A Wiener-Hopf type factorization for the exponential functional of Levy processes

For a Lévy process ξ=(ξt)t≥0 drifting to −∞, we define the so-called exponential functional as follows: Formula Under mild conditions on ξ, we show that the following factorization of exponential functionals: Formula holds, where × stands for the product of independent random variables, H− is the descending ladder height process of ξ and Y is a spectrally positive Lévy process with a negative mean constructed from its ascending ladder height process. As a by-product, we generate an integral or power series representation for the law of Iξ for a large class of Lévy processes with two-sided jumps and also derive some new distributional properties. The proof of our main result relies on a fine Markovian study of a class of generalized Ornstein–Uhlenbeck processes, which is itself of independent interest. We use and refine an alternative approach of studying the stationary measure of a Markov process which avoids some technicalities and difficulties that appear in the classical method of employing the generator of the dual Markov process.

Small time Chung-type LIL for Lévy processes

We prove Chung-type laws of the iterated logarithm for general Lévy processes at zero. In particular, we provide tools to translate small deviation estimates directly into laws of the iterated logarithm. This reveals laws of the iterated logarithm for Lévy processes at small times in many concrete examples. In some cases, exotic norming functions are derived.

Forecasting VaR using analytic higher moments for GARCH processes

It is widely accepted that some of the most accurate Value-at-Risk (VaR) estimates are based on an appropriately specified GARCH process. But when the forecast horizon is greater than the frequency of the GARCH model, such predictions have typically required time-consuming simulations of the aggregated returns distributions. This paper shows that fast, quasi-analytic GARCH VaR calculations can be based on new formulae for the first four moments of aggregated GARCH returns. Our extensive empirical study compares the Cornish–Fisher expansion with the Johnson SU distribution for fitting distributions to analytic moments of normal and Student t, symmetric and asymmetric (GJR) GARCH processes to returns data on different financial assets, for the purpose of deriving accurate GARCH VaR forecasts over multiple horizons and significance levels.

What processes drive the ocean heat transport?

The ocean contributes to regulating the Earth’s climate through its ability to transport heat from the equator to the poles. In this study we use long simulations of an ocean model to investigate whether the heat transport is carried primarily by wind-driven gyres or whether it is dominated by deep circulations associated with abyssal mixing and high latitude convection. The heat transport is computed as a function of temperature classes. In the Pacific and Indian ocean, the bulk of the heat transport is associated with wind-driven gyres confined to the thermocline. In the Atlantic, the thermocline gyres account for only 40% of the total heat transport. The remaining 60% is associated with a circulation reaching down to cold waters below the thermocline. Using a series of sensitivity experiments, we show that this deep heat transport is primarily set by the strength and patterns of surface winds and only secondarily by diabatic processes at high latitudes in the North Atlantic. Abyssal mixing below 2000 m has hardly any impact on ocean heat transport. A major implication is that the role of the ocean in regulating Earth’s climate strongly depends on how surface winds change across different climates in both hemispheres at low and high latitudes.

Balanced excitation and inhibition: Model based analysis of local field potentials

We have developed a model of the local field potential (LFP) based on the conservation of charge, the independence principle of ionic flows and the classical Hodgkin–Huxley (HH) type intracellular model of synaptic activity. Insights were gained through the simulation of the HH intracellular model on the nonlinear relationship between the balance of synaptic conductances and that of post-synaptic currents. The latter is dependent not only on the former, but also on the temporal lag between the excitatory and inhibitory conductances, as well as the strength of the afferent signal. The proposed LFP model provides a method for decomposing the LFP recordings near the soma of layer IV pyramidal neurons in the barrel cortex of anaesthetised rats into two highly correlated components with opposite polarity. The temporal dynamics and the proportional balance of the two components are comparable to the excitatory and inhibitory post-synaptic currents computed from the HH model. This suggests that the two components of the LFP reflect the underlying excitatory and inhibitory post-synaptic currents of the local neural population. We further used the model to decompose a sequence of evoked LFP responses under repetitive electrical stimulation (5 Hz) of the whisker pad. We found that as neural responses adapted, the excitatory and inhibitory components also adapted proportionately, while the temporal lag between the onsets of the two components increased during frequency adaptation. Our results demonstrated that the balance between neural excitation and inhibition can be investigated using extracellular recordings. Extension of the model to incorporate multiple compartments should allow more quantitative interpretations of surface Electroencephalography (EEG) recordings into components reflecting the excitatory, inhibitory and passive ionic current flows generated by local neural populations.

Lower stratospheric processes

Chapter 7 of Scientific Assessment of Ozone Depletion: 1998

Online bayesian inference in some time-frequency representations of non-stationary processes

The use of Bayesian inference in the inference of time-frequency representations has, thus far, been limited to offline analysis of signals, using a smoothing spline based model of the time-frequency plane. In this paper we introduce a new framework that allows the routine use of Bayesian inference for online estimation of the time-varying spectral density of a locally stationary Gaussian process. The core of our approach is the use of a likelihood inspired by a local Whittle approximation. This choice, along with the use of a recursive algorithm for non-parametric estimation of the local spectral density, permits the use of a particle filter for estimating the time-varying spectral density online. We provide demonstrations of the algorithm through tracking chirps and the analysis of musical data.

The competition–performance relation: a meta-analytic review and test of the opposing processes model of competition and performance

What is the relation between competition and performance? The present research addresses this important multidisciplinary question by conducting a meta-analysis of existing empirical work and by proposing a new conceptual model—the opposing processes model of competition and performance. This model was tested by conducting an additional meta-analysis and 3 new empirical studies. The first meta-analysis revealed that there is no noteworthy relation between competition and performance. The second meta-analysis showed, in accord with the opposing processes model, that the absence of a direct effect is the result of inconsistent mediation via achievement goals: Competition prompts performance-approach goals which, in turn, facilitate performance; and competition also prompts performance-avoidance goals which, in turn, undermine performance. These same direct and mediational findings were also observed in the 3 new empirical studies (using 3 different conceptualizations of competition and attending to numerous control variables). Our findings provide both interpretational clarity regarding past research and conceptual guidance regarding future research on the competition–performance relation.

Parameterised diabatic processes in numerical simulations of an extratropical cyclone

The parameterisation of diabatic processes in numerical models is critical for the accuracy of weather forecasts and for climate projections. A novel approach to the evaluation of these processes in models is introduced in this contribution. The approach combines a suite of on-line tracer diagnostics with off-line trajectory calculations. Each tracer tracks accumulative changes in potential temperature associated with a particular parameterised diabatic process in the model. A comparison of tracers therefore allows the identification of the most active diabatic processes and their downstream impacts. The tracers are combined with trajectories computed using model-resolved winds, allowing the various diabatic contributions to be tracked back to their time and location of occurrence. We have used this approach to investigate diabatic processes within a simulated extratropical cyclone. We focus on the warm conveyor belt, in which the dominant diabatic contributions come from large-scale latent heating and parameterised convection. By contrasting two simulations, one with standard convection parameterisation settings and another with reduced parameterised convection, the effects of parameterised convection on the structure of the cyclone have been determined. Under reduced parameterised convection conditions, the large-scale latent heating is forced to release convective instability that would otherwise have been released by the convection parameterisation. Although the spatial distribution of precipitation depends on the details of the split between parameterised convection and large-scale latent heating, the total precipitation amount associated with the cyclone remains largely unchanged. For reduced parameterised convection, a more rapid and stronger latent heating episode takes place as air ascends within the warm conveyor belt.

