Classifying general nonlinear force laws in cell-based models via the continuum limit

though discrete cell-based frameworks are now commonly used to simulate a whole range of biological phenomena, it is typically not obvious how the numerous different types of model are related to one another, nor which one is most appropriate in a given context. Here we demonstrate how individual cell movement on the discrete scale modeled using nonlinear force laws can be described by nonlinear diffusion coefficients on the continuum scale. A general relationship between nonlinear force laws and their respective diffusion coefficients is derived in one spatial dimension and, subsequently, a range of particular examples is considered. For each case excellent agreement is observed between numerical solutions of the discrete and corresponding continuum models. Three case studies are considered in which we demonstrate how the derived nonlinear diffusion coefficients can be used to (a) relate different discrete models of cell behavior; (b) derive discrete, intercell force laws from previously posed diffusion coefficients, and (c) describe aggregative behavior in discrete simulations.

Stable Nonlinear Receding Horizon Regulator Using RBF Neural Network Models

The general stability theory of nonlinear receding horizon controllers has attracted much attention over the last fifteen years, and many algorithms have been proposed to ensure closed-loop stability. On the other hand many reports exist regarding the use of artificial neural network models in nonlinear receding horizon control. However, little attention has been given to the stability issue of these specific controllers. This paper addresses this problem and proposes to cast the nonlinear receding horizon control based on neural network models within the framework of an existing stabilising algorithm.

Bifurcation Analysis of Eigenstructure Assignment Control in a Simple Nonlinear Aircraft Model

Aircraft systems are highly nonlinear and time varying. High-performance aircraft at high angles of incidence experience undesired coupling of the lateral and longitudinal variables, resulting in departure from normal controlled � ight. The construction of a robust closed-loop control that extends the stable and decoupled � ight envelope as far as possible is pursued. For the study of these systems, nonlinear analysis methods are needed. Previously, bifurcation techniques have been used mainly to analyze open-loop nonlinear aircraft models and to investigate control effects on dynamic behavior. Linear feedback control designs constructed by eigenstructure assignment methods at a � xed � ight condition are investigated for a simple nonlinear aircraft model. Bifurcation analysis, in conjunction with linear control design methods, is shown to aid control law design for the nonlinear system.

Precise calculations of the existence of multiple AMOC equilibria in coupled climate models Part I: equilibrium states

This study examines criteria for the existence of two stable states of the Atlantic Meridional Overturning Circulation (AMOC) using a combination of theory and simulations from a numerical coupled atmosphere–ocean climate model. By formulating a simple collection of state parameters and their relationships, the authors reconstruct the North Atlantic Deep Water (NADW) OFF state behavior under a varying external salt-flux forcing. This part (Part I) of the paper examines the steady-state solution, which gives insight into the mechanisms that sustain the NADW OFF state in this coupled model; Part II deals with the transient behavior predicted by the evolution equation. The nonlinear behavior of the Antarctic Intermediate Water (AAIW) reverse cell is critical to the OFF state. Higher Atlantic salinity leads both to a reduced AAIW reverse cell and to a greater vertical salinity gradient in the South Atlantic. The former tends to reduce Atlantic salt export to the Southern Ocean, while the latter tends to increases it. These competing effects produce a nonlinear response of Atlantic salinity and salt export to salt forcing, and the existence of maxima in these quantities. Thus the authors obtain a natural and accurate analytical saddle-node condition for the maximal surface salt flux for which a NADW OFF state exists. By contrast, the bistability indicator proposed by De Vries and Weber does not generally work in this model. It is applicable only when the effect of the AAIW reverse cell on the Atlantic salt budget is weak.

Closed loop design for a simple nonlinear aircraft model using eigenstructure assignment

Aircraft systems are highly nonlinear and time varying. High-performance aircraft at high angles of incidence experience undesired coupling of the lateral and longitudinal variables, resulting in departure from normal controlled flight. The aim of this work is to construct a robust closed-loop control that optimally extends the stable and decoupled flight envelope. For the study of these systems nonlinear analysis methods are needed. Previously, bifurcation techniques have been used mainly to analyze open-loop nonlinear aircraft models and investigate control effects on dynamic behavior. In this work linear feedback control designs calculated by eigenstructure assignment methods are investigated for a simple aircraft model at a fixed flight condition. Bifurcation analysis in conjunction with linear control design methods is shown to aid control law design for the nonlinear system.

