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An Efficient Algorithm for Eigenvalue Problem of Latin Squares in a Bipartite Min-Max-Plus System

Mubasher Umer, Umar Hayat, Fazal Abbas, Anurag Agarwal, Petko Kitanov
2020 Symmetry  
In this paper, we consider the eigenproblems for Latin squares in a bipartite min-max-plus system.  ...  The focus is upon developing a new algorithm to compute the eigenvalue and eigenvectors (trivial and non-trivial) for Latin squares in a bipartite min-max-plus system.  ...  Acknowledgments: We thank the referees for their valuable suggestions and helpful remarks. Conflicts of Interest: The authors declare no conflict of interest.  ... 
doi:10.3390/sym12020311 fatcat:zmbzgsy7cfefheouqrucwfabaa

An Efficient Algorithm for Latin Squares in a Bipartite Min-Max-Plus System [article]

Mubasher Umer, Umar Hayat, Fazal Abbas, Anurag Agarwal, Petko Kitanov
2019 arXiv   pre-print
In this paper, we consider the eigenproblems for Latin squares in a bipartite min-max-plus system.  ...  The focus is upon developing a new algorithm to compute the eigenvalue and eigenvectors (trivial and non-trivial) for Latin squares in a bipartite min-max-plus system.  ...  In [11] , authors show that for Latin squares in a system of type (2), the eigenvalue λ is determined as λ = max(A) + min(B) 2 . (6) Therefore eigenproblems for Latin squares in a system of type (2) are  ... 
arXiv:1908.08371v1 fatcat:zth36pgj6jafbeabiw3kwbltau

An Efficient Algorithm for Nontrivial Eigenvectors in Max-Plus Algebra

Mubasher Umer, Umar Hayat, Fazal Abbas
2019 Symmetry  
In this paper, we propose an algorithm to compute the eigenvalue and the corresponding eigenvectors of a square matrix in an iterative way.  ...  The algorithm is extended to compute the nontrivial eigenvectors for Latin squares in max-plus algebra.  ...  The funding sponsors had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, and in the decision to publish the results.  ... 
doi:10.3390/sym11060738 fatcat:dmefx6nfv5djrayyeka2wpjfce

Entanglement, randomness and chaos [article]

Giuliano Benenti
2008 arXiv   pre-print
In particular, quantum chaotic maps are efficient generators of multipartite entanglement among the qubits, close to that expected for random states.  ...  ; (iii) the decoherence induced by the coupling of a system to a chaotic environment, that is, by the entanglement established between the system and the environment.  ...  Quantum algorithm. -In the following, we describe an exponentially efficient quantum algorithm for simulation of the map (46) [46] .  ... 
arXiv:0807.4364v1 fatcat:difkqlx4rbhidhzuhrbdp3f4fq

The forwarding indices of graphs - a survey

Jun-Ming Xu, Min Xu
2013 Opuscula Mathematica  
The load of any vertex is limited by the capacity of the vertex, for otherwise it would affect the efficiency of transmission and even result in the malfunction of the network.  ...  Let G be a connected graph of order n. A routing R in G is a set of n(n − 1) fixed paths for all ordered pairs (x, y) of vertices of G.  ...  The work was supported partially by NNSF of China (No. 11071233; No. 61272008 ) and Fundamental Research Funds for the Central Universities.  ... 
doi:10.7494/opmath.2013.33.2.345 fatcat:47zeik3anjam5ghhxyqdiehm4e

Vital nodes identification in complex networks

Linyuan Lü, Duanbing Chen, Xiao-Long Ren, Qian-Ming Zhang, Yi-Cheng Zhang, Tao Zhou
2016 Physics reports  
In this review, we clarify the concepts and metrics, classify the problems and methods, as well as review the important progresses and describe the state of the art.  ...  In despite of the emphasis on physics-rooted approaches, the unification of the language and comparison with cross-domain methods would trigger interdisciplinary solutions in the near future.  ...  We also acknowledge the team lead by Zi-Ke Zhang (some members are the authors of the companying review) for useful exchange of research. This work is supported by the National Natural Science  ... 
doi:10.1016/j.physrep.2016.06.007 fatcat:3zecrlkydfex3gv5o62fozgksu

Reference list of indexed articles

2000 Discrete Applied Mathematics  
Salkin, An efficient algorithm for the complete set partitioning problem 6 (1983) 149-156 174. W.  ...  Ibaraki, An efficient algorithm for the parametric resource allocation problem 10 (1985) 261-274 293. T.  ... 
doi:10.1016/s0166-218x(00)00209-2 fatcat:l53yxlj45ffdrdecl3uah2gj3y

Minimal matrices in the Bruhat order for symmetric (0,1)-matrices

Henrique F. da Cruz, Rosário Fernandes, Susana Furtado
2017 Linear Algebra and its Applications  
We have received 150 abstracts for 20-minute contributed talks which will run in four parallel sessions and cover a large variety of areas within graph theory and combinatorics.  ...  Twenty-seven years later we are gathered here for the second such conference organised in the Island of Malta.  ...  We show that, unlike for trees, all containments in the Venn diagram are proper for MOPs, a subfamily of 2-trees.  ... 
doi:10.1016/j.laa.2017.05.014 fatcat:zlcp5rb2sjeqvlyaajvf2nyoby

