Asymmetric circular graph with Hosoya index and negative continued fractions

It has been known that the Hosoya index of caterpillar graph can be calculated as the numerator of the simple continued fraction. Recently in [MATCH Commun. Math. Comput. Chem. 2020, 84 (2), 399-428], the author introduces a more general graph called caterpillar-bond graph and shows that its Hosoya index can be calculated as the numerator of the general continued fraction. In this paper, we show how the Hosoya index of the graph with non-uniform ring structure can be calculated from the negative continued fraction. We also give the relation between some radial graphs and multidimensional continued fractions in the sense of the Hosoya index.

Discrete-time quantum walk on circular graph: Simulations and effect of gate depth and errors

We investigate the counterparts of random walks in universal quantum computing and their implementation using standard quantum circuits. Quantum walks have been recently well investigated for traversing graphs with certain oracles. We focus our study on traversing a 1D graph, namely a circle, and show how to implement a discrete-time quantum walk in quantum circuits built with universal CNOT and single qubit gates. We review elementary quantum gates and circuit decomposition techniques and propose a generalized version of all CNOT-based circuits of the quantum walk. We simulated these circuits on five different qubits IBM-Q quantum devices. This quantum computer has nonperfect gates based on superconducting qubits, and, therefore, we analyzed the impact of the CNOT errors and CNOT-depth on the fidelity of the circuit.

Graph-Based Visual Analytics Tools for Digital Humanities Research

This paper is devoted to the development of the Web application for the visual analytics of the interconnected data within digital humanities research highly adaptable to the specifics of application domain and personal analytics preferences. The circular graph is proposed as a visual model to depict the interconnected data in a comprehensive way. The graph rendering software is organized according to the model-driven architecture utilizing ontology engineering methods and means, which ensure configuration flexibility and modification ease. The functioning scenarios of the application’s visualization component can be changed without its source code modifications, just by editing the under- lying ontology that describes data processing and rendering mechanisms. Extraction, transformation, loading and rendering of the data are con- figured in the intuitive way by data flow diagrams with the help of a high-level graphical editor. The described features are demonstrated on the real-world examples from the digital humanities application domain.

Environmental spatial and temporal variability and its role in non-favoured mutant dynamics

Understanding how environmental variability (or randomness) affects evolution is of fundamental importance for biology. The presence of temporal or spatial variability significantly affects the competition dynamics in populations, and gives rise to some counterintuitive observations. In this paper, we consider both birth–death (BD) or death–birth (DB) Moran processes, which are set up on a circular or a complete graph. We investigate spatial and temporal variability affecting division and/or death parameters. Assuming that mutant and wild-type fitness parameters are drawn from an identical distribution, we study mutant fixation probability and timing. We demonstrate that temporal and spatial types of variability possess fundamentally different properties. Under temporal randomness, in a completely mixed system, minority mutants experience (i) higher than neutral fixation probability and a higher mean conditional fixation time, if the division rates are affected by randomness and (ii) lower fixation probability and lower mean conditional fixation time if the death rates are affected. Once spatial restrictions are imposed, however, these effects completely disappear, and mutants in a circular graph experience neutral dynamics, but only for the DB update rule in case (i) and for the BD rule in case (ii) above. In contrast to this, in the case of spatially variable environment, both for BD/DB processes, both for complete/circular graph and both for division/death rates affected, minority mutants experience a higher than neutral probability of fixation. Fixation time, however, is increased by randomness on a circle, while it decreases for complete graphs under random division rates. A basic difference between temporal and spatial kinds of variability is the types of correlations that occur in the system. Under temporal randomness, mutants are spatially correlated with each other (they simply have equal fitness values at a given moment of time; the same holds for wild-types). Under spatial randomness, there are subtler, temporal correlations among mutant and wild-type cells, which manifest themselves by cells of each type ‘claiming’ better spots for themselves. Applications of this theory include cancer generation and biofilm dynamics.

IslandHunter – A Java-based GI detection software

Over the past decade, researchers have discovered that apart from the essential genes, bacterial genomes also contain a variable amount of accessory genes acquired by horizontal gene transfer (HGT) that are categorized as genomic islands (GIs). GIs encode adaptive traits, which might be beneficial for the species under certain growth or environmental conditions. It has always been a challenge for biologists to identify GIs within a bacterial genome as they evolve very rapidly. This paper proposes a standalone software, IslanHunter, that has been developed using Java and BioJava and can extract GI regions using GC content, codon usage bias, dinucleotide frequency bias, tetranucleotide frequency bias, k-mer signature analysis (2-mer, 3-mer, 4-mer, 5-mer, and 6-mer) and presence of mobility genes. IslandHunter provides a simple graphical user interface where disclosed GIs are displayed in a tree-view and a circular graph. Users are presented with options to save the GI regions as blocks of DNA sequences in FASTA format. They can later use these predicted GI regions for further analysis. IslandHunter can take as input, files in GenBank, EMBL or FASTA formats. IslandHunter provides flexible display options and save options. The software has been evaluated against exiting tools with good performance. It is available for evaluation at https://github.com/ShakunBaichoo/IslandHunter .

IslandHunter – A Java-based GI detection software

Over the past decade, researchers have discovered that apart from the essential genes, bacterial genomes also contain a variable amount of accessory genes acquired by horizontal gene transfer (HGT) that are categorized as genomic islands (GIs). GIs encode adaptive traits, which might be beneficial for the species under certain growth or environmental conditions. It has always been a challenge for biologists to identify GIs within a bacterial genome as they evolve very rapidly. This paper proposes a standalone software, IslanHunter, that has been developed using Java and BioJava and can extract GI regions using GC content, codon usage bias, dinucleotide frequency bias, tetranucleotide frequency bias, k-mer signature analysis (2-mer, 3-mer, 4-mer, 5-mer, and 6-mer) and presence of mobility genes. IslandHunter provides a simple graphical user interface where disclosed GIs are displayed in a tree-view and a circular graph. Users are presented with options to save the GI regions as blocks of DNA sequences in FASTA format. They can later use these predicted GI regions for further analysis. IslandHunter can take as input, files in GenBank, EMBL or FASTA formats. IslandHunter provides flexible display options and save options. The software has been evaluated against exiting tools with good performance. It is available for evaluation at https://github.com/ShakunBaichoo/IslandHunter .