Order Kernel Research Articles

Development of an MRI Radiomic Machine-Learning Model to Predict Triple-Negative Breast Cancer Based on Fibroglandular Tissue of the Contralateral Unaffected Breast in Breast Cancer Patients

Aim: The purpose of this study was to develop a radiomic-based machine-learning model to predict triple-negative breast cancer (TNBC) based on the contralateral unaffected breast’s fibroglandular tissue (FGT) in breast cancer patients. Materials and methods: This study retrospectively included 541 patients (mean age, 51 years; range, 26–82) who underwent a screening breast MRI between November 2016 and September 2018 and who were subsequently diagnosed with biopsy-confirmed, treatment-naïve breast cancer. Patients were divided into training (n = 250) and validation (n = 291) sets. In the training set, 132 radiomic features were extracted using the opensource CERR platform. Following feature selection, the final prediction model was created, based on a support vector machine with a polynomial kernel of order 2. Results: In the validation set, the final prediction model, which included four radiomic features, achieved an F1 score of 0.66, an area under the curve of 0.71, a sensitivity of 54% [47–60%], a specificity of 74% [65–84%], a positive predictive value of 84% [78–90%], and a negative predictive value of 39% [31–47%]. Conclusions: TNBC can be predicted based on radiomic features extracted from the FGT of the contralateral unaffected breast of patients, suggesting the potential for risk prediction specific to TNBC.

A sixth order kernel functions approach for nonlinear fourth order boundary value problems

A sixth order kernel functions approach for nonlinear fourth order boundary value problems

Influence of Conservation Methods on the sour cherry (Cerasus vulgaris Mill.) fruits quality

Objective: Sour cherry fruits (Cerasus vulgaris Mill.) belong to the Rosaceae family and are designed as a GRAS ingredient based on the FDA data. Animal experiments and clinical practice confirm that there are many positive pharmacological effects mainly related to anthocyanins. Development of standard regulations for this kind of medicinal plant raw materials is actual to introduce sour cherry fruits into official medical practice. In our research, we investigate macroscopic and microscopic properties and determine the content of tanning substances and anthocyanins in sour cherry fruits of various kinds of conservation. Materials and methods: Modern complex of physicochemical methods was used in pharmacognostical research. Microscopic analysis was performed on a LOMO Micmed-6 microscope with 10× eyepieces, 4×, 10×, 40× and 100× objectives, photographies were taken with a Sony Xperia Z3 compact digital camera. The content of total anthocyanins in terms of cyanidin-3-О-glucoside was determined by differential UV-spectrophotometry, total tannins content – by redox titration. Results and discussion: The anomocytic stomatal complex, fruits pulp druses, anthocyanins containing in the epidermis and fruits pulp cells, and vessels are typical signs for the sour cherry fruits anatomy structure. A conservation method has not to effect on visual representation of diagnostic signs. The contents of tanning substances are little; it is from 2.73±0.08% to 4.12±0.13% in terms of tannin. Maximal anthocyanin contents (in terms of cyanidin-3-glucoside and in absolutely dried raw material) were determined in fresh-frozen sour cherry fruits (after defrosting (with juice and without kernel) is 5.40±0.15% or in terms of moisture-containing raw materials (without kernel) – 0.690±0.019%. In the defrosted fruits without juice, the content of anthocyanins is two times lower in terms of completely dried raw material (without kernel), it is 2.77±0.12% or in terms of moisture-containing raw material (without kernel), it is 0.410±0.018%. In the juice released from cherry fruits after defrosting anthocyanin content in terms of cyanidin-3-glucoside is of 0.450±0.007% (g/100ml juice), in dried sour cherry fruits (without kernel) – 4.34±0.17%, which is lower than in fresh-frozen raw materials. It can be explained by the varietal features, as well by the conservation conditions; this matter is to be further studied. Contents of tanning substances in fresh-frozen and dried sour cherry fruits when storage during 4 months is insignificantly reduced, but it is established that contents of anthocyanin in terms of cyanidin-3-glucoside reduces 1.5 times in 4 months, if the raw material is frozen, and it reduces by 10% if the raw material is dried. Conclusion: Diagnostic signs of macroscopic and microscopic structures, contents of tanning substances and anthocyanins in terms of cyanidin 3-glycoside in sour cherry fruits were studied. The content of the main groups of biologically active substances decreases equally during storage of dried and frozen cherry fruits. When defrosting, it is necessary to carefully collect the juice, as it contains the bulk of the anthocyanins. It is promising to study various options for freezing and drying of cherry fruits with kernels in order to reduce the loss of fruits juice to a minimum. In this case, it is important to ensure that the kernels are whole (not destroyed), in order to avoid the ingress of cyanogenic glycosides into the medicinal plant material. The results will be used to develop normative documentation for sour cherry fruits.

