In this study, we analyze the minimum control node set problem for Boolean networks (BNs) with degree constraints. Our major contribution is the derivation of nontrivial lower and upper bounds on the size of the minimum control node set through combinatorial analysis of four types of BNs (i.e., $k$ - $k$ -XOR-BNs, simple $k$ - $k$ -AND-BNs, $k$ - $k$ -AND-BNs with negation, and $k$ - $k$ -NC-BNs, where the indegree and outdegree of each node are both $k$ , and the $k$ - $k$ -AND-BN with negation is an extension of the simple $k$ - $k$ -AND-BN that considers the occurrence of negation and NC means nested canalyzing). More specifically, four bounds for the size of the minimum control node set: general lower bound, best case upper bound, worst-case lower bound, and general upper bound are analyzed. By dividing nodes into three disjoint sets, extending the time to reach the target state, and utilizing necessary conditions for controllability, these bounds are obtained. Further, meaningful results and phenomena are discovered. Notably, all of the above results involving the AND function also apply to the OR function.

Current research on undulatory propulsion robots has predominantly centered on hydrodynamic performance simulations. However, challenges such as limited mobility and difficulties in parameter identification during underwater bio-mimetic motion remain unresolved. To address these issues, this study proposes a novel undulating fin robot featuring passive rotational joints, aiming to enhance motion capabilities and facilitate more accurate modeling. These joints enhance both the agility and stability of the robot's movements. Initially, the research develops models for the undulatory motion of the undulating fin and the rotational passive degrees of freedom in the fin rays. Based on fluid drag theory, a hydrodynamic model for undulating fin propulsion is constructed to analyze the thrust, lateral force, and lift generated at varying frequencies. Furthermore, a comprehensive dynamics model for the underwater motion of the biomimetic undulating fin robot is developed. Numerical simulations of the robot's non-steady-state motion are conducted to identify the hydrodynamic parameters of the model, thereby enabling the solution of the dynamic model. The experimental results demonstrate that the robot achieves an underwater straight-line motion speed exceeding 0.5m/s, a turning speed of approximately 45°/s, and an inclined upward motion speed of 0.21 m/s. This study provides a novel approach for the design of underwater undulating fin robots and the resolution of kinematic models for underwater robots. It is hoped that this research can contribute to the further development of undulatory propulsion robot technology.

In this article, we mainly study the depth and width of autoencoders consisting of rectified linear unit (ReLU) activation functions. An autoencoder is a layered neural network consisting of an encoder, which compresses an input vector to a lower-dimensional vector, and a decoder, which transforms the low-dimensional vector back to the original input vector exactly (or approximately). In a previous study, Melkman et al. (2023) studied the depth and width of autoencoders using linear threshold activation functions with binary input and output vectors. We show that similar theoretical results hold if autoencoders using ReLU activation functions with real input and output vectors are used. Furthermore, we show that it is possible to compress input vectors to one-dimensional vectors using ReLU activation functions, although the size of compressed vectors is trivially Ω(log n) for autoencoders with linear threshold activation functions, where n is the number of input vectors. We also study the cases of linear activation functions. The results suggest that the compressive power of autoencoders using linear activation functions is considerably limited compared with those using ReLU activation functions.

This article presents a distributed pinning control strategy aimed at achieving global stabilization of Markovian jump Boolean control networks. The strategy relies on network matrix information to choose controlled nodes and adopts the algebraic state space representation approach for designing pinning controllers. Initially, a sufficient criterion is established to verify the global stability of a given Markovian jump Boolean network (MJBN) with probability one at a specific state within finite time. To stabilize an unstable MJBN at a predetermined state, the selection of pinned nodes involves removing the minimal number of entries, ensuring that the network matrix transforms into a strictly lower (or upper) triangular form. For each pinned node, two types of state feedback controllers are developed: 1) mode-dependent and 2) mode-independent, with a focus on designing a minimally updating controller. The choice of controller type is determined by the feasibility condition of the mode-dependent pinning controller, which is articulated through the solvability of matrix equations. Finally, the theoretical results are illustrated by studying the T cell large granular lymphocyte survival signaling network consisting of 54 genes and 6 stimuli.

MOTIVATION: From a systematic perspective, it is crucial to infer and analyze gene regulatory network (GRN) from high-throughput single-cell RNA sequencing data. However, most existing GRN inference methods mainly focus on the network topology, only few of them consider how to explicitly describe the updated logic rules of regulation in GRNs to obtain their dynamics. Moreover, some inference methods also fail to deal with the over-fitting problem caused by the noise in time series data. RESULTS: In this article, we propose a novel embedded Boolean threshold network method called LogBTF, which effectively infers GRN by integrating regularized logistic regression and Boolean threshold function. First, the continuous gene expression values are converted into Boolean values and the elastic net regression model is adopted to fit the binarized time series data. Then, the estimated regression coefficients are applied to represent the unknown Boolean threshold function of the candidate Boolean threshold network as the dynamical equations. To overcome the multi-collinearity and over-fitting problems, a new and effective approach is designed to optimize the network topology by adding a perturbation design matrix to the input data and thereafter setting sufficiently small elements of the output coefficient vector to zeros. In addition, the cross-validation procedure is implemented into the Boolean threshold network model framework to strengthen the inference capability. Finally, extensive experiments on one simulated Boolean value dataset, dozens of simulation datasets, and three real single-cell RNA sequencing datasets demonstrate that the LogBTF method can infer GRNs from time series data more accurately than some other alternative methods for GRN inference. AVAILABILITY AND IMPLEMENTATION: The source data and code are available at https://github.com/zpliulab/LogBTF.

