247 research outputs found
A Heterosynaptic Learning Rule for Neural Networks
In this article we intoduce a novel stochastic Hebb-like learning rule for
neural networks that is neurobiologically motivated. This learning rule
combines features of unsupervised (Hebbian) and supervised (reinforcement)
learning and is stochastic with respect to the selection of the time points
when a synapse is modified. Moreover, the learning rule does not only affect
the synapse between pre- and postsynaptic neuron, which is called homosynaptic
plasticity, but effects also further remote synapses of the pre- and
postsynaptic neuron. This more complex form of synaptic plasticity has recently
come under investigations in neurobiology and is called heterosynaptic
plasticity. We demonstrate that this learning rule is useful in training neural
networks by learning parity functions including the exclusive-or (XOR) mapping
in a multilayer feed-forward network. We find, that our stochastic learning
rule works well, even in the presence of noise. Importantly, the mean learning
time increases with the number of patterns to be learned polynomially,
indicating efficient learning.Comment: 19 page
Predicting Cell Cycle Regulated Genes by Causal Interactions
The fundamental difference between classic and modern biology is that technological innovations allow to generate high-throughput data to get insights into molecular interactions on a genomic scale. These high-throughput data can be used to infer gene networks, e.g., the transcriptional regulatory or signaling network, representing a blue print of the current dynamical state of the cellular system. However, gene networks do not provide direct answers to biological questions, instead, they need to be analyzed to reveal functional information of molecular working mechanisms. In this paper we propose a new approach to analyze the transcriptional regulatory network of yeast to predict cell cycle regulated genes. The novelty of our approach is that, in contrast to all other approaches aiming to predict cell cycle regulated genes, we do not use time series data but base our analysis on the prior information of causal interactions among genes. The major purpose of the present paper is to predict cell cycle regulated genes in S. cerevisiae. Our analysis is based on the transcriptional regulatory network, representing causal interactions between genes, and a list of known periodic genes. No further data are used. Our approach utilizes the causal membership of genes and the hierarchical organization of the transcriptional regulatory network leading to two groups of periodic genes with a well defined direction of information flow. We predict genes as periodic if they appear on unique shortest paths connecting two periodic genes from different hierarchy levels. Our results demonstrate that a classical problem as the prediction of cell cycle regulated genes can be seen in a new light if the concept of a causal membership of a gene is applied consequently. This also shows that there is a wealth of information buried in the transcriptional regulatory network whose unraveling may require more elaborate concepts than it might seem at first
New approaches to model and study social networks
We describe and develop three recent novelties in network research which are
particularly useful for studying social systems. The first one concerns the
discovery of some basic dynamical laws that enable the emergence of the
fundamental features observed in social networks, namely the nontrivial
clustering properties, the existence of positive degree correlations and the
subdivision into communities. To reproduce all these features we describe a
simple model of mobile colliding agents, whose collisions define the
connections between the agents which are the nodes in the underlying network,
and develop some analytical considerations. The second point addresses the
particular feature of clustering and its relationship with global network
measures, namely with the distribution of the size of cycles in the network.
