Hard Instances of the Constrained Discrete Logarithm Problem

The discrete logarithm problem (DLP) generalizes to the constrained DLP, where the secret exponent $x$ belongs to a set known to the attacker. The complexity of generic algorithms for solving the constrained DLP depends on the choice of the set. Motivated by cryptographic applications, we study sets with succinct representation for which the constrained DLP is hard. We draw on earlier results due to Erd\"os et al. and Schnorr, develop geometric tools such as generalized Menelaus' theorem for proving lower bounds on the complexity of the constrained DLP, and construct sets with succinct representation with provable non-trivial lower bounds

Holographic phase transitions at finite baryon density

We use holographic techniques to study SU(Nc) super Yang-Mills theory coupled to Nf << Nc flavours of fundamental matter at finite temperature and baryon density. We focus on four dimensions, for which the dual description consists of Nf D7-branes in the background of Nc black D3-branes, but our results apply in other dimensions as well. A non-zero chemical potential mu or baryon number density n is introduced via a nonvanishing worldvolume gauge field on the D7-branes. Ref. [1] identified a first order phase transition at zero density associated with `melting' of the mesons. This extends to a line of phase transitions for small n, which terminates at a critical point at finite n. Investigation of the D7-branes' thermodynamics reveals that (d mu / dn)_T <0 in a small region of the phase diagram, indicating an instability. We comment on a possible new phase which may appear in this region.Comment: 33 pages, 22 figure

Direct Constraints on Minimal Supersymmetry from Fermi-LAT Observations of the Dwarf Galaxy Segue 1

The dwarf galaxy Segue 1 is one of the most promising targets for the indirect detection of dark matter. Here we examine what constraints 9 months of Fermi-LAT gamma-ray observations of Segue 1 place upon the Constrained Minimal Supersymmetric Standard Model (CMSSM), with the lightest neutralino as the dark matter particle. We use nested sampling to explore the CMSSM parameter space, simultaneously fitting other relevant constraints from accelerator bounds, the relic density, electroweak precision observables, the anomalous magnetic moment of the muon and B-physics. We include spectral and spatial fits to the Fermi observations, a full treatment of the instrumental response and its related uncertainty, and detailed background models. We also perform an extrapolation to 5 years of observations, assuming no signal is observed from Segue 1 in that time. Results marginally disfavour models with low neutralino masses and high annihilation cross-sections. Virtually all of these models are however already disfavoured by existing experimental or relic density constraints.Comment: 22 pages, 5 figures; added extra scans with extreme halo parameters, expanded introduction and discussion in response to referee's comment

A Numerical Investigation of the Effects of Classical Phase Space Structure on a Quantum System

We present a detailed numerical study of a chaotic classical system and its quantum counterpart. The system is a special case of a kicked rotor and for certain parameter values possesses cantori dividing chaotic regions of the classical phase space. We investigate the diffusion of particles through a cantorus; classical diffusion is observed but quantum diffusion is only significant when the classical phase space area escaping through the cantorus per kicking period greatly exceeds Planck's constant. A quantum analysis confirms that the cantori act as barriers. We numerically estimate the classical phase space flux through the cantorus per kick and relate this quantity to the behaviour of the quantum system. We introduce decoherence via environmental interactions with the quantum system and observe the subsequent increase in the transport of quantum particles through the boundary.Comment: 15 pages, 22 figure

Extreme Ultra-Violet Spectroscopy of the Lower Solar Atmosphere During Solar Flares

The extreme ultraviolet portion of the solar spectrum contains a wealth of diagnostic tools for probing the lower solar atmosphere in response to an injection of energy, particularly during the impulsive phase of solar flares. These include temperature and density sensitive line ratios, Doppler shifted emission lines and nonthermal broadening, abundance measurements, differential emission measure profiles, and continuum temperatures and energetics, among others. In this paper I shall review some of the advances made in recent years using these techniques, focusing primarily on studies that have utilized data from Hinode/EIS and SDO/EVE, while also providing some historical background and a summary of future spectroscopic instrumentation.Comment: 34 pages, 8 figures. Submitted to Solar Physics as part of the Topical Issue on Solar and Stellar Flare

Loop Operators and the Kondo Problem

We analyse the renormalisation group flow for D-branes in WZW models from the point of view of the boundary states. To this end we consider loop operators that perturb the boundary states away from their ultraviolet fixed points, and show how to regularise and renormalise them consistently with the global symmetries of the problem. We pay particular attention to the chiral operators that only depend on left-moving currents, and which are attractors of the renormalisation group flow. We check (to lowest non-trivial order in the coupling constant) that at their stable infrared fixed points these operators measure quantum monodromies, in agreement with previous semiclassical studies. Our results help clarify the general relationship between boundary transfer matrices and defect lines, which parallels the relation between (non-commutative) fields on (a stack of) D-branes and their push-forwards to the target-space bulk.Comment: 22 pages, 2 figure

