Abstract: Nonlinear models have been widely employed to characterize the
underlying structure in a time series. It has been shown that the
in-sample fit of nonlinear models is better than linear models, however,
the superiority of nonlinear models over linear models, from the
perspective of out-of-sample forecasting accuracy remains doubtful. We
compare forecast accuracy of nonlinear regime switching models against
classical linear models using different performance scores, such as root
mean square error (RMSE), mean absolute error (MAE), and the continuous
ranked probability score (CRPS). We propose and investigate the efficacy
of a class of simple nonparametric, nonlinear models that are based on
estimation of a few parameters, and can generate more accurate forecasts
when compared with the classical models. Also, given the importance of
gauging uncertainty in forecasts for proper risk assessment and well
informed decision making, we focus on generating and evaluating both point
and density forecasts.
Keywords: Nonlinear, Forecasting, Performance scores.
This talk will introduce various aspects of modern cryptography. After introducing RSA and some factoring algorithms, I will move on to how elliptic curves can be used to produce a more complex form of Diffie--Hellman key exchange.
We investigate a class of weakly interactive particle systems with absorption. We assume that the coefficients in our model depend on an "absorbing" factor and prove the existence and uniqueness of the proposed model. Then we investigate the convergence of the empirical measure of the particle system and derive the Stochastic PDE satisfied by the density of the limit empirical measure. This result can be applied to credit modelling. This is a joint work with Dr. Ben Hambly.
Abstract: Cell migration and growth are essential components of the development of multicellular organisms. The role of various cues in directing cell migration is widespread, in particular, the role of signals in the environment in the control of cