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The central issue of the development of the multivariate public key algorithms is the design of reversible non-linear mappings of $n$-dimensional vectors over a finite field, which can be represented in a form of a set of power polynomials. For the first time, finite fields $GF\left((2^d)^m\right)$ of characteristic two, represented in the form of $m$-dimensional finite algebras over the fields $GF(2^d)$ are introduced for implementing the said mappings as exponentiation operation. This technique allows one to eliminate the use of masking linear mappings, usually used in the known approaches to the design of multivariate cryptography algorithms and causing the sufficiently large size of the public key. The issues of using the fields $GF\left((2^d)^m\right)$ as algebraic support of non-linear mappings are considered, including selection of appropriate values of $m$ and $d$. In the proposed approach to development of the multivariate cryptography algorithms, a superposition of two non-linear mappings is used to define resultant hard-to-reverse mapping with a secret trap door. The used two non-linear mappings provide mutual masking of the corresponding reverse maps, due to which the size of the public key significantly reduces as compared with the known algorithms-analogues at a given security level.

The central issue of the development of the multivariate public key algorithms is the design of reversible non-linear mappings of n-dimensional vectors over a finite field, which can be represented in a form of a set of power polynomials. For the first time, finite fields GF ((2d)m) of characteristic two, represented in the form of m-dimensional finite algebras over the fields GF(2d) are introduced for implementing the said mappings as exponentiation operation. This technique allows one to eliminate the use of masking linear mappings, usually used in the known approaches to the design of multivariate cryptography algorithms and causing the sufficiently large size of the public key. The issues of using the fields GF ((2d)m) as algebraic support of non-linear mappings are considered, including selection of appropriate values of m and d. In the proposed approach to development of the multivariate cryptography algorithms, a superposition of two non-linear mappings is used to define resultant hard-to-reverse mapping with a secret trap door. The used two non-linear mappings provide mutual masking of the corresponding reverse maps, due to which the size of the public key significantly reduces as compared with the known algorithms-analogues at a given security level. [ABSTRACT FROM AUTHOR]

The use of neural network models to monitor bearing vibration signals can easily be affected by noise, which leads to a decrease in the model test accuracy. Therefore, the existence of noise problems increases the requirements for non-linear mapping capability and robustness of deep neural network (DNN) models. In order to deal with the noise problem, the concept of qubit neurons is introduced into a deep learning stacked autoencoder (SAE) model, and a quantum stacked autoencoder (QSAE) model based on qubits and quantum gates is proposed. The properties of SAE layer-by-layer coding and the arithmetic of qubit neurons are combined in the QSAE. The quantum state signal is taken as the input signal to the encoder and the coding activation function and coding weight matrix are redefined by quantum-controlled non-gates and quantum revolving gates, so that the quantum state signal can be coded layer by layer. Experimental results show that the QSAE can train and diagnose noisy experimental data and maintain high test accuracy in an anti-attack test. This shows that the QSAE has non-linear mapping capability and robustness. [ABSTRACT FROM AUTHOR]

A new approach to the design of multivariate public-key cryptalgorithms is introduced. It envisages using non-linear mappings defined as squaring and cubic operations in finite fields represented as finite algebras. The developed approach allows significant reduction of the size of public key and thereby make post-quantum algorithms of multivariate cryptography much more practical. In the developed algorithms, the secret key includes a set of values of structural constants that determine the modifications of the finite fields used and the coefficients in the set of sixth degree polynomials that make up the public key. [ABSTRACT FROM AUTHOR]

For the problems of darkness, insufficient contrast, and color cast in the images captured by CMOS image sensors in the $\gamma $ radiation environment, this paper proposed a joint contrast improvement and color cast correction approach for the $\gamma $ radiation image enhancement, which improved the image effects from enhancing detail expression and color expression. For the problem of overall darkness of $\gamma $ radiation image, we first utilized logarithmic mapping to improve the image brightness. Secondly, for the insufficient contrast of image details, a contrast enhancement method with an adaptive Gamma coefficient is proposed, which adaptively adjusts the image brightness at the pixel level, so that the image detail expression is more in line with the human visual characteristics (HVC). Lastly, the color level remapping method is exploited for color cast correction. Extensive experiments are conducted on the $\gamma $ radiation images collected in the Co60 environment. With the help of the proposed method, we can achieve the best results in quantitative and visual comparison. Experimental results demonstrate that the proposed method enjoys state-of-the-art performance in $\gamma $ radiation image enhancement.

