Genes and human languages are discrete combinatorial systems (DCSs), in which the basic building blocks are finite sets of elementary units: nucleotides or codons in a DNA sequence, and letters or words in a language. Different combinations of these finite units give rise to potentially infinite numbers of genes or sentences. This type of DCSs can be represented as an alphabetic bipartite network (ABN) where there are two kinds of nodes, one type represents the elementary units while the other type represents their combinations. Here, we extend and generalize recent analytical findings for ABNs derived in [Peruani, Europhys. Lett. 79, 28001 (2007)] and empirically investigate two real world systems in terms of ABNs, the codon gene and the phoneme-language network. The one-mode projections onto the elementary basic units are also studied theoretically as well as in real world ABNs. We propose the use of ABNs as a means for inferring the mechanisms underlying the growth of real world DCSs.
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PLoS One
January 2025
Computer Science and Engineering Discipline, Khulna University, Khulna, Bangladesh.
The objective of the max-cut problem is to cut any graph in such a way that the total weight of the edges that are cut off is maximum in both subsets of vertices that are divided due to the cut of the edges. Although it is an elementary graph partitioning problem, it is one of the most challenging combinatorial optimization-based problems, and tons of application areas make this problem highly admissible. Due to its admissibility, the problem is solved using the Harris Hawk Optimization algorithm (HHO).
View Article and Find Full Text PDFTheory Biosci
December 2024
Department of Biochemical Engineering and Biotechnology, Indian Institute of Technology Delhi, Hauz Khas, New Delhi, 110016, India.
Can mathematical proofs be employed for the solution of fundamental molecular-level problems in biology? Recently, I mathematically tackled complex mechanistic problems arising during the synthesis of the universal biological currency, adenosine triphosphate (ATP) by the FF-ATP synthase, nature's smallest rotary molecular motor, using graph-theoretical and combinatorial approaches for the membrane-bound F and water-soluble F domains of this fascinating molecule (see Nath in Theory Biosci 141:249‒260, 2022 and Theory Biosci 143:217‒227, 2024). In the third part of this trilogy, I investigate another critical aspect of the molecular mechanism-that of coupling between the F and F domains of the ATP synthase mediated by the central γ-subunit of nanometer diameter. According to Nath's torsional mechanism of energy transduction and ATP synthesis the γ-subunit twists during ATP synthesis and the release of stored torsional energy in the central γ-stalk causes conformational changes in the catalytic sites that lead to ATP synthesis, with 1 ATP molecule synthesized per discrete 120° rotation.
View Article and Find Full Text PDFBiomimetics (Basel)
November 2024
College of Mechanical and Electrical Engineering, Harbin Engineering University, Harbin 150001, China.
In recent years, twin stacker crane units have been increasingly integrated into large automated storage and retrieval systems (AS/RSs) in shipyards to enhance operational efficiency. These common rail units often encounter conflicts, and the additional time costs incurred during collision avoidance significantly diminish AS/RS efficiency. Therefore, addressing the twin stacker cranes' scheduling problem (TSSP) with a collision-free constraint is essential.
View Article and Find Full Text PDFJ Appl Comput Topol
September 2024
Laboratory for Topology and Neuroscience, École Polytechnique Fédérale de Lausanne (EPFL), Lausanne, Switzerland.
At the intersection of Topological Data Analysis (TDA) and machine learning, the field of cellular signal processing has advanced rapidly in recent years. In this context, each signal on the cells of a complex is processed using the combinatorial Laplacian, and the resultant Hodge decomposition. Meanwhile, discrete Morse theory has been widely used to speed up computations by reducing the size of complexes while preserving their global topological properties.
View Article and Find Full Text PDFCarbohydr Polym
January 2025
Key Laboratory of Agricultural Environmental Microbiology, Ministry of Agriculture and Rural Affairs, College of Life Sciences, Nanjing Agricultural University, Nanjing 210095, China. Electronic address:
As attractive functional ingredients, maltooligosaccharides (MOS) are typically prepared by controlled enzymatic hydrolysis of starch. However, the random attack mode of amylase often leads to discrete product distribution, thereby reducing yields and purities. In this study, a novel glycoside hydrolase family 13 amylase AmyEs from marine myxobacteria Enhygromyxa salina was identified efficient maltohexaose (G6)-forming ability (40 %, w/w).
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