Matching of orbits of certain NN-expansions with a finite set of digits

In this paper we consider a class of continued fraction expansions: the so-called $N$-expansions with a finite digit set, where $N\geq 2$ is an integer. These \emph{$N$-expansions with a finite digit set} were introduced in [KL,L], and further studied in [dJKN,S]. For $N$ fixed they are steered by a parameter $\alpha\in (0,\sqrt{N}-1]$. In [KL], for $N=2$ an explicit interval $[A,B]$ was determined, such that for all $\alpha\in [A,B]$ the entropy $h(T_{\alpha})$ of the underlying Gauss-map $T_{\alpha}$ is equal. In this paper we show that for all $N\in \mathbb N$, $N\geq 2$, such plateaux exist. In order to show that the entropy is constant on such plateaux, we obtain the underlying planar natural extension of the maps $T_{\alpha}$, the $T_{\alpha}$-invariant measure, ergodicity, and we show that for any two $\alpha,\alpha'$ from the same plateau, the natural extensions are metrically isomorphic, and the isomorphism is given explicitly. The plateaux are found by a property called matching

Stability of port-Hamiltonian systems with mixed time delays subject to input saturation

In this paper, we investigate the stability of port-Hamiltonian systems with mixed time-varying delays as well as input saturation. Three types of time delays, including state delay, input delay, and output delay, are all assumed to be bounded. By introducing the output feedback control law and utilizing serval Lyapunov–Krasovskii functionals, we present three delay-dependent stability criteria in terms of the linear matrix inequality. Meanwhile, we use Wirtinger’s inequality, constraint conditions, and Lyapunov–Krasovskii functionals of triple and quadruple integral form to obtain less conservative results. Some numerical examples demonstrate and support our results

GSAE: an autoencoder with embedded gene-set nodes for genomics functional characterization

Bioinformatics tools have been developed to interpret gene expression data at the gene set level, and these gene set based analyses improve the biologists' capability to discover functional relevance of their experiment design. While elucidating gene set individually, inter gene sets association is rarely taken into consideration. Deep learning, an emerging machine learning technique in computational biology, can be used to generate an unbiased combination of gene set, and to determine the biological relevance and analysis consistency of these combining gene sets by leveraging large genomic data sets. In this study, we proposed a gene superset autoencoder (GSAE), a multi-layer autoencoder model with the incorporation of a priori defined gene sets that retain the crucial biological features in the latent layer. We introduced the concept of the gene superset, an unbiased combination of gene sets with weights trained by the autoencoder, where each node in the latent layer is a superset. Trained with genomic data from TCGA and evaluated with their accompanying clinical parameters, we showed gene supersets' ability of discriminating tumor subtypes and their prognostic capability. We further demonstrated the biological relevance of the top component gene sets in the significant supersets. Using autoencoder model and gene superset at its latent layer, we demonstrated that gene supersets retain sufficient biological information with respect to tumor subtypes and clinical prognostic significance. Superset also provides high reproducibility on survival analysis and accurate prediction for cancer subtypes.Comment: Presented in the International Conference on Intelligent Biology and Medicine (ICIBM 2018) at Los Angeles, CA, USA and published in BMC Systems Biology 2018, 12(Suppl 8):14

MicroRNA-like RNAs from the same miRNA precursors play a role in cassava chilling responses

Abstract MicroRNAs (miRNAs) are known to play important roles in various cellular processes and stress responses. MiRNAs can be identified by analyzing reads from high-throughput deep sequencing. The reads realigned to miRNA precursors besides canonical miRNAs were initially considered as sequencing noise and ignored from further analysis. Here we reported a small-RNA species of phased and half-phased miRNA-like RNAs different from canonical miRNAs from cassava miRNA precursors detected under four distinct chilling conditions. They can form abundant multiple small RNAs arranged along precursors in a tandem and phased or half-phased fashion. Some of these miRNA-like RNAs were experimentally confirmed by re-amplification and re-sequencing, and have a similar qRT-PCR detection ratio as their cognate canonical miRNAs. The target genes of those phased and half-phased miRNA-like RNAs function in process of cell growth metabolism and play roles in protein kinase. Half-phased miR171d.3 was confirmed to have cleavage activities on its target gene P-glycoprotein 11, a broad substrate efflux pump across cellular membranes, which is thought to provide protection for tropical cassava during sharp temperature decease. Our results showed that the RNAs from miRNA precursors are miRNA-like small RNAs that are viable negative gene regulators and may have potential functions in cassava chilling responses

Supervised Sparsity Preserving Projections for Face Recognition

Recently feature extraction methods have commonly been used as a principled approach to understand the intrinsic structure hidden in high-dimensional data. In this paper, a novel supervised learning method, called Supervised Sparsity Preserving Projections (SSPP), is proposed. SSPP attempts to preserve the sparse representation structure of the data when identifying an efficient discriminant subspace. First, SSPP creates a concatenated dictionary by class-wise PCA decompositions and learns the sparse representation structure of each sample under the constructed dictionary using the least squares method. Second, by maximizing the ratio of non-local scatter to local scatter, a Laplacian discriminant function is defined to characterize the separability of the samples in the different sub-manifolds. Then, to achieve improved recognition results, SSPP integrates the learned sparse representation structure as a regular term into the Laplacian discriminant function. Finally, the proposed method is converted into a generalized eigenvalue problem. The extensive and promising experimental results on several popular face databases validate the feasibility and effectiveness of the proposed approach

Physically Interpretable Feature Learning and Inverse Design of Supercritical Airfoils

Machine-learning models have demonstrated a great ability to learn complex patterns and make predictions. In high-dimensional nonlinear problems of fluid dynamics, data representation often greatly affects the performance and interpretability of machine learning algorithms. With the increasing application of machine learning in fluid dynamics studies, the need for physically explainable models continues to grow. This paper proposes a feature learning algorithm based on variational autoencoders, which is able to assign physical features to some latent variables of the variational autoencoder. In addition, it is theoretically proved that the remaining latent variables are independent of the physical features. The proposed algorithm is trained to include shock wave features in its latent variables for the reconstruction of supercritical pressure distributions. The reconstruction accuracy and physical interpretability are also compared with those of other variational autoencoders. Then, the proposed algorithm is used for the inverse design of supercritical airfoils, which enables the generation of airfoil geometries based on physical features rather than the complete pressure distributions. It also demonstrates the ability to manipulate certain pressure distribution features of the airfoil without changing the others

Study of transfer learning from 2D supercritical airfoils to 3D transonic swept wings

Machine learning has been widely utilized in fluid mechanics studies and aerodynamic optimizations. However, most applications, especially flow field modeling and inverse design, involve two-dimensional flows and geometries. The dimensionality of three-dimensional problems is so high that it is too difficult and expensive to prepare sufficient samples. Therefore, transfer learning has become a promising approach to reuse well-trained two-dimensional models and greatly reduce the need for samples for three-dimensional problems. This paper proposes to reuse the baseline models trained on supercritical airfoils to predict finite-span swept supercritical wings, where the simple swept theory is embedded to improve the prediction accuracy. Two baseline models for transfer learning are investigated: one is commonly referred to as the forward problem of predicting the pressure coefficient distribution based on the geometry, and the other is the inverse problem that predicts the geometry based on the pressure coefficient distribution. Two transfer learning strategies are compared for both baseline models. The transferred models are then tested on the prediction of complete wings. The results show that transfer learning requires only approximately 500 wing samples to achieve good prediction accuracy on different wing planforms and different free stream conditions. Compared to the two baseline models, the transferred models reduce the prediction error by 60% and 80%, respectively