Chapter 9 Gene Drive Strategies for Population Replacement

Gene drive systems are selfish genetic elements capable of spreading into a population despite a fitness cost. A variety of these systems have been proposed for spreading disease-refractory genes into mosquito populations, thus reducing their ability to transmit diseases such as malaria and dengue fever to humans. Some have also been proposed for suppressing mosquito populations. We assess the alignment of these systems with design criteria for their safety and efficacy. Systems such as homing endonuclease genes, which manipulate inheritance through DNA cleavage and repair, are highly invasive and well-suited to population suppression efforts. Systems such as Medea, which use combinations of toxins and antidotes to favor their own inheritance, are highly stable and suitable for replacing mosquito populations with disease-refractory varieties. These systems offer much promise for future vector-borne disease control

Thermal Quench at Finite t'Hooft Coupling

Using holography we have studied thermal electric field quench for infinite and finite t'Hooft coupling constant. The set-up we consider here is D7-brane embedded in ($\alpha'$ corrected) AdS-black hole background. It is well-known that due to a time-dependent electric field on the probe brane, a time-dependent current will be produced and it will finally relax to its equilibrium value. We have studied the effect of different parameters of the system on equilibration time. As the most important results, we have observed a universal behaviour in the rescaled equilibration time in the very fast quench regime for different values of the temperature and $\alpha'$ correction parameter. It seems that in the slow quench regime the system behaves adiabatically. We have also observed that the equilibration time decreases in finite t'Hooft coupling limit.Comment: 6 pages, 9 figure

On the Unit Graph of a Noncommutative Ring

Let $R$ be a ring (not necessary commutative) with non-zero identity. The unit graph of $R$, denoted by $G(R)$, is a graph with elements of $R$ as its vertices and two distinct vertices $a$ and $b$ are adjacent if and only if $a+b$ is a unit element of $R$. It was proved that if $R$ is a commutative ring and \fm is a maximal ideal of $R$ such that |R/\fm|=2, then $G(R)$ is a complete bipartite graph if and only if (R, \fm) is a local ring. In this paper we generalize this result by showing that if $R$ is a ring (not necessary commutative), then $G(R)$ is a complete $r$-partite graph if and only if (R, \fm) is a local ring and $r=|R/m|=2^n$, for some $n \in \N$ or $R$ is a finite field. Among other results we show that if $R$ is a left Artinian ring, $2 \in U(R)$ and the clique number of $G(R)$ is finite, then $R$ is a finite ring.Comment: 6 pages. To appear in Algebra Colloquiu