The development of computer assisted permanent Brachytherapy for prostate cancer by Shi, Xiaoming.

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A deterministic approximation algorithm for computing the permanent of a 0, 1 matrix by Gamarnik, David, Rogozhnikov, Dmitriy A.

“…We consider the problem of computing the permanent of a n by n matrix. For a class of matrices corresponding to constant degree expanders we construct a deterministic polynomial time approximation algorithm to within a multiplicative factor ( 1 + ∈)[superscript η] for arbitrary∈ > 0. …”
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خوارزميتان فعالتان لحساب دائم مصفوفة باستخدام نظرية البيانات الموجهة by أحمد الكردي

“…Because of the importance of matrices permanents in several applications such as Combinatorics, Graph theory, Statistics and Probability, the researchers started to find closed and analytical forms for computing the permanent of matrix. But computing the permanent is a difficult problem. …”
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خوارزميتان فعالتان لحساب دائم مصفوفة باستخدام نظرية البيانات الموجهة by أحمد الكردي

“…Because of the importance of matrices permanents in several applications such as Combinatorics, Graph theory, Statistics and Probability, the researchers started to find closed and analytical forms for computing the permanent of matrix. But computing the permanent is a difficult problem. …”
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Three complexity classification questions at the quantum/classical boundary by Grier, Daniel.

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Quantum-inspired permanent identities by Ulysse Chabaud, Abhinav Deshpande, Saeed Mehraban

“…The permanent is pivotal to both complexity theory and combinatorics. In quantum computing, the permanent appears in the expression of output amplitudes of linear optical computations, such as in the Boson Sampling model. …”
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Polynomial computational complexity of matrix elements of finite-rank-generated single-particle operators in products of finite bosonic states by Dmitri A. Ivanov

“…It is known that computing the permanent of the matrix 1+A, where A is a finite-rank matrix, requires a number of operations polynomial in the matrix size. …”
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A linear-optical proof that the permanent is #P-hard by Aaronson, Scott

“…One of the crown jewels of complexity theory is Valiant's theorem that computing the permanent of an n×n matrix is #P-hard. Here we show that, by using the model of linear-optical quantum computing—and in particular, a universality theorem owing to Knill, Laflamme and Milburn—one can give a different and arguably more intuitive proof of this theorem.…”
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Faster classical boson sampling by Clifford, P, Clifford, R

“…The advantage was reduced by Clifford and Clifford (2018), who gave a significantly faster classical solution taking O(n2n+poly(m, n)) time and linear space, matching the complexity of computing the permanent of a single matrix when m is polynomial in n. …”

Approximating the Permanent with Fractional Belief Propagation by Chertkov, Michael, Yedidia, Adam B.

“…We discuss schemes for exact and approximate computations of permanents, and compare them with each other. …”
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Computing permanents and counting Hamiltonian cycles by listing dissimilar vectors by Williams, Richard Ryan, Björklund, Andreas

“…A key tool in our approach is a reduction from computing the permanent to listing pairs of dissimilar vectors from two sets of vectors, i.e., vectors over a finite set that differ in each coordinate, building on an observation of [Bax and Franklin, Algorithmica 2002]. …”
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From object to process. Interface politics of networked computerization by Jan Distelmeyer

“…Both developments are profoundly related to the establishment of computers as permanently networked machines, whereby their functionality, depresentations, and ideology come into focus.…”
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Evaluating roadblocks to implementing a green freight transportation system: an interval valued intuitionistic fuzzy digraph matrix approach by Singh, Suneet, Barve, Akhilesh, Muduli, Kamalakanta, Kumar, Anil, Luthra, Sunil

“…The PERMAN algorithm is used to compute the permanent function of matrices. Findings suggest that the freight logistics industries in third world nations should pay more attention to societal and managerial barriers for successful implementation of green freight. …”
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Rank-Based Comparative Research Flow Benchmarking the Effectiveness of AHP–GTMA on Aiding Decisions of Shredder Selection by Reference to AHP–TOPSIS by Zheng-Yun Zhuang, Chang-Ching Lin, Chih-Yung Chen, Chia-Rong Su

“…In addition, along with this study, some contributable points are also rendered for implementing the decision models, e.g., the optimized recursive implementation in R to compute the permanent value of a square ASAM (alternative selection attribute matrix, which is the computational basis required by AHP–GTMA) of any dimension. …”
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CBCT Evaluation of Periapical Pathologies in Maxillary Posterior Teeth and Their Relationship with Maxillary Sinus Mucosal Thickening by Rizwan Jouhar, Hussain Mohammed Alkhames, Muhammad Adeel Ahmed, Naji Mohammad Almadeh, Muhammad Faheemuddin, Muhammad Farooq Umer

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