scholarly journals DEFORMATION CONDITIONS FOR PSEUDOREPRESENTATIONS

2019 ◽  
Vol 7 ◽  
Author(s):  
PRESTON WAKE ◽  
CARL WANG-ERICKSON
Keyword(s):  
Stability Condition ◽  
Deformation Theory ◽  
Axiomatic Definition ◽  
Galois Deformation ◽  
Definition Of

Given a property of representations satisfying a basic stability condition, Ramakrishna developed a variant of Mazur’s Galois deformation theory for representations with that property. We introduce an axiomatic definition of pseudorepresentations with such a property. Among other things, we show that pseudorepresentations with a property enjoy a good deformation theory, generalizing Ramakrishna’s theory to pseudorepresentations.

scholarly journals Quasi-Perfect Stackelberg Equilibrium

2019 ◽  
Vol 33 ◽  
pp. 2117-2124 ◽  
Author(s):  
Alberto Marchesi ◽  
Gabriele Farina ◽  
Christian Kroer ◽  
Nicola Gatti ◽  
Tuomas Sandholm
Keyword(s):  
Broad Class ◽  
Stackelberg Equilibrium ◽  
Correlated Equilibrium ◽  
Equilibrium Concept ◽  
Extensive Form ◽  
Tree Form ◽  
Axiomatic Definition ◽  
Security Games ◽  
Definition Of ◽  
Perfect Equilibria

Equilibrium refinements are important in extensive-form (i.e., tree-form) games, where they amend weaknesses of the Nash equilibrium concept by requiring sequential rationality and other beneficial properties. One of the most attractive refinement concepts is quasi-perfect equilibrium. While quasiperfection has been studied in extensive-form games, it is poorly understood in Stackelberg settings—that is, settings where a leader can commit to a strategy—which are important for modeling, for example, security games. In this paper, we introduce the axiomatic definition of quasi-perfect Stackelberg equilibrium. We develop a broad class of game perturbation schemes that lead to them in the limit. Our class of perturbation schemes strictly generalizes prior perturbation schemes introduced for the computation of (non-Stackelberg) quasi-perfect equilibria. Based on our perturbation schemes, we develop a branch-and-bound algorithm for computing a quasi-perfect Stackelberg equilibrium. It leverages a perturbed variant of the linear program for computing a Stackelberg extensive-form correlated equilibrium. Experiments show that our algorithm can be used to find an approximate quasi-perfect Stackelberg equilibrium in games with thousands of nodes.

scholarly journals Cladistic hypotheses as degree of equivalence relational structures: implications for three-item statements

2021 ◽  
Author(s):  
Valentin Rineau ◽  
Stéphane Prin
Keyword(s):  
Phylogenetic Trees ◽  
Phylogenetic Reconstruction ◽  
Equivalence Relations ◽  
Strong Connection ◽  
Relational Structures ◽  
Degree Of Equivalence ◽  
Axiomatic Definition ◽  
Finite Set ◽  
Definition Of ◽  
Supertree Methods

AbstractThree-item statements, as minimal informative rooted binary phylogenetic trees on three items, are the minimal units of cladistic information. Their importance for phylogenetic reconstruction, consensus and supertree methods relies on both (i) the fact that any cladistic tree can always be decomposed into a set of three-item statements, and (ii) the possibility, at least under some conditions, to build a new cladistic tree by combining all or part of the three-item statements deduced from several prior cladistic trees. In order to formalise such procedures, several k-adic rules of inference, i.e., rules that allow us to deduce at least one new three-item statement from exactly k other ones, have been identified. However, no axiomatic background has been proposed, and it remains unknown if a particular k-adic rule of inference can be reduced to more basic rules. In order to solve this problem, we propose here to define three-item statements in terms of degree of equivalence relations. Given both the axiomatic definition of the latter and their strong connection to hierarchical classifications, we establish a list of the most basic properties for three-item statements. With such an approach, we show that it is possible to combine five three-item statements from basic rules although they are not combinable only from dyadic rules. Such a result suggests that all higher k-adic rules are well reducible to a finite set of simpler rules.

Self-Consistent Approaches and Strain Heterogeneities in Two-Phase Elastoplastic Materials

1994 ◽  
Vol 47 (1S) ◽  
pp. S66-S76 ◽  
Author(s):  
Michel Bornert ◽  
Eveline Herve´ ◽  
Claude Stolz ◽  
Andre´ Zaoui
Keyword(s):  
Deformation Theory ◽  
Shear Bands ◽  
Local Concentration ◽  
Two Phase ◽  
Self Consistent ◽  
Measured Strain ◽  
Elastoplastic Materials ◽  
Hardening Parameter ◽  
Analytical Result ◽  
Definition Of

The Generalized Self Consistent Scheme [GSCS] extended to the nonlinear case with help of a deformation theory of elastoplasticity is used to predict the strain heterogeneities that spread out in two phase elastoplastic materials submitted to a monotonic uniaxial load. Materials with different microstructural morphologies are considered. The single composite inclusion of the GSCS is an accurate representation of “matrix/inclusion” microstructures but it does not give a sufficient representation of the considered morphologies. That’s why this model is extended to more general cases by using two or even more different spherical composite inclusions: local concentration fluctuations and local morphological inversions can then be modeled. The nonlinear extension is also modified: the composite inclusions are discretized into several concentric layers in order to take into better account the strain gradient along the radius and a new definition of the work-hardening parameter of each of these layers is proposed. The elastoplastic strain field in the single composite inclusion is also computed numerically by means of finite element methods and compared to the analytical result. Unfortunately, these modifications do not basically modify the strain heterogeneity predictions of the GSCS, which widely underestimate the measured strain heterogeneities in most of the cases. In fact, the inaccuracy of the GSCS in these cases is basically due to the appearance of long range shear bands that cannot be described by a local self-consistent approach.

scholarly journals A New Entropy and Its Properties Based on the Improved Axiomatic Definition of Intuitionistic Fuzzy Entropy

2018 ◽  
Vol 2018 ◽  
pp. 1-6 ◽  
Author(s):  
Dengying Jiang ◽  
Yaxiong Wang
Keyword(s):  
Fuzzy Sets ◽  
Intuitionistic Fuzzy Sets ◽  
Fuzzy Entropy ◽  
Constraint Condition ◽  
Entropy Formula ◽  
Intuitionistic Fuzzy ◽  
Intuitionistic Fuzzy Entropy ◽  
Axiomatic Definition ◽  
Definition Of

Regarding the problem of the existing intuitionistic fuzzy entropy formulas in ordering the partial entropy, the constraint condition that is consistent with the intuitionistic facts is proposed in this paper, the axiomatic definition of entropy which fully reflects the intuition and fuzziness of intuitionistic fuzzy sets is given, and the improved intuitionistic fuzzy entropy formula is constructed according to the entropy axiomatic definition and its properties are studied. Finally, we compare the improved formula with the existing intuitionistic fuzzy entropy formulas, and the result turns out that the improved formula can solve the problem in the entropy ordering theoretically and practically.

Sign in / Sign up

Export Citation Format

Share Document