Controlling the Chaos of the CMMI Continuous Representation

2006 ◽  
pp. 2-2
Author(s):  
Jan Jaap Cannegieter
Keyword(s):  
Continuous Representation

scholarly journals Canonical transformations for fermions in superanalysis

2014 ◽  
Vol 26 (06) ◽  
pp. 1450009
Author(s):  
Joachim Kupsch
Keyword(s):  
Infinite Number ◽  
Orthogonal Group ◽  
Degrees Of Freedom ◽  
Fock Space ◽  
Continuous Representation ◽  
Canonical Transformations ◽  
Module Extension ◽  
Bogoliubov Transformations

Canonical transformations (Bogoliubov transformations) for fermions with an infinite number of degrees of freedom are studied within a calculus of superanalysis. A continuous representation of the orthogonal group is constructed on a Grassmann module extension of the Fock space. The pull-back of these operators to the Fock space yields a unitary ray representation of the group that implements the Bogoliubov transformations.

scholarly journals A 4D continuous representation of myocardial velocity fields from tissue phase mapping magnetic resonance imaging

PLoS ONE ◽  
2021 ◽  
Vol 16 (3) ◽  
pp. e0247826
Author(s):  
Bård A. Bendiksen ◽  
Gary McGinley ◽  
Ivar Sjaastad ◽  
Lili Zhang ◽  
Emil K. S. Espe
Keyword(s):  
Velocity Field ◽  
Velocity Fields ◽  
Tissue Phase Mapping ◽  
Continuous Representation ◽  
Resonance Imaging ◽  
Limits Of Agreement ◽  
B Splines ◽  
End Point ◽  
Tissue Phase ◽  
Linear B

Myocardial velocities carry important diagnostic information in a range of cardiac diseases, and play an important role in diagnosing and grading left ventricular diastolic dysfunction. Tissue Phase Mapping (TPM) Magnetic Resonance Imaging (MRI) enables discrete sampling of the myocardium’s underlying smooth and continuous velocity field. This paper presents a post-processing framework for constructing a spatially and temporally smooth and continuous representation of the myocardium’s velocity field from TPM data. In the proposed scheme, the velocity field is represented through either linear or cubic B-spline basis functions. The framework facilitates both interpolation and noise reducing approximation. As a proof-of-concept, the framework was evaluated using artificially noisy (i.e., synthetic) velocity fields created by adding different levels of noise to an original TPM data. The framework’s ability to restore the original velocity field was investigated using Bland-Altman statistics. Moreover, we calculated myocardial material point trajectories through temporal integration of the original and synthetic fields. The effect of noise reduction on the calculated trajectories was investigated by assessing the distance between the start and end position of material points after one complete cardiac cycle (end point error). We found that the Bland-Altman limits of agreement between the original and the synthetic velocity fields were reduced after application of the framework. Furthermore, the integrated trajectories exhibited consistently lower end point error. These results suggest that the proposed method generates a realistic continuous representation of myocardial velocity fields from noisy and discrete TPM data. Linear B-splines resulted in narrower limits of agreement between the original and synthetic fields, compared to Cubic B-splines. The end point errors were also consistently lower for Linear B-splines than for cubic. Linear B-splines therefore appear to be more suitable for TPM data.

scholarly journals Linearization and discretization risks in knowledge management

2019 ◽  
Vol 13 (1) ◽  
pp. 448-456
Author(s):  
Constantin Bratianu
Keyword(s):  
Decision Making ◽  
Knowledge Management ◽  
Continuous Representation ◽  
Negative Consequences ◽  
Complex Activity ◽  
Managerial Decision ◽  
Managerial Decision Making ◽  
Discretization Methods ◽  
Intangible Resources ◽  
Discretized Systems

Abstract The purpose of this paper is to analyze the limitations induced in Knowledge Management by the processes of linearization and discretization, which happen frequently in decision-making. Linearization is a result of applying linear thinking models in decision-making, regardless of the complexity of knowledge management phenomena. Knowledge and all the other intangible resources are nonlinear entities and they should be evaluated with nonlinear metrics. However, in many situations managers use simple solutions based on linear thinking models and get large errors in their decision-making, with significant negative consequences in management. Also, linear thinking model is dominant in legislation, which may lead to significant errors in managerial decision-making. Discretization is a process in which an entity with a continuous representation, like a knowledge field, is transformed into a piecewise entity to be handled more easily. Also, social media uses discretized systems for different evaluations which should be interpreted accordingly. For instance, counting the number of “like” on Facebook for a certain message or image may lead to the conclusion that friendship is proportional with the number of “friends”, which might not be in concordance with reality. Knowledge management is a complex activity dealing with knowledge, which means nonlinear entities. Using linear thinking models and discretization methods in evaluations and decision-making may lead to significant errors and negative consequences.

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