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PubMed2006

Generative model for feedback networks.

We propose a model for network formation and study some of its statistical properties. The motivation for the model comes from the growth of several kinds of real networks (i.e., kinship and trading networks, networks of corporate alliances, networks of autocatalytic chemical reactions). These networks grow either by establishing closer connections by adding links in the existing network or by adding new nodes. A node in these networks lacks the information of the entire network. In order to establish a closer connection to other nodes it starts a search in the neighboring part of the network and waits for a possible feedback from a distant node that received the "searching signal." Our model imitates this behavior by growing the network via the addition of a link that creates a cycle in the network or via the addition of a new node with a link to the network. The forming of a cycle creates feedback between the two ending nodes. After choosing a starting node, a search is made for another node at a suitable distance; if such a node is found, a link is established between this and the starting node, otherwise (such a node cannot be found) a new node is added and is linked to the starting node. We simulate this algorithm and find that we cannot reject the hypothesis that the empirical degree distribution is a q-exponential function, which has been used to model long-range processes in nonequilibrium statistical mechanics.

Journal Article↗
PubMed2026

PaNDA: Efficient Optimization of Phylogenetic Diversity in Networks.

Phylogenetic diversity (PD) plays an important role in biodiversity, conservation, and evolutionary studies by measuring the diversity of a set of taxa based on their phylogenetic relationships. In phylogenetic trees, a subset of k taxa with maximum PD can be found by a simple and efficient greedy algorithm. However, this algorithmic tractability is lost when considering phylogenetic networks, which incorporate reticulate evolutionary events such as hybridization and horizontal gene transfer. To address this challenge, we introduce PaNDA (Phylogenetic Network Diversity Algorithms), the first software package and interactive graphical user-interface for exploring, visualizing, and maximizing diversity in phylogenetic networks. PaNDA includes a novel algorithm to find a subset of k taxa with maximum diversity, running in polynomial time for networks of bounded scanwidth, a measure of tree-likeness of a network that grows slower than the well-known level measure. This algorithm considers the variant of PD on networks in which the branch lengths of all paths from the root to the selected taxa contribute towards their diversity. We demonstrate the scalability of this algorithm on simulated networks, successfully analyzing level-15 networks with up to 200 taxa in seconds. We also provide a proof-of-concept analysis using a phylogenetic network on Xiphophorus species, illustrating how the tool can support diversity studies based on real genomic data. The software is easily installable and freely available at https://github.com/nholtgrefe/panda. Additionally, we extend the definition of PD to semi-directed phylogenetic networks, which are mixed graphs increasingly used in phylogenetic analysis to model uncertainty of the root location. We prove that finding a subset of k taxa with maximum diversity remains NP-hard on semi-directed networks, but do present a polynomial-time algorithm for networks with bounded level.

network↗
PubMed2006

A thermodynamic view of networks.

Networks can be described by the frequency distribution of the number of links associated with each node (the degree of the node). Of particular interest are the power law distributions, which give rise to the so-called scale-free networks, and the distributions of the form of the simplified canonical law (SCL) introduced by Mandelbrot, which give what we shall call the Mandelbrot networks. Many dynamical methods have been obtained for the construction of scale-free networks, but no dynamical construction of Mandelbrot networks has been demonstrated. Here we develop a systematic technique to obtain networks with any given distribution of the degrees of the nodes. This is done using a thermodynamic approach in which we maximise the entropy associated with degree distribution of the nodes of the network subject to certain constraints. These constraints can be chosen systematically to produce the desired network architecture. For large networks we therefore replace a dynamical approach to the stationary state by a thermodynamical viewpoint. We use the method to generate scale-free and Mandelbrot networks with arbitrarily chosen parameters. We emphasise that this approach opens the possibility of insights into a thermodynamics of networks by suggesting thermodynamic relations between macroscopic variables for networks.

Computer Simulation↗
PubMed2000

Basic concepts of artificial neural network (ANN) modeling and its application in pharmaceutical research.