Since in social bipartite networks it is not possible to measure the clustering
from standard procedures, we propose an alternative clustering coefficient that
can be used to extract an improved normalized cycle distribution in any
network. Finally, the third point addresses dynamical processes occurring on
networks, namely when studying the propagation of information in them. In
particular, we focus on the particular features of gossip propagation which
impose some restrictions in the propagation rules. To this end we introduce a
quantity, the spread factor, which measures the average maximal fraction of
nearest neighbors which get in contact with the gossip, and find the striking
result that there is an optimal non-trivial number of friends for which the
spread factor is minimized, decreasing the danger of being gossiped.Comment: 16 Pages, 9 figure
Connections between Classical and Parametric Network Entropies
This paper explores relationships between classical and parametric measures of graph (or network) complexity. Classical measures are based on vertex decompositions induced by equivalence relations. Parametric measures, on the other hand, are constructed by using information functions to assign probabilities to the vertices. The inequalities established in this paper relating classical and parametric measures lay a foundation for systematic classification of entropy-based measures of graph complexity
Hierarchical coordination of periodic genes in the cell cycle of Saccharomyces cerevisiae
<p>Abstract</p> <p>Background</p> <p>Gene networks are a representation of molecular interactions among genes or products thereof and, hence, are forming causal networks. Despite intense studies during the last years most investigations focus so far on inferential methods to reconstruct gene networks from experimental data or on their structural properties, e.g., degree distributions. Their structural analysis to gain functional insights into organizational principles of, e.g., pathways remains so far under appreciated.</p> <p>Results</p> <p>In the present paper we analyze cell cycle regulated genes in <it>S. cerevisiae</it>. Our analysis is based on the transcriptional regulatory network, representing causal interactions and not just associations or correlations between genes, and a list of known periodic genes. No further data are used. Partitioning the transcriptional regulatory network according to a graph theoretical property leads to a hierarchy in the network and, hence, in the information flow allowing to identify two groups of periodic genes. This reveals a novel conceptual interpretation of the working mechanism of the cell cycle and the genes regulated by this pathway.</p> <p>Conclusion</p> <p>Aside from the obtained results for the cell cycle of yeast our approach could be exemplary for the analysis of general pathways by exploiting the rich causal structure of inferred and/or curated gene networks including protein or signaling networks.</p
Uniform random generation of large acyclic digraphs
Directed acyclic graphs are the basic representation of the structure
underlying Bayesian networks, which represent multivariate probability
distributions. In many practical applications, such as the reverse engineering
of gene regulatory networks, not only the estimation of model parameters but
the reconstruction of the structure itself is of great interest. As well as for
the assessment of different structure learning algorithms in simulation
studies, a uniform sample from the space of directed acyclic graphs is required
to evaluate the prevalence of certain structural features. Here we analyse how
to sample acyclic digraphs uniformly at random through recursive enumeration,
an approach previously thought too computationally involved. Based on
complexity considerations, we discuss in particular how the enumeration
directly provides an exact method, which avoids the convergence issues of the
alternative Markov chain methods and is actually computationally much faster.
The limiting behaviour of the distribution of acyclic digraphs then allows us
to sample arbitrarily large graphs. Building on the ideas of recursive
enumeration based sampling we also introduce a novel hybrid Markov chain with
much faster convergence than current alternatives while still being easy to
adapt to various restrictions. Finally we discuss how to include such
restrictions in the combinatorial enumeration and the new hybrid Markov chain
method for efficient uniform sampling of the corresponding graphs.Comment: 15 pages, 2 figures. To appear in Statistics and Computin
Integrative Network Biology: Graph Prototyping for Co-Expression Cancer Networks
Network-based analysis has been proven useful in biologically-oriented areas, e.g., to explore the dynamics and complexity of biological networks. Investigating a set of networks allows deriving general knowledge about the underlying topological and functional properties. The integrative analysis of networks typically combines networks from different studies that investigate the same or similar research questions. In order to perform an integrative analysis it is often necessary to compare the properties of matching edges across the data set. This identification of common edges is often burdensome and computational intensive. Here, we present an approach that is different from inferring a new network based on common features. Instead, we select one network as a graph prototype, which then represents a set of comparable network objects, as it has the least average distance to all other networks in the same set. We demonstrate the usefulness of the graph prototyping approach on a set of prostate cancer networks and a set of corresponding benign networks. We further show that the distances within the cancer group and the benign group are statistically different depending on the utilized distance measure
Comparing community structure identification
We compare recent approaches to community structure identification in terms
of sensitivity and computational cost. The recently proposed modularity measure
is revisited and the performance of the methods as applied to ad hoc networks
with known community structure, is compared. We find that the most accurate
methods tend to be more computationally expensive, and that both aspects need
to be considered when choosing a method for practical purposes. The work is
intended as an introduction as well as a proposal for a standard benchmark test
of community detection methods.Comment: 10 pages, 3 figures, 1 table. v2: condensed, updated version as
appears in JSTA
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