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1012. An embedding theorem for a weighted space of Sobolev type and correct solvability of the Sturm-Liouville equation
- Creator:
- Chernyavskaya, Nina A. and Shuster, Leonid A.
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- Sobolev space, embedding theorem, and Sturm-Liouville equation
- Language:
- English
- Description:
- We consider the weighted space $W_1^{(2)}(\mathbb R,q)$ of Sobolev type $$ W_1^{(2)}(\mathbb R,q)=\left \{y\in A_{\rm loc}^{(1)}(\mathbb R)\colon \|y''\|_{L_1(\mathbb R)}+\|qy\|_{L_1(\mathbb R)}<\infty \right \} $$ and the equation $$ - y''(x)+q(x)y(x)=f(x),\quad x\in \mathbb R. \leqno (1) $$ Here $f\in L_1(\mathbb R)$ and $0\le q\in L_1^{\rm loc}(\mathbb R).$ \endgraf We prove the following: \item {1)} The problems of embedding $W_1^{(2)}(\mathbb R,q)\hookrightarrow L_1(\mathbb R)$ and of correct solvability of (1) in $L_1(\mathbb R) $ are equivalent; \item {2)} an embedding $W_1^{(2)}(\mathbb R,q)\hookrightarrow L_1(\mathbb R) $ exists if and only if $$\exists a>0\colon \inf _{x\in \mathbb R}\int _{x-a}^{x+a} q(t) {\rm d} t>0.$$.
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public
1013. An empirical study of dimensionality reduction in support vector machine
- Creator:
- Cao, L. J., JingQing , Zhang, Zongwu, Cai, and Guan, Liam Kian
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- Support vector machines, principal component analysis, kernel principal component analysis, and independent component analysis
- Language:
- English
- Description:
- Recently, the the support vector machine (SVM) has become a popular tool in time series forecasting. In developing a successful SVM forecaster, the first step is feature extraction. This paper proposes the applications of principal component analysis (PCA), kernel principal component analysis (KPCA) and independent component analysis (ICA) to SVM for feature extraction. The PCA linearly transforms the original inputs into new uncorrelated features. The KPCA is a nonlinear PCA developed by using the kernel method. In ICA, the original inputs are linearly transformed into features which are mutually statistically independent. By examining the sunspot data, Santa Fe data set A and five real futures contracts, the experiment shows that SVM by feature extraction using PCA, KPCA or ICA can perform better than that without feature extraction. Furthermore, among the three methods, there is the best performance in the KPCA feature extraction, followed by the ICA feature extraction.
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public
1014. An empirical study of feature selection in support vector machines
- Creator:
- Cao, L. J. and Jingqing , Zhang
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- Feature selection, support vector machines, structural risk minimization principle, saliency analysis, and genetic algorithm
- Language:
- English
- Description:
- Recently, a support vector machine (SVM) has been receiving increasing attention in the field of regression estimation due to its remarkable characteristics such as good generalization performance, the absence of local minima and sparse representation of the solution. However, within the SVMs framework, there are very few established approaches for identifying important features. Selecting significant features from all candidate features is the first step in regression estimation, and this procedure can improve the network performance, reduce the network complexity, and speed up the training of the network. This paper investigates the use of saliency analysis (SA) and genetic algorithm (GA) in SVMs for selecting important features in the context of regression estimation. The SA measures the importance of features by evaluating the sensitivity of the network output with respect to the feature input. The derivation of the sensitivity of the network output to the feature input in terms of the partial derivative in SVMs is presented, and a systematic approach to remove irrelevant features based on the sensitivity is developed. GA is an efficient search method based on the mechanics of natural selection and population genetics. A simple GA is used where all features are mapped into binary chromosomes with a bit "1" representing the inclusion of the feature and a bit of "0" representing the absence of the feature. The performances of SA and GA are tested using two simulated non-linear time series and five real financial time series. The experiments show that with the simulated data, GA and SA detect the same true feature set from the redundant feature set, and the method of SA is also insensitive to the kernel function selection. With the real financial data, GA and SA select different subsets of the features. Both selected feature sets achieve higher generation performance in SVMs than that of the full feature set. In addition, the generation performance between the selected feature sets of GA and SA is similar. All the results demonstrate that that both SA and GA are effective in the SVMs for identifying important features.
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public
1015. An endogenous human resources selection model based on linguistic assessments
- Creator:
- de Andrés, Rocío and García-Lapresta, José Luis
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- Management endogenous personnel selection, multi-criteria decision making, and aggregation operators
- Language:
- English
- Description:
- This paper proposes an endogenous human resources selection process by using linguistic information from a competency management perspective. We consider different sets of appraisers taking part in the evaluation process, having a different knowledge about the candidates that are being evaluated. Then, appraisers can express their assessments in different linguistic domains according to their knowledge. The proposed method converts each linguistic label into a fuzzy set on a common domain. Candidates are ranked by using different aggregation operators in order to allow the management team to make a final decision.
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public
1016. An EnKF-based scheme for snow multivariable data assimilation at an Alpine site
- Creator:
- Piazzi, Gaia, Campo, Lorenzo, Gabellani, Simone, Castelli, Fabio, Cremonese, Edoardo, di Cella, Umberto Morra, Stevenin, Hervé, and Ratto, Sara Maria
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- snow modeling, energy-balance model, data assimilation, and Ensemble Kalman Filter
- Language:
- Slovak
- Description:
- The knowledge of snowpack dynamics is of critical importance to several real-time applications especially in mountain basins, such as agricultural production, water resource management, flood prevention, hydropower generation. Since simulations are affected by model biases and forcing data uncertainty, an increasing interest focuses on the assimilation of snow-related observations with the purpose of enhancing predictions on snowpack state. The study aims at investigating the effectiveness of snow multivariable data assimilation (DA) at an Alpine site. The system consists of a snow energy-balance model strengthened by a multivariable DA system. An Ensemble Kalman Filter (EnKF) scheme allows assimilating ground-based and remotely sensed snow observations in order to improve the model simulations. This research aims to investigate and discuss: (1) the limitations and constraints in implementing a multivariate EnKF scheme in the framework of snow modelling, and (2) its performance in consistently updating the snowpack state. The performance of the multivariable DA is shown for the study case of Torgnon station (Aosta Valley, Italy) in the period June 2012 – December 2013. The results of several experiments are discussed with the aim of analyzing system sensitivity to the DA frequency, the ensemble size, and the impact of assimilating different observations.