Artificial neural networks (ANNs) are biologically inspired computer programs designed to simulate the way in which the human brain processes information. ANNs gather their knowledge by detecting the patterns and relationships in data and learn (or are trained) through experience, not from programming. An ANN is formed from hundreds of single units, artificial neurons or processing elements (PE), connected with coefficients (weights), which constitute the neural structure and are organised in layers. The power of neural computations comes from connecting neurons in a network. Each PE has weighted inputs, transfer function and one output. The behavior of a neural network is determined by the transfer functions of its neurons, by the learning rule, and by the architecture itself. The weights are the adjustable parameters and, in that sense, a neural network is a parameterized system. The weighed sum of the inputs constitutes the activation of the neuron. The activation signal is passed through transfer function to produce a single output of the neuron. Transfer function introduces non-linearity to the network. During training, the inter-unit connections are optimized until the error in predictions is minimized and the network reaches the specified level of accuracy. Once the network is trained and tested it can be given new input information to predict the output. Many types of neural networks have been designed already and new ones are invented every week but all can be described by the transfer functions of their neurons, by the learning rule, and by the connection formula. ANN represents a promising modeling technique, especially for data sets having non-linear relationships which are frequently encountered in pharmaceutical processes. In terms of model specification, artificial neural networks require no knowledge of the data source but, since they often contain many weights that must be estimated, they require large training sets. In addition, ANNs can combine and incorporate both literature-based and experimental data to solve problems. The various applications of ANNs can be summarised into classification or pattern recognition, prediction and modeling. Supervised 'associating networks can be applied in pharmaceutical fields as an alternative to conventional response surface methodology. Unsupervised feature-extracting networks represent an alternative to principal component analysis. Non-adaptive unsupervised networks are able to reconstruct their patterns when presented with noisy samples and can be used for image recognition. The potential applications of ANN methodology in the pharmaceutical sciences range from interpretation of analytical data, drug and dosage form design through biopharmacy to clinical pharmacy.

Algorithms↗
PubMed2003

External excitatory stimuli can terminate bursting in neural network models.

The concept of modulating or terminating seizure activity by brain stimulation is attracting considerable attention. The ability of such external excitatory stimuli to terminate repetitive bursting may depend upon identifiable parameters. We investigate the ability of external stimuli to terminate bursting under various conditions in defined neural network models. Networks of multiple neurons (n=90), with both inhibitory and excitatory synaptic connections were modeled using conductance-based models with a reduced number of variables. Each neuron in the network has synaptic connections from randomly chosen excitatory and inhibitory neurons. The type and number of connections were kept constant. The initial parameters of the networks were chosen to simulate synchronized repetitive bursting activity. Two basic models of repetitive bursting activity were developed. The first model is a single network with constant random excitatory input, the second incorporates two networks with no random background input, but with a feedback loop with a delay of 600-900ms connecting two networks. The ability of external excitatory stimuli to terminate repetitive bursting in each model was studied. External excitatory stimulation terminates repetitive bursting in both models; however, only in the models with a feedback loop, is the burst termination long-lasting. In the single network model with constant random excitatory input, termination is of short duration and recurrent bursting resumes. Timing of the application of the stimulus to the dual network model is critical; long-lasting termination occurs only when the stimuli to the first network are during a time when the connected network is still relatively refractory. The delay in the loop determines the exact timing of the stimulus. Synaptic inhibition is not required for burst termination. Neural network models provide systems for the study of burst termination and can help define the requirements for such stimuli to successfully terminate bursts. Studies in these models can guide the development and application of such stimuli in intact systems.

Algorithms↗
PubMed2005

Are scale-free networks robust to measurement errors?

BACKGROUND: Many complex random networks have been found to be scale-free. Existing literature on scale-free networks has rarely considered potential false positive and false negative links in the observed networks, especially in biological networks inferred from high-throughput experiments. Therefore, it is important to study the impact of these measurement errors on the topology of the observed networks. RESULTS: This article addresses the impact of erroneous links on network topological inference and explores possible error mechanisms for scale-free networks with an emphasis on Saccharomyces cerevisiae protein interaction networks. We study this issue by both theoretical derivations and simulations. We show that the ignorance of erroneous links in network analysis may lead to biased estimates of the scale parameter and recommend robust estimators in such scenarios. Possible error mechanisms of yeast protein interaction networks are explored by comparisons between real data and simulated data. CONCLUSION: Our studies show that, in the presence of erroneous links, the connectivity distribution of scale-free networks is still scale-free for the middle range connectivities, but can be greatly distorted for low and high connecitivities. It is more appropriate to use robust estimators such as the least trimmed mean squares estimator to estimate the scale parameter gamma under such circumstances. Moreover, we show by simulation studies that the scale-free property is robust to some error mechanisms but untenable to others. The simulation results also suggest that different error mechanisms may be operating in the yeast protein interaction networks produced from different data sources. In the MIPS gold standard protein interaction data, there appears to be a high rate of false negative links, and the false negative and false positive rates are more or less constant across proteins with different connectivities. However, the error mechanism of yeast two-hybrid data may be very different, where the overall false negative rate is low and the false negative rates tend to be higher for links involving proteins with more interacting partners.

