Network Structure and Inflection Class Predictability: Modeling the Emergence of Marginal Detraction

The lack of studying the complex organization of directed network usually limits the understanding of the underlying relationship between network structures and functions. Structural controllability and structural predictability, two seemingly unrelated subjects, are revealed in this article to be both highly dependent on the critical links previously thought to only be able to influence the number of driver nodes in controllable directed networks. Here, we show that critical links can not only contribute to structural controllability but can also have a significant impact on the structural predictability of networks, suggesting the universal pattern of structural reciprocity in directed networks. In addition, it is shown that the fraction and location of critical links have a strong influence on the performance of prediction algorithms. Moreover, these empirical results are interpreted by introducing the link centrality based on corresponding line graphs. This work bridges the gap between the two independent research fields, and it provides indications of developing advanced control strategies and prediction algorithms from a microscopic perspective.

The structure of networks that provide optimal transport properties has been investigated in a variety of contexts. While many different formulations of this problem have been considered, it is recurrently found that optimal networks are trees. It is shown here that this result is contingent on the assumption of a stationary flow through the network. When time variations or fluctuations are allowed for, a different class of optimal structures is found, which share the hierarchical organization of trees yet contain loops. The transitions between different network topologies as the parameters of the problem vary are examined. These results may have strong implications for the structure and formation of natural networks, as is illustrated by the example of leaf venation networks.

Chapter 5 - Protein Structure Prediction

Interactive microcomputer-aided analysis of tensile network structures

Structure prediction is an important and widely studied problem in network science and machine learning, finding its applications in various fields. Despite the significant progress in prediction algorithms, the fundamental predictability of structures remains unclear, as networks’ complex underlying formation dynamics are usually unobserved or difficult to describe. As such, there has been a lack of theoretical guidance on the practical development of algorithms for their absolute performances. Here, for the first time, we find that the normalized shortest compression length of a network structure can directly assess the structure predictability. Specifically, shorter binary string length from compression leads to higher structure predictability. We also analytically derive the origin of this linear relationship in artificial random networks. In addition, our finding leads to analytical results quantifying maximum prediction accuracy, and allows the estimation of the network dataset potential values through the size of the compressed network data file.

Can network structure predict cross-sectional stock returns? Evidence from co-attention networks in China

Deciphering the native conformation of proteins from their amino acid sequences is one of the greatest challenges in the field of molecular biology. The successful prediction of structural class may help to improve the accuracy levels of structure (secondary and tertiary) predictive schemes in globular proteins. In our earlier works we developed a new surrounding hydrophobicity scale for the 20 amino acid residues applicable for both globular and membrane proteins and used it successfully to predict the transmembrane helical and strand segments in membrane proteins. In this article we propose (i) rules to predict the structural class of proteins and (ii) a new predictive scheme for forecasting secondary structures of globular proteins, with the use of the new hydrophobicity scale. This scheme predicts the structural class and secondary structures of globular proteins to 92 and 82% levels of accuracy, respectively, far better than the levels from other existing methods.

PreSSAPro: A software for the prediction of secondary structure by amino acid properties

The space-group distribution of molecular organic structures is reviewed. Topics discussed include: a priori classifications of space groups; special positions of given symmetry; empirical space-group frequencies; the use of molecular symmetry; structural classes; a statistical model for space-group frequency; molecular packing; and a priori predictions of molecular crystal structures. Keywords: antimorphism; basic structural features; hydrogen bonding; Kitajgorodskij’s categories; molecular packing; packing; space groups; space-group frequencies; statistical modelling; structural classes; structure prediction; symmorphism

Group composition and network structure in school classes: a multilevel application of the p∗ model

The properties of social networks have been used to explain the behaviour and performance of diverse economic and social systems. Recently, attention has been given to a class of network structures identified as ‘small‐worlds’, due to their apparent efficiency in connecting different actors through short path lengths within a relatively sparse network. Intuitively, such network structures should also be conducive for innovation due to better flows of information and the possibility of new connections between skills and ideas. While there is some evidence for this hypothesis, we urge caution in interpreting the results of small‐world studies of innovation and suggest future improvements for empirical research.

The network and dimensionality structure of affective psychoses: an exploratory graph analysis approach

We present HotKnots, a new heuristic algorithm for the prediction of RNA secondary structures including pseudoknots. Based on the simple idea of iteratively forming stable stems, our algorithm explores many alternative secondary structures, using a free energy minimization algorithm for pseudoknot free secondary structures to identify promising candidate stems. In an empirical evaluation of the algorithm with 43 sequences taken from the Pseudobase database and from the literature on pseudoknotted structures, we found that overall, in terms of the sensitivity and specificity of predictions, HotKnots outperforms the well-known Pseudoknots algorithm of Rivas and Eddy and the NUPACK algorithm of Dirks and Pierce, both based on dynamic programming approaches for limited classes of pseudoknotted structures. It also outperforms the heuristic Iterated Loop Matching algorithm of Ruan and colleagues, and in many cases gives better results than the genetic algorithm from the STAR package of van Batenburg and colleagues and the recent pknotsRG-mfe algorithm of Reeder and Giegerich. The HotKnots algorithm has been implemented in C/C++ and is available from http://www.cs.ubc.ca/labs/beta/Software/HotKnots.

The classification of the structures of proteins provides preliminary information for the further detailed theoretical analyses. Classified information of protein folds might be utilized for the structural alignment while fold class prediction might help ab inito prediction of protein structures. Here, prediction of structural fold class of proteins with torsion angle based secondary structure profile library and multi-class linear discriminant analysis was performed. All-versus-all method was utilized to circumvent the problem of data imbalance of one-versus-others approach. From nonredundant structure files, a tripeptide secondary structure profile library was constructed and used to calculate the probable secondary structure content of protein folds. The mean and covariance matrices of the reference classes of the training set were derived using this library. Based on this information, fold classes of test set proteins were predicted using multi-class linear discriminant analysis. The result was highly accurate according to the low error rates. This highly accurate fold class prediction might be further utilized in the application of secondary structure predictions exploiting the benefits of larger scrutinizing windows. Appropriateness of the torsion angle representation in local structure analysis has also been partly proved.

Classification of protein structures is important in the prediction of the tertiary structures of proteins. In this paper, we propose to decompose the chaos game representation of proteins in to two time series, from which the protein sequences can be uniquely reconstructed. Multifractal analysis is applied to measures constructed from these two time series. A total of 26 characteristic parameters are calculated for each protein, which are used to construct a 26-dimensional space. Each protein is represented by one point in this space. A procedure is proposed to classify the structures of 100 large proteins consisting of four structural classes. Fisher's linear discriminant algorithmdemonstrates that the average accuracy for our classification can reach 84.67%. Compared with the results for the 46 large proteins reported before, the method proposed here has much better performance.