During breast cancer metastasis, the developmental process epithelial-mesenchymal (EM) transition is abnormally activated. Transcriptional regulatory networks controlling EM transition are well-studied; however, alternative RNA splicing also plays a critical regulatory role during this process. Alternative splicing was proved to control the EM transition process, and RNA-binding proteins were determined to regulate alternative splicing. A comprehensive understanding of alternative splicing and the RNA-binding proteins that regulate it during EM transition and their dynamic impact on breast cancer remains largely unknown. To accurately study the dynamic regulatory relationships, time-series data of the EM transition process are essential. However, only cross-sectional data of epithelial and mesenchymal specimens are available. Therefore, we developed a pseudotemporal causality-based Bayesian (PCB) approach to infer the dynamic regulatory relationships between alternative splicing events and RNA-binding proteins. Our study sheds light on facilitating the regulatory network-based approach to identify key RNA-binding proteins or target alternative splicing events for the diagnosis or treatment of cancers. The data and code for PCB are available at: http://hkumath.hku.hk/~wkc/PCB(data+code).zip.

This paper first investigates the synchronization design problem for both Boolean networks (BNs) and singular BNs. According to the complete family of reachable sets, all possible synchronized response BNs and all possible weakly synchronized response singular BNs can be constructed. Subsequently, it is noted that there is similarity between synchronized response (singular) BNs and state observers. The synchronized response (singular) BN is constructed based on the state of a given drive (singular) BN, making its state gradually tend to be consistent with the state of the given drive (singular) BN. While the state observer is designed based on the output of a given real (singular) BN, making its state (state estimation) gradually tend to be consistent with the state of the given real (singular) BN. Therefore, consider applying the results for constructing synchronized response (singular) BNs to designing state observers for (singular) BNs. Specifically, the real (singular) BN to be observed can be regarded as a drive (singular) BN. Consequently, the problem for designing state observers can be transformed into the problem for constructing response (singular) BNs that achieve synchronization with a given real (singular) BN, and then the gain matrix of the designed state observer can be obtained by solving a matrix equation. The method for designing state observers is superior to other methods in that the accurate estimated time for designed state observers can be determined and adjusted to some certain extent, and all possible state observers in the considered form can be designed.

We aim to further study the global stability of Boolean control networks (BCNs) under aperiodic sampled-data control (ASDC). According to our previous work, it is known that a BCN under ASDC can be transformed into a switched Boolean network (SBN), and further global stability of the BCN under ASDC can be obtained by studying the global stability of the transformed SBN. Unfortunately, since the major idea of our previous work is to use stable subsystems to offset the state divergence caused by unstable subsystems, the SBN considered has at least one stable subsystem. The central thought in this paper is that switching behavior also has good stabilization; i.e., the SBN can also be stable with appropriate switching laws designed, even if all subsystems are unstable. This is completely different from that in our previous work. Specifically, for this case, the dwell time (DT) should be limited within a pair of upper and lower bounds. By means of the discretized Lyapunov function and DT, a sufficient condition for global stability is obtained. Finally, the above results are demonstrated by a biological example.

In this letter, we investigate the sampled-data state feedback control (SDSFC) problem of Boolean control networks (BCNs). Some necessary and sufficient conditions are obtained for the global stabilization of BCNs by SDSFC. Different from conventional state feedback controls, new phenomena observed the study of SDSFC. Based on the controllability matrix, we derive some necessary and sufficient conditions under which the trajectories of BCNs can be stabilized to a fixed point by piecewise constant control (PCC). It is proved that the global stabilization of BCNs under SDSFC is equivalent to that by PCC. Moreover, algorithms are given to construct the sampled-data state feedback controllers. Numerical examples are given to illustrate the efficiency of the obtained results.

This brief investigates the partial and complete synchronization of two Boolean control networks (BCNs). Necessary and sufficient conditions for partial and complete synchronization are established by the algebraic representations of logical dynamics. An algorithm is obtained to construct the feedback controller that guarantees the synchronization of master and slave BCNs. Two biological examples are provided to illustrate the effectiveness of the obtained results.

A CSR-Based (Contextual Sparse Representation) classification method for PolSAR image is proposed based on the idea of sparse representation and spatial correlation, which incorporates the intrinsic polarimetric information and the spatial contextual information in the sparse representation procedure. Firstly, multiple useful features are extracted to describe PolSAR images at various aspects. Then, the feature vectors of training samples construct an over-complete dictionary. Then sparsely represent the training samples using the over-complete dictionary and obtain the corresponding coefficients. In this step, the spatial neighboring feature-vectors are assumed to have a similar sparse representation way. Specifically, they can be linearly represented by the same atoms while the weights are different. That is the kernel of CSR. In this way, the efficiency of sparse classification can be highly raised and the result can also be improved by adding the contextual information. The proposed method is validated by the Danish EMISAR L-band fully polarimetric SAR data and the experimental results confirm the performance of the proposed method in PolSAR image classification.

In this paper, a supervised PolSAR images classification method based on sparse representation is proposed. Firstly, Polarimetric decomposition based on Multiple-component Scattering Model, Cloude-Pottier decomposition and Gray-level Co-occurrence Matrix are implemented to obtain features which can describe PolSAR images at multiple aspects. Then, the training samples are represented in an overcomplete dictionary in which the basic elements are the feature vectors of the training samples and this can be computed by minimize l1-norm. Through comparing the residuals of the reconstructed training samples corresponding to different classes with the original training sample, the optimization problem can be solved and obtain the classification result. The proposed method is validated by the Danish EMISAR L-band fully polarimetric SAR data of Foulum Area (DK) and the preliminary experimental results confirm the performance and potential of the proposed method in PolSAR image interpretation.