The Fueling and Evolution of AGN: Internal and External Triggers

In this chapter, I review the fueling and evolution of active galactic nuclei (AGN) under the influence of internal and external triggers, namely intrinsic properties of host galaxies (morphological or Hubble type, color, presence of bars and other non-axisymmetric features, etc) and external factors such as environment and interactions. The most daunting challenge in fueling AGN is arguably the angular momentum problem as even matter located at a radius of a few hundred pc must lose more than 99.99 % of its specific angular momentum before it is fit for consumption by a BH. I review mass accretion rates, angular momentum requirements, the effectiveness of different fueling mechanisms, and the growth and mass density of black BHs at different epochs. I discuss connections between the nuclear and larger-scale properties of AGN, both locally and at intermediate redshifts, outlining some recent results from the GEMS and GOODS HST surveys.Comment: Invited Review Chapter to appear in LNP Volume on "AGN Physics on All Scales", Chapter 6, in press. 40 pages, 12 figures. Typo in Eq 5 correcte

Suppression of nuclear factor-κB activity in macrophages by chylomicron remnants: modulation by the fatty acid composition of the particles

Current evidence indicates that chylomicron remnants (CMR) induce macrophage foam cell formation, an early event in atherosclerosis. Inflammation also plays a part in atherogenesis and the transcription factor nuclear factor-κB (NF-κB) has been implicated. In this study, the influence of CMR on the activity of NF-κB in macrophages and its modulation by the fatty acid composition of the particles were investigated using macrophages derived from the human monocyte cell line THP-1 and CMR-like particles (CRLPs). Incubation of THP-1 macrophages with CRLPs caused decreased NF-κB activation and downregulated the expression of phospho-p65–NF-κB and phospho-IκBα (pIκBα). Secretion of the inflammatory cytokines tumour necrosis factor α, interleukin-6 and monocyte chemoattractant protein-1, which are under NF-κB transcriptional control, was inhibited and mRNA expression for cyclooxygenase-2, an NF-κB target gene, was reduced. CRLPs enriched in polyunsaturated fatty acids compared with saturated or monounsaturated fatty acids had a markedly greater inhibitory effect on NF-κB binding to DNA and the expression of phospho-p65–NF-κB and pIκB. Lipid loading of macrophages with CRLPs enriched in polyunsaturated fatty acids compared with monounsaturated fatty acids or saturated fatty acids also increased the subsequent rate of cholesterol efflux, an effect which may be linked to the inhibition of NF-κB activity. These findings demonstrate that CMR suppress NF-κB activity in macrophages, and that this effect is modulated by their fatty acid composition. This downregulation of inflammatory processes in macrophages may represent a protective effect of CMR which is enhanced by dietary polyunsaturated fatty acids

Fascicles and the interfascicular matrix show decreased fatigue life with ageing in energy storing tendons

Tendon is composed of rope-like fascicles bound together by interfascicular matrix (IFM). The IFM is critical for the function of energy storing tendons, facilitating sliding between fascicles to allow these tendons to cyclically stretch and recoil. This capacity is required to a lesser degree in positional tendons. We have previously demonstrated that both fascicles and IFM in energy storing tendons have superior fatigue resistance compared with positional tendons, but the effect of ageing on the fatigue properties of these different tendon subunits has not been determined. Energy storing tendons become more injury-prone with ageing, indicating reduced fatigue resistance, hence we tested the hypothesis that the decline in fatigue life with ageing in energy storing tendons would be more pronounced in the IFM than in fascicles. We further hypothesised that tendon subunit fatigue resistance would not alter with ageing in positional tendons. Fascicles and IFM from young and old energy storing and positional tendons were subjected to cyclic fatigue testing until failure, and mechanical properties were calculated. The results show that both IFM and fascicles from the SDFT exhibit a similar magnitude of reduced fatigue life with ageing. By contrast, the fatigue life of positional tendon subunits was unaffected by ageing. The age-related decline in fatigue life of tendon subunits in energy storing tendons is likely to contribute to the increased risk of injury in aged tendons. Full understanding of the mechanisms resulting in this reduced fatigue life will aid in the development of treatments and interventions to prevent age-related tendinopathy

Nuclear relocalisation of cytoplasmic poly(A)-binding proteins PABP1 and PABP4 in response to UV irradiation reveals mRNA-dependent export of metazoan PABPs

Poly(A)-binding protein 1 (PABP1) has a fundamental role in the regulation of mRNA translation and stability, both of which are crucial for a wide variety of cellular processes. Although generally a diffuse cytoplasmic protein, it can be found in discrete foci such as stress and neuronal granules. Mammals encode several additional cytoplasmic PABPs that remain poorly characterised, and with the exception of PABP4, appear to be restricted in their expression to a small number of cell types. We have found that PABP4, similarly to PABP1, is a diffusely cytoplasmic protein that can be localised to stress granules. However, UV exposure unexpectedly relocalised both proteins to the nucleus. Nuclear relocalisation of PABPs was accompanied by a reduction in protein synthesis but was not linked to apoptosis. In examining the mechanism of PABP relocalisation, we found that it was related to a change in the distribution of poly(A) RNA within cells. Further investigation revealed that this change in RNA distribution was not affected by PABP knockdown but that perturbations that block mRNA export recapitulate PABP relocalisation. Our results support a model in which nuclear export of PABPs is dependent on ongoing mRNA export, and that a block in this process following UV exposure leads to accumulation of cytoplasmic PABPs in the nucleus. These data also provide mechanistic insight into reports that transcriptional inhibitors and expression of certain viral proteins cause relocation of PABP to the nucleus. © 2011. Published by The Company of Biologists Ltd