Nearest Neighbor Technique for a Positive Definite Correlation Matrix in Advanced Stressed VAR

2016 ◽  
Author(s):  
Jan W Dash ◽  
Xipei Yang
Keyword(s):  
Correlation Matrix ◽  
Nearest Neighbor ◽  
Positive Definite ◽  
Definite Correlation

scholarly journals Positive Definite Norm Dependent Matrices In Stochastic Modeling

2014 ◽  
Vol 47 (1) ◽  
Author(s):  
Sebastian P. Kuniewski ◽  
Jolanta K. Misiewicz
Keyword(s):  
Stochastic Modeling ◽  
Mathematical Analysis ◽  
Spatial Data ◽  
Correlation Matrix ◽  
Positive Definiteness ◽  
Positive Definite ◽  
Necessary Condition ◽  
The Family ◽  
Definite Correlation

AbstractPositive definite norm dependent matrices are of interest in stochastic modeling of distance/norm dependent phenomena in nature. An example is the application of geostatistics in geographic information systems or mathematical analysis of varied spatial data. Because the positive definiteness is a necessary condition for a matrix to be a valid correlation matrix, it is desirable to give a characterization of the family of the distance/norm dependent functions that form a valid (positive definite) correlation matrix. Thus, the main reason for writing this paper is to give an overview of characterizations of norm dependent real functions and consequently norm dependent matrices, since this information is somehow hidden in the theory of geometry of Banach spaces

scholarly journals The Impact of Emotional Music on Active ROI in Patients with Depression Based on Deep Learning: A Task-State fMRI Study

2019 ◽  
Vol 2019 ◽  
pp. 1-14
Author(s):  
Renzhou Gui ◽  
Tongjie Chen ◽  
Han Nie
Keyword(s):  
Neural Network ◽  
Deep Learning ◽  
Correlation Matrix ◽  
Nearest Neighbor ◽  
Learning Model ◽  
Fmri Data ◽  
Support Vector ◽  
K Nearest Neighbor ◽  
The Impact ◽  
Deep Learning Model

With the continuous development of science, more and more research results have proved that machine learning is capable of diagnosing and studying the major depressive disorder (MDD) in the brain. We propose a deep learning network with multibranch and local residual feedback, for four different types of functional magnetic resonance imaging (fMRI) data produced by depressed patients and control people under the condition of listening to positive- and negative-emotions music. We use the large convolution kernel of the same size as the correlation matrix to match the features and obtain the results of feature matching of 264 regions of interest (ROIs). Firstly, four-dimensional fMRI data are used to generate the two-dimensional correlation matrix of one person’s brain based on ROIs and then processed by the threshold value which is selected according to the characteristics of complex network and small-world network. After that, the deep learning model in this paper is compared with support vector machine (SVM), logistic regression (LR), k-nearest neighbor (kNN), a common deep neural network (DNN), and a deep convolutional neural network (CNN) for classification. Finally, we further calculate the matched ROIs from the intermediate results of our deep learning model which can help related fields further explore the pathogeny of depression patients.

Strictly positive definite correlation functions

2006 ◽  
Author(s):  
John Dolloff ◽  
Brian Lofy ◽  
Alan Sussman ◽  
Charles Taylor
Keyword(s):  
Correlation Functions ◽  
Positive Definite ◽  
Definite Correlation

Theory of Pressure Broadening in an Adiabatic Representation

1974 ◽  
Vol 52 (18) ◽  
pp. 1816-1842 ◽  
Author(s):  
Antoine Royer
Keyword(s):  
Correlation Matrix ◽  
Quantum Interference ◽  
Nearest Neighbor ◽  
Interatomic Interaction ◽  
Projection Operators ◽  
Pressure Broadening ◽  
Spectral Matrix ◽  
Dipole Moment Operator ◽  
Adiabatic Representation ◽  
Moment Operator

The theory of pressure broadening by foreign atoms is formulated within the framework of an adiabatic representation (which we distinguish from the adiabatic approximation). This allows us to treat all the electrons in the gas as indistinguishable, and thus include the possibility of electron exchange between atoms; this effect, which is responsible for much of the interatomic interaction, is neglected in all previous theories, apart from the adiabatic and 'nearest neighbor' theories which are of limited applicability. By means of projection operators, we define a spectral matrix, whose dimension is equal to the number of distinct frequencies characteristic of the isolated radiator. The spectrum is equal to the sum of all the elements of the spectral matrix; the diagonal elements correspond to the different lines of the spectrum, and the off diagonal elements represent quantum interference between overlapping lines. The Fourier transform of the spectral matrix is the correlation matrix, whose elements time correlate components of the dipole moment operator responsible for different lines of the spectrum. The time evolution of the zero perturber correlation matrix is given by eiΩτ, where Ω is a diagonal matrix whose elements are the different frequencies characteristic of the radiator. The perturbing gas causes the 'reduced Liouvillian' Ω to acquire a time dependent or frequency dependent non-Hermitian nondiagonal part. To obtain low density approximations, we treat that non-Hermitian 'perturbation' to first order in the gas density.

Observation of Superlattice Dislocations on Cube Planes in Ni3Al

1973 ◽  
Vol 31 ◽  
pp. 174-175 ◽  
Author(s):  
J. M. Oblak ◽  
W. H. Rand
Keyword(s):  
Nearest Neighbor ◽  
Antiphase Boundary ◽  
Nearest Neighbors ◽  
High Energy ◽  
Cross Slip ◽  
Octahedral Plane ◽  
Trapping Mechanism ◽  
Slip Traces

The energy of an a/2 <110> shear antiphase. boundary in the Ll2 expected to be at a minimum on {100} cube planes because here strue ture is there is no violation of nearest-neighbor order. The latter however does involve the disruption of second nearest neighbors. It has been suggested that cross slip of paired a/2 <110> dislocations from octahedral onto cube planes is an important dislocation trapping mechanism in Ni3Al; furthermore, slip traces consistent with cube slip are observed above 920°K.Due to the high energy of the {111} antiphase boundary (> 200 mJ/m2), paired a/2 <110> dislocations are tightly constricted on the octahedral plane and cannot be individually resolved.

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