Spiky Strings, Giant Magnons and beta-deformations

We study rigid string solutions rotating on the S^3 subspace of the beta-deformed AdS_5xS^5 background found by Lunin and Maldacena. For particular values of the parameters of the solutions we find the known giant magnon and single spike strings. We present a single spike string solution on the deformed S^3 and find how the deformation affects the dispersion relation. The possible relation of this string solution to spin chains and the connection of the solutions on the undeformed S^3 to the sine-Gordon model are briefly discussed.Comment: 20 pages, 2 figures; v2: typos corrected, references adde

Stability of Cross-Feeding Polymorphisms in Microbial Communities

This is the final version of the article. Available from Public Library of Science via the DOI in this record.Cross-feeding, a relationship wherein one organism consumes metabolites excreted by another, is a ubiquitous feature of natural and clinically-relevant microbial communities and could be a key factor promoting diversity in extreme and/or nutrient-poor environments. However, it remains unclear how readily cross-feeding interactions form, and therefore our ability to predict their emergence is limited. In this paper we developed a mathematical model parameterized using data from the biochemistry and ecology of an E. coli cross-feeding laboratory system. The model accurately captures short-term dynamics of the two competitors that have been observed empirically and we use it to systematically explore the stability of cross-feeding interactions for a range of environmental conditions. We find that our simple system can display complex dynamics including multi-stable behavior separated by a critical point. Therefore whether cross-feeding interactions form depends on the complex interplay between density and frequency of the competitors as well as on the concentration of resources in the environment. Moreover, we find that subtly different environmental conditions can lead to dramatically different results regarding the establishment of cross-feeding, which could explain the apparently unpredictable between-population differences in experimental outcomes. We argue that mathematical models are essential tools for disentangling the complexities of cross-feeding interactions.IG was supported by a Natural Environment Research Council (NERC) Advanced Fellowship NE/E013007/3 and a European Research Council (ERC) Consolidator grant MathModExp 647292, MK was funded by a National Aeronautics and Space Administration (NASA) NPP Fellowship and NASA NNX12AD87G, IG and PR were funded by a Biotechnology and Biological Sciences Research Council (BBSRC) grant BB/J010340/1, KS was supported by National Human Genome Research Institute (NHGRI) 2R01HG003328 - 07A1 and FR was supported by NASA NNX12AD87G. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript

Kinase inhibition leads to hormesis in a dual phosphorylation-dephosphorylation cycle

This is the final version of the article. Available from the publisher via the DOI in this record.Many antimicrobial and anti-tumour drugs elicit hormetic responses characterised by low-dose stimulation and high-dose inhibition. While this can have profound consequences for human health, with low drug concentrations actually stimulating pathogen or tumour growth, the mechanistic understanding behind such responses is still lacking. We propose a novel, simple but general mechanism that could give rise to hormesis in systems where an inhibitor acts on an enzyme. At its core is one of the basic building blocks in intracellular signalling, the dual phosphorylation-dephosphorylation motif, found in diverse regulatory processes including control of cell proliferation and programmed cell death. Our analytically-derived conditions for observing hormesis provide clues as to why this mechanism has not been previously identified. Current mathematical models regularly make simplifying assumptions that lack empirical support but inadvertently preclude the observation of hormesis. In addition, due to the inherent population heterogeneities, the presence of hormesis is likely to be masked in empirical population-level studies. Therefore, examining hormetic responses at single-cell level coupled with improved mathematical models could substantially enhance detection and mechanistic understanding of hormesis.Funding bodies: BBSRC (BB/J010340/1); EPSRC (EP/I00503X/1); Wellcome Trust (ISSF to University of Exeter)

On semiclassical calculation of three-point functions in AdS_5 \times T^(1,1)

Recently there has been progress on the computation of two- and three-point correlation functions with two "heavy" states via semiclassical methods. We extend this analysis to the case of AdS_5 \times T^(1,1), and examine the suggested procedure for the case of several simple string solutions. By making use of AdS/CFT duality, we derive the relevant correlation functions of operators belonging to the dual gauge theory.Comment: 18 pages, added referenc

Magnon-Like Dispersion Relation from M-Theory

We investigate classical rotating membranes in two different backgrounds. First, we obtain membrane solution in $AdS_4\times S^7$ background, analogous to the solution obtained by Hofman and Maldacena in the case of string theory. We find a magnon type dispersion relation similar to that of Hofman and Maldacena and to the one found by Dorey for the two spin case. In the appendix of the paper, we consider membrane solutions in $AdS_7\times S^4$, which give new relations between the conserved charges.Comment: 16 pages, typos corrected; V3: New section and comments added, to appear in Nucl. Phys.

Correlation functions in the Coulomb branch of N=4 SYM from AdS/CFT correspondence

In the present paper we study SU(N)->S(U(N/2)xU(N/2)) symmetry breaking in N=4 SYM via AdS/CFT correspondence. We consider two stacks of N/2 parallel D3 branes separated by a distance 2\vec d. In this case there is mixing between the different l-wave dilatonic KK modes. We calculate certain the two point correlation functions in the dual gauge theory. Due to mode mixing, the diagonal correlation functions have 1/N conformal-like correction as well as deformation terms. The off-diagonal correlators are also non-vanishing and their leading order is 1/N. We discuss briefly the spectrum of the glueball exitations.Comment: 25 pages, more comments on two throat geometry, decoupling limit and correction terms, a few typos corrected, two references added; to appear in Phys.Rev.

Boundary Action of N=2 Super-Liouville Theory

We derive a boundary action of N=2 super-Liouville theory which preserves both N=2 supersymmetry and conformal symmetry by imposing explicitly $T={\bar T}$ and $G={\bar G}$. The resulting boundary action shows a new duality symmetry.Comment: 15 pages; One reference is adde