RBFNN-based Minimum Entropy Filtering for a Class of Stochastic Nonlinear Systems

The file attached to this record is the author's final peer reviewed version. The Publisher's final version can be found by following the DOI link.This paper presents a novel minimum entropy filter design for a class of stochastic nonlinear systems which are subjected to non-Gaussian noises. Motivated by stochastic distribution control, an output entropy model is developed using RBF neural network while the parameters of the model can be identified by the collected data. Based upon the presented model, the filtering problem has been investigated while the system dynamics have been represented. As the model output is the entropy of the estimation error, the optimal nonlinear filter is obtained based on the Lyapunov design which makes the model output minimum. Moreover, the entropy assignment problem has been discussed as an extension of the presented approach. To verify the presented design procedure, a numerical example is given which illustrates the effectiveness of the presented algorithm. The contributions of this paper can be included as 1) an output entropy model is presented using neural network; 2) a nonlinear filter design algorithm is developed as the main result and 3) a solution of entropy assignment problem is obtained which is an extension of the presented framework

Hadamard Matrices, dd-Linearly Independent Sets and Correlation-Immune Boolean Functions with Minimum Hamming Weights

It is known that correlation-immune (CI) Boolean functions used in the framework of side channel attacks need to have low Hamming weights. In 2013, Bhasin et al. studied the minimum Hamming weight of $d$-CI Boolean functions, and presented an open problem: the minimal weight of a $d$-CI function in $n$ variables might not increase with $n$. Very recently, Carlet and Chen proposed some constructions of low-weight CI functions, and gave a conjecture on the minimum Hamming weight of $3$-CI functions in $n$ variables. In this paper, we determine the values of the minimum Hamming weights of $d$-CI Boolean functions in $n$ variables for infinitely many $n$\u27s and give a negative answer to the open problem proposed by Bhasin et al. We then present a method to construct minimum-weight 2-CI functions through Hadamard matrices, which can provide all minimum-weight 2-CI functions in $4k-1$ variables. Furthermore, we prove that the Carlet-Chen conjecture is equivalent to the famous Hadamard conjecture. Most notably, we propose an efficient method to construct low-weight $n$-variable CI functions through $d$-linearly independent sets, which can provide numerous minimum-weight $d$-CI functions. Particularly, we obtain some new values of the minimum Hamming weights of $d$-CI functions in $n$ variables for $n\leq 13$. We conjecture that the functions constructed by us are of the minimum Hamming weights if the sets are of absolute maximum $d$-linearly independent. If our conjecture holds, then all the values for $n\leq 13$ and most values for general $n$ are determined

A Novel Data-based Stochastic Distribution Control for Non-Gaussian Stochastic Systems

YesThis note presents a novel data-based approach to investigate the non-Gaussian stochastic distribution control problem. As the motivation of this note, the existing methods have been summarised regarding to the drawbacks, for example, neural network weights training for unknown stochastic distribution and so on. To overcome these disadvantages, a new transformation for dynamic probability density function is given by kernel density estimation using interpolation. Based upon this transformation, a representative model has been developed while the stochastic distribution control problem has been transformed into an optimisation problem. Then, data-based direct optimisation and identification-based indirect optimisation have been proposed. In addition, the convergences of the presented algorithms are analysed and the effectiveness of these algorithms has been evaluated by numerical examples. In summary, the contributions of this note are as follows: 1) a new data-based probability density function transformation is given; 2) the optimisation algorithms are given based on the presented model; and 3) a new research framework is demonstrated as the potential extensions to the existing s

The SAT-Based Automatic Searching and Experimental Verification for Differential Characteristics with Application to Midori64

In this paper, we show that it is inaccurate to apply the hypothesis of independent round keys to search for differential characteristics of a block cipher with a simple key schedule. Therefore, the derived differential characteristics may be invalid. We develop a SAT-based algorithm to verify the validity of differential characteristics. Furthermore, we take the key schedule into account and thus put forward an algorithm to directly find the valid differential characteristics. All experiments are performed on Midori64 and we find some interesting results

Parametric covariance assignment using a reduced-order closed-form covariance model

YesThis paper presents a novel closed-form covariance model using covariance matrix decomposition for both continuous-time and discrete-time stochastic systems which are subjected to Gaussian noises. Different from the existing covariance models, it has been shown that the order of the presented model can be reduced to the order of original systems and the parameters of the model can be obtained by Kronecker product and Hadamard product which imply a uniform expression. Furthermore, the associated controller design can be simplified due to the use of the reduced-order structure of the model. Based on this model, the state and output covariance assignment algorithms have been developed with parametric state and output feedback, where the computational complexity is reduced and the extended free parameters of parametric feedback supply flexibility to the optimization. As an extension, the reduced-order closed-form covariance model for stochastic systems with parameter uncertainties is also presented in this paper. A simulated example is included to show the effectiveness of the proposed control algorithm, where encouraging results have been obtained.National Natural Science Foundation of China [grant number 61573022], [grant number 61290323] and [grant number 61333007

Exploring the Structural Transformation Mechanism of Chinese and Thailand Silk Fibroin Fibers and Formic-Acid Fabricated Silk Films

Silk fibroin (SF) is a protein polymer derived from insects, which has unique mechanical properties and tunable biodegradation rate due to its variable structures. Here, the variability of structural, thermal, and mechanical properties of two domesticated silk films (Chinese and Thailand B. Mori) regenerated from formic acid solution, as well as their original fibers, were compared and investigated using dynamic mechanical analysis (DMA) and Fourier transform infrared spectrometry (FTIR). Four relaxation events appeared clearly during the temperature region of 25 °C to 280 °C in DMA curves, and their disorder degree (fdis) and glass transition temperature (Tg) were predicted using Group Interaction Modeling (GIM). Compared with Thai (Thailand) regenerated silks, Chin (Chinese) silks possess a lower Tg, higher fdis, and better elasticity and mechanical strength. As the calcium chloride content in the initial processing solvent increases (1%–6%), the Tg of the final SF samples gradually decrease, while their fdis increase. Besides, SF with more non-crystalline structures shows high plasticity. Two α- relaxations in the glass transition region of tan δ curve were identified due to the structural transition of silk protein. These findings provide a new perspective for the design of advanced protein biomaterials with different secondary structures, and facilitate a comprehensive understanding of the structure-property relationship of various biopolymers in the futu