On sign-symmetric signed graphs

A signed graph is said to be sign-symmetric if it is switching isomorphic to its negation. Bipartite signed graphs are trivially sign-symmetric. We give new constructions of non-bipartite sign-symmetric signed graphs. Sign-symmetric signed graphs have a symmetric spectrum but not the other way around. We present constructions of signed graphs with symmetric spectra which are not sign-symmetric. This, in particular answers a problem posed by Belardo, Cioabă, Koolen, and Wang (2018)

Evaluation of effective resistances in pseudo-distance-regular resistor networks

In Refs.[1] and [2], calculation of effective resistances on distance-regular networks was investigated, where in the first paper, the calculation was based on the stratification of the network and Stieltjes function associated with the network, whereas in the latter one a recursive formula for effective resistances was given based on the Christoffel-Darboux identity. In this paper, evaluation of effective resistances on more general networks called pseudo-distance-regular networks [21] or QD type networks \cite{obata} is investigated, where we use the stratification of these networks and show that the effective resistances between a given node such as $\alpha$ and all of the nodes $\beta$ belonging to the same stratum with respect to $\alpha$ ($R_{\alpha\beta^{(m)}}$, $\beta$ belonging to the $m$-th stratum with respect to the $\alpha$) are the same. Then, based on the spectral techniques, an analytical formula for effective resistances $R_{\alpha\beta^{(m)}}$ such that $L^{-1}_{\alpha\alpha}=L^{-1}_{\beta\beta}$ (those nodes $\alpha$, $\beta$ of the network such that the network is symmetric with respect to them) is given in terms of the first and second orthogonal polynomials associated with the network, where $L^{-1}$ is the pseudo-inverse of the Laplacian of the network. From the fact that in distance-regular networks, $L^{-1}_{\alpha\alpha}=L^{-1}_{\beta\beta}$ is satisfied for all nodes $\alpha,\beta$ of the network, the effective resistances $R_{\alpha\beta^{(m)}}$ for $m=1,2,...,d$ ($d$ is diameter of the network which is the same as the number of strata) are calculated directly, by using the given formula.Comment: 30 pages, 7 figure

Understanding Marine Mussel Adhesion

In addition to identifying the proteins that have a role in underwater adhesion by marine mussels, research efforts have focused on identifying the genes responsible for the adhesive proteins, environmental factors that may influence protein production, and strategies for producing natural adhesives similar to the native mussel adhesive proteins. The production-scale availability of recombinant mussel adhesive proteins will enable researchers to formulate adhesives that are water-impervious and ecologically safe and can bind materials ranging from glass, plastics, metals, and wood to materials, such as bone or teeth, biological organisms, and other chemicals or molecules. Unfortunately, as of yet scientists have been unable to duplicate the processes that marine mussels use to create adhesive structures. This study provides a background on adhesive proteins identified in the blue mussel, Mytilus edulis, and introduces our research interests and discusses the future for continued research related to mussel adhesion