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public
1017. An entire function sharing a polynomial with its linear differential polynomial
- Creator:
- Kaish, Imrul and Rahaman, Md. Majibur
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- entire function, differential polynomial, and derivative; sharing
- Language:
- English
- Description:
- We study the uniqueness of entire functions which share a polynomial with their linear differential polynomials.
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public
1018. An evaluation of velocity estimates with a correlated noise: case study of IGS ITRF2014 European stations
- Creator:
- Klos, Anna and Bogusz, Janusz
- Format:
- print, bez média, and svazek
- Type:
- article, články, journal articles, model:article, and TEXT
- Subject:
- Geologie. Meteorologie. Klimatologie, GPS sítě, GPS netwoks, ITRF2014, noise analysis, velocity, 7, and 551
- Language:
- English
- Description:
- The velocities of the Global Positioning System (GPS) stations are widely employed for numerous geodynamical studies. The aim of this paper is to investigate the reliability of station velocities and to draw reader’s attention that for proper estimates of velocity, we need to consider the optimal character of noise. We focus on a set of 115 European GPS stations which contributed to the newest release of the International Terrestrial Reference Frame (ITRF), i.e. ITRF2014. Based on stacked Power Spectral Densities (PSDs), we show that amplitudes o f seasonal signals are significant for nine harmonics of tropical year (365.25 days) and two harmonics of draconitic year (351.60 days). The amplitudes of tropical annual signal fall between 0.1-8.4 mm and are much higher for vertical component than for horizontal. Draconitic annual signal reaches the maximum amplitudes of 1.2 and 0.9 mm for North and East, respectively, whereas is slightly higher for the Up component with a maximum of 3.1 mm. We performed a noise analysis with Maximum Like lihood Estimation (MLE) and found that stations in Central and Northern Europe are characterized by spectral index between flicker and random-walk noise, while stations in Southern and Western Europe: between white and flicker noise. Both amplitudes and spectral indices of power-law noise show a spatial correlation for Up component. We compared the uncertainties of velocities derived in this study with a combination of power-law and white noises to the ones offici ally released in the ITRF2014 with a pure white noise. A ratio of the two estimates is larger than 10 for 13 % and 30 % of stations in horizontal and vertical direction, respectively with medians of 6 and 7. The large differences support the fact that at the velocity determination the proper noise characteristic should be taken into account to avoid any mislead interpretation., Anna Klos and Janusz Bogusz., and Obsahuje bibliografické odkazy
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public
1019. An evolutionary RBF network configuration using adaptive width adjustment based on vaccination
- Creator:
- Zang, Xiaogang, Gong, Xinbao, Ling, Xiaofeng, Chang, Cheng , and Tang , Bin
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- Computational learning theory, evolutionary computation, neural networks, RBF networks, and vaccination operation
- Language:
- English
- Description:
- In this paper, a mechanism of adaptive width adjustment based on immunological vaccination is proposed for the evolutionary training of RBF neural networks. Inspired by the vaccination process of the natural immune system, the algorithm implements an individual-orientated adaptation of the width in training stages to optimize the potential solutions, therefore reinforces the evolutionary capability and efficiency. A two-layer genotype-coding scheme, which enables a simultaneous evolution of network structure and parameters, is presented to achieve a compact and consistent-in-form solution. The proposed learning strategy is tested on several benchmark problems and results demonstrate promise.
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public
1020. An evolutionary simulation of modularity emergence of genotype-phenotype mappings
- Creator:
- Kvasnička, Vladimír
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- modularity, genotype-phenotype mapping, evolutionary simulation, evolutionary algorithms, and evolvability
- Language:
- English
- Description:
- A novel rriethod that allows us to study the emergence of modularity for genotype-phenotype mapping in the course of Darwinian evolution is described. The evolutionary method used is based on cornposite chromosomes with two parts; One is a binary genotype whereas the other corresponds to the mapping of genes onto phenotype characters. For such generalized chromosomes the modularity is determined by the following intuitive way: The genes are divided into two subgroups; simultaneously with this decomposition also an accompanied decomposition of the set of phenotype characters is defined. We expect that for chromosomes with rnodular structures the genes frorn one group are rnapped onto characters from the respective group, an appearance of “crosslink” mappings is rnaximally suppressed. A fundamental question for the whole evolutionary biology (and also for evolutioriary algorithms and connectionist cognitive science) is the nature of mechanism of evolutionary emergence of modular structures. An idea of effective fitness is used in the presented explanatory simulations. It is based on the rnetaphor of Hinton and Nowlan theory of the Baldwin eífect, and was ušed as an effective idea for generalization of evolutionary algorithms. The effective fitness reflects not only a static concept of the phenotype, but also its ability to be adapted (learned) within a neighborhood of the respective chromosome. The chromosomes determined in the presented paper inay be understood as objects with the type of plasticity. The rnetaphor of the Baldwin effect (or effective fitness) applied to evolutionary algorithms offers an evolutionary tool that is potentially able to produce the emergence of modularity.
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public