Self-Duality of Polytopes and its Relations to Vertex Enumeration and Graph Isomorphism

2013 ◽  
Vol 30 (3) ◽  
pp. 729-742 ◽  
Author(s):  
Hans Raj Tiwary ◽  
Khaled Elbassioni
1992 ◽  
Vol 07 (23) ◽  
pp. 2077-2085 ◽  
Author(s):  
A. D. POPOV

The anti-self-duality equations for gauge fields in d = 4 and a generalization of these equations to dimension d = 4n are considered. For gauge fields with values in an arbitrary semisimple Lie algebra [Formula: see text] we introduce the ansatz which reduces the anti-self-duality equations in the Euclidean space ℝ4n to a system of equations breaking up into the well known Nahm's equations and some linear equations for scalar field φ.


2021 ◽  
Vol 11 (9) ◽  
pp. 4011
Author(s):  
Dan Wang ◽  
Jindong Zhao ◽  
Chunxiao Mu

In the field of modern bidding, electronic bidding leads a new trend of development, convenience and efficiency and other significant advantages effectively promote the reform and innovation of China’s bidding field. Nowadays, most systems require a strong and trusted third party to guarantee the integrity and security of the system. However, with the development of blockchain technology and the rise of privacy protection, researchers has begun to emphasize the core concept of decentralization. This paper introduces a decentralized electronic bidding system based on blockchain and smart contract. The system uses blockchain to replace the traditional database and uses chaincode to process business logic. In data interaction, encryption techniques such as zero-knowledge proof based on graph isomorphism are used to improve privacy protection, which improves the anonymity of participants, the privacy of data transmission, and the traceability and verifiable of data. Compared with other electronic bidding systems, this system is more secure and efficient, and has the nature of anonymous operation, which fully protects the privacy information in the bidding process.


2021 ◽  
Vol 82 (1) ◽  
Author(s):  
Javier Gutiérrez García ◽  
Ulrich Höhle ◽  
Tomasz Kubiak

2021 ◽  
Vol 183 (3) ◽  
Author(s):  
Mario Ayala ◽  
Gioia Carinci ◽  
Frank Redig

AbstractWe study the symmetric inclusion process (SIP) in the condensation regime. We obtain an explicit scaling for the variance of the density field in this regime, when initially started from a homogeneous product measure. This provides relevant new information on the coarsening dynamics of condensing interacting particle systems on the infinite lattice. We obtain our result by proving convergence to sticky Brownian motion for the difference of positions of two SIP particles in the sense of Mosco convergence of Dirichlet forms. Our approach implies the convergence of the probabilities of two SIP particles to be together at time t. This, combined with self-duality, allows us to obtain the explicit scaling for the variance of the fluctuation field.


2020 ◽  
Vol 2020 (9) ◽  
Author(s):  
Guido Festuccia ◽  
Anastasios Gorantis ◽  
Antonio Pittelli ◽  
Konstantina Polydorou ◽  
Lorenzo Ruggeri

Abstract We construct a large class of gauge theories with extended supersymmetry on four-dimensional manifolds with a Killing vector field and isolated fixed points. We extend previous results limited to super Yang-Mills theory to general $$ \mathcal{N} $$ N = 2 gauge theories including hypermultiplets. We present a general framework encompassing equivariant Donaldson-Witten theory and Pestun’s theory on S4 as two particular cases. This is achieved by expressing fields in cohomological variables, whose features are dictated by supersymmetry and require a generalized notion of self-duality for two-forms and of chirality for spinors. Finally, we implement localization techniques to compute the exact partition function of the cohomological theories we built up and write the explicit result for manifolds with diverse topologies.


2020 ◽  
Vol 12 (1) ◽  
Author(s):  
Jördis-Ann Schüler ◽  
Steffen Rechner ◽  
Matthias Müller-Hannemann

AbstractAn important task in cheminformatics is to test whether two molecules are equivalent with respect to their 2D structure. Mathematically, this amounts to solving the graph isomorphism problem for labelled graphs. In this paper, we present an approach which exploits chemical properties and the local neighbourhood of atoms to define highly distinctive node labels. These characteristic labels are the key for clever partitioning molecules into molecule equivalence classes and an effective equivalence test. Based on extensive computational experiments, we show that our algorithm is significantly faster than existing implementations within , and . We provide our Java implementation as an easy-to-use, open-source package (via GitHub) which is compatible with . It fully supports the distinction of different isotopes and molecules with radicals.


2021 ◽  
Vol 860 ◽  
pp. 51-71
Author(s):  
Pavel Klavík ◽  
Dušan Knop ◽  
Peter Zeman
Keyword(s):  

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