Search results for "Theorem"
showing 10 items of 1250 documents
Splineapproximationen von beliebigem Defekt zur numerischen L�sung gew�hnlicher Differentialgleichungen. Teil III
1980
In the first part [5] a general procedure is presented to obtain polynomial spline approximations of arbitrary defect for the solution of the initial value problem of ordinary differential equations. The essential result is a divergence theorem in dependence of the polynomial degree and the defect of the spline functions. In this second part the convergent procedures are investigated and two convergence theorems are proved. Furthermore the question is treated, whether the convergent procedures are appropriate for the numerical solution of stiff equations. The paper is finished by a convergence theorem for a procedure producing spline approximations in a natural way by the discrete approxima…
BELM: Bayesian Extreme Learning Machine
2011
The theory of extreme learning machine (ELM) has become very popular on the last few years. ELM is a new approach for learning the parameters of the hidden layers of a multilayer neural network (as the multilayer perceptron or the radial basis function neural network). Its main advantage is the lower computational cost, which is especially relevant when dealing with many patterns defined in a high-dimensional space. This brief proposes a bayesian approach to ELM, which presents some advantages over other approaches: it allows the introduction of a priori knowledge; obtains the confidence intervals (CIs) without the need of applying methods that are computationally intensive, e.g., bootstrap…
Complex group algebras of finite groups: Brauer’s Problem 1
2005
Brauer’s Problem 1 asks the following: what are the possible complex group algebras of finite groups? It seems that with the present knowledge of representation theory it is not possible to settle this question. The goal of this paper is to announce a partial solution to this problem. We conjecture that if the complex group algebra of a finite group does not have more than a fixed number m m of isomorphic summands, then its dimension is bounded in terms of m m . We prove that this is true for every finite group if it is true for the symmetric groups.
A Bayesian unified framework for risk estimation and cluster identification in small area health data analysis.
2020
Many statistical models have been proposed to analyse small area disease data with the aim of describing spatial variation in disease risk. In this paper, we propose a Bayesian hierarchical model that simultaneously allows for risk estimation and cluster identification. Our model formulation assumes that there is an unknown number of risk classes and small areas are assigned to a risk class by means of independent allocation variables. Therefore, areas within each cluster are assumed to share a common risk but they may be geographically separated. The posterior distribution of the parameter representing the number of risk classes is estimated using a novel procedure that combines its prior …
On Contextuality in Behavioral Data
2015
Dzhafarov, Zhang, and Kujala (Phil. Trans. Roy. Soc. A 374, 20150099) reviewed several behavioral data sets imitating the formal design of the quantum-mechanical contextuality experiments. The conclusion was that none of these data sets exhibited contextuality if understood in the generalized sense proposed in Dzhafarov, Kujala, and Larsson (Found. Phys. 7, 762-782, 2015), while the traditional definition of contextuality does not apply to these data because they violate the condition of consistent connectedness (also known as marginal selectivity, no-signaling condition, no-disturbance principle, etc.). In this paper we clarify the relationship between (in)consistent connectedness and (non…
A new Adaptive and Progressive Image Transmission Approach using Function Superpositions
2010
International audience; We present a novel approach to adaptive and progressive image transmission, based on the decomposition of an image into compositions and superpositions of monovariate functions. The monovariate functions are iteratively constructed and transmitted, one after the other, to progressively reconstruct the original image: the progressive transmission is performed directly in the 1D space of the monovariate functions and independently of any statistical properties of the image. Each monovariate function contains only a fraction of the pixels of the image. Each new transmitted monovariate function adds data to the previously transmitted monovariate functions. After each tra…
A Comparative Study to Analyze the Performance of Advanced Pattern Recognition Algorithms for Multi-Class Classification
2021
This study aims to implement the following four advanced pattern recognition algorithms, such as “optimal Bayesian classifier,” “anti-Bayesian classifier,” “decision trees (DTs),” and “dependence trees (DepTs)” on both artificial and real datasets for multi-class classification. Then, we calculated the performance of individual algorithms on both real and artificial data for comparison. In Sect. 1, a brief introduction is given about the study. In the second section, the different types of datasets used in this study are discussed. In the third section, we compared the classification accuracies of Bayesian and anti-Bayesian methods for both the artificial and real-life datasets. In the four…
Statistical classification and proportion estimation - an application to a macroinvertebrate image database
2010
We apply and compare a random Bayes forest classifier and three traditional classification methods to a dataset of complex benthic macroinvertebrate images of known taxonomical identity. Since in biomonitoring changes in benthic macroinvertebrate taxa proportions correspond to changes in water quality, their correct estimation is pivotal. As classification errors are passed on to the allocated proportions, we explore a correction method known as a confusion matrix correction. Classification methods were compared using the misclassification error and the χ2 distance measures of the true proportions to the allocated and to the corrected proportions. Using low misclassification error and small…
Evaluation of an Optical Energy Harvester for SHM Application
2019
Abstract In this paper a preliminary study on an array configuration of rectified optical nanoantennas for energy harvesting application is proposed. Currently, the major impediments for the use of the rectified optical nanoantenna known as rectenna are the relatively low conversion efficiency and low power transfer to the load, both of them caused mainly by the mismatch between the impedance of the rectifier (several kilo ohms) and that of the antenna (hundreds of ohm). For this reason, the design of the array represents a crucial point to obtain the maximum energy transfer from the rectenna to the load, represented as a typical DC/DC boost power converter, and modeled by an equivalent inp…
Direct method for calculating temperature-dependent transport properties
2015
We show how temperature-induced disorder can be combined in a direct way with first-principles scattering theory to study diffusive transport in real materials. Excellent (good) agreement with experiment is found for the resistivity of Cu, Pd, Pt (and Fe) when lattice (and spin) disorder are calculated from first principles. For Fe, the agreement with experiment is limited by how well the magnetization (of itinerant ferromagnets) can be calculated as a function of temperature. By introducing a simple Debye-like model of spin disorder parameterized to reproduce the experimental magnetization, the temperature dependence of the average resistivity, the anisotropic magnetoresistance and the spi…