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Self-assembling amphiphilic peptides have recently received special attention in medicine. Nonetheless, testing the myriad of combinations generated from at least 20 coded and several hundreds of noncoded amino acids to obtain candidate sequences for each application, if possible, is time-consuming and expensive. Therefore, rapid and accurate approaches are needed to select candidates from countless combinations. In the current study, we examined three conventional descriptor sets along with a novel descriptor set derived from the simulated aggregation propensity of di- and tripeptides to model the critical aggregation concentration (CAC) of amphiphilic peptides. In contrast to the conventional descriptors, the radial kernel model derived from the novel descriptor set accurately predicted the critical aggregation concentration of the test set with a residual standard error of 0.10. The importance of aromatic side chains, as well as neighboring amino acids in the self-assembly, was emphasized by analysis of the influential descriptors. The addition of very long peptides (70–100 residues) to the data set decreased the model accuracy and changed the influential descriptors. The developed model can be used to predict the CAC of self-assembling amphiphilic peptides and also to derive rules to apply in designing novel amphiphilic peptides with desired properties.

Tourism in Bali is one of the major industries which play an important role in developing the global economy in Indonesia. Good forecasting of tourist arrival, especially from foreign countries, is needed to predict the number of tourists based on past information to minimize the prediction error rate. This study compares the performance of SVM and Backpropagation to find the model with the best prediction algorithm using data from foreign tourists in Bali Province. The results of this study recommend the best forecasting using the SVM model with the radial kernel function. The best accuracy of the SVM model obtained the lowest error values of MSE 0.0009, MAE 0.0186, and MAPE 0.0276, compared to Backpropagation which obtained MSE 0.0170, MAE 0.1066, and MAPE 0.1539.

Objective Early diagnosis of many diseases is essential for their treatment. Furthermore, the existence of abundant and unknown variables makes more complicated decision making. For this reason, the diagnosis and classification of diseases using machine learning algorithms have attracted a lot of attention. Therefore, this study aimed to design a support vector machine (SVM) based decision-making support system to diagnosis various periodontal diseases. Data were collected from 300 patients referring to Periodontics department of Hamadan University of Medical Sciences, west of Iran. Among these patients, 160 were Gingivitis, 60 were localized periodontitis and 80 were generalized periodontitis. In the designed classification model, 11 variables such as age, sex, smoking, gingival index, plaque index and so on used as input and output variable show the individual’s status as a periodontal disease. Results Using different kernel functions in the design of the SVM classification model showed that the radial kernel function with an overall correct classification accuracy of 88.7% and the overall hypervolume under the manifold (HUM) value was to 0.912 has the best performance. The results of the present study show that the designed classification model has an acceptable performance in predicting periodontitis.

The purpose of this paper is to provide necessary and sufficient conditions on a continuous and matrix valued radial kernel on a Euclidean space in order that it be conditionally positive definite of a fixed order. Except for the one dimensional Euclidean space, the strict conditional positive definiteness of the kernel is fully characterized.

In this paper, we estimate the dynamic parameters of a time-varying coefficient model through radial kernel functions in the context of a longitudinal study. Our proposal is based on a linear combination of weighted kernel functions involving a bandwidth, centered around a given set of time points. In addition, we study different alternatives of estimation and inference including a Frequentist approach using weighted least squares along with bootstrap methods, and a Bayesian approach through both Markov chain Monte Carlo and variational methods. We compare the estimation strategies mention above with each other, and our radial kernel functions proposal with an expansion based on regression spline, by means of an extensive simulation study considering multiples scenarios in terms of sample size, number of repeated measurements, and subject-specific correlation. Our experiments show that the capabilities of our proposal based on radial kernel functions are indeed comparable with or even better than those obtained from regression splines. We illustrate our methodology by analyzing data from two AIDS clinical studies.

