amidohydrolase (6-APA forming) activities <it>in vivo</it>. When the canonical ARL motif (leading to peroxisomal targeting) was added to the C-terminus of the IAL protein (IAL^ARL) by site-directed mutagenesis, no penicillin biosynthetic activity was detected. Since the IAT is only active after an accurate self-processing of the preprotein into α and β subunits, self-processing of the IAL was tested in <it>Escherichia coli</it>. Overexpression experiments and SDS-PAGE analysis revealed that IAL is also self-processed in two subunits, but despite the correct processing, the enzyme remained inactive <it>in vitro</it>.</p> <p>Conclusion</p> <p>No activity related to the penicillin biosynthesis was detected for the IAL. Sequence comparison among the <it>P. chrysogenum </it>IAL, the <it>A. nidulans </it>IAL homologue and the IAT, revealed that the lack of enzyme activity seems to be due to an alteration of the essential Ser309 in the thioesterase active site. Homologues of the <it>ial </it>gene have been found in many other ascomycetes, including non-penicillin producers. Our data suggest that like in <it>A. nidulans</it>, the <it>ial </it>and <it>penDE </it>genes might have been formed from a single ancestral gene that became duplicated during evolution, although a separate evolutive origin for the <it>ial </it>and <it>penDE </it>genes, is also discussed.</p

Exploring the “Middle Earth” of network spectra via a Gaussian matrix function

We study a Gaussian matrix function of the adjacency matrix of artificial and real-world networks. We motivate the use of this function on the basis of a dynamical process modeled by the time-dependent Schrodinger equation with a squared Hamiltonian. In particular, we study the Gaussian Estrada index - an index characterizing the importance of eigenvalues close to zero. This index accounts for the information contained in the eigenvalues close to zero in the spectra of networks. Such method is a generalization of the so-called "Folded Spectrum Method" used in quantum molecular sciences. Here we obtain bounds for this index in simple graphs, proving that it reaches its maximum for star graphs followed by complete bipartite graphs. We also obtain formulas for the Estrada Gaussian index of Erdos-Renyi random graphs as well as for the Barabasi-Albert graphs. We also show that in real-world networks this index is related to the existence of important structural patters, such as complete bipartite subgraphs (bicliques). Such bicliques appear naturally in many real-world networks as a consequence of the evolutionary processes giving rise to them. In general, the Gaussian matrix function of the adjacency matrix of networks characterizes important structural information not described in previously used matrix functions of graphs

Invasive pulmonary aspergillosis post extracorporeal membrane oxygenation support and literature review

The use of extracorporeal membrane oxygenation (ECMO) for reversible pulmonary failure in critically ill patients has increased over the last few decades. Nosocomial infections are a major complication of ECMO and fungi have been found to be a common cause. Herein, we describe a case of invasive pulmonary aspergillosis following ECMO, which was successfully treated with combination antifungal therapy and interferon-gamma

Linearly scaling direct method for accurately inverting sparse banded matrices

In many problems in Computational Physics and Chemistry, one finds a special kind of sparse matrices, termed "banded matrices". These matrices, which are defined as having non-zero entries only within a given distance from the main diagonal, need often to be inverted in order to solve the associated linear system of equations. In this work, we introduce a new O(n) algorithm for solving such a system, being n X n the size of the matrix. We produce the analytical recursive expressions that allow to directly obtain the solution, as well as the pseudocode for its computer implementation. Moreover, we review the different options for possibly parallelizing the method, we describe the extension to deal with matrices that are banded plus a small number of non-zero entries outside the band, and we use the same ideas to produce a method for obtaining the full inverse matrix. Finally, we show that the New Algorithm is competitive, both in accuracy and in numerical efficiency, when compared to a standard method based in Gaussian elimination. We do this using sets of large random banded matrices, as well as the ones that appear when one tries to solve the 1D Poisson equation by finite differences.Comment: 24 pages, 5 figures, submitted to J. Comp. Phy