Robust Emergent Activity in Dynamical Networks

We study the evolution of a random weighted network with complex nonlinear dynamics at each node, whose activity may cease as a result of interactions with other nodes. Starting from a knowledge of the micro-level behaviour at each node, we develop a macroscopic description of the system in terms of the statistical features of the subnetwork of active nodes. We find the asymptotic characteristics of this subnetwork to be remarkably robust: the size of the active set is independent of the total number of nodes in the network, and the average degree of the active nodes is independent of both the network size and its connectivity. These results suggest that very different networks evolve to active subnetworks with the same characteristic features. This has strong implications for dynamical networks observed in the natural world, notably the existence of a characteristic range of links per species across ecological systems.Comment: 4 pages, 5 figure

Natural Supersymmetry, Muon g−2g-2, and the Last Crevices for the Top Squark

We study the interplay of natural supersymmetry and a supersymmetric solution to the discrepancy observed in measurements of the muon magnetic moment. The strongest constraints on the parameter space currently come from chargino searches in the trilepton channel and slepton searches in the dilepton channel at the LHC, and vast regions are currently allowed, especially at large $\tan{\beta}$. With light top squarks in the spectrum, as required from naturalness arguments, the situation changes dramatically; stop-assisted chargino and neutralino production via $\tilde{t} \rightarrow b \tilde{\chi}_{1}^{\pm}$ and $\tilde{t} \rightarrow t \tilde{\chi}_{1}^0$ are already probing the entire parameter space compatible with the muon magnetic moment at $\tan{\beta} \sim \mathcal{O}(10)$, while upcoming stop searches will probe most of the parameter space at larger $\tan{\beta} \sim 40$. Direct Higgsino searches as well as compressed slepton and stop searches are crucial to close out corners of parameter space. We consider one such example: in the presence of light sleptons and charginos as required to obtain appreciable contributions to the muon magnetic moment, compressed stops can dominantly undergo the following decay $\tilde{t} \, \rightarrow \, b \tilde{\ell} \nu (\tilde{\nu} \ell) \, \rightarrow \, b \ell \nu \tilde{\chi}_{1}^0$, facilitated by off-shell charginos. We find that the enhanced branching to leptons leads to a $5 \sigma$ mass reach (with $3000$ fb$^{-1}$ of data at LHC14) of $m_{\tilde{t}} \, \sim \, 350$ GeV, with the mass difference between stops and the lightest neutralino being $\sim 80$ GeV. This will further close out a significant part of the parameter space compatible with naturalness and the muon magnetic moment.Comment: 13 pages, 14 figures. Matches published versio

Coupling the PLANKTOM5.0 marine ecosystem model to the OCCAM 1º ocean general circulation model for investigation of the sensitivity of global biogeochemical cycles to variations in ecosystem complexity and physical environment

The earliest marine ecosystem models consisted of a simple representation of the main features of marine ecosystems, including, typically, variables for phytoplankton, zooplankton, nutrient and detritus (NPZD models). These have been incorporated into ocean general circulation models to give a basic representation of ecosystem function, providing predictions of bulk quantities such as global primary production, export and biomass which can be compared with available observations. A recent trend has been to increase the number of phytoplankton and zooplankton groups modelled, as analogues of different plankton groups observed to exist in the ocean, for example diatoms and cocolithophores (the so-called plankton functional type or PFT approach). It is usually assumed that the increase in complexity of the model will result in simulated ecosystems which more faithfully reproduce observations than NPZD models, but this has not been demonstrated systematically. The robustness of the PFT models to changes in model parameters and to changes to the physical environment in which it is embedded, have not been investigated. As a first step towards these goals, we incorporate a state-of-the-art PFT model, PLANKTOM5.0 into the OCCAM ocean general circulation model. A 6 year simulation is performed, covering the years 1989-1994 with identical parameter choices to an existing run of PLANKTOM5.0 coupled to the OPA general circulation model. This document describes the development of the coupled model and the 6 year simulation. Comparison with the OPA model and sensitivity of the solution to parameter choices will be described in a forthcoming journal paper

Mixing of the RR and NSNS sectors in the BMN limit

This paper concerns instanton contributions to two-point correlation functions of BMN operators in N=4 supersymmetric Yang-Mills that vanish in planar perturbation theory. Two-point functions of operators with even numbers of fermionic impurities (dual to RR string states) and with purely scalar impurities (dual to NSNS string states) are considered. This includes mixed RR - NSNS two-point functions. The gauge theory correlation functions are shown to respect BMN scaling and their behaviour is found to be in good agreement with the corresponding D-instanton contributions to two-point amplitudes in the maximally supersymmetric IIB plane-wave string theory. The string theory calculation also shows a simple dependence of the mass matrix elements on the mode numbers of states with an arbitrary number of impurities, which is difficult to extract from the gauge theory. For completeness, a discussion is also given of the perturbative mixing of two-impurity states in the RR and NSNS sectors at the first non-planar level.Comment: latex, 29 pages, 4 figure