Similarity learning which is useful for the purpose of comparing various characteristics of images in the computer vision field has been often applied for deep metric learning (DML). Also, a lot of combinations of pairwise similarity metrics such as Euclidean distance and cosine similarity have been studied actively. However, such a local similarity-based approach can be rather a bottleneck for a retrieval task in which global characteristics of images must be considered important. Therefore, this paper proposes a new similarity metric structure that considers the local similarity as well as the global characteristic on the representation space, i.e., class variability. Also, based on an insight that better class variability analysis can be accomplished on the Stiefel (or Riemannian) manifold, manifold geometry is employed to generate class variability information. Finally, we show that the proposed method designed through in-depth analysis of generalization bound of DML outperforms conventional DML methods theoretically and experimentally.

Soft sensors driven by data are very common in industrial plants to perform indirect measurements of difficult to measure critical variables by using other variables that are relatively easier to obtain. The use of soft sensors implies some challenges, such as the colinearity of the predictor variables, the time-varying and possible non-linear nature of the industrial process. To deal with the first challenge, the partial least square (PLS) regression has been employed in many applications to model the linear relations between process variables, with noisy and highly correlated data. However, the PLS model needs to deal with the other two issues: the non-linear and time-varying characteristics of the processes. In this work, a new knowledge-based methodology for a recursive non-linear PLS algorithm (RNPLS) is systematized to deal with these issues. Here, the non-linear PLS algorithm is set up by carrying out the PLS regression over the augmented input matrix, which includes knowledge based non-linear transformations of some of the variables. This transformation depends on the system's nature, and takes into account the available knowledge about the process, which is provided by expert knowledge or emulated using software tools. Then, the recursive exponential weighted PLS is used to modify and adapt the model according to the process changes. This RNPLS algorithm has been tested using two case studies according to the available knowledge, a real industrial evaporation station of the sugar industry, where the expert knowledge about the process permits the formulation of the relationships, and a simulated wastewater treatment plant, where the necessary knowledge about the process is obtained by a software tool. The results show that the methodology involving knowledge regarding the process is able to adjust the process changes, providing highly accurate predictions. • Use expert knowledge about the process to develop a knowledge based non-linear PLS. • Consider the time-varying nature of industrial processes to perform a recursive PLS. • Combine the knowledge-based NPLS with recursion to develop a Recursive NPLS (RNPLS). • The knowledge based RNPLS algorithm has been tested into two case studies. [ABSTRACT FROM AUTHOR]

• BP ANN and GRNN were proposed to quantify interfacial energy related to fouling. • BP ANN and GRNN well captured the relations between interfacial energy and factors. • BP ANN and GRNN showed quick response to quantify interfacial energy and fouling. • this study showed breakthrough of the fundamental methodology in membrane fouling. Interfacial energy between sludge foulants and rough membrane surface critically determines adhesive fouling in membrane bioreactors (MBRs). As a current available method, the advanced extensive Derjaguin-Landau-Verwey-Overbeek (XDLVO) approach cannot efficiently quantify the interfacial energy. In this study, novel methods including back propagation (BP) artificial neural network (ANN) and generalized regression neural network (GRNN) were proposed to quantify the interfacial energy associated with the membrane fouling in an MBR. Different levels of 5 apparent input factors and the resulted interfacial energies were used as training and testing databases for establishment of ANN models. The established BP ANN and GRNN models exhibited high regression coefficients and accuracies, suggesting the high capacity of ANN models to capture the complicated non-linear mapping relations between interfacial energy and various factors. As compared with the advanced XDLVO approach, both BP ANN and GRNN showed remarkably improved quantification efficiency. Meanwhile, BP ANN showed better prediction performance than GRNN model. Case study further demonstrated the robustness and feasibility of BP ANN for interfacial energy quantification. This study provided a new approach to quantify interfacial energy associated with membrane fouling. [ABSTRACT FROM AUTHOR]

Cross-domain recommendation is a promising solution in recommendation systems by using relatively rich information from the source domain to improve the recommendation accuracy of the target domain. Most of the existing methods consider the rating information of users in different domains, the label information of users and items and the review information of users on items. However, they do not effectively use the latent sentiment information to find the accurate mapping of latent features in reviews between domains. User reviews usually include user’s subjective views, which can reflect the user’s preferences and sentiment tendencies to various attributes of the items. Therefore, in order to solve the cold-start problem in the recommendation process, this paper proposes a cross-domain recommendation algorithm (CDR-SAFM) based on sentiment analysis and latent feature mapping by combining the sentiment information implicit in user reviews in different domains. Different from previous sentiment research, this paper divides sentiment into three categories based on three-way decision ideas—namely, positive, negative and neutral—by conducting sentiment analysis on user review information. Furthermore, the Latent Dirichlet Allocation (LDA) is used to model the user’s semantic orientation to generate the latent sentiment review features. Moreover, the Multilayer Perceptron (MLP) is used to obtain the cross domain non-linear mapping function to transfer the user’s sentiment review features. Finally, this paper proves the effectiveness of the proposed CDR-SAFM framework by comparing it with existing recommendation algorithms in a cross-domain scenario on the Amazon dataset.

