A Scalable IoT Protocol via an Efficient DAG-Based Distributed Ledger Consensus

The Internet of Things (IoT) suffers from various security vulnerabilities. The use of blockchain technology can help resolve these vulnerabilities, but some practical problems in terms of scalability continue to hinder the adaption of blockchain for application in the IoT. The directed acyclic graph (DAG)-based Tangle model proposed by the IOTA Foundation aims to avoid transaction fees by employing a different protocol from that used in the blockchain. This model uses the Markov chain Monte Carlo (MCMC) algorithm to update a distributed ledger. However, concerns about centralization by the coordinator nodes remain. Additionally, the economic incentive to choose the algorithm is insufficient. The present study proposes a light and efficient distributed ledger update algorithm that regards only the subtangle of each step by considering the Bayesian inference. Experimental results have confirmed that the performance of the proposed methodology is similar to that of the existing methodology, and the proposed methodology enables a faster computation time. It also provides the same resistance to possible attacks, and for the same reasons, as does the MCMC algorithm.

Application of a skein relation to difference topology experiments

Difference topology is a technique used to study any protein that can stably bind to DNA. This technique is used to determine the conformation of DNA bound by protein. Motivated by difference topology experiments, we use the skein relation tangle model as a novel technique to study experiments using topoisomerase to study SMC proteins, a family of proteins that stably bind to DNA. The oriented skein relation involves an oriented knot, [Formula: see text], with a distinguished positive crossing; a knot [Formula: see text], obtained by changing the distinguished positive crossing of [Formula: see text] to a negative crossing; a knot, [Formula: see text], resulting from the non-orientation persevering resolution of the distinguished crossing; and a link [Formula: see text], the orientation preserving resolution of the distinguished crossing. We refer to [Formula: see text] as the skein quadruple. Topoisomerases are proteins that break one segment of DNA allowing a DNA segment to pass through before resealing the break. Recombinases are proteins that cut two segments of DNA and recombine them in some manner. They can act on direct repeat or inverted repeat sites, resulting in a link or knot, respectively. Thus, the skein quadruple is now viewed as [Formula: see text] circular DNA substrate, [Formula: see text] product of topoisomerase action, [Formula: see text] product of recombinase action on directed repeat sites, and [Formula: see text] product of recombinase action of inverted repeat sites.

A 4-string tangle analysis of DNA-protein complexes based on difference topology

An n-string tangle is a three-dimensional ball with n-strings properly embedded in it. In the late 1980s, Ernst and Sumners introduced a tangle model for protein-DNA complexes. The protein is modeled by a three-dimensional ball and the protein-bound DNA is modeled by strings embedded inside the ball. Originally the tangle model was applied to proteins such as Tn3 resolvase which binds two DNA segments. This protein breaks and rejoins two DNA segments and can create knotted DNA. A 2-string tangle model can be used for this complex. More recently, Pathania, Jayaram and Harshey determined that the topological structure of DNA within a Mu protein complex consists of three DNA segments containing five crossings. Since Mu binds DNA sequences at three sites, this Mu protein-DNA complex can be modeled by a 3-string tangle. Darcy, Leucke and Vazquez analyzed Pathania et al.'s experimental results by using 3-string tangle analysis. There are protein-DNA complexes that involve four or more DNA sites. When a protein binds circular DNA at four sites, a protein-DNA complex can be modeled by a 4-string tangle with four loops outside of the tangle. We determine a biologically relevant 4-string tangle model. We also develop mathematics for solving 4-string tangle equations to determine the topology of DNA within a protein complex.

Connect sum of lens spaces surgeries: application to Hin recombination

We extend the tangle model, originally developed by Ernst and Sumners [18], to include composite knots. We show that, for any prime tangle, there are no rational tangle attachments of distance greater than one that first yield a 4-plat and then a connected sum of 4-plats. This is done by studying the corresponding Dehn filling problem via double branched covers. In particular, we build on results on exceptional Dehn fillings at maximal distance to show that if Dehn filling on an irreducible manifold gives a lens space and then a connect sum of lens spaces, the distance between the slopes must be one. We then apply our results to the action of the Hin recombinase on mutated sites. In particular, after solving the tangle equations for processive recombination, we use our work to give a complete set of solutions to the tangle equations modelling distributive recombination.

BRAID SOLUTIONS TO THE ACTION OF THE GIN ENZYME

The topological analysis of enzymes, an active research topic, has allowed the application of the tangle model of Ernst and Sumners to deduce the action mechanism of several enzymes, modeled as 2-string tangles. By first deriving some results in the theory of 3-braids, in this paper we analyze knotted and linked products of site-specific recombination mediated by the Gin DNA invertase, an enzyme that involves 3-string tangles. Provided that the 3-tangles involved are 3-braids, we determine four families of solutions to its action, two families for each of the directly and inversely repeated site cases. For each case, one of the given solutions had not previously been reported in the related literature. These solutions were found using a computer algorithm, based on our theoretical results, which allows one to solve tangle equations under the assumption that the product of two or more rounds of recombinations is known.