Autism Spectrum Disorder (ASD) is on the rise and constantly growing. Earlier identify of ASD with the best outcome will allow someone to be safe and healthy by proper nursing. Humans are hard to estimate the present condition and stage of ASD by measuring primary symptoms. Therefore, it is being necessary to develop a method that will provide the best outcome and measurement of ASD. This paper aims to show several measurements that implemented in several classifiers. Among them, Support Vector Machine (SVM) provides the best result and under SVM, there are also some kernels to perform. Among them, the Gaussian Radial Kernel gives the best result. The proposed classifier achieves 95% accuracy using the publicly available standard ASD dataset.

We overview recent developments in the study of alignment hydrodynamics, driven by a general class of symmetric communication kernels. A main question of interest is to characterize the emergent behavior of such systems, which we quantify in terms of the spectral gap of a weighted Laplacian associated with the alignment operator. Our spectral analysis of energy fluctuation covers both long-range and short-range kernels and does not require thermal equilibrium (no closure for the pressure). In particular, in the prototypical case of metric-based short-range kernels, the spectral gap admits a lower-bound expressed in terms of the discrete Fourier coefficients of the radial kernel, which enables us to quantify an emerging flocking behavior for non-vacuous solutions. These large-time behavior results apply as long as the solutions remain smooth. It is known that global smooth solutions exist in one and two spatial dimensions, subject to sub-critical initial data. We settle the question for arbitrary dimension, obtaining non-trivial initial threshold conditions which guarantee existence of multiD global smooth solutions.

The objective of this paper is to compare the accuracy of different kernel functions of the SVM method for text classification. As a basis for the research film reviews are used. The authors try to detect the kernel functions and their parameters to achieve high accuracy in movie reviews classification. The studied kernel functions are: polynomial kernel of degree 2, a linear kernel and a radial base kernel. The achieved accuracy is higher than 83%. The experiments show that the sigmoid radial kernel is an inappropriate choice in text classification.

In this paper, we prove some properties of algebraic cone metric spaces and introduce the notion of algebraic distance in an algebraic cone metric space. As an application, we obtain some famous fixed point results in the framework of this algebraic distance.

Sufficient conditions on the kernel and the grandizer that ensure the boundedness of integral operators with homogeneous kernels in grand Lebesgue spaces on ℝ n as well as an upper bound for their norms are obtained. For some classes of grandizers, necessary conditions and lower bounds for the norm of these operators are also obtained. In the case of a radial kernel, stronger estimates are established in terms of one-dimensional grand norms of spherical means of the function. A sufficient condition for the boundedness of the operator with homogeneous kernel in classical Lebesgue spaces with arbitrary radial weight is obtained. As an application, boundedness in grand spaces of the one-dimensional operator of fractional Riemann–Liouville integration and of a multidimensional Hilbert-type operator is studied.

In this paper we show an interior discontinuity and its piecewise regularity for a stationary compressible Stokes problem with inflow jump datum. The discontinuity is preserved along the interior curve directed by the ambient vector field. The difficulty lies in controlling the gradient of the pressure across the interior curve starting at the jump point that the inflow datum has. We deal with this issue by constructing a vector function K corresponding to the interior jump and splitting the vector K from the velocity vector. Finally the remainder for the velocity vector and pressure function is shown to be in the space H 2 , q × H 1 , q for q ≥ 2 .

Machine Learning (ML) algorithms have been used for assessing soil quality parameters along with non-destructive methodologies. Among spectroscopic analytical methodologies, energy dispersive X-ray fluorescence (EDXRF) is one of the more quick, environmentally friendly and less expensive when compared to conventional methods. However, some challenges in EDXRF spectral data analysis still demand more efficient methods capable of providing accurate outcomes. Using Multi-target Regression (MTR) methods, multiple parameters can be predicted, and also taking advantage of inter-correlated parameters the overall predictive performance can be improved. In this study, we proposed the Multi-target Stacked Generalisation (MTSG), a novel MTR method relying on learning from different regressors arranged in stacking structure for a boosted outcome. We compared MTSG and 5 MTR methods for predicting 10 parameters of soil fertility. Random Forest and Support Vector Machine (with linear and radial kernels) were used as learning algorithms embedded into each MTR method. Results showed the superiority of MTR methods over the Single-target Regression (the traditional ML method), reducing the predictive error for 5 parameters. Particularly, MTSG obtained the lowest error for phosphorus, total organic carbon and cation exchange capacity. When observing the relative performance of Support Vector Machine with a radial kernel, the prediction of base saturation percentage was improved in 19%. Finally, the proposed method was able to reduce the average error from 0.67 (single-target) to 0.64 analysing all targets, representing a global improvement of 4.48%., 20 pages, 5 figures

Skin condition closely reflects human health, and skin roughness is one of the factors to analyze skin condition. This paper presents a classification algorithm of skin roughness based on improved support vector machine. The improved gray co-occurrence matrix, Tamura texture feature, fractal dimension, Gabor feature and other 24 properties affecting skin roughness were extracted by using human skin samples captured by visible light as data sources. Genetic algorithm was used to optimize the feature space, and the most important feature combinations were selected according to the fitness values. In order to improve the performance of classifier, the improved particle swarm optimization algorithm is used to optimize the penalty factor C and radial kernel function coefficient Gamma of support vector machine. The experiment shows that the model established in this paper has an obvious effect on the classification of skin roughness.

In this paper, we analyse three interior point continuous trajectories for convex programming with general linear constraints. The three continuous trajectories are derived from the primal–dual path-following method, the primal–dual affine scaling method and the central path, respectively. Theoretical properties of the three interior point continuous trajectories are fully studied. The optimality and convergence of all three interior point continuous trajectories are obtained for any interior feasible point under some mild conditions. In particular, with proper choice of some parameters, the convergence for all three interior point continuous trajectories does not require the strict complementarity or the analyticity of the objective function. These results are new in the literature.

By means of the Minkowski-type nonlinear scalarization functional, in this paper, we establish some nonlinear separation theorems via relative algebraic interior and vector closure in a general real linear space, via relative topological interior and topological closure in a real topological linear space and via quasi relative interior and topological closure in a real separated locally convex topological linear space, respectively. These new separation theorems can be applied to study those vector optimization problems with the ordering cones having possibly empty topological interior and even relative topological interior or relative algebraic interior. As their applications, we give some nonlinear scalarization characterizations of the corresponding weak efficient solutions of vector optimization problems. Moreover, we also present some concrete examples to illustrate the main results in some infinite dimensional spaces.

Article focuses on the prediction of bankruptcy of the 850 medium-sized retail business companies in EU from which 48 companies gone bankrupt in 2014 with respect to lag of the used features. From various types of classification models we chose Support vector machines method with linear, polynomial and radial kernels to acquire best results. Pre-processing is enhanced with filter based feature selection like Gain ratio, Chi-square and Relief algorithm to acquire attributes with the best information value. On this basis we deal with random samples of financial data to measure prediction accuracy with the confusion matrices and area under curve values for different kernel types and selected features. From the results it is obvious that with the rising distance to the bankruptcy there drops precision of bankruptcy prediction. The last year (2013) with avaible financial data offers best total prediction accuracy, thus we also infer both the Error I and II types for better recognizance. The 3rd order polynomial kernel offers better accuracy for bankruptcy prediction than linear and radial versions. But in terms of the total accuracy we recommend to use radial kernel without feature selection.

Log-based reservoir characterization is one of the widely used techniques to estimate the reservoir properties and make decisions about future plans for hydrocarbon production. Use of the machine learning tools is becoming a more accessible approach for predictive model development in oil and gas engineering. The objective of this research is to identify and rank the most contributing log variables for estimation of water saturation using the machine learning tools. The multilayer perception artificial neural network (MLP-ANN) and kernel function-based least-squares support vector machine (LS-SVM) techniques are employed to develop predictive models for water saturation. The model can capture the non-linear behaviors and high-dimensional complex relationships among field log data variables. Based on the prediction performance of the models, the Levenberg-Marquardt algorithm-based MLP-ANN and the radial kernel function-based LS-SVM model optimized with coupled simulated annealing optimization technique were found to perform better compared to other models. The MLP-ANN and radial kernel function-based LS-SVM approaches lead to the same feature ranking of predictor variables. It was found that the significance order (higher to lower) of influential log variables are the true resistivity, bulk density, neutron porosity, photoelectric factor, gamma-ray, and sonic travel time based on their relative contribution to the water saturation. The strategy introduced in this study assists to forecast water saturation with a relatively few number of log variables, and thus, reduces the number of necessary logs to run during exploration stage, considerably lowering the exploration costs.

—Metal oxide (MOX) gas detectors based on SnO2 provide low-cost solutions for real-time sensing of complex gas mixtures for indoor ambient monitoring. With high sensitivity under ideal conditions, MOX detectors may have poor longterm response accuracy due to environmental factors (humidity and temperature) along with sensor aging, leading to calibration drifts. Finding a simple and efficient solution to correct such calibration drifts has been the subject of numerous studies but remains an open problem. In this work, we present an efficient approach to MOX calibration using active and transfer sampling techniques coupled with non-linear machine learning algorithms, namely neural networks, extreme gradient boosting (XGBoost) and radial kernel support vector machines (SVM). Applied on the UCI’s HT detectors dataset, the study evaluates methods for active sampling, makes an assessment of suitable neural networks architectures and compares the performance of neural networks, XGBoost and radial kernel SVM to classify gas mixtures (banana and wine odours, clean air) in the presence of humidity and temperature changes. The results show high classification accuracy levels (above 90%) and confirm that active sampling can provide a suitable solution. Index Terms—Neural Networks, Extreme Gradient Boosting, XGBoost, Support Vector Machines, Non-Linear Learning Methods, Machine Learning

As inorganic nitrogen compounds are essential for basic building blocks of life (e.g., nucleotides and amino acids), the role of biological nitrogen-fixation (BNF) is indispensible. All nitrogen fixing microbes rely on the same nitrogenase enzyme for nitrogen reduction, which is in fact an enzyme complex consists of as many as 20 genes. However, the occurrence of six genes viz., nifB, nifD, nifE, nifH, nifK, and nifN has been proposed to be essential for a functional nitrogenase enzyme. Therefore, identification of these genes is important to understand the mechanism of BNF as well as to explore the possibilities for improving BNF from agricultural sustainability point of view. Further, though the computational tools are available for the annotation and phylogenetic analysis of nifH gene sequences alone, to the best of our knowledge no tool is available for the computational prediction of the above mentioned six categories of nitrogen-fixation (nif) genes or proteins. Thus, we proposed an approach, which is first of its kind for the computational identification of nif proteins encoded by the six categories of nif genes. Sequence-derived features were employed to map the input sequences into vectors of numeric observations that were subsequently fed to the support vector machine as input. Two types of classifier were constructed: (i) a binary classifier for classification of nif and non-nitrogen-fixation (non-nif) proteins, and (ii) a multi-class classifier for classification of six categories of nif proteins. Higher accuracies were observed for the combination of composition-transition-distribution (CTD) feature set and radial kernel, as compared to the other feature-kernel combinations. The overall accuracies were observed >90% in both binary and multi-class classifications. The developed approach further achieved >92% accuracy, while evaluated with blind (independent) test datasets. The developed approach also produced higher accuracy in identifying nif proteins, while evaluated using proteome-wide datasets of several species. Furthermore, we established a prediction server nifPred (http://webapp.cabgrid.res.in/nifPred) to assist the scientific community for proteome-wide identification of six categories of nif proteins. Besides, the source code of nifPred is also available at https://github.com/PrabinaMeher/nifPred. The developed web server is expected to supplement the transcriptional profiling and comparative genomics studies for the identification and functional annotation of genes related to BNF.

In this work, we apply stochastic collocation methods with radial kernel basis functions for an uncertainty quantification of the random incompressible two-phase Navier-Stokes equations. Our approach is non-intrusive and we use the existing fluid dynamics solver NaSt3DGPF to solve the incompressible two-phase Navier-Stokes equation for each given realization. We are able to empirically show that the resulting kernel-based stochastic collocation is highly competitive in this setting and even outperforms some other standard methods.

Background Statistical and machine learning applications are increasingly popular in animal breeding and genetics, especially to compute genomic predictions for phenotypes of interest. Noise (errors) in the data may have a negative impact on the accuracy of predictions. The effects of noisy data have been investigated in genome-wide association studies for case–control experiments, and in genomic predictions for binary traits in plants. No studies have been published yet on the impact of noisy data in animal genomics. In this work, the susceptibility to noise of five classification models (Lasso-penalised logistic regression—Lasso, K-nearest neighbours—KNN, random forest—RF, support vector machines with linear—SVML—or radial—SVMR—kernel) was tested. As illustration, the identification of carriers of a recessive mutation in cattle (Bos taurus) was used. A population of 3116 Fleckvieh animals with SNP genotypes on the same chromosome as the mutation locus (BTA 19) was available. The carrier status (0/1 phenotype) was randomly sampled to generate noise. Increasing proportions of noise—up to 20%— were introduced in the data. Results SVMR and Lasso were relatively more robust to noise in the data, with total accuracy still above 0.975 and TPR (true positive rate; accuracy in the minority class) in the range 0.5–0.80 also with 17.5–20% mislabeled observations. The performance of SVML and RF decreased monotonically with increasing noise in the data, while KNN constantly failed to identify mutation carriers (observations in the minority class). The computation time increased with noise in the data, especially for the two support vector machines classifiers. Conclusions This work was the first to assess the impact of phenotyping errors on the accuracy of genomic predictions in animal genetics. The choice of the classification method can influence results in terms of higher or lower susceptibility to noise. In the presented problem, SVM with radial kernel performed relatively well even when the proportion of errors in the data reached 12.5%. Lasso was the second best method, while SVML, RF and KNN were very sensitive to noise. Taking into account both accuracy and computation time, Lasso provided the best combination., BMC Research Notes, 10, ISSN:1756-0500

The objective of this research was to recognize the hand gestures of Arabic Sign Language (ArSL) words using two depth sensors. The researchers developed a model to examine 143 signs gestured by 10 users for 5 ArSL words (the dataset). The sensors captured depth images of the upper human body, from which 235 angles (features) were extracted for each joint and between each pair of bones. The dataset was divided into a training set (109 observations) and a testing set (34 observations). The support vector machine (SVM) classifier was set using different parameters on the gestured words’ dataset to produce four SVM models, with linear kernel (SVMLD and SVMLT) and radial kernel (SVMRD and SVMRT) functions. The overall identification accuracy for the corresponding words in the training set for the SVMLD, SVMLT, SVMRD, and SVMRT models was 88.92%, 88.92%, 90.88%, and 90.884%, respectively. The accuracy from the testing set for SVMLD, SVMLT, SVMRD, and SVMRT was 97.059%, 97.059%, 94.118%, and 97.059%, respectively. Therefore, since the two kernels in the models were close in performance, it is far more efficient to use the less complex model (linear kernel) set with a default parameter.

Helitrons, eukaryotic transposable elements (TEs), were discovered 18 years ago in various genomes. In the Cænorhabditis elegans (C.elegans) genome, helitron sequences have high variability in terms of size by base pairs (bp) varied from 11 to 8965 bp from one sequence to another. These TEs are not uniformly dispersed sequences, and they have the ability to mobilize within a genome by a rolling-circle mechanism. This ability to move and reproduce in genomes enables these elements to play a major role in genomic evolution. In order to follow the evolution, we predicted helitron families (10 classes) in the C.elegans genome using the combination of the features extracted from signals corresponding to DNA sequences and the Support Vector Machine (SVM) classifier. In our classification system, the features extracted from the signals were shown to be efficient to automatically predict helitronic sequences. As a result, the Gaussian radial kernel over 100-fold cross-validation gave the best accuracy rates, ranging from 68% to 97%, with an overall mean score of 83.7%, and we successfully identified the Helitron Y1A class for a specific value of c and gamma, reaching an accuracy rate of 100%. In addition, other notable helitrons (NDNAX2, NDNAX3 Helitron_Y2) were predicted with interesting accuracy rates. Keywords: Helitrons classification, Signal, FCGS coding technique, Machine learning, SVM

For any finite planar point set in general position, an interior point of the set is a point of the set such that it is not on the boundary of the convex hull of the set . For any positive integer , let be the smallest integer such that every finite planar point set with no three collinear points and with at least interior points has a subset for which the interior of the convex hull of the set contains exactly or interior points of the set . In this paper, we prove that .

Simplex algorithms governed by some pivot rule and interior point algorithms are two diverging and competitive types of algorithms for solving linear programming problems. The former moves on the underlying polyhedron, from vertex to adjacent vertex, along edges until an optimal vertex is reached while the latter approaches an optimal point by moving across interior of the polyhedron. In this article, we derive an algorithm that may be regarded as a pivot as well as interior point one. It produces a sequence of interior as well as boundary points, including vertices, until reaching a pair of exact primal and dual optimal solutions. We report encouraging computational results with dense implementation of the algorithm on a set of Netlib test problems.

At this time, the players Forex Trading generally still use the data exchange in the form of a Forex Trading figures from different sources. Thus they only receive or know the data rate of a Forex Trading prevailing at the time just so difficult to analyze or predict exchange rate movements future. Forex players usually use the indicators to enable them to analyze and memperdiksi future value. Indicator is a decision making tool. Trading forex is trading currency of a country, the other country's currency. Trading took place globally between the financial centers of the world with the involvement of the world's major banks as the major transaction. Trading Forex offers profitable investment type with a small capital and high profit, with relatively small capital can earn profits doubled. This is due to the forex trading systems exist leverage which the invested capital will be doubled if the predicted results of buy / sell is accurate, but Trading Forex having high risk level, but by knowing the right time to trade (buy or sell), the losses can be avoided. Traders who invest in the foreign exchange market is expected to have the ability to analyze the circumstances and situations in predicting the difference in currency exchange rates. Forex price movements that form the pattern (curve) up and down greatly assist traders in making decisions. The movement of the curve used as an indicator in the decision to purchase (buy) or sell (sell). This study compares (Comparation) type algorithm kernel on Support Vector Machine (SVM) to predict the movement of the curve in live time trading forex using the data GBPUSD, 1H. Results of research on the study of the results and discussion can be concluded that the Kernel Dot, Kernel Multiquaric, Kernel Neural inappropriately used for data is non-linear in the case of data forex to follow the pattern of trend curves, because curves generated curved linear (straight) and then to type of kernel is the closest curve similar to the curve trend of online forex trading is Anova kernel and kernel radial, a little closer Combination Gaussian kernel, kernel Epachnenikof and to kernel polynomial form a parabolic curve open. key words: Trading Forex, Support Vector Machine, Kernel Anova, Dot Kernel, Kernel Multiquaric, Kernel Neural, Prediction, radial Kernel, Kernel Gaussian Combination, Epachnenikof kernel, polynomial kernel, EURUSD H1

The modeling of cracks and identification of dam behavior changes are difficult issues in dam health monitoring research. In this paper, a time-varying identification model for crack monitoring data is built using support vector regression (SVR) and the Bayesian evidence framework (BEF). First, the SVR method is adopted for better modeling of the nonlinear relationship between the crack opening displacement (COD) and its influencing factors. Second, the BEF approach is applied to determine the optimal SVR modeling parameters, including the penalty coefficient, the loss coefficient, and the width coefficient of the radial kernel function, under the principle that the prediction errors between the monitored and the model forecasted values are as small as possible. Then, considering the predicted COD, the historical maximum COD, and the time-dependent component, forewarning criteria are proposed for identifying the time-varying behavior of cracks and the degree of abnormality of dam health. Finally, an example of modeling and forewarning analysis is presented using two monitoring subsequences from a real structural crack in the Chencun concrete arch-gravity dam. The findings indicate that the proposed time-varying model can provide predicted results that are more accurately nonlinearity fitted and is suitable for use in evaluating the behavior of cracks in dams.

In this paper we propose a crash-start technique for interior point methods applicable to multi-stage stochastic programming problems. The main idea is to generate an initial point for the interior point solver by decomposing the barrier problem associated with the deterministic equivalent at the second stage and using a concatenation of the solutions of the subproblems as a warm-starting point for the complete instance. We analyse this scheme and produce theoretical conditions under which the warm-start iterate is successful. We describe the implementation within the OOPS solver and the results of the numerical tests we performed.

Using advanced machine learning techniques as an alternative to conventional double-entry volume equations, a regression model of the inside-bark volume (dependent variable) for standing Eucalyptus globulus trunks (or main stems) has been built as a function of the following three independent variables: age, height and outside-bark diameter at breast height (DBH). The experimental observed data (age, height, outside-bark DBH and inside-bark volume) for 142 trees ( E. globulus ) were measured and a nonlinear model was built using a data-mining methodology based on support vector machines (SVM) and multilayer perceptron networks (MLP) for regression problems. Coefficients of determination and Furnival’s indices indicate the superiority of the SVM with a radial kernel over the allometric regression models and the MLP.

A new strategy to improve the selection of interior points inside an element of finite element methods is proposed. The novelty is to use the element boundary information in selecting the internal points. The new strategy is compared to the classical strategy in several examples and the main benefits are qualitatively and quantitatively explained.

RNA-sample pooling is sometimes inevitable, but should be avoided in classification tasks like biomarker studies. Our simulation framework investigates a two-class classification study based on gene expression profiles to point out how strong the outcomes of single sample designs differ to those of pooling designs. The results show how the effects of pooling depend on pool size, discriminating pattern, number of informative features and the statistical learning method used (support vector machines with linear and radial kernel, random forest (RF), linear discriminant analysis, powered partial least squares discriminant analysis (PPLS-DA) and partial least squares discriminant analysis (PLS-DA)). As a measure for the pooling effect, we consider prediction error (PE) and the coincidence of important feature sets for classification based on PLS-DA, PPLS-DA and RF. In general, PPLS-DA and PLS-DA show constant PE with increasing pool size and low PE for patterns for which the convex hull of one class is not a cover of the other class. The coincidence of important feature sets is larger for PLS-DA and PPLS-DA as it is for RF. RF shows the best results for patterns in which the convex hull of one class is a cover of the other class, but these depend strongly on the pool size. We complete the PE results with experimental data which we pool artificially. The PE of PPLS-DA and PLS-DA are again least influenced by pooling and are low. Additionally, we show under which assumption the PLS-DA loading weights, as a measure for importance of features regarding classification, are equal for the different designs.

The aim of this work is to introduce the concept of L-fuzzy interior systems and L-fuzzy interior operators. We start by establishing a connection between L-fuzzy interior systems and L-fuzzy interior operators. It is shown that an L-fuzzy interior system is precisely the fuzzy system in opposition to the crisp system, and an L-fuzzy interior operator is a suitable interior operator that has a close relation to an L-fuzzy interior system. It is also shown that there is a Galois correspondence between the category of L-fuzzy interior system spaces and that of L-fuzzy interior spaces.

This paper studies the vector optimization problem of finding weakly efficient points for maps from R n to R m , with respect to the partial order induced by a closed, convex, and pointed cone C ⊂ R m , with nonempty interior. We develop for this problem an extension of the proximal point method for scalar-valued convex optimization problem with a modified convergence sensing condition that allows us to construct an interior proximal method for solving VOP on nonpolyhedral set.

An interior point of a finite planar point set is a point of the set that is not on the boundary of the convex hull of the set. For any integer k ≥ 1, let h(k) be the smallest integer such that every point set in the plane, no three collinear, with at least h(k) interior points, has a subset with k or k + 2 interior points of P. We prove that h(3) = 8.

An H-triangle is a triangle with corners in the set of vertices of a tiling of R^2 by regular hexagons of unit edge. It is known that any H-triangle with exactly 1 interior H-point can have at most 10 H-points on its boundary. In this note we prove that any H-triangle with exactly k interior H-points can have at most 3k+7 boundary H-points. Moreover we form two conjectures dealing with H-polygons.

