The minimum rank of universal adjacency matrices

In this paper we introduce a new parameter for a graph called the {\it minimum universal rank}. This parameter is similar to the minimum rank of a graph. For a graph $G$ the minimum universal rank of $G$ is the minimum rank over all matrices of the form $$U(\alpha, \beta, \gamma, \delta) = \alpha A + \beta I + \gamma J + \delta D$$ where $A$ is the adjacency matrix of $G$, $J$ is the all ones matrix and $D$ is the matrix with the degrees of the vertices in the main diagonal, and $\alpha\neq 0, \beta, \gamma, \delta$ are scalars. Bounds for general graphs based on known graph parameters are given, as is a formula for the minimum universal rank for regular graphs based on the multiplicity of the eigenvalues of $A$. The exact value of the minimum universal rank of some families of graphs are determined, including complete graphs, complete bipartite graph, paths and cycles. Bounds on the minimum universal rank of a graph obtained by deleting a single vertex are established. It is shown that the minimum universal rank is not monotone on induced subgraphs, but bounds based on certain induced subgraphs, including bounds on the union of two graphs, are given. Finally we characterize all graphs with minimum universal rank equal to 0 and to 1

CsrA impacts survival of Yersinia enterocolitica by affecting a myriad of physiological activities.

BackgroundA previous study identified a Yersinia enterocolitica transposon mutant, GY448, that was unable to export the flagellar type three secretion system (T3SS)-dependent phospholipase, YplA. This strain was also deficient for motility and unable to form colonies on Lauria-Bertani agar medium. Preliminary analysis suggested it carried a mutation in csrA. CsrA in Escherichia coli is an RNA-binding protein that is involved in specific post-transcriptional regulation of a myriad of physiological activities. This study investigated how CsrA affects expression of the flagellar regulatory cascade that controls YplA export and motility. It also explored the effect of csrA mutation on Y. enterocolitica in response to conditions that cue physiological changes important for growth in environments found both in nature and the laboratory.ResultsThe precise location of the transposon insertion in GMY448 was mapped within csrA. Genetic complementation restored disruptions in motility and the YplA export phenotype (Yex), which confirmed this mutation disrupted CsrA function. Mutation of csrA affected expression of yplA and flagellar genes involved in flagellar T3SS dependent export and motility by altering expression of the master regulators flhDC. Mutation of csrA also resulted in increased sensitivity of Y. enterocolitica to various osmolytes, temperatures and antibiotics.ConclusionsThe results of this study reveal unique aspects of how CsrA functions in Y. enterocolitica to control its physiology. This provides perspective on how the Csr system is susceptible to adaptation to particular environments and bacterial lifestyles

The NGO's Dilemma: How to Influence Firms to Replace a Potentially Hazardous Substance

We study a nongovernmental organization's (NGO's) decisions when it attempts to remove a potentially hazardous substance from commercial use in a market with competing firms. Specifically, we determine under what market and regulatory conditions an NGO should target the industry versus the regulatory body to influence firms to replace the substance. We examine how the NGO's strategy changes as the NGO's pragmatism (i.e., the extent to which the NGO incorporates firms' profits into its decision making) increases. Our results demonstrate that when the NGO is less pragmatic, it should examine the existing market structure to determine whether to target the industry or the regulatory body. However, as the pragmatism of the NGO increases, the NGO should increasingly leverage the competition between firms to ensure that a replacement is available to consumers. We examine multiple extensions including varying the competition dynamics, the NGO targeting both the industry and the regulatory body, the time discounting of replacement costs, and a firm potentially lobbying to counteract an NGO's activism. We show that the potential for a firm to lobby can benefit consumers by motivating the NGO to exert more effort and increase the market sensitivity to a substance, thereby forcing the firm to replace.National Science Foundation (U.S.) (Grant NSF/CAREER-0547021

Deciphering in situ electron dynamics of ultrarelativistic plasma via polarization pattern of emitted gamma photons

Understanding and interpretation of the dynamics of ultrarelativistic plasma is a challenge, which calls for the development of methods for \textit{in situ} probing the plasma dynamical characteristics. We put forward a new method, harnessing polarization properties of $\gamma$-photons emitted from a non-pre-polarized plasma irradiated by a circularly polarized pulse. We show that the angular pattern of $\gamma$-photon linear polarization is explicitly correlated with the dynamics of the radiating electrons, which provides information on the laser-plasma interaction regime. Furthermore, with the $\gamma$-photon circular polarization originating from the electron radiative spin-flips, the plasma susceptibility to quantum electrodynamical processes is gauged. Our study demonstrates that the polarization signal of emitted $\gamma$-photons can be a versatile information source, which would be beneficial for the research fields of laser-driven plasma, accelerator science, and laboratory astrophysics