Abstract Vowel-like regions (VLRs) in a speech signal include vowel, semivowel and diphthong sound units. In the existing VLRs detection methods, front-end speech parameterization have been done by complex algorithms. Those approaches require more hardware and hence delay the process. To address this issue, a simple and robust signal processing approach and it's hardware architecture is proposed for discriminating VLRs in the speech signal. In the proposed approach, non-local slope difference (NSD) at each time instant is computed by processing the speech signal through a single pole filter. The NSD is then averaged over an analysis frame and non-linearly mapped using negative exponential to reduce the fluctuations present in the input speech signal. The non-linearly mapped averaged NSD (NL-ANSD) is used as the front-end feature for discriminating VLRs. The NL-ANSD exhibits significantly sharp transition at the starting and ending points of the VLRs. The regions wherein the proposed feature exhibits significant transition and attains lower magnitude for a considerable duration of time are hypothesized as the VLRs. The proposed approach is very simple and requires significantly less hardware when compared with the existing zero-frequency filtering (ZFF) based methods. On the other hand, the proposed approach outperforms the existing ZFF based approaches for the task of detecting VLRs in clean as well as noisy speech signals. The hardware architecture of the proposed approach is verified by implementing it on the Nexys video Artix − 7(XC 7 A 200T − 1 SBG 484C) field-programmable gate array (FPGA) trainer board for multimedia applications using Xilinx system generator-2016.2. Highlights • A simple and highly effective approach for detecting VLRs using non-local slope difference (NSD) is proposed. • A non-linearly mapped averaged NSD which discriminates the starting and ending points of the VLRs is proposed. • An efficient hardware architecture for real-time VLRs detection is designed and implemented on FPGA. [ABSTRACT FROM AUTHOR]

Spatiotemporal fusion provides an effective way to fuse two types of remote sensing data featured by complementary spatial and temporal properties (typical representatives are Landsat and MODIS images) to generate fused data with both high spatial and temporal resolutions. This paper presents a very deep convolutional neural network (VDCN) based spatiotemporal fusion approach to effectively handle massive remote sensing data in practical applications. Compared with existing shallow learning methods, especially for the sparse representation based ones, the proposed VDCN-based model has the following merits: (1) explicitly correlating the MODIS and Landsat images by learning a non-linear mapping relationship; (2) automatically extracting effective image features; and (3) unifying the feature extraction, non-linear mapping, and image reconstruction into one optimization framework. In the training stage, we train a non-linear mapping between downsampled Landsat and MODIS data using VDCN, and then we train a multi-scale super-resolution (MSSR) VDCN between the original Landsat and downsampled Landsat data. The prediction procedure contains three layers, where each layer consists of a VDCN-based prediction and a fusion model. These layers achieve non-linear mapping from MODIS to downsampled Landsat data, the two-times SR of downsampled Landsat data, and the five-times SR of downsampled Landsat data, successively. Extensive evaluations are executed on two groups of commonly used Landsat−MODIS benchmark datasets. For the fusion results, the quantitative evaluations on all prediction dates and the visual effect on one key date demonstrate that the proposed approach achieves more accurate fusion results than sparse representation based methods.

Conventional coupled dictionary learning approaches are designed for noiseless image super-resolution (SR), but quite sensitive to noisy images. We find that the cause is the commonly used ℓ F -norm coefficients transition term. In this paper, we propose a robust ℓ 1 -norm solution by introducing two sub-terms: LR coefficient sparsity constraint term and HR coefficient conversion term , which are able to prevent the noise transmission from noisy input to output. By incorporating our simple yet effective non-linear model inspired by auto-encoder, the proposed ℓ 1 -norm dictionary learning achieves a more accurate coefficients conversion. Moreover, to make the coefficients conversion more reliable in the iterative process, we bring the non-local self-similarity constraint to regularize the HR sparse coefficients updates. The improved sparse representation further enhances SR inference on both synthesized noisy and noiseless images. Using standard metrics, we show that results are significantly clearer than state-of-the-arts on noisy images and sharper on denoised images. In addition, experiments on real-world data further demonstrate the superiority of our method in practice. [ABSTRACT FROM AUTHOR]

