Divergences have become a very useful tool for measuring similarity (or dissimilarity) between probability distributions. Depending on the field of application a more appropriate measure may be necessary. In this paper we introduce a family of divergences we call gamma-divergences. They are based on the convexity property of the functions that generate them. We demonstrate that these divergences verify all the usually required properties, and we extend them to weighted probability distribution. We investigate their properties in the context of kernel theory. Finally, we apply our findings to the analysis of simulated and real time series.

This paper presents a new method : HIVEC to learn latent vector representations of graphs in a manner that captures the semantic dependencies of sub-structures. The representations can then be used in machine learning algorithms for tasks such as graph classification, clustering etcetera. The method proposed is unsupervised and uses the information of co-occurrence of sub-structures. It introduces a notion of hierarchical embeddings that allows us to avoid repetitive learning of sub-structures for every new graph. As an alternative to deep learning methods, the edit distance similarity between sub-structures is also used to learn vector representations. We compare the performance of these methods against previous work.

We address the dynamics of two-dimensional Navier-Stokes models with infinite delay and hereditary memory, whose kernels are a much larger class of functions than the one considered in the literature, on a bounded domain. We prove the existence and uniqueness of weak solutions by means of Faedo-Galerkin method. Moreover, we establish the existence of global attractor for the system with the existence of a bounded absorbing set and asymptotic compact property.

This paper presents a new algorithm for semi-supervised action recognition using adaptive feature analysis. We model the samples of the same action as the same manifold and those of different actions as different manifolds, and integrate feature correlation mining and visual similarity mining into a joint framework. By maximizing the separability between different classes based on the labeled data, the proposed algorithm learns multiple features from labeled data and utilizes the intrinsic geometric structure of the data distribution between labeled and unlabeled data to boost the recognition. We introduce Projected Barzilai-Borwein (PBB) to train a subspace projection matrix as classifier. Extensive experiments on three benchmark datasets demonstrate that our algorithm outperforms the existing semi-supervised action recognition algorithms when there are a few labeled training samples.

The aim of this study was to determine the correlation between the external friction angle of cereal kernels and the roughness of a steel friction plate. The experiment was performed on the kernels of five principal cereals: wheat, rye, barley, oats and triticale. Flat seed units composed of three spaced kernels joined by adhesive tape were analyzed in each experimental variant. The external friction angle of flat seed units was determined on 9 steel friction plates with different roughness. Measurements were performed in 3 replications with a photosensor device which registered the external friction angle of cereal kernels. On friction plates with surface roughness Ra=0.36 to Ra=6.72, the average values of the angle of external friction ranged from 17.56° in rye kernels to 34.01° in oat kernels. The greatest similarities in the angle of external friction were observed between wheat and triticale kernels, whereas the greatest differences were noted between barley and oat kernels and between barley and triticale kernels. Friction plates made of ST3S steel should be characterized by the lowest surface roughness to minimize energy consumption during grain processing. The optimal surface roughness of steel friction plates was determined at Ra=0.9.

The aim of this study was to determine the correlation between the external friction angle of cereal kernels and the roughness of a steel friction plate. The experiment was performed on the kernels of five principal cereals: wheat, rye, barley, oats and triticale. Flat seed units composed of three spaced kernels joined by adhesive tape were analyzed in each experimental variant. The external friction angle of flat seed units was determined on 9 steel friction plates with different roughness. Measurements were performed in 3 replications with a photosensor device which registered the external friction angle of cereal kernels. On friction plates with surface roughness Ra=0.36 to Ra=6.72, the average values of the angle of external friction ranged from 17.56° in rye kernels to 34.01° in oat kernels. The greatest similarities in the angle of external friction were observed between wheat and triticale kernels, whereas the greatest differences were noted between barley and oat kernels and between barley and triticale kernels. Friction plates made of ST3S steel should be characterized by the lowest surface roughness to minimize energy consumption during grain processing. The optimal surface roughness of steel friction plates was determined at Ra=0.9.