Impact of oceanic processes on the carbon cycle during the last termination

During the last termination (from ~18 000 years ago to ~9000 years ago), the climate significantly warmed and the ice sheets melted. Simultaneously, atmospheric CO2 increased from ~190 ppm to ~260 ppm. Although this CO2 rise plays an important role in the deglacial warming, the reasons for its evolution are difficult to explain. Only box models have been used to run transient simulations of this carbon cycle transition, but by forcing the model with data constrained scenarios of the evolution of temperature, sea level, sea ice, NADW formation, Southern Ocean vertical mixing and biological carbon pump. More complex models (including GCMs) have investigated some of these mechanisms but they have only been used to try and explain LGM versus present day steady-state climates. In this study we use a coupled climate-carbon model of intermediate complexity to explore the role of three oceanic processes in transient simulations: the sinking of brines, stratification-dependent diffusion and iron fertilization. Carbonate compensation is accounted for in these simulations. We show that neither iron fertilization nor the sinking of brines alone can account for the evolution of CO2, and that only the combination of the sinking of brines and interactive diffusion can simultaneously simulate the increase in deep Southern Ocean δ13C. The scenario that agrees best with the data takes into account all mechanisms and favours a rapid cessation of the sinking of brines around 18 000 years ago, when the Antarctic ice sheet extent was at its maximum. In this scenario, we make the hypothesis that sea ice formation was then shifted to the open ocean where the salty water is quickly mixed with fresher water, which prevents deep sinking of salty water and therefore breaks down the deep stratification and releases carbon from the abyss. Based on this scenario, it is possible to simulate both the amplitude and timing of the long-term CO2 increase during the last termination in agreement with ice core data. The atmospheric δ13C appears to be highly sensitive to changes in the terrestrial biosphere, underlining the need to better constrain the vegetation evolution during the termination.

Automatic control of food manufacturing processes. 2nd edition

In the ten years since the first edition of this book appeared there have been significant developments in food process engineering, notably in biotechnology and membrane application. Advances have been made in the use of sensors for process control, and the growth of information technology and on-line computer applications continues apace. In addition, plant investment decisions are increasingly determined by quality assurance considerations and have to incorporate a greater emphasis on health and safety issues. The content of this edition has been rearranged to include descriptions of recent developments and to reflect the influence of new technology on the control and operations of automated plant. Original examples have been retained where relevant and these, together with many new illustrations, provide a comprehensive guide to good practice.

Improved evaporative flux partitioning and carbon flux in the land surface model JULES: impact on the simulation of land surface processes in temperate Europe

The primary role of land surface models embedded in climate models is to partition surface available energy into upwards, radiative, sensible and latent heat fluxes. Partitioning of evapotranspiration, ET, is of fundamental importance: as a major component of the total surface latent heat flux, ET affects the simulated surface water balance, and related energy balance, and consequently the feedbacks with the atmosphere. In this context it is also crucial to credibly represent the CO2 exchange between ecosystems and their environment. In this study, JULES, the land surface model used in UK weather and climate models, has been evaluated for temperate Europe. Compared to eddy covariance flux measurements, the CO2 uptake by the ecosystem is underestimated and the ET overestimated. In addition, the contribution to ET from soil and intercepted water evaporation far outweighs the contribution of plant transpiration. To alleviate these biases, adaptations have been implemented in JULES, based on key literature references. These adaptations have improved the simulation of the spatio-temporal variability of the fluxes and the accuracy of the simulated GPP and ET, including its partitioning. This resulted in a shift of the seasonal soil moisture cycle. These adaptations are expected to increase the fidelity of climate simulations over Europe. Finally, the extreme summer of 2003 was used as evaluation benchmark for the use of the model in climate change studies. The improved model captures the impact of the 2003 drought on the carbon assimilation and the water use efficiency of the plants. It, however, underestimates the 2003 GPP anomalies. The simulations showed that a reduction of evaporation from the interception and soil reservoirs, albeit not of transpiration, largely explained the good correlation between the carbon and the water fluxes anomalies that was observed during 2003. This demonstrates the importance of being able to discriminate the response of individual component of the ET flux to environmental forcing.