
Life and language 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 DCS can be represented as an Alphabetic Bipartite Network ($��$-BiN) where there are two kinds of nodes, one type represents the elementary units while the other type represents their combinations. There is an edge between a node corresponding to an elementary unit $u$ and a node corresponding to a particular combination $v$ if $u$ is present in $v$. Naturally, the partition consisting of the nodes representing elementary units is fixed, while the other partition is allowed to grow unboundedly. Here, we extend recently analytical findings for $��$-BiNs derived in [Peruani et al., Europhys. Lett. 79, 28001 (2007)] and empirically investigate two real world systems: the codon-gene network and the phoneme-language network. The evolution equations for $��$-BiNs under different growth rules are derived, and the corresponding degree distributions computed. It is shown that asymptotically the degree distribution of $��$-BiNs can be described as a family of beta distributions. The one-mode projections of the theoretical as well as the real world $��$-BiNs are also studied. We propose a comparison of the real world degree distributions and our theoretical predictions as a means for inferring the mechanisms underlying the growth of real world systems.
Time Factors, FOS: Physical sciences, Phonetics, Databases, Genetic, Animals, Humans, Computer Simulation, Physics - Biological Physics, Codon, Language, Stochastic Processes, [INFO.INFO-NI] Computer Science [cs]/Networking and Internet Architecture [cs.NI], Base Sequence, Models, Genetic, DNA, Models, Theoretical, Genes, Nonlinear Dynamics, Biological Physics (physics.bio-ph), Physics - Data Analysis, Statistics and Probability, [INFO.INFO-MO] Computer Science [cs]/Modeling and Simulation, Algorithms, Data Analysis, Statistics and Probability (physics.data-an)
Time Factors, FOS: Physical sciences, Phonetics, Databases, Genetic, Animals, Humans, Computer Simulation, Physics - Biological Physics, Codon, Language, Stochastic Processes, [INFO.INFO-NI] Computer Science [cs]/Networking and Internet Architecture [cs.NI], Base Sequence, Models, Genetic, DNA, Models, Theoretical, Genes, Nonlinear Dynamics, Biological Physics (physics.bio-ph), Physics - Data Analysis, Statistics and Probability, [INFO.INFO-MO] Computer Science [cs]/Modeling and Simulation, Algorithms, Data Analysis, Statistics and Probability (physics.data-an)
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