PhD thesis: Multipartite entanglement and quantum algorithms [article]

Daniel Alsina
2017 arXiv   pre-print
Also some quantum algorithms run with the IBM quantum computer are covered, together with others applied to adiabatic quantum computation and quantum thermodynamics.  ...  PhD thesis dealing with various aspects of multipartite entanglement, such as entanglement measures, absolutely maximally entangled states, bell inequalities, entanglement spectrum and quantum frustration  ...  Efficient algorithms remain to be created in order to solve practical problems for real-life hamiltonians.  ... 
arXiv:1706.08318v2 fatcat:ishnubdzvnew3kvfhdjhkjyjnm

Characterizing Attitudinal Network Graphs through Frustration Cloud [article]

Lucas Rusnak, Jelena Tešić
2021 arXiv   pre-print
We propose an efficient scalable algorithm for calculating frustration cloud-based measures in social network and survey data of up to 80,000 vertices and half-a-million edges.  ...  We also introduce a new global measure of controversy for a given signed graph and show that vertex status is a zero-sum game in the signed network.  ...  Acknowledgements: We would like to thank Data Lab alumni students Joshua Mitchell for initial implementation and graphB 1.0 proof-of-concept and Eric Hull for graphB 2.0 proof-of-concept and code release  ... 
arXiv:2009.07776v3 fatcat:azohmosfbvbdvltcjqwlp7ngwi

Characterizing attitudinal network graphs through frustration cloud

Lucas Rusnak, Jelena Tešić
2021 Data mining and knowledge discovery  
We propose an efficient scalable algorithm for calculating frustration cloud-based measures in social network and survey data of up to 80,000 vertices and half-a-million edges.  ...  We also introduce a new global measure of controversy for a given signed graph and show that vertex status is a zero-sum game in the signed network.  ...  Acknowledgements We would like to thank Data Lab alumni students Joshua Mitchell for initial implementation and graphB 1.0 proof-of-concept and Eric Hull for graphB 2.0 proof-of-concept and code release  ... 
doi:10.1007/s10618-021-00795-z fatcat:otqsophdvjghphjfhtcznbwv2q

Synchronization and Linearity: An Algebra for Discrete Event Systems

Charles Leake, Francois Baccelli, Guy Cohen, Geert Jan Olsder, Jean-Pierre Quadrat
1994 Journal of the Operational Research Society  
In the present release, alterations of the original text are mild and need no special mention: they concern typographic style (which may result in a different pagination with respect to the original paper  ...  Some sentences may even have been rephrased for better clarity without altering the original meaning. There are, however, no changes in the numbering of equations, theorems, remarks, etc..  ...  In Chapter 3 it will be shown that under quite general conditions an eigenvalue (λ) and corresponding eigenvector (v) also exist in the max-plus algebra context for a square matrix (A).  ... 
doi:10.2307/2583959 fatcat:cx7pfvwhk5cshanzmfjwzjyizy

Cryptography in a Quantum World [article]

Stephanie Wehner
2008 arXiv   pre-print
Shor's discovery of an efficient quantum algorithm for factoring large integers implies that many existing classical systems based on computational assumptions can be broken, once a quantum computer is  ...  In particular, we investigate several questions that are crucial to the security of quantum protocols: How can we find good uncertainty relations for a large number of measurement settings?  ...  First , we consider MUBs based on mutually orthogonal Latin squares [WB05] .Informally, an s × s Latin square over the symbol set [s] is an arrangement of elements of [s] into an s × s square such that  ... 
arXiv:0806.3483v1 fatcat:br4tirmaundxnbvud3cjdoamgy

The density-matrix renormalization group

U. Schollwöck
2005 Reviews of Modern Physics  
The density-matrix renormalization group (DMRG) is a numerical algorithm for the efficient truncation of the Hilbert space of low-dimensional strongly correlated quantum systems based on a rather general  ...  This algorithm has achieved unprecedented precision in the description of one-dimensional quantum systems.  ...  This work has been supported by The Young Academy at the Berlin-Brandenburg Academy of Sciences and the Leopoldina.  ... 
doi:10.1103/revmodphys.77.259 fatcat:kin23dbcffd65h267nghsmhz2i

Recommender systems

Linyuan Lü, Matúš Medo, Chi Ho Yeung, Yi-Cheng Zhang, Zi-Ke Zhang, Tao Zhou
2012 Physics reports  
Extensive research for recommender systems is conducted by a broad range of communities including social and computer scientists, physicists, and interdisciplinary researchers.  ...  In addition to algorithms, physical aspects are described to illustrate macroscopic behavior of recommender systems. Potential impacts and future directions are discussed.  ...  TZ is supported by the Research Funds for the Central Universities (UESTC).  ... 
doi:10.1016/j.physrep.2012.02.006 fatcat:cywkeyu2wjdzhdqkg2545v5f7a
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