Abstract: In order to improve the accuracy of the medical image segmentation and reduce the effect of selecting seed points using region growing algorithm, an improved region growing method is proposed in this paper. First, the source images are pre-processed using non-linear mapping method and the region of interest in the liver is selected by man–machine interaction; Quasi-Monte Carlo method is used for generating low-dispersion sequences points in the region of interest and the optical seed points are selected by computing these points; In addition, the region growing criteria is also improved. The improved region growing algorithm is used for segmenting three discontinuous abdomen CT images. Compared with the traditional region growing method, the improved method can get better liver segmentation effects. The proposed method can be effectively applied to liver segmentation and it can improve the accuracy of liver segmentation. [Copyright &y& Elsevier]

Multidimensional scaling is a must-have tool for visual data miners, projecting multidimensional data onto a two-dimensional plane. However, what we see is not necessarily what we think about. In many cases, end-users do not take care of scaling the projection space with respect to the multidimensional space. Anyway, when using non-linear mappings, scaling is not even possible. Yet, without scaling geometrical structures which might appear do not make more sense than considering a random map. Without scaling, we shall not make inference from the display back to the multidimensional space. No clusters, no trends, no outliers, there is nothing to infer without first quantifying the mapping quality. Several methods to qualify mappings have been devised. Here, we propose CheckViz, a new method belonging to the framework of Verity Visualization. We define a two-dimensional perceptually uniform colour coding which allows visualizing tears and false neighbourhoods, the two elementary and complementary types of geometrical mapping distortions, straight onto the map at the location where they occur. As examples shall demonstrate, this visualization method is essential to help users make sense out of the mappings and to prevent them from over interpretations. It could be applied to check other mappings as well. [ABSTRACT FROM AUTHOR]

The antifungal activity of 14 anthracene-based synthetic dyes and 6 reference compounds was measured on 36 fungal strains and the data matrix was evaluated separately by principal component analysis (PCA) and using a spectral mapping technique (SPM). The dimensionality of the maps of principal component loadings and variables and the selectivity maps was reduced to two by non-linear mapping. Except for two compounds, the dyes showed marked antifungal activity. Calculations proved that both the strength and selectivity of the biological effect of anthracene-based dyes were highly dependent on the chemical structure of the dye and on the type of fungi. PCA and SPM revealed different aspects of the antifungal activity, therefore, their simultaneous application in future quantitative structure-activity relationship studies is highly recommended. [ABSTRACT FROM AUTHOR]

In this article, we shall give practical and numerical representations of inverse mappings of two-dimensional mappings (of the solutions of two non-linear simultaneous equations) and show their numerical experiments by using computers. We derive a concrete formula from a very general idea for the representation of the inverse functions. [ABSTRACT FROM AUTHOR]

Abstract: Vibrational Raman optical activity (ROA), measured as a small difference in the intensity of Raman scattering from chiral molecules in right and left-circularly polarized incident light, or as the intensity of a small circularly polarized component in the scattered light, is a powerful probe of the aqueous solution structure of proteins. On account of the large number of structure-sensitive bands in protein ROA spectra, multivariate analysis techniques such as non-linear mapping (NLM) are especially favourable for determining structural relationships between different proteins. Here NLM is used to map a dataset of 80 polypeptide, protein and virus ROA spectra, considered as points in a multidimensional space with axes representing the digitized wavenumbers, into readily visualizable two and three-dimensional spaces in which points close to or distant from each other, respectively, represent similar or dissimilar structures. Discrete clusters are observed which correspond to the seven structure classes all α, mainly α, αβ, mainly β, all β, mainly disordered/irregular and all disordered/irregular. The average standardised ROA spectra of the proteins falling within each structure class have distinct features characteristic of each class. A distinct cluster containing the wheat protein A-gliadin and the plant viruses potato virus X, narcissus mosaic virus, papaya mosaic virus and tobacco rattle virus, all of which appear in the mainly α cluster in the two-dimensional representation, becomes clearly separated in the direction of increasing disorder in the three-dimensional representation. This suggests that the corresponding five proteins, none of which to date has yielded high-resolution X-ray structures, consist mainly of α-helix and disordered structure with little or no β-sheet. This combination of structural elements may have functional significance, such as facilitating disorder-to-order transitions (and vice versa) and suppressing aggregation, in these proteins and also in sequences within other proteins. The use of ROA to identify proteins containing significant amounts of disordered structure will, inter alia, be valuable in structural genomics/proteomics since disordered regions often inhibit crystallization. [Copyright &y& Elsevier]