Orthonormal expansions for translation-invariant kernels

We present a general Fourier analytic technique for constructing orthonormal basis expansions of translation-invariant kernels from orthonormal bases of ℒ2(R). This allows us to derive explicit expansions on the real line for (i) Matérn kernels of all half-integer orders in terms of associated Laguerre functions, (ii) the Cauchy kernel in terms of rational functions, and (iii) the Gaussian kernel in terms of Hermite functions.

Robust Bayesian estimation via the [formula omitted]-divergence

In this paper, we introduce a novel framework for robust Bayesian parameter estimation using the K-divergence. The framework incorporates an outlier resilient pseudo-posterior density function, called the K-posterior, which is based on an empirical version of the K-divergence. The latter involves utilizing Parzen’s non-parametric Kernel density estimator to mitigate the influence of outliers. Under the quadratic loss, a new robust analog of the posterior mean estimator (PME), referred here to as the KPME, is obtained. In the paper, we examine the asymptotic behavior of the KPME and investigate its robustness in the presence of outliers. Furthermore, we tackle the task of data-guided selection for the bandwidth parameter of the kernel in order to optimize a performance-oriented objective. Lastly, the KPME is successfully applied to robust Bayesian source localization under intermittent jamming.

A new method to design energy-conserving surrogate models for the coupled, nonlinear responses of intervertebral discs

The aim of this study was to design physics-preserving and precise surrogate models of the nonlinear elastic behaviour of an intervertebral disc (IVD). Based on artificial force-displacement data sets from detailed finite element (FE) disc models, we used greedy kernel and polynomial approximations of second, third and fourth order to train surrogate models for the scalar force-torque -potential. Doing so, the resulting models of the elastic IVD responses ensured the conservation of mechanical energy through their structure. At the same time, they were capable of predicting disc forces in a physiological range of motion and for the coupling of all six degrees of freedom of an intervertebral joint. The performance of all surrogate models for a subject-specific L4|\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\vert$$\\end{document}5 disc geometry was evaluated both on training and test data obtained from uncoupled (one-dimensional), weakly coupled (two-dimensional), and random movement trajectories in the entire six-dimensional (6d) physiological displacement range, as well as on synthetic kinematic data. We observed highest precisions for the kernel surrogate followed by the fourth-order polynomial model. Both clearly outperformed the second-order polynomial model which is equivalent to the commonly used stiffness matrix in neuro-musculoskeletal simulations. Hence, the proposed model architectures have the potential to improve the accuracy and, therewith, validity of load predictions in neuro-musculoskeletal spine models.

An efficient method for generalised Wiener series estimation of nonlinear systems using Gaussian processes

System identification of dynamical systems aims to predict the output of a system for a given input by inferring model details from data. This is particularly challenging for nonlinear vibrating systems with long memory, which often have complex dynamics for which the physics is not fully understood. However, in many engineering applications, it is important to capture as much of the nonlinearity in the response as possible. The Wiener series is a classical data-driven technique that decomposes the system response into a set of orthogonal functionals of increasing order. Unlike standard black-box algorithms, such as neural networks, the series is highly interpretable and can offer insight into the nonlinearities present. However, current methods require vast quantities of data to calculate higher order terms in the Wiener series. In this paper, a novel generalised formulation of the Wiener series is developed by framing the series explicitly as a QR decomposition. Then by placing a Gaussian process prior over the kernels, their inherent structure is exploited to significantly reduce the quantity of data required for inference. Initial investigations were carried out using two systems: first pre-defined kernels and second an idealised nonlinear oscillatory system with unknown kernels. It is demonstrated that the Gaussian Process Generalised Wiener Series (GPGWS) enables the calculation of up to and including the third order kernel for systems with long memory and improves the robustness to noise.

Mathematical study of polycystic ovarian syndrome disease including medication treatment mechanism for infertility in women.

Among women of reproductive age, PCOS (polycystic ovarian syndrome) is one of the most prevalent endocrine illnesses. In addition to decreasing female fertility, this condition raises the risk of cardiovascular disease, diabetes, dyslipidemia, obesity, psychiatric disorders and other illnesses. In this paper, we constructed a fractional order model for polycystic ovarian syndrome by using a novel approach with the memory effect of a fractional operator. The study population was divided into four groups for this reason: Women who are at risk for infertility, PCOS sufferers, infertile women receiving therapy (gonadotropin and clomiphene citrate), and improved infertile women. We derived the basic reproductive number, and by utilizing the Jacobian matrix and the Routh-Hurwitz stability criterion, it can be shown that the free and endemic equilibrium points are both locally stable. Using a two-step Lagrange polynomial, solutions were generated in the generalized form of the power law kernel in order to explore the influence of the fractional operator with numerical simulations, which shows the impact of the sickness on women due to the effect of different parameters involved.

A New Second Order Kernel of the Beta Polynomial Family in Density Estimation

A New Second Order Kernel of the Beta Polynomial Family in Density Estimation

Memory-dependent derivative grey Bernoulli model and its application in electricity generation forecast

PurposeThis paper aims to develop a novel grey Bernoulli model with memory characteristics, which is designed to dynamically choose the optimal memory kernel function and the length of memory dependence period, ultimately enhancing the model's predictive accuracy.Design/methodology/approachThis paper enhances the traditional grey Bernoulli model by introducing memory-dependent derivatives, resulting in a novel memory-dependent derivative grey model. Additionally, fractional-order accumulation is employed for preprocessing the original data. The length of the memory dependence period for memory-dependent derivatives is determined through grey correlation analysis. Furthermore, the whale optimization algorithm is utilized to optimize the cumulative order, power index and memory kernel function index of the model, enabling adaptability to diverse scenarios.FindingsThe selection of appropriate memory kernel functions and memory dependency lengths will improve model prediction performance. The model can adaptively select the memory kernel function and memory dependence length, and the performance of the model is better than other comparison models.Research limitations/implicationsThe model presented in this article has some limitations. The grey model is itself suitable for small sample data, and memory-dependent derivatives mainly consider the memory effect on a fixed length. Therefore, this model is mainly applicable to data prediction with short-term memory effect and has certain limitations on time series of long-term memory.Practical implicationsIn practical systems, memory effects typically exhibit a decaying pattern, which is effectively characterized by the memory kernel function. The model in this study skillfully determines the appropriate kernel functions and memory dependency lengths to capture these memory effects, enhancing its alignment with real-world scenarios.Originality/valueBased on the memory-dependent derivative method, a memory-dependent derivative grey Bernoulli model that more accurately reflects the actual memory effect is constructed and applied to power generation forecasting in China, South Korea and India.

Efficient Approximate Kernel Based Spike Sequence Classification.

Machine learning (ML) models, such as SVM, for tasks like classification and clustering of sequences, require a definition of distance/similarity between pairs of sequences. Several methods have been proposed to compute the similarity between sequences, such as the exact approach that counts the number of matches between k-mers (sub-sequences of length k) and an approximate approach that estimates pairwise similarity scores. Although exact methods yield better classification performance, they pose high computational costs, limiting their applicability to a small number of sequences. The approximate algorithms are proven to be more scalable and perform comparably to (sometimes better than) the exact methods - they are designed in a "general" way to deal with different types of sequences (e.g., music, protein, etc.). Although general applicability is a desired property of an algorithm, it is not the case in all scenarios. For example, in the current COVID-19 (coronavirus) pandemic, there is a need for an approach that can deal specifically with the coronavirus. To this end, we propose a series of ways to improve the performance of the approximate kernel (using minimizers and information gain) in order to enhance its predictive performance pm coronavirus sequences. More specifically, we improve the quality of the approximate kernel using domain knowledge (computed using information gain) and efficient preprocessing (using minimizers computation) to classify coronavirus spike protein sequences corresponding to different variants (e.g., Alpha, Beta, Gamma). We report results using different classification and clustering algorithms and evaluate their performance using multiple evaluation metrics. Using two datasets, we show that our proposed method helps improve the kernel's performance compared to the baseline and state-of-the-art approaches in the healthcare domain.