Cannabidiol exerts anti-convulsant effects in animal models of temporal lobe and partial seizures

Cannabis sativa has been associated with contradictory effects upon seizure states despite its medicinal use by numerous people with epilepsy. We have recently shown that the phytocannabinoid cannabidiol (CBD) reduces seizure severity and lethality in the well-established in vivo model of pentylenetetrazoleinduced generalised seizures, suggesting that earlier, small-scale clinical trials examining CBD effects in people with epilepsy warrant renewed attention. Here, we report the effects of pure CBD (1, 10 and 100 mg/kg) in two other established rodent seizure models, the acute pilocarpine model of temporal lobe seizure and the penicillin model of partial seizure. Seizure activity was video recorded and scored offline using model-specific seizure severity scales. In the pilocarpine model CBD (all doses) significantly reduced the percentage of animals experiencing the most severe seizures. In the penicillin model, CBD (�10 mg/kg) significantly decreased the percentage mortality as a result of seizures; CBD (all doses) also decreased the percentage of animals experiencing the most severe tonic–clonic seizures. These results extend the anticonvulsant profile of CBD; when combined with a reported absence of psychoactive effects, this evidence strongly supports CBD as a therapeutic candidate for a diverse range of human epilepsies.

Potential anti-cancer effects of virgin olive oil phenols on colorectal carcinogenesis models in vitro

The traditional Mediterranean diet is thought to represent a healthy lifestyle; especially given the incidence of several cancers including colorectal cancer is lower in Mediterranean countries compared to Northern Europe. Olive oil, a central component of the Mediterranean diet, is believed to beneficially affect numerous biological processes. We used phenols extracted from virgin olive oil on a series of in vitro systems that model important stages of colon carcinogenesis. The effect the extract on DNA damage induced by hydrogen peroxide was measured in HT29 cells using single cell microgel-electrophoresis. A significant anti-genotoxic linear trend (p=0.011) was observed when HT29 cells were pre-incubated with olive oil phenols (0, 5, 10, 25, 50, 75, 100 microg/ml) for 24 hr, then challenged with hydrogen peroxide. The olive oil phenols (50, 100 microg/ml) significantly (p=0.004, p=0.002) improved barrier function of CACO2 cells after 48 hr as measured by trans-epithelial resistance. Significant inhibition of HT115 invasion (p<0.01) was observed at olive oil phenols concentrations of 25, 50, 75, 100 microg/ml using the matrigel invasion assay. No effect was observed on HT115 viability over the concentration range 0, 25, 50 75, 100 microg/ml after 24 hr, although 75 and 100 microg/ml olive oil phenols significantly inhibited HT115 cell attachment (p=0.011, p=0.006). Olive oil phenols had no significant effect on metastasis-related gene expression in HT115 cells. We have demonstrated that phenols extracted from virgin olive oil are capable of inhibiting several stages in colon carcinogenesis in vitro.

Anti-proliferative effects of physiological concentrations of enterolactone in models of prostate tumourigenesis

SCOPE: There is evidence that a mammalian lignan, enterolactone (ENL), decreases the proliferation rate of prostate cancer cells, although previous studies have used concentrations difficult to achieve through dietary modification. We have therefore investigated the anti-proliferative effects of ENL in an in vitro model of prostate tumourigenesis at concentrations reported to occur in a range of male populations. METHODS AND RESULTS: The effects of 0.1 and 1 μM ENL on three markers of viability and proliferation (metabolic activity, growth kinetics, and cell cycle progression) were assessed in the RWPE-1, WPE1-NA22, WPE1-NB14, WPE1-NB11, WPE1-NB26, LNCaP, and PC-3 cell lines over 72 h. Based on these data, we quantified the expression levels of 12 genes involved in the control of DNA replication initiation using TaqMan real-time PCR in the WPE1-NA22, WPE1-NB14, WPE1-NB11, and WPE1-NB26 cell lines. ENL significantly inhibited the abnormal proliferation of the WPE1-NB14 and WPE1-NB11 cell lines and appears to be a consequence of decreased expression of abnormal chromatin licensing and DNA replication factor 1. CONCLUSION: In contrast to previous studies, concentrations of ENL that are reported after dietary intervention restrict the proliferation of early-stage tumourigenic prostate cell lines by inhibiting the abnormal formation of complexes that initiate DNA replication.

A spectral view of nonlinear fluxes and stationary-transient interaction in the atmosphere

Nonlinear spectral transfers of kinetic energy and enstrophy, and stationary-transient interaction, are studied using global FGGE data for January 1979. It is found that the spectral transfers arise primarily from a combination, in roughly equal measure, of pure transient and mixed stationary-transient interactions. The pure transient interactions are associated with a transient eddy field which is approximately locally homogeneous and isotropic, and they appear to be consistently understood within the context of two-dimensional homogeneous turbulence. Theory based on spatial wale separation concepts suggests that the mixed interactions may be understood physically, to a first approximation, as a process of shear-induced spectral transfer of transient enstrophy along lines of constant zonal wavenumber. This essentially conservative enstrophy transfer generally involves highly nonlocal stationary-transient energy conversions. The observational analysis demonstrates that the shear-induced transient enstrophy transfer is mainly associated with intermediate-scale (zonal wavenumber m > 3) transients and is primarily to smaller (meridional) scales, so that the transient flow acts as a source of stationary energy. In quantitative terms, this transient-eddy rectification corresponds to a forcing timescale in the stationary energy budget which is of the same order of magnitude as most estimates of the damping timescale in simple stationary-wave models (5 to 15 days). Moreover, the nonlinear interactions involved are highly nonlocal and cover a wide range of transient scales of motion.

