Determining Tanimoto Similarity Neighborhoods of Real-Valued Vectors by Means of the Triangle Inequality and Bounds on Lengths

2021 ◽  
pp. 18-34
Author(s):  
Marzena Kryszkiewicz
1982 ◽  
Vol 89 (2) ◽  
pp. 123-154 ◽  
Author(s):  
Amos Tversky ◽  
Itamar Gati
Keyword(s):  

2014 ◽  
Vol 13 (1) ◽  
pp. 4127-4145
Author(s):  
Madhushi Verma ◽  
Mukul Gupta ◽  
Bijeeta Pal ◽  
Prof. K. K. Shukla

Orienteering problem (OP) is an NP-Hard graph problem. The nodes of the graph are associated with scores or rewards and the edges with time delays. The goal is to obtain a Hamiltonian path connecting the two necessary check points, i.e. the source and the target along with a set of control points such that the total collected score is maximized within a specified time limit. OP finds application in several fields like logistics, transportation networks, tourism industry, etc. Most of the existing algorithms for OP can only be applied on complete graphs that satisfy the triangle inequality. Real-life scenario does not guarantee that there exists a direct link between all control point pairs or the triangle inequality is satisfied. To provide a more practical solution, we propose a stochastic greedy algorithm (RWS_OP) that uses the roulette wheel selectionmethod, does not require that the triangle inequality condition is satisfied and is capable of handling both complete as well as incomplete graphs. Based on several experiments on standard benchmark data we show that RWS_OP is faster, more efficient in terms of time budget utilization and achieves a better performance in terms of the total collected score ascompared to a recently reported algorithm for incomplete graphs.


2020 ◽  
Vol 70 (4) ◽  
pp. 849-862
Author(s):  
Shagun Banga ◽  
S. Sivaprasad Kumar

AbstractIn this paper, we use the novel idea of incorporating the recently derived formula for the fourth coefficient of Carathéodory functions, in place of the routine triangle inequality to achieve the sharp bounds of the Hankel determinants H3(1) and H2(3) for the well known class 𝓢𝓛* of starlike functions associated with the right lemniscate of Bernoulli. Apart from that the sharp bound of the Zalcman functional: $\begin{array}{} |a_3^2-a_5| \end{array}$ for the class 𝓢𝓛* is also estimated. Further, a couple of interesting results of 𝓢𝓛* are also discussed.


2021 ◽  
Vol 13 (1) ◽  
Author(s):  
Kohulan Rajan ◽  
Achim Zielesny ◽  
Christoph Steinbeck

AbstractChemical compounds can be identified through a graphical depiction, a suitable string representation, or a chemical name. A universally accepted naming scheme for chemistry was established by the International Union of Pure and Applied Chemistry (IUPAC) based on a set of rules. Due to the complexity of this ruleset a correct chemical name assignment remains challenging for human beings and there are only a few rule-based cheminformatics toolkits available that support this task in an automated manner. Here we present STOUT (SMILES-TO-IUPAC-name translator), a deep-learning neural machine translation approach to generate the IUPAC name for a given molecule from its SMILES string as well as the reverse translation, i.e. predicting the SMILES string from the IUPAC name. In both cases, the system is able to predict with an average BLEU score of about 90% and a Tanimoto similarity index of more than 0.9. Also incorrect predictions show a remarkable similarity between true and predicted compounds.


2017 ◽  
Vol 657 ◽  
pp. 111-126 ◽  
Author(s):  
Usha Mohan ◽  
Sivaramakrishnan Ramani ◽  
Sounaka Mishra

2005 ◽  
Vol 112 (3) ◽  
pp. 280
Author(s):  
Razvan Satnoianu ◽  
Walther Janous
Keyword(s):  

2021 ◽  
pp. 105-113
Author(s):  
N. D. Moskin ◽  

The work is devoted to methods for comparing and classifying graphs. This trend is known as "graph matching". An overview of metrics for comparing graphs based on the maximum common subgraph is given. A modification of the distance based on the maximum common subgraph, which takes into account the ordering of the vertices, is proposed. It is shown that this function satisfies all the properties of the metric (non-negativity, identity, symmetry, triangle inequality).


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