Pattern memory analysis based on stability theory of cellular neural networks

AbstractIn this paper, several sufficient conditions are obtained to guarantee that the n-dimensional cellular neural network can have even (⩽2n) memory patterns. In addition, the estimations of attractive domain of such stable memory patterns are obtained. These conditions, which can be directly derived from the parameters of the neural networks, are easily verified. A new design procedure for cellular neural networks is developed based on stability theory (rather than the well-known perceptron training algorithm), and the convergence in the new design procedure is guaranteed by the obtained local stability theorems. Finally, the validity and performance of the obtained results are illustrated by two examples

One-loop correction to the enhanced curvature perturbation with local-type non-Gaussianity for the formation of primordial black holes

As one of the promising candidates of cold dark matter (DM), primordial black holes (PBHs) were formed due to the collapse of over-densed regions generated by the enhanced curvature perturbations during the radiation-dominated era. The enhanced curvature perturbations are expected to be non-Gaussian in some relevant inflation models and hence the higher-order loop corrections to the curvature power spectrum might be non-negligible as well as altering the abundance of PBHs. In this paper, we calculate the one-loop correction to the curvature power spectrum with local-type non-Gaussianities characterizing by $F_{\mathrm{NL}}$ and $G_{\mathrm{NL}}$ standing for the quadratic and cubic non-Gaussian parameters, respectively. Requiring that the one-loop correction be subdominant, we find a perturbativity condition, namely $|2cAF_{\mathrm{NL}}^2+6AG_{\mathrm{NL}}|\ll 1$, where $c$ is a constant coefficient which can be explicitly calculated in the given model and $A$ denotes the variance of Gaussian part of enhanced curvature perturbation, and such a perturbativity condition can provide a stringent constraint on the relevant inflation models for the formation of PBHs.Comment: 6 pages, 5 figure

Full analysis of the scalar-induced gravitational waves for the curvature perturbation with local-type non-Gaussianities

Primordial black holes (PBHs) are supposed to form through the gravitational collapse of regions with large density fluctuations. The formation of PBHs inevitably leads to the emission of scalar-induced gravitational wave (SIGW) signals, offering a unique opportunity to test the hypothesis of PBHs as a constituent of dark matter (DM). Previous studies have calculated the energy spectrum of SIGWs in local-type non-Gaussian models, primarily considering the contributions from the $F_{\mathrm{NL}}$-order or the $G_{\mathrm{NL}}$-order while neglecting connected diagrams. In this study, we extend the previous work by (i) considering the full contribution of non-Gaussian diagrams up to the $G_{\mathrm{NL}}$-order; (ii) deriving the generic scaling of the SIGW energy spectrum in the infrared region. We derive semi-analytical results applicable to arbitrary primordial power spectra and numerically evaluate the energy spectrum of SIGWs for a log-normal power spectrum.Comment: 21 pages, 2 figure

An Algorithm for Finding Functional Modules and Protein Complexes in Protein-Protein Interaction Networks

Biological processes are often performed by a group of proteins rather than by individual proteins, and proteins in a same biological group form a densely connected subgraph in a protein-protein interaction network. Therefore, finding a densely connected subgraph provides useful information to predict the function or protein complex of uncharacterized proteins in the highly connected subgraph. We have developed an efficient algorithm and program for finding cliques and near-cliques in a protein-protein interaction network. Analysis of the interaction network of yeast proteins using the algorithm demonstrates that 59% of the near-cliques identified by our algorithm have at least one function shared by all the proteins within a near-clique, and that 56% of the near-cliques show a good agreement with the experimentally determined protein complexes catalogued in MIPS

APIS: accurate prediction of hot spots in protein interfaces by combining protrusion index with solvent accessibility

<p>Abstract</p> <p>Background</p> <p>It is well known that most of the binding free energy of protein interaction is contributed by a few key hot spot residues. These residues are crucial for understanding the function of proteins and studying their interactions. Experimental hot spots detection methods such as alanine scanning mutagenesis are not applicable on a large scale since they are time consuming and expensive. Therefore, reliable and efficient computational methods for identifying hot spots are greatly desired and urgently required.</p> <p>Results</p> <p>In this work, we introduce an efficient approach that uses support vector machine (SVM) to predict hot spot residues in protein interfaces. We systematically investigate a wide variety of 62 features from a combination of protein sequence and structure information. Then, to remove redundant and irrelevant features and improve the prediction performance, feature selection is employed using the F-score method. Based on the selected features, nine individual-feature based predictors are developed to identify hot spots using SVMs. Furthermore, a new ensemble classifier, namely APIS (A combined model based on Protrusion Index and Solvent accessibility), is developed to further improve the prediction accuracy. The results on two benchmark datasets, ASEdb and BID, show that this proposed method yields significantly better prediction accuracy than those previously published in the literature. In addition, we also demonstrate the predictive power of our proposed method by modelling two protein complexes: the calmodulin/myosin light chain kinase complex and the heat shock locus gene products U and V complex, which indicate that our method can identify more hot spots in these two complexes compared with other state-of-the-art methods.</p> <p>Conclusion</p> <p>We have developed an accurate prediction model for hot spot residues, given the structure of a protein complex. A major contribution of this study is to propose several new features based on the protrusion index of amino acid residues, which has been shown to significantly improve the prediction performance of hot spots. Moreover, we identify a compact and useful feature subset that has an important implication for identifying hot spot residues. Our results indicate that these features are more effective than the conventional evolutionary conservation, pairwise residue potentials and other traditional features considered previously, and that the combination of our and traditional features may support the creation of a discriminative feature set for efficient prediction of hot spot residues. The data and source code are available on web site <url>http://home.ustc.edu.cn/~jfxia/hotspot.html</url>.</p