374 research outputs found
Comparison of the Representational Power of Random Forests, Binary Decision Diagrams, and Neural Networks
In this letter, we compare the representational power of random forests, binary decision diagrams (BDDs), and neural networks in terms of the number of nodes. We assume that an axis-aligned function on a single variable is assigned to each edge in random forests and BDDs, and the activation functions of neural networks are sigmoid, rectified linear unit, or similar functions. Based on existing studies, we show that for any random forest, there exists an equivalent depth-3 neural network with a linear number of nodes. We also show that for any BDD with balanced width, there exists an equivalent shallow depth neural network with a polynomial number of nodes. These results suggest that even shallow neural networks have the same or higher representation power than deep random forests and deep BDDs. We also show that in some cases, an exponential number of nodes are required to express a given random forest by a random forest with a much fewer number of trees, which suggests that many trees are required for random forests to represent some specific knowledge efficiently
Structurally Robust Control of Complex Networks
Robust control theory has been successfully applied to numerous real-world
problems using a small set of devices called {\it controllers}. However, the
real systems represented by networks contain unreliable components and modern
robust control engineering has not addressed the problem of structural changes
on a large network. Here, we introduce the concept of structurally robust
control of complex networks and provide a concrete example using an algorithmic
framework that is widely applied in engineering. The developed analytical
tools, computer simulations and real network analyses lead herein to the
discovery that robust control can be achieved in scale-free networks with
exactly the same order of controllers required in a standard non-robust
configuration by adjusting only the minimum degree. The presented methodology
also addresses the probabilistic failure of links in real systems, such as
neural synaptic unreliability in {\it C. elegans}, and suggests a new direction
to pursue in studies of complex networks in which control theory has a role.Comment: 36 pages, 22 figures. This paper was submitted to a journal in May
2014 and still under review. Please cite the arxiv version if your work is
related to our researc
Prediction of RNA secondary structure with pseudoknots using integer programming
<p>Abstract</p> <p>Background</p> <p>RNA secondary structure prediction is one major task in bioinformatics, and various computational methods have been proposed so far. Pseudoknot is one of the typical substructures appearing in several RNAs, and plays an important role in some biological processes. Prediction of RNA secondary structure with pseudoknots is still challenging since the problem is NP-hard when arbitrary pseudoknots are taken into consideration.</p> <p>Results</p> <p>We introduce a new method of predicting RNA secondary structure with pseudoknots based on integer programming. In our formulation, we aim at minimizing the value of the objective function that reflects free energy of a folding structure of an input RNA sequence. We focus on a practical class of pseudoknots by setting constraints appropriately. Experimental results for a set of real RNA sequences show that our proposed method outperforms several existing methods in sensitivity. Furthermore, for a set of sequences of small length, our approach achieved good performance in both sensitivity and specificity.</p> <p>Conclusion</p> <p>Our integer programming-based approach for RNA structure prediction is flexible and extensible.</p
Analysis of the impact degree distribution in metabolic networks using branching process approximation
Theoretical frameworks to estimate the tolerance of metabolic networks to
various failures are important to evaluate the robustness of biological complex
systems in systems biology. In this paper, we focus on a measure for robustness
in metabolic networks, namely, the impact degree, and propose an approximation
method to predict the probability distribution of impact degrees from metabolic
network structures using the theory of branching process. We demonstrate the
relevance of this method by testing it on real-world metabolic networks.
Although the approximation method possesses a few limitations, it may be a
powerful tool for evaluating metabolic robustness.Comment: 17 pages, 4 figures, 4 table
Conditional random field approach to prediction of protein-protein interactions using domain information
For understanding cellular systems and biological networks, it is important to analyze functions and interactions of proteins and domains. Many methods for predicting protein-protein interactions have been developed. It is known that mutual information between residues at interacting sites can be higher than that at non-interacting sites. It is based on the thought that amino acid residues at interacting sites have coevolved with those at the corresponding residues in the partner proteins. Several studies have shown that such mutual information is useful for identifying contact residues in interacting proteins
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