Relativistic extended thermodynamics: General assumptions and mathematical procedure

1989 ◽  
pp. 269-277 ◽  
Author(s):  
Tommaso Ruggeri
Keyword(s):  
Extended Thermodynamics ◽  
Mathematical Procedure

scholarly journals Transporting Deformations of Face Emotions in the Shape Spaces: A Comparison of Different Approaches

2021 ◽  
Author(s):  
Paolo Piras ◽  
Valerio Varano ◽  
Maxime Louis ◽  
Antonio Profico ◽  
Stanley Durrleman ◽  
...  
Keyword(s):  
Computer Vision ◽  
Shape Change ◽  
Surface Matching ◽  
Human Face ◽  
Matching Algorithm ◽  
Mathematical Procedure ◽  
Shape Spaces ◽  
Diffeomorphic Deformation ◽  
Common Application ◽  
Scientific Fields

AbstractStudying the changes of shape is a common concern in many scientific fields. We address here two problems: (1) quantifying the deformation between two given shapes and (2) transporting this deformation to morph a third shape. These operations can be done with or without point correspondence, depending on the availability of a surface matching algorithm, and on the type of mathematical procedure adopted. In computer vision, the re-targeting of emotions mapped on faces is a common application. We contrast here four different methods used for transporting the deformation toward a target once it was estimated upon the matching of two shapes. These methods come from very different fields such as computational anatomy, computer vision and biology. We used the large diffeomorphic deformation metric mapping and thin plate spline, in order to estimate deformations in a deformational trajectory of a human face experiencing different emotions. Then we use naive transport (NT), linear shift (LS), direct transport (DT) and fanning scheme (FS) to transport the estimated deformations toward four alien faces constituted by 240 homologous points and identifying a triangulation structure of 416 triangles. We used both local and global criteria for evaluating the performance of the 4 methods, e.g., the maintenance of the original deformation. We found DT, LS and FS very effective in recovering the original deformation while NT fails under several aspects in transporting the shape change. As the best method may differ depending on the application, we recommend carefully testing different methods in order to choose the best one for any specific application.

scholarly journals Validation of a mathematical procedure for computer analysis of flow cytometric DNA data in human tumors

Cytometry ◽  
1985 ◽  
Vol 6 (1) ◽  
pp. 31-36 ◽  
Author(s):  
G. Del Bino ◽  
C. Bruni ◽  
G. Koch ◽  
G. Mazzini ◽  
A. Costa ◽  
...  
Keyword(s):  
Computer Analysis ◽  
Human Tumors ◽  
Mathematical Procedure ◽  
Flow Cytometric

An overview of entropy principle

2021 ◽  
pp. 1-6
Author(s):  
I-Shih Liu
Keyword(s):  
Mathematical Formulation ◽  
Irreversible Thermodynamics ◽  
Extended Thermodynamics ◽  
Basic Assumptions ◽  
Entropy Principle ◽  
Linear Irreversible Thermodynamics

A brief overview of the development from classical linear irreversible thermodynamics to the modern rational thermodynamics with Coleman–Noll and Müller–Liu procedures is presented, emphasizing the basic assumptions and formulation details. The major arguments concerned are the improvement of physical assumptions and mathematical formulation differences. Extended thermodynamics is also briefly commented.

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