Measuring β-cell function in vivo to understand the pathophysiology of type 2 diabetes

Diabetes arises when insulin secretion is inadequate for the prevailing metabolic conditions. As such appropriate measurement of β-cell function is necessary for a better understanding of the pathophysiology of prediabetes and diabetes. Unfortunately this is not a straightforward process and requires utilization of mathematical modelling to best appreciate its complexities. This is because insulin concentrations in the plasma represent a balance between the processes of secretion, hepatic extraction and clearance. In isolation such simple measures reveal very little about β-cell function. Moreover, since insulin lowers glucose accounting for the effect of the former on the latter it is a key part of understanding insulin action. The development of the minimal model has allowed simultaneous measurement of the dynamic relationship between insulin secretion and insulin action and produces a quantitative number – the Disposition Index – which quantifies β-cell function. At present this remains the best functional measure of islet health, however, it may not capture other phenotypes such as β-cell senescence or the effect of incretin hormones on β-cell function. Future ongoing development and interaction with other technologies, such as functional imaging, should enhance the contribution of this functional testing to the prevention, treatment and understanding of type 2 diabetes.peer-reviewe

A stochastic approach to path-dependent nonlinear Kolmogorov equations via BSDEs with time-delayed generators and applications to finance

We prove the existence of a viscosity solution of the following path dependent nonlinear Kolmogorov equation: $$\begin{cases} \partial_{t}u(t,\phi)+\mathcal{L}u(t,\phi)+f(t,\phi,u(t,\phi),\partial_{x}u(t,\phi) \sigma(t,\phi),(u(\cdot,\phi))_{t})=0,\;t\in[0,T),\;\phi\in\mathbb{\Lambda}\, ,u(T,\phi)=h(\phi),\;\phi\in\mathbb{\Lambda}, \end{cases}$$ where $\mathbb{\Lambda}=\mathcal{C}([0,T];\mathbb{R}^{d})$, $(u(\cdot ,\phi))_{t}:=(u(t+\theta,\phi))_{\theta\in[-\delta,0]}$ and $$\mathcal{L}u(t,\phi):=\langle b(t,\phi),\partial_{x}u(t,\phi)\rangle+\dfrac {1}{2}\mathrm{Tr}\big[\sigma(t,\phi)\sigma^{\ast}(t,\phi)\partial_{xx} ^{2}u(t,\phi)\big].$$ The result is obtained by a stochastic approach. In particular we prove a new type of nonlinear Feynman-Kac representation formula associated to a backward stochastic differential equation with time-delayed generator which is of non-Markovian type. Applications to the large investor problem and risk measures via $g$-expectations are also provided.Comment: 45 page

Dynamic Model Averaging in Large Model Spaces Using Dynamic Occam's Window

Bayesian model averaging has become a widely used approach to accounting for uncertainty about the structural form of the model generating the data. When data arrive sequentially and the generating model can change over time, Dynamic Model Averaging (DMA) extends model averaging to deal with this situation. Often in macroeconomics, however, many candidate explanatory variables are available and the number of possible models becomes too large for DMA to be applied in its original form. We propose a new method for this situation which allows us to perform DMA without considering the whole model space, but using a subset of models and dynamically optimizing the choice of models at each point in time. This yields a dynamic form of Occam's window. We evaluate the method in the context of the problem of nowcasting GDP in the Euro area. We find that its forecasting performance compares well that of other methods. Keywords: Bayesian model averaging; Model uncertainty; Nowcasting; Occam's window

Assessment of malaria transmission changes in Africa, due to the climate impact of land use change using Coupled Model Intercomparison Project Phase 5 earth system models

Using mathematical modelling tools, we assessed the potential for land use change (LUC) associated with the Intergovernmental Panel on Climate Change low- and high-end emission scenarios (RCP2.6 and RCP8.5) to impact malaria transmission in Africa. To drive a spatially explicit, dynamical malaria model, data from the four available earth system models (ESMs) that contributed to the LUC experiment of the Fifth Climate Model Intercomparison Project are used. Despite the limited size of the ESM ensemble, stark differences in the assessment of how LUC can impact climate are revealed. In three out of four ESMs, the impact of LUC on precipitation and temperature over the next century is limited, resulting in no significant change in malaria transmission. However, in one ESM, LUC leads to increases in precipitation under scenario RCP2.6, and increases in temperature in areas of land use conversion to farmland under both scenarios. The result is a more intense transmission and longer transmission seasons in the southeast of the continent, most notably in Mozambique and southern Tanzania. In contrast, warming associated with LUC in the Sahel region reduces risk in this model, as temperatures are already above the 25-30°C threshold at which transmission peaks. The differences between the ESMs emphasise the uncertainty in such assessments. It is also recalled that the modelling framework is unable to adequately represent local-scale changes in climate due to LUC, which some field studies indicate could be significant