scholarly journals Minimax-Optimal Bounds for Detectors Based on Estimated Prior Probabilities

2012 ◽  
Vol 58 (9) ◽  
pp. 6101-6109 ◽  
Author(s):  
Jiantao Jiao ◽  
Lin Zhang ◽  
Robert D. Nowak
Keyword(s):  
Prior Probabilities ◽  
Optimal Bounds

scholarly journals Mathematical Properties of Variable Topological Indices

Symmetry ◽  
2020 ◽  
Vol 13 (1) ◽  
pp. 43
Author(s):  
José M. Sigarreta
Keyword(s):  
Real Number ◽  
Large Class ◽  
Symmetric Functions ◽  
Topological Indices ◽  
Current Interest ◽  
Zagreb Indices ◽  
Mathematical Properties ◽  
Connectivity Indices ◽  
Optimal Bounds ◽  
New Framework

A topic of current interest in the study of topological indices is to find relations between some index and one or several relevant parameters and/or other indices. In this paper we study two general topological indices Aα and Bα, defined for each graph H=(V(H),E(H)) by Aα(H)=∑ij∈E(H)f(di,dj)α and Bα(H)=∑i∈V(H)h(di)α, where di denotes the degree of the vertex i and α is any real number. Many important topological indices can be obtained from Aα and Bα by choosing appropriate symmetric functions and values of α. This new framework provides new tools that allow to obtain in a unified way inequalities involving many different topological indices. In particular, we obtain new optimal bounds on the variable Zagreb indices, the variable sum-connectivity index, the variable geometric-arithmetic index and the variable inverse sum indeg index. Thus, our approach provides both new tools for the study of topological indices and new bounds for a large class of topological indices. We obtain several optimal bounds of Aα (respectively, Bα) involving Aβ (respectively, Bβ). Moreover, we provide several bounds of the variable geometric-arithmetic index in terms of the variable inverse sum indeg index, and two bounds of the variable inverse sum indeg index in terms of the variable second Zagreb and the variable sum-connectivity indices.

scholarly journals Optimal bounds on finding fixed points of contraction mappings

2010 ◽  
Vol 411 (16-18) ◽  
pp. 1742-1749 ◽  
Author(s):  
Ching-Lueh Chang ◽  
Yuh-Dauh Lyuu
Keyword(s):  
Fixed Points ◽  
Contraction Mappings ◽  
Optimal Bounds

scholarly journals Proof of a conjecture of Granath on optimal bounds of the Landau constants

2016 ◽  
Vol 204 ◽  
pp. 17-33 ◽  
Author(s):  
Chun-Ru Zhao ◽  
Wen-Gao Long ◽  
Yu-Qiu Zhao
Keyword(s):  
Optimal Bounds

scholarly journals Data Assimilation with Gaussian Mixture Models Using the Dynamically Orthogonal Field Equations. Part I: Theory and Scheme

2013 ◽  
Vol 141 (6) ◽  
pp. 1737-1760 ◽  
Author(s):  
Thomas Sondergaard ◽  
Pierre F. J. Lermusiaux
Keyword(s):  
Data Assimilation ◽  
Mixture Models ◽  
Gaussian Mixture Models ◽  
Expectation Maximization Algorithm ◽  
Planck Equation ◽  
Information Criterion ◽  
Gaussian Mixture ◽  
Field Equations ◽  
Dynamical Equations ◽  
Prior Probabilities

Abstract This work introduces and derives an efficient, data-driven assimilation scheme, focused on a time-dependent stochastic subspace that respects nonlinear dynamics and captures non-Gaussian statistics as it occurs. The motivation is to obtain a filter that is applicable to realistic geophysical applications, but that also rigorously utilizes the governing dynamical equations with information theory and learning theory for efficient Bayesian data assimilation. Building on the foundations of classical filters, the underlying theory and algorithmic implementation of the new filter are developed and derived. The stochastic Dynamically Orthogonal (DO) field equations and their adaptive stochastic subspace are employed to predict prior probabilities for the full dynamical state, effectively approximating the Fokker–Planck equation. At assimilation times, the DO realizations are fit to semiparametric Gaussian Mixture Models (GMMs) using the Expectation-Maximization algorithm and the Bayesian Information Criterion. Bayes’s law is then efficiently carried out analytically within the evolving stochastic subspace. The resulting GMM-DO filter is illustrated in a very simple example. Variations of the GMM-DO filter are also provided along with comparisons with related schemes.

Prior probabilities modulate cortical surprise responses: A study of event-related potentials

2016 ◽  
Vol 106 ◽  
pp. 78-89 ◽  
Author(s):  
Caroline Seer ◽  
Florian Lange ◽  
Moritz Boos ◽  
Reinhard Dengler ◽  
Bruno Kopp
Keyword(s):  
Event Related Potentials ◽  
Prior Probabilities ◽  
Related Potentials
Sign in / Sign up

Export Citation Format

Share Document