X-ray images are often of low contrast due to the subtle distinction of attenuation coefficients and scatter effect, which makes it difficult to distinguish signals from background. This paper proposes an image enhancement algorithm using the multi-scale dyadic wavelet transform. The algorithm includes two steps: 1) In order to enhance contrast, a non-linear mapping is performed on wavelet coefficients at different scales. Inhibition factors are then applied to reduce the impact of scatter; 2) In order to reduce the negative impact of noise amplification from the first step, wavelet coefficients are classified into two categories: irregular coefficients and edge-related and regular coefficients, and then filtered with different schemes for each category. Experimental results demonstrate that this algorithm effectively enhance the contrast of x-ray images. Examination is also done on CT reconstructions from multi-view projection data processed by the proposed method and significant improvement of image quality is observed. Our results are expected to offer great help to follow-up detection and recognition tasks. [ABSTRACT FROM AUTHOR]

Recent advances in gene sequencing and rational drug design have re-emphasized the need for new methods for protein analysis, classification, and structure and function prediction. In this article, we introduce a new method for analyzing protein sequences based on Sammon's non-linear mapping algorithm. When applied to a family of homologous sequences, the method is able to capture the essential features of the similarity matrix, and provides a faithful representation of chemical or evolutionary distance in a simple and intuitive way. The merits of the new algorithm are demonstrated using examples from the protein kinase family. [ABSTRACT FROM AUTHOR]

Cross-domain recommendation is a promising solution in recommendation systems by using relatively rich information from the source domain to improve the recommendation accuracy of the target domain. Most of the existing methods consider the rating information of users in different domains, the label information of users and items and the review information of users on items. However, they do not effectively use the latent sentiment information to find the accurate mapping of latent features in reviews between domains. User reviews usually include user's subjective views, which can reflect the user's preferences and sentiment tendencies to various attributes of the items. Therefore, in order to solve the cold-start problem in the recommendation process, this paper proposes a cross-domain recommendation algorithm (CDR-SAFM) based on sentiment analysis and latent feature mapping by combining the sentiment information implicit in user reviews in different domains. Different from previous sentiment research, this paper divides sentiment into three categories based on three-way decision ideas—namely, positive, negative and neutral—by conducting sentiment analysis on user review information. Furthermore, the Latent Dirichlet Allocation (LDA) is used to model the user's semantic orientation to generate the latent sentiment review features. Moreover, the Multilayer Perceptron (MLP) is used to obtain the cross domain non-linear mapping function to transfer the user's sentiment review features. Finally, this paper proves the effectiveness of the proposed CDR-SAFM framework by comparing it with existing recommendation algorithms in a cross-domain scenario on the Amazon dataset. [ABSTRACT FROM AUTHOR]

Spatiotemporal fusion provides an effective way to fuse two types of remote sensing data featured by complementary spatial and temporal properties (typical representatives are Landsat and MODIS images) to generate fused data with both high spatial and temporal resolutions. This paper presents a very deep convolutional neural network (VDCN) based spatiotemporal fusion approach to effectively handle massive remote sensing data in practical applications. Compared with existing shallow learning methods, especially for the sparse representation based ones, the proposed VDCN-based model has the following merits: (1) explicitly correlating the MODIS and Landsat images by learning a non-linear mapping relationship; (2) automatically extracting effective image features; and (3) unifying the feature extraction, non-linear mapping, and image reconstruction into one optimization framework. In the training stage, we train a non-linear mapping between downsampled Landsat and MODIS data using VDCN, and then we train a multi-scale super-resolution (MSSR) VDCN between the original Landsat and downsampled Landsat data. The prediction procedure contains three layers, where each layer consists of a VDCN-based prediction and a fusion model. These layers achieve non-linear mapping from MODIS to downsampled Landsat data, the two-times SR of downsampled Landsat data, and the five-times SR of downsampled Landsat data, successively. Extensive evaluations are executed on two groups of commonly used Landsat–MODIS benchmark datasets. For the fusion results, the quantitative evaluations on all prediction dates and the visual effect on one key date demonstrate that the proposed approach achieves more accurate fusion results than sparse representation based methods. [ABSTRACT FROM AUTHOR]