On Bogomolny-Schmit conjecture

Bogomolny and Schmit proposed that the critical edge percolation on the square lattice is a good model for the nodal domains of a random plane wave. Based on this they made a conjecture about the number of nodal domains. Recent computer experiments showed that the mean number of clusters per vertex and the mean number of nodal domains per unit area are very close but different. Since the original argument was mostly supported by numerics, it was believed that the percolation model is wrong. In this paper we give some numerical evidence in favour of the percolation model.Comment: 6 pages, 2 figures. To be published in Journal of Physics A: Mathematical and Theoretica

Analisis Pengaruh Kualitas Pelayanan Terhadap Kepuasan Pelanggan Pada Perusahaan Daerah Air Minum (PDAM) Kabupaten Flores Timur

PDAM is one of the agencies that often gets complaints from customers regarding the quality of service. These include complaints about the handling of complaints that the response was slow, slow handling of the pipe leak. This study aims to analyze (1) the extent to which the influence of service quality (reliability, responsiveness, assurance, empathy, and tangible) to customer satisfaction in the PDAM Kabupaten Flores Timur together, and (2) the extent to which the influence of service quality (reliability, responsiveness, assurance, empathy, and tangible) to customer satisfaction in the PDAM Kabupaten Flores Timur partially. The method used in this research is descriptive quantitative research methods. The independent variable in this study is the quality of service, which consists of reliability (X1), responsiveness (X2), assurance (X3), empathy (X4), and tangible (X5). Meanwhile, the dependent variable in this study is customer satisfaction (Y). As for the population in this study is the PDAM Kabupaten Flores Timur customers. Specified number of respondents of 100 respondents. The samples using nonprobability sampling, is by purposive sampling.. The data was collected through questionnaires and observations. Analysis of data using multiple regression analysis. The results showed that (1) Taken together or simultaneously all the variables, namely the reliability factor (reliability) (X1), factor responsiveness (responsiveness) (X2), the belief factor (assurance) (X3), factor empathy (empathy) ( X4), and intangible factors (tangible) (X5) and a significant positive effect on customer satisfaction PDAM Kabupaten Flores Timur, and (2) Partially reliability factor (reliability) (X1), security (assurance) (X3), and intangible factors (tangible) (X5) and a significant positive effect on customer satisfaction PDAM Kabupaten Flores Timur. In contrast, factor responsiveness (responsiveness) (X2) and factor empathy (empathy) (X4) in this model and no significant positive effect on customer satisfaction PDAM Kabupaten Flores Timur

On the Convergence of Stochastic Gradient Descent for Linear Inverse Problems in Banach Spaces

In this work we consider stochastic gradient descent (SGD) for solving linear inverse problems in Banach spaces. SGD and its variants have been established as one of the most successful optimization methods in machine learning, imaging, and signal processing, to name a few. At each iteration SGD uses a single datum, or a small subset of data, resulting in highly scalable methods that are very attractive for large-scale inverse problems. Nonetheless, the theoretical analysis of SGD-based approaches for inverse problems has thus far been largely limited to Euclidean and Hilbert spaces. In this work we present a novel convergence analysis of SGD for linear inverse problems in general Banach spaces: we show the almost sure convergence of the iterates to the minimum norm solution and establish the regularizing property for suitable a priori stopping criteria. Numerical results are also presented to illustrate features of the approach

On an unsupervised method for parameter selection for the elastic net

Despite recent advances in regularization theory, the issue of parameter selection still remains a challenge for most applications. In a recent work the framework of statistical learning was used to approximate the optimal Tikhonov regularization parameter from noisy data. In this work, we improve their results and extend the analysis to the elastic net regularization. Furthermore, we design a data-driven, automated algorithm for the computation of an approximate regularization parameter. Our analysis combines statistical learning theory with insights from regularization theory. We compare our approach with state-of-the-art parameter selection criteria and show that it has superior accuracy

Estimating covariance and precision matrices along subspaces

We study the accuracy of estimating the covariance and the precision matrix of a D-variate sub-Gaussian distribution along a prescribed subspace or direction using the finite sample covariance. Our results show that the estimation accuracy depends almost exclusively on the components of the distribution that correspond to desired subspaces or directions. This is relevant and important for problems where the behavior of data along a lower-dimensional space is of specific interest, such as dimension reduction or structured regression problems. We also show that estimation of precision matrices is almost independent of the condition number of the covariance matrix. The presented applications include direction-sensitive eigenspace perturbation bounds, relative bounds for the smallest eigenvalue, and the estimation of the single-index model. For the latter, a new estimator, derived from the analysis, with strong theoretical guarantees and superior numerical performance is proposed

Development of Early Warning Systems in Croatian Companies

The challenge to predict the direction of market requirements is an increasingly pronounced challenge of today\u27s management structures, i.e., how to make timely decisions that ensure the sustainability of the business. In predicting when and where the potential for success will arise or what the sources of threats will be, it is essential to properly implement and continuously use the early warning system by monitoring indicators from the environment. This paper presents a theoretical and practical contribution to understanding the importance of early warning systems in Croatian companies operating in international markets. The introduction includes a discussion on current business conditions, and then the term "early warning system" is conceptually discussed. The research part of the paper presents the results of empirical research on the perception of respondents on the level of development of early warning systems in their companies operating in the international market according to the legal form, size, headquarters, and ownership of the company. The established attitude of the respondents was that the level of development of the early warning system is low, i.e., that they are used primarily by large foreign-owned companies based in more economically developed counties