Estrogen hormones interact with cellular ERs to exert their biological effects in vertebrate animals. Similar to other animals, fishes have two distinct ER subtypes, ERα (NR3A1) and ERβ (NR3A2). The ERβ subtype is found as two different isoforms in several fish species because of a gene duplication event. Although predicted, two different isoforms of ERα have not been demonstrated in any fish s...

Let H be a fixed graph on k vertices. For an edge-coloring c of H , we say that H is rainbow, or totally multicolored if c assigns distinct colors to all edges of H . We show, that it is easy to avoid rainbow induced graphs H . Specifically, we prove that for any graph H (with some notable exceptions), and for any graphs G, G 6= H , there is an edge-coloring of G with k colors which contains no...

A conjecture by Aharoni and Berger states that every family of n matchings of size n + 1 in a bipartite multigraph contains a rainbow matching of size n. In this paper we prove that matching sizes of ( 3 2 + o(1) ) n suffice to guarantee such a rainbow matching, which is asymptotically the same bound as the best-known one in the case where we only aim to find a rainbow matching of size n − 1. T...

Password recovery tools are often used in digital forensic investigations to obtain the passwords that are used by suspects to encrypt potential evidentiary data. This paper presents a new method for deterministically generating and efficiently storing password recovery tables. The method, which involves the virtual expansion of rainbow tables, achieves improvements of 16.92% to 28.15% in the p...

A new class of rainbows is created when a droplet is illuminated from the inside by a point light source. The position of the rainbow depends on both the index of refraction of the droplet and the position of the light source, and the rainbow vanishes when the point source is too close to the center of the droplet. Here we experimentally measure the position of the transmission and one-internal...

Let G be an edge-colored graph and v a vertex of G. The color degree of v is the number of colors appearing on the edges incident to v. A rainbow triangle in G is one in which all edges have distinct colors. In this paper, we first prove that an edge-colored graph on n vertices contains a rainbow triangle if the color degree sum of any two adjacent vertices is at least n+ 1. Afterwards, we char...