Algorithms↗
PubMed2006

Global similarity and local divergence in human and mouse gene co-expression networks.

BACKGROUND: A genome-wide comparative analysis of human and mouse gene expression patterns was performed in order to evaluate the evolutionary divergence of mammalian gene expression. Tissue-specific expression profiles were analyzed for 9,105 human-mouse orthologous gene pairs across 28 tissues. Expression profiles were resolved into species-specific coexpression networks, and the topological properties of the networks were compared between species. RESULTS: At the global level, the topological properties of the human and mouse gene coexpression networks are, essentially, identical. For instance, both networks have topologies with small-world and scale-free properties as well as closely similar average node degrees, clustering coefficients, and path lengths. However, the human and mouse coexpression networks are highly divergent at the local level: only a small fraction (<10%) of coexpressed gene pair relationships are conserved between the two species. A series of controls for experimental and biological variance show that most of this divergence does not result from experimental noise. We further show that, while the expression divergence between species is genuinely rapid, expression does not evolve free from selective (functional) constraint. Indeed, the coexpression networks analyzed here are demonstrably functionally coherent as indicated by the functional similarity of coexpressed gene pairs, and this pattern is most pronounced in the conserved human-mouse intersection network. Numerous dense network clusters show evidence of dedicated functions, such as spermatogenesis and immune response, that are clearly consistent with the coherence of the expression patterns of their constituent gene members. CONCLUSION: The dissonance between global versus local network divergence suggests that the interspecies similarity of the global network properties is of limited biological significance, at best, and that the biologically relevant aspects of the architectures of gene coexpression are specific and particular, rather than universal. Nevertheless, there is substantial evolutionary conservation of the local network structure which is compatible with the notion that gene coexpression networks are subject to purifying selection.

Animals↗
PubMed1997

A proposed classification of veterinary epidemiosurveillance networks.

With the signing of the General Agreement on Tariffs and Trade and the establishment of the World Trade Organisation, the trading environment for animal products has changed. Disease control measures can no longer be applied as trade barriers unless supported by scientific epidemiological data. In this context, it has become necessary, if not obligatory, to gain accurate and up-to-date knowledge about the epidemiological status of important infectious animal diseases. The role of veterinary epidemiosurveillance networks is therefore gaining importance. Furthermore, epidemiosurveillance contributes to the protection of animal populations from exotic or emerging diseases, as well as to the development and evaluation of disease control programmes. Despite the large diversity of surveillance networks, the authors propose a method of network classification. The criteria for classification are as follows: the type of disease being monitored (i.e., surveillance of exotic versus endemic diseases). The number of diseases concerned (i.e., focused networks versus broad-based networks). The area being covered (i.e., local, national or international networks). The population being monitored (i.e., whether the network is targeted at suspect or susceptible animals). The sampling strategy of the network (i.e., sample-based networks versus exhaustive networks). The method of collecting data (i.e., passive data collection versus active collection). The type of network management (i.e., autonomous management versus that which is integrated with other programmes). This classification is discussed and illustrated by examples published in the literature. It may aid in the future development of a grid for the evaluation of veterinary epidemiosurveillance networks.

Animals↗
PubMed1995

Artificial neural networks for decision support in clinical medicine.