The financial effects of uniform and mixed corporate social performance

Firms typically present a mixed picture of corporate social performance (CSP), with positive and negative indicators exhibited by the same firm. Thus, stakeholders’ judgements of corporate social responsibility (CSR) typically evaluate positives in the context of negatives, and vice versa. Building on social judgement theory, we present two alternative accounts of how stakeholders respond to such complexity, which provide differing implications for the financial effects of CSP: reciprocal dampening and rewarding uniformity. Echoing notable findings on strategic consistency, our US panel study finds that firms that exhibit uniformly positive or uniformly negative indicators in particular dimensions of CSP outperform firms that exhibit a mixed picture of positives and negatives, which supports the notion that stakeholders’ judgements of CSR reward uniformity.

Asymmetric output gap effects in Phillips Curve and mark-up pricing models: evidence for the US and the UK

A number of studies have found an asymmetric response of consumer price index inflation to the output gap in the US in simple Phillips curve models. We consider whether there are similar asymmetries in mark-up pricing models, that is, whether the mark-up over producers' costs also depends upon the sign of the (adjusted) output gap. The robustness of our findings to the price series is assessed, and also whether price-output responses in the UK are asymmetric.

Estimating Lorenz's reference state in an ocean with a nonlinear equation of state for seawater

The study of the mechanical energy budget of the oceans using Lorenz available potential energy (APE) theory is based on knowledge of the adiabatically re-arranged Lorenz reference state of minimum potential energy. The compressible and nonlinear character of the equation of state for seawater has been thought to cause the reference state to be ill-defined, casting doubt on the usefulness of APE theory for investigating ocean energetics under realistic conditions. Using a method based on the volume frequency distribution of parcels as a function of temperature and salinity in the context of the seawater Boussinesq approximation, which we illustrate using climatological data, we show that compressibility effects are in fact minor. The reference state can be regarded as a well defined one-dimensional function of depth, which forms a surface in temperature, salinity and density space between the surface and the bottom of the ocean. For a very small proportion of water masses, this surface can be multivalued and water parcels can have up to two statically stable levels in the reference density profile, of which the shallowest is energetically more accessible. Classifying parcels from the surface to the bottom gives a different reference density profile than classifying in the opposite direction. However, this difference is negligible. We show that the reference state obtained by standard sorting methods is equivalent, though computationally more expensive, to the volume frequency distribution approach. The approach we present can be applied systematically and in a computationally efficient manner to investigate the APE budget of the ocean circulation using models or climatological data.

Trends in the CERES dataset, 2000–13: the effects of sea ice and jet shifts and comparison to climate models

We review the effects of dynamical variability on clouds and radiation in observations and models and discuss their implications for cloud feedbacks. Jet shifts produce robust meridional dipoles in upper-level clouds and longwave cloud-radiative effect (CRE), but low-level clouds, which do not simply shift with the jet, dominate the shortwave CRE. Because the effect of jet variability on CRE is relatively small, future poleward jet shifts with global warming are only a second-order contribution to the total CRE changes around the midlatitudes, suggesting a dominant role for thermodynamic effects. This implies that constraining the dynamical response is unlikely to reduce the uncertainty in extratropical cloud feedback. However, we argue that uncertainty in the cloud-radiative response does affect the atmospheric circulation response to global warming, by modulating patterns of diabatic forcing. How cloud feedbacks can affect the dynamical response to global warming is an important topic of future research.

Mixed-phase cloud physics and Southern Ocean cloud feedback in climate models

Increasing optical depth poleward of 45° is a robust response to warming in global climate models. Much of this cloud optical depth increase has been hypothesized to be due to transitions from ice-dominated to liquid-dominated mixed-phase cloud. In this study, the importance of liquid-ice partitioning for the optical depth feedback is quantified for 19 Coupled Model Intercomparison Project Phase 5 models. All models show a monotonic partitioning of ice and liquid as a function of temperature, but the temperature at which ice and liquid are equally mixed (the glaciation temperature) varies by as much as 40 K across models. Models that have a higher glaciation temperature are found to have a smaller climatological liquid water path (LWP) and condensed water path and experience a larger increase in LWP as the climate warms. The ice-liquid partitioning curve of each model may be used to calculate the response of LWP to warming. It is found that the repartitioning between ice and liquid in a warming climate contributes at least 20% to 80% of the increase in LWP as the climate warms, depending on model. Intermodel differences in the climatological partitioning between ice and liquid are estimated to contribute at least 20% to the intermodel spread in the high-latitude LWP response in the mixed-phase region poleward of 45°S. It is hypothesized that a more thorough evaluation and constraint of global climate model mixed-phase cloud parameterizations and validation of the total condensate and ice-liquid apportionment against observations will yield a substantial reduction in model uncertainty in the high-latitude cloud response to warming.