An interior point of a finite planar point set is a point of the set that is not on the boundary of the convex hull of the set. For any integer k≥1, let g(k) be the smallest integer such that every planar point set in general position with at least g(k) interior points has a convex subset of points with exactly k interior points of P. In this article, we prove that g(3)=9.

An interior point of a finite planar point set is a point of the set that is not on the boundary of the convex hull of the set. For any integer k ≥ 1, let g(k) be the smallest integer such that every set P of points in the plane with no three collinear points and with at least g(k) interior points has a subset containing precisely k interior point of P. We prove that g(k) ≥ 3k for k ≥ 3, which improves the known result that g(k) ≥ 3k − 1 for k ≥ 3.

One commonly finds in applications of smooth radial basis functions (RBFs) that scaling the kernels so they are `flat' leads to smaller discretization errors. However, the direct numerical approach for computing with flat RBFs (RBF-Direct) is severely ill-conditioned. We present an algorithm for bypassing this ill-conditioning that is based on a new method for rational approximation (RA) of vector-valued analytic functions with the property that all components of the vector share the same singularities. This new algorithm (RBF-RA) is more accurate, robust, and easier to implement than the Contour-Pad\'e method, which is similarly based on vector-valued rational approximation. In contrast to the stable RBF-QR and RBF-GA algorithms, which are based on finding a better conditioned base in the same RBF-space, the new algorithm can be used with any type of smooth radial kernel, and it is also applicable to a wider range of tasks (including calculating Hermite type implicit RBF-FD stencils). We present a series of numerical experiments demonstrating the effectiveness of this new method for computing RBF interpolants in the flat regime. We also demonstrate the flexibility of the method by using it to compute implicit RBF-FD formulas in the flat regime and then using these for solving Poisson's equation in a 3D spherical shell., Comment: 27 pages, lots of figures, Matlab code included

In [G.C. Feng, Z.H. Lin, B. Yu, Existence of an interior pathway to a Karush–Kuhn–Tucker point of a nonconvex programming problem, Nonlinear Anal. 32 (1998) 761–768; G.C. Feng, B. Yu, Combined homotopy interior point method for nonlinear programming problems, in: H. Fujita, M. Yamaguti (Eds.), Advances in Numerical Mathematics, Proceedings of the Second Japan–China Seminar on Numerical Mathematics, Lecture Notes in Numerical and Applied Analysis, vol. 14, Kinokuniya, Tokyo, 1995, pp. 9–16; Z.H. Lin, B. Yu, G.C. Feng, A combined homotopy interior point method for convex programming problem, Appl. Math. Comput. 84 (1997) 193–211.], a combined homotopy was constructed for solving non-convex programming and convex programming with weaker conditions, without assuming the logarithmic barrier function to be strictly convex and the solution set to be bounded. It was proven that a smooth interior path from an interior point of the feasible set to a K–K–T point of the problem exists. This shows that combined homotopy interior point methods can solve the problem that commonly used interior point methods cannot solve. However, so far, there is no result on its complexity, even for linear programming. The main difficulty is that the objective function is not monotonically decreasing on the combined homotopy path. In this paper, by taking a piecewise technique, under commonly used conditions, polynomiality of a combined homotopy interior point method is given for convex nonlinear programming.

We consider a homogeneous self-dual interior-point algorithm for solving multistage stochastic linear programs. The algorithm is particularly suitable for the so-called “scenario formulation” of the problem, whose constraint system consists of a large block-diagonal matrix together with a set of sparse nonanticipativity constraints. Due to this structure, the major computational work required by the homogeneous self-dual interior-point method can be split into three steps, each of which is highly decomposable. Numerical results on some randomly generated problems and a multistage production-planning problem are reported.

Using the idea of quasi-coincidence of a fuzzy point with a fuzzy set, the concept of an (@a,@b)-fuzzy interior ideal, which is a generalization of a fuzzy interior ideal, in a semigroup is introduced, and related properties are investigated.

An interior point approach for medium and large non-negative linear least-squares problems is proposed. Global and locally quadratic convergence is shown even if a degenerate solution is approached. Viable approaches for implementation are discussed and numerical results are provided. Copyright © 2006 John Wiley & Sons, Ltd.