Continuity in law for solutions of SPDES with space-time homogeneous Gaussian noise

In this paper, we study the continuity in law of the solutions of two linear multiplicative SPDEs (the parabolic Anderson model and the hyperbolic Anderson model) with respect to the spatial parameter of the noise. The solution is interpreted in the Skorohod sense, using Malliavin calculus. We consider two cases: (i) the regular noise, whose spatial covariance is given by the Riesz kernel of order [Formula: see text], in spatial dimension [Formula: see text]; (ii) the rough noise, which is fractional in space with Hurst index [Formula: see text], in spatial dimension [Formula: see text]. We assume that the noise is colored in time.

Toward an Online Monitoring of Structural Performance Based on Physics-Informed Hybrid Modeling Method

Abstract To optimize structures and monitor their health, it is essential to build an accurate dynamic analysis model. However, traditional modeling methods based solely on physical information or data-driven techniques may not suffice for many engineering applications. While physical models can accurately simulate complex equipment, they may also incur high computational time. On the other hand, data-driven models may improve computational efficiency but are subject to significant deviations due to the influence of training data. To address these challenges, the Physics-Informed Neural Network (PINN) has gained popularity for imposing physical constraints during the training process, leading to better generalization capabilities with fewer data samples. This paper proposes a physics-informed hybrid modeling (PIHM) approach that combines a reduced-order model, kernel functions, and dynamic equations to predict dynamic output with limited training data and physical information. The method integrates prior physics information into function approximation by incorporating the reduced dynamic equation into a surrogate modeling framework. The loss function considers inertial and damping effects, ensuring physical plausibility. Unlike traditional PINN applications, the proposed modeling method is more explainable, as the trained model can be expressed in function form with engineering interpretation. The approach is verified with a real-world engineering example (telehandler boom) under complex load conditions, demonstrating accuracy, efficiency, and physical plausibility. Overall, the proposed method offers promising capabilities in solving problems where high-fidelity simulation is challenging.

Harnack inequalities and Hölder estimates for fully nonlinear integro-differential equations with weak scaling conditions

Hölder estimates and Harnack inequalities are studied for fully nonlinear integro-differential equations under some mild assumptions. We allow the kernels of variable order and critically close to 2.

Analysis of a fractional order Bovine Brucellosis disease model with discrete generalized Mittag–Leffler kernels

Bovine Brucellosis, a zoonotic disease, can infect cattle in tropical and subtropical areas. It remains a critical issue for both human and animal health in many parts of the world, especially those where livestock is an important source of food and income. An efficient method for monitoring the illness’s increasing prevalence and developing low-cost prevention strategies for both its effects and recurrence is brucellosis disease modeling. We create a fractional-order model of Bovine Brucellosis using a discrete modified Atangana–Baleanu fractional difference operator of the Liouville–Caputo type. An analysis of the suggested system’s well-posedness and a qualitative investigation are both conducted. The examination of the Volterra-type Lyapunov function for global stability is supported by the first and derivative tests. The Lipschitz condition is also used for the model in order to meet the criterion of the uniqueness of the exact solution. We created an endemic and disease-free equilibrium. Solutions are built in the discrete generalized form of the Mittag-Leffler kernel in order to analyze the effect of the fractional operator with numerical simulations and emphasize the effects of the sickness due to the many factors involved. The capacity of the suggested model to forecast an infectious disease like brucellosis can help researchers and decision-makers take preventive actions.

Classical solutions to integral equations with zero order kernels

Classical solutions to integral equations with zero order kernels

Peach (Prunus persica (L.) Batsch) seeds and kernels as potential plant-based functional food ingredients: A review of bioactive compounds and health-promoting activities

Prunus persica (L.) Batsch (or peach) (Rosaceae) is the most important stone fruit crop in many areas, including North Africa, South Africa, and Europe. Peaches are well known for their flavor, nutritional value, and potential health benefits. During the consumption of peach fruit, usually jams, jellies, juices, and other food products, the seed and kernel (stone) is disposed of as waste. However, the seeds and kernels of peach fruit are considered remarkably rich sources of sodium, potassium, zinc, copper, iron, fatty acids (linolenic, oleic, palmitic, and linoleic acids), fiber, and carbohydrate (sucrose, glucose, and fructose) content. The preliminary results of various studies demonstrated that seed and kernels of peach fruit contain high amount of protein and bioactive peptides. Seed and kernels extract showed anti-ageing, anti-biofilm properties, protection against oxidative stress, cancer cell proliferation, inhibit type II diabetes, Alzheimer’s disease and obesity. It was concluded that biological properties are stimulated by the presence of hydroxycinnamic acids, polymeric procyanidins, cyanogenic glycosides, carotenoids and other metabolites. Oil extracted from the seeds of peach extracted via, supercritical CO2 shows the presence of phytosterols (stigmasterol, β-sitosterol, campesterol) that were widely known for their cholesterol-lowering effects, while additional research showed peach kernels as a potent source of phenolic compounds with high concentration of phenolic acids and catechin. Amygdalin is present in the seed extract of peach fruit, that changes into cyanide and supposed to kill cancer cells. A variety of studies are being conducted to recover possible bioactive compounds from peach seed and/or kernels in order to prevent environmental pollution and also economic losses. Thus, peach wastes, by-products, and their valorized compounds can be used as a sustainable resource of various important compounds that can be of great importance in different functional foods, pharmaceuticals, animal feed industry and cosmetics.

A Comparative Study of Higher Order Kernel Estimation and Kernel Density Derivative Estimation of the Gaussian Kernel Estimator with Data Application

Higher-order kernel estimation and kernel density derivative estimation are techniques for reducing the asymptotic mean integrated squared error in nonparametric kernel density estimation. A reduction in the error criterion is an indication of better performance. The estimation of kernel function relies greatly on bandwidth and the identified reduction methods in the literature are bandwidths reliant for their implementation. This study examines the performance of higher order kernel estimation and kernel density derivatives estimation techniques with reference to the Gaussian kernel estimator owing to its wide applicability in real-life-settings. The explicit expressions for the bandwidth selectors of the two techniques in relation to the Gaussian kernel and the bandwidths were accurately obtained. Empirical results using two data sets obviously revealed that kernel density derivative estimation outperformed the higher order kernel estimation excellently well with the asymptotic mean integrated squared error as the criterion function.

New classes of density estimates of low bias

A desirable property of a kernel used for a density estimate is that it has high order as this gives low bias. Given a kernel K, a basis pj(z),j≥0, and q≥1, we show how to choose a=a0,…,aq−1′ such that K̂q(z)=K(z)∑j=0q−1ajpj(z) is a kernel of order at least q. a is given in terms of the mixed moments, EZjpk(Z). Some of the kernels involve the complex unit. A simulation study is performed to compare density estimates based on some of the proposed kernels to competitive ones including those in Withers and Nadarajah [1]. The proposed estimates are shown to have smaller biases and smaller mean squared errors.

Identifying impacts of global climate teleconnection patterns on land water storage using machine learning

Study RegionThe Zambezi River Basin in southern Africa Study focusModelling global freshwater systems is difficult because of the complexities of climate and anthropogenic influence on hydrological systems, especially at local scales. The rapid changes in hydrological systems caused by the influence of global climate trigger complex processes that make traditional machine learning algorithms limited in quantifying impacts of climate variability on freshwater. In this study, we developed a novel machine learning routine based on the Gaussian process regression (GPR) technique to improve understanding of the interaction of non-linear climatic variables with hydrological stores (includes surface water and terrestrial water storage-TWS). The GPR is built on the principle of the Gaussian process, which is a stochastic process that simplifies multivariate Gaussian distribution to infinite-dimensional space, such that the distributions over function values can be defined. The prediction of the GPR is tested using twenty-three independent climate variables against satellite observations of TWS between April 2002 and June 2017. We explored the use of a characteristic length scale for the kernels, which we tagged as ‘first order kernels’, and another set of kernels having a separate length scale for each discrete predictor. The latter was implemented using the automatic relevance determination (ARD), tagged as ‘higher order kernels’. The first and higher order kernels of the GPR technique were further examined using multivariate statistical indices to reveal the close relationship among hydro-climatic similarity and predictability. New hydrological insights for the regionOur results indicate that the large fluctuations of TWS in our tentative test-bed (the Zambezi Basin) for the GPR technique are largely caused by strong changes in sea surface temperature and global teleconnection patterns of the nearby oceans. The GPR introduced in this study provides an improved modelling framework to keep track on the influence of these global climate teleconnection patterns on major hydrological systems, like the Zambezi Basin, which contributes to global hydro-climatology but currently showing large amplitudes of land water storage loss.