Connectionist models such as neural networks are alternatives to linear, parametric statistical methods. Neural networks are computer-based pattern recognition methods with loose similarities with the nervous system. Individual variables of the network, usually called 'neurones', can receive inhibitory and excitatory inputs from other neurones. The networks can define relationships among input data that are not apparent when using other approaches, and they can use these relationships to improve accuracy. Thus, neural nets have substantial power to recognize patterns even in complex datasets. Neural network methodology has outperformed classical statistical methods in cases where the input variables are interrelated. Because clinical measurements usually derive from multiple interrelated systems it is evident that neural networks might be more accurate than classical methods in multivariate analysis of clinical data. This paper reviews the use of neural networks in medical decision support. A short introduction to the basics of neural networks is given, and some practical issues in applying the networks are highlighted. The current use of neural networks in image analysis, signal processing and laboratory medicine is reviewed. It is concluded that neural networks have an important role in image analysis and in signal processing. However, further studies are needed to determine the value of neural networks in the analysis of laboratory data.

Clinical Medicine↗
PubMed1989

A neural network model for limb trajectory formation.

This paper deals with the problem of representing and generating unconstrained aiming movements of a limb by means of a neural network architecture. The network produced time trajectories of a limb from a starting posture toward targets specified by sensory stimuli. Thus the network performed a sensory-motor transformation. The experimenters trained the network using a bell-shaped velocity profile on the trajectories. This type of profile is characteristic of most movements performed by biological systems. We investigated the generalization capabilities of the network as well as its internal organization. Experiments performed during learning and on the trained network showed that: (i) the task could be learned by a three-layer sequential network; (ii) the network successfully generalized in trajectory space and adjusted the velocity profiles properly; (iii) the same task could not be learned by a linear network; (iv) after learning, the internal connections became organized into inhibitory and excitatory zones and encoded the main features of the training set; (v) the model was robust to noise on the input signals; (vi) the network exhibited attractor-dynamics properties; (vii) the network was able to solve the motor-equivalence problem. A key feature of this work is the fact that the neural network was coupled to a mechanical model of a limb in which muscles are represented as springs. With this representation the model solved the problem of motor redundancy.

Extremities↗
PubMed2005

Modulations among the alerting, orienting and executive control networks.

This paper reports a series of experiments that were carried out in order to study the attentional system. Three networks make up this system, and each of them specializes in particular processes. The executive control network specializes in control processes, such as conflict resolution or detection of errors; the orienting network directs the processing system to the source of input and enhances its processing; the alerting network prepares the system for a fast response by maintaining an adequate level of activation in the cognitive system. Recently, Fan and collaborators [J Cogn Neurosci 14(3):340-347, 2002] designed a task to measure the efficiency of each network. We modified Fan's task to test the influences among the networks. We found that the executive control network is inhibited by the alerting network, whereas the orienting network raises the efficiency of the executive control network (Experiment 1). We also found that the alerting network influences the orienting network by speeding up its time course function (Experiment 2). Results were replicated in a third experiment, proving the effects to be stable over time, participants and experimental context, and to be potentially important as a tool for neuropsychological assessment.

Acoustic Stimulation↗
PubMed1979

Structure and dynamics of neural network oscillators.

Techniques are given to represent oscillating neural networks by asynchronous logical switching networks, and to analyze the oscillating networks using a directed graph called a state transition diagram. Consideration is restricted to network oscillators containing no rhythm determining pacemaker neurons, and no neurons exhibiting self-limiting properties such as post-inhibitory rebound or accumulating refractoriness. In the state transition diagrams, stable oscillations are associated with a particular geometric configuration called a cyclic attractor (the heavy cycle in Fig. 2). We show that given the network connectivity it is possible to predict autonomous dynamic behaviour, as well as behaviour following hyperpolarizing or depolarizing inputs to neurons of the network. Conversely, given information about patterns of firing activity during cycles and transients of neural networks, the network connectivity can be predicted. The theoretical techniques can be used to generate a census of network structures capable of generating stable oscillations. Several representative network oscillators are discussed in the context of previous theoretical and experimental studies of the structure of neural network oscillators. Although the number of theoretically possile network oscillators capable of generating sustained oscillations is very large, the techniques which are given should be useful in the design of experiments capable of distinguishing between equally plausible hypotheses.

Action Potentials↗
PubMed1983

'Core' and 'extended' social networks in relation to health and illness.

This paper considers several models of the nature of the association that has been found between characteristics of social networks and health. Such an association does not appear to be adequately accounted for by a deleterious effect of illness on social contact, nor by the role of social networks in mediating health-related practices or in buffering the effects of stress. Thus the proposition is tentatively warranted that the social network is more directly and causally involved in health outcomes--perhaps through the impact of social feedback as mediated by the network. It is argued that the social processes that affect the association between networks and health involve a larger social unit than the small core networks that have generally been the focus of study. Assuming that the individual's susceptibility to illness is affected by the adequacy of the core network, we must deal with the fact that the vulnerability of the core network to loss without adequate replacement is, in turn, affected by the structure of the larger, extended network in which the core network is embedded. By shifting attention to these extended networks, it should also become possible to integrate findings from network studies with more traditional epidemiological findings relating such macro-variables as social class to illness.

Adult↗
PubMed1994

The relevance of drug injectors' social and risk networks for understanding and preventing HIV infection.

Focusing on the social environment as well as the individual should both enhance our understanding of HIV transmission and assist in the development of more effective prevention programs. Networks are an important aspect of drug injectors' social environment. We distinguish between (1) risk networks (the people among whom HIV risk behaviors occur) as vectors of disease transmission, and (2) social networks (the people among whom there are social interactions with a mutual orientation to one another) as generators and disseminators of social influence. These concepts are applied to analyses of data from interviews with drug injectors in two studies. In the first study drug injectors' risk networks converge with their social networks: 70% inject or share syringes with a spouse or sex partner, a running partner, or with friends or others whom they know. Qualitative data from interviews with injectors in the second study also show that the social relationships between drug injectors and members of their risk network are often based on long-standing and multiplex relationships, such as those based on kinship, friendship, marital and sexual ties, and economic activity. In the first study the vast majority of injectors, over 90%, have social ties with non-injectors. Injectors with more frequent social contacts with non-injectors engage in lower levels of injecting risk behavior. Risk settings may function as risk networks: injectors in this study who inject at shooting galleries are more likely than those who do not to rent used syringes, borrow used syringes and inject with strangers. Since the adoption of a network approach is relatively new, a number of issues require further attention. These include: how to utilize social networks among drug injectors to reduce risk through peer pressure; how to promote risk reduction by encouraging ties between injectors and non-injectors; and how to integrate biographical and historical change into understanding network processes. Appropriate methodologies to study drug injectors' networks should be developed, including techniques to reach hidden populations, computer software for managing and analyzing network data bases, and statistical methods for drawing inferences from data gathered through dependent sampling designs.

Adult↗
PubMed2005

Inference of signaling and gene regulatory networks by steady-state perturbation experiments: structure and accuracy.

One of the fundamental problems of cell biology is the understanding of complex regulatory networks. Such networks are ubiquitous in cells and knowledge of their properties is essential for the understanding of cellular behavior. In earlier work (Kholodenko et al. (PNAS 99: 12841), it was shown how the structure of biological networks can be quantified from experimental measurements of steady-state concentrations of key intermediates as a result of perturbations using a simple algorithm called "unravelling". Here, we study the effect of experimental uncertainty on the accuracy of the inferred structure (i.e. whether interactions are excitatory or inhibitory) of the networks determined using the unravelling algorithm. We show that the accuracy of the network structure depends not only on the noise level but on the strength of the interactions within the network. In particular, both very small and very large values of the connection strengths lead to large uncertainty in the inferred network. We describe a powerful geometric tool for the intuitive understanding of the effect of experimental error on the qualitative accuracy of the inferred network. In addition, we show that the use of additional data beyond that needed to minimally constrain the network not only improves the accuracy of the inferred network, but also may allow the detection of situations in which the initial assumptions of unravelling with respect to the network and the perturbations have been violated. Our ideas are illustrated using the mitogen-activated protein kinase (MAPK) signaling network as an example.

Algorithms↗
PubMed2005

Modelling the evolution of genetic regulatory networks.

An evolutionary model of genetic regulatory networks is developed, based on a model of network encoding and dynamics called the Artificial Genome (AG). This model derives a number of specific genes and their interactions from a string of (initially random) bases in an idealized manner analogous to that employed by natural DNA. The gene expression dynamics are determined by updating the gene network as if it were a simple Boolean network. The generic behaviour of the AG model is investigated in detail. In particular, we explore the characteristic network topologies generated by the model, their dynamical behaviours, and the typical variance of network connectivities and network structures. These properties are demonstrated to agree with a probabilistic analysis of the model, and the typical network structures generated by the model are shown to lie between those of random networks and scale-free networks in terms of their degree distribution. Evolutionary processes are simulated using a genetic algorithm, with selection acting on a range of properties from gene number and degree of connectivity through periodic behaviour to specific patterns of gene expression. The evolvability of increasingly complex patterns of gene expression is examined in detail. When a degree of redundancy is introduced, the average number of generations required to evolve given targets is reduced, but limits on evolution of complex gene expression patterns remain. In addition, cyclic gene expression patterns with periods that are multiples of shorter expression patterns are shown to be inherently easier to evolve than others. Constraints imposed by the template-matching nature of the AG model generate similar biases towards such expression patterns in networks in initial populations, in addition to the somewhat scale-free nature of these networks. The significance of these results on current understanding of biological evolution is discussed.

Algorithms↗
PubMed2006

Network analysis of Danish cattle industry trade patterns as an evaluation of risk potential for disease spread.

Trade patterns of animal movements in a specific industry are complex and difficult to study because there are many stakeholders, premises that are heterogeneously spread over the country, and a highly dynamic flow of animals exists among them. The Danish cattle industry was defined as a network of animal movements and graph theory was used to analyse the movements of cattle within this network. A premise was defined as a farm, an abattoir or a market. These premises constituted the network nodes in the graph and the animal movements between them were the links. In this framework, each premise had a sub-network of other premises to which it was linked by these animal movements. If no movement of animals were registered for a specific farm, then the sub-network for that premise consisted of only that premise. Otherwise, the sub-network linked the premise of interest to all premises from which and to which animals were moved, as long as there was a path linking animal movements to that specific premise. This approach allowed visualization and analyses of four levels of organization that existed in Denmark animal registers: (1) the animal that was moved, (2) the movements of all animals between two premises, (3) the specific premise network, and (4) the overall industry network. When contagious animals are moved from one premise to another, then to a third and so forth, these movements create a path for potential transfer of pathogens. The paths within which pathogens are present identify the transmission risks. A network of animal movements should provide information about pathogen transmission and disease spread. The network of the Danish cattle industry network was a directed scale-free graph (the direction of a movement was known), with an in-degree power of 2 an out-degree power of 1.46, consisted of 29,999 nodes, and 130,265 movements during a 6-month period. The in clustering coefficient was calculated to be 0.52 for the inward direction (movement to), while it was 0.02 for the outward direction (movement from). In Denmark, the cattle movements between premises demonstrated a large degree of heterogeneity. This heterogeneity in movements between farms should be used to evaluate the risk potential of disease transmission for each premise and must be considered when modelling disease spread between premises. The objective of this research was to describe the network of animal movements and not just the animal movements per se.

Animals↗
PubMed2003

Response delays and the structure of transcription networks.

Sensory transcription networks generally control rapid and reversible gene expression responses to external stimuli. Developmental transcription networks carry out slow and irreversible temporal programs of gene expression during development. It is important to understand the design principles that underlie the structure of sensory and developmental transcription networks. Cascades, which are chains of regulatory reactions, are a basic structural element of transcription networks. When comparing databases of sensory and developmental transcription networks, a striking difference is found in the distribution of cascade lengths. Here, we suggest that delay times in the responses of the network present a design constraint that influences the network architecture. We experimentally studied the response times in simple cascades constructed of well-characterized repressors in Escherichia coli. Accurate kinetics at high temporal resolution was measured using green fluorescent protein (GFP) reporters. We find that transcription cascades can show long delays of about one cell-cycle time per cascade step. Mathematical analysis suggests that such a delay is characteristic of cascades that are designed to minimize the response times for both turning-on and turning-off gene expression. The need to achieve rapid reversible responses in sensory transcription networks may help explain the finding that long cascades are very rare in databases of E.coli and Saccharomyces cerevisiae sensory transcription networks. In contrast, long cascades are common in developmental transcription networks from sea urchin and from Drosophila melanogaster. Response delay constraints are likely to be less important for developmental networks, since they control irreversible processes on the timescale of cell-cycles. This study highlights a fundamental difference between the architecture of sensory and developmental transcription networks.

Algorithms↗