In recent years, there has been significant growth in the ubiquity and popularity of three dimensional(3D) point clouds, with an increasing focus on the classification of 3D point clouds. To extract richer features from point clouds, many researchers have turned their attention to various point set regions and channels within irregular point clouds. However, this approach has limited capability in attending to crucial regions of interest in 3D point clouds and may overlook valuable information from neighboring features during feature aggregation. Therefore, this paper proposes a novel 3D point cloud classification method based on global attention and adaptive graph convolution. The method consists of two main branches: the first branch com-putes attention masks for each point, while the second branch employs adaptive graph convolu-tion to extract global features from the point set. It dynamically learns features based on point interactions, generating adaptive kernels to effectively and precisely capture diverse relationships among points from different semantic parts. Experimental results demonstrate that the proposed model achieves 93.8% in overall accuracy and 90.8% in average accuracy on the ModeNet40 dataset.

This study develops a new definition of fractional derivative that mixes the definitions of fractional derivatives with singular and non-singular kernels. Such developed definition encompasses many types of fractional derivatives, such as the Riemann-Liouville and Caputo fractional derivatives for singular kernel type as well as the Caputo-Fabrizio, the Atangana-Baleanu and the generalized Hattaf fractional derivatives for non-singular kernel type. The associate fractional integral of the new mixed fractional derivative is rigorously introduced. Furthermore, newly numerical scheme is developed to approximate the solutions of a class of fractional differential equations (FDEs) involving the mixed fractional derivative. Finally, an application to computational biology is presented.

We say that a system {zmF(z)}m=0∞ is a Beurling system if F is an outer function. Beurling’s approximation theorem asserts that if F is an outer function from H2(D) then the system {zmF(z)}m=0∞ is complete in the space H2(D). We prove that a Beurling system with F∈Hp(D),1≤p<∞ is an M−bases in Hp(D) with an explicit dual system. Any function f∈Hp(D),1≤p<∞ can be expanded as a series by the system {zmF(z)}m=0∞. For different methods of summation we characterize outer functions F for which the expansion converges to f. Related results for weighted Hardy spaces in the unit disc are studied. Particularly we prove Rosenblum’s hypothesis.

In recent years, different deep learning frameworks were introduced for hyperspectral image (HSI) classification. However, the proposed network models have a higher model complexity and do not provide high classification accuracy if few-shot learning is used. This paper pre-sents an HSI classification method that combines random patches network (RPNet) and re-cursive filtering (RF) to obtain informative deep features. The proposed method first convolves image bands with random patches to extract multi-level deep RPNet features. Thereafter, the RPNet feature set is subjected to dimension reduction through principal component analysis (PCA) and the extracted components are filtered using the RF procedure. Finally, HSI spectral features and the obtained RPNet-RF features are combined to classify the HSI using a support vector machine (SVM) classifier. In order to test the performance of the proposed RPNet-RF method, some experiments were performed on three widely known datasets using a few training samples for each class and classification results were compared with those obtained by other advanced HSI classification methods adopted for small training samples. The comparison showed that the RPNet-RF classification is characterized by higher values of such evaluation metrics as overall accuracy and Kappa coefficient (https://github.com/UchaevD/RPNet-RF).

In this article, we establish some new generalized inequalities of Hilbert-type on time scales delta calculus which considered as similar formulas for inequalities of Hilbert type proved by Chang-Jian, Lian-Ying and Cheung [7]. These inequalities will proved by applying Hölder’s inequality, chain rule on time scales and the mean inequality. As special cases of our results (when T = N and T = R), we get the discrete and continuous inequalities. Also, we can obtain other inequalities in different time scale, like T = q^Z, q > 1.

This study aims to focus on using the Volterra series and machine learning for forecasting random and chaotic wind speed regimes, since the calm weather is mostly noticed at the local site, making the dataset selection difficult. A novel method is proposed to predict Volterra kernels up to the third order, using a forward-back propagation neural network with 12-month measurements at Fujairah site (UAE). Both daily and monthly wind speed data sets are investigated for forecasting. The three dominant hourly and daily kernels are extracted for each day and each month. Predicted future Volterra kernels are estimated from past values using both statistical analysis and individual neuro networks for each of the Volterra kernel coefficients. Due to the random nature of wind speed at the local site, a two-layer with 4 neurons per layer neuro network is used to locate the most variable and intense speed during 8-hours in the day. Forecasted wind speed is determined with errors arising from different sources such as the utilization of only 3rd-order Volterra kernels and the difficulty of machine training of the employed shallow network. Nevertheless, this work depicts a useful algorithm to forecast chaotic and random wind speed regimes. Computational time is a trade of the complexity of Volterra mathematical analysis.

Dietary polyphenols exist in two forms; extractable polyphenols (EPP) or compounds solubilised by aqueous/organic solvents, and non-extractable polyphenols (NEPP) or compounds remain in the corresponding residues after the extraction. At present, most researchers focus on EEP fractions, while NEPP is neglected. Thus, this study aimed to release NEPP from the remaining powder residue of Barhi date palm kernels (BDPK) with acid hydrolysis. The related extraction conditions were determined and optimised using response surface methodology (RSM) for maximisation of NEPP with highest cytotoxic and antioxidant activities. The face-centred central composite design (FCCCD) was used to establish treatments based on three independent variables, namely; extraction temperature, time, and solvent/sample ratio. Under the optimal conditions, the experimental values for DPPH radical-scavenging capacity of NEPP (IC50=57.52µg/mL), and cytotoxicity of NEPP against A549 and HT29 cells were IC50=17.4 µg/mL and 31.4µg/mL, respectively. The experimental values were in agreement with those predicted by RSM models, confirming the suitability of the model employed and the success of RSM for optimisation of the extraction conditions for NEPP from BDPK. These results indicate that NEPP from industrial date fruit waste could be a promising candidate as natural antioxidants with significant antiproliferation effect against A549 and HT29 cancer cells in-vitro.

In this paper, two types of the general fractional derivatives of distributed order as well as a corresponding fractional integral of distributed type are defined and their basic properties are investigated. The general fractional derivatives of distributed order are constructed for a special class of the one-parametric Sonin kernels with a power law singularities at the origin. The conventional fractional derivatives of distributed order based on the Riemann-Liouville and the Caputo fractional derivatives are particular cases of the general fractional derivatives of distributed order introduced in this paper.

Background and objectives: The initiation of apoptotic death in cancer cells is the aim of many chemotherapeutic strategies. As many anticancer agents have been discovered in natural plant sources, the search for novel phytochemicals displaying anticancer activities continues at a tremendous rate. This study was conducted to evaluate the effect of extractable polyphenols (EPP); non-extractable polyphenols (NEPP); nobiletin (NOB); tectorigenin (TEC) and persicogenin (PERS) from Barhi date palm kernels (BDPK) extracts on the induction of apoptosis in human lung cancer A549 and colon cancer HT29 cell lines. Materials and Methods: The anticancer activities were determined using MTT and trypan blue exclusion assays. Flow cytometry analysis was performed to study the cell viability, cell cycle arrest and apoptosis. The underlying mechanism of apoptosis induced by crude extracts and the purified compounds was investigated using caspase-3, -8 and -9 assays and the mitochondrial membrane potential assay. Results: The findings indicate that both BDPK extracts and the purified compounds do exert induced cell death on A549 and HT29 cells. The results observed from MTT- assay and trypan blue exclusion indicate that the cytotoxic effects of both plant extracts and the three isolated flavonoids are dose-dependent with higher cell death after 72 hours treatment. Treatment of human lung and colon cancer cells with EPP, NEPP, NOB, TEC and PERSI induced late stages of apoptosis as there was evidence of the DNA degradation and high percentage of the cells population was situated at sub-G1 phase, indicating a high population of apoptotic cells. Conclusions: Study of the apoptotic mechanism demonstrated that EPP and NEPP exhibited dependent mitochondrial signalling pathway as seen with caspase-9 and induced receptor-mediated (extrinsic) apoptotic pathway as seen with caspase-8. Therefore, our results suggest that BDPK extracts and the three isolated flavonoids could be a good candidate for developing anticancer agents.