scholarly journals A geometrical method for consensus building in GDM with incomplete heterogeneous preference information

2021 ◽  
Vol 105 ◽  
pp. 107224
Author(s):  
Gang Kou ◽  
Yi Peng ◽  
Xiangrui Chao ◽  
Enrique Herrera-Viedma ◽  
Fawaz E. Alsaadi
Keyword(s):  
Consensus Building ◽  
Geometrical Method ◽  
Preference Information ◽  
Heterogeneous Preference

CHAOTIC DYNAMICS FOR MAPS IN ONE AND TWO DIMENSIONS: A GEOMETRICAL METHOD AND APPLICATIONS TO ECONOMICS

2009 ◽  
Vol 19 (10) ◽  
pp. 3283-3309 ◽  
Author(s):  
ALFREDO MEDIO ◽  
MARINA PIREDDU ◽  
FABIO ZANOLIN
Keyword(s):  
Dynamical Systems ◽  
Discrete Time ◽  
Chaotic Dynamics ◽  
Economic Models ◽  
Two Dimensions ◽  
Geometrical Method ◽  
Mathematical Ideas ◽  
Definition Of ◽  
Applications To Economics ◽  
Discrete Time Dynamical Systems

This article describes a method — called here "the method of Stretching Along the Paths" (SAP) — to prove the existence of chaotic sets in discrete-time dynamical systems. The method of SAP, although mathematically rigorous, is based on some elementary geometrical considerations and is relatively easy to apply to models arising in applications. The paper provides a description of the basic mathematical ideas behind the method, as well as three applications to economic models. Incidentally, the paper also discusses some questions concerning the definition of chaos and some problems arising from economic models in which the dynamics are defined only implicitly.

Cell behaviour in a polygonal cell sheet*

Development ◽  
1984 ◽  
Vol 83 (Supplement) ◽  
pp. 313-327
Author(s):  
H. Honda ◽  
R. Kodama ◽  
T. Takeuchi ◽  
H. Yamanaka ◽  
K. Watanabe ◽  
...  
Keyword(s):  
Cell Sheet ◽  
Cell Monolayer ◽  
Time Lapse ◽  
Geometrical Method ◽  
Cell Behaviour ◽  
Cell Monolayers ◽  
Polygonal Cell ◽  
Computer Based ◽  
Insight Into

Cell monolayers on culture dishes were divided into two groups: tensile monolayers and non-tensile ones. In the development of an epithelium, a non-tensile cell monolayer turns into a tightly bound tensile one. Detection of these states was carried out by using the boundary shortening procedure, a computer-based geometrical method to show how much the polygonal cell boundary contracts. Non-tensile monolayers were divided further into two groups according to their motility: a fluctuating monolayer in which cells move laterally, and a stable monolayer in which cells are immobilized. Quantitative determination of cell motility was performed by analysing time-lapse cellular patterns. These computer-based geometrical analyses enabled us to divide monolayers into three groups: tensile stable monolayers, non-tensile stable monolayers and fluctuating monolayers, and this study therefore gives an insight into the way in which changing conformations of cells may be assayed.

scholarly journals A survey on the cutting and packing problems

2020 ◽  
Vol 13 (4) ◽  
pp. 567-572
Author(s):  
Loris Faina
Keyword(s):  
Three Dimensional ◽  
Cutting And Packing ◽  
Unified Approach ◽  
Geometrical Method ◽  
Packing Problems ◽  
Enumeration Scheme

Abstract This paper presents a unified approach, based on a geometrical method (see Faina in Eur J Oper Res 114:542–556, 1999; Eur J Oper Res 126:340–354, 2000), which reduces the general two and three dimensional cutting and packing type problems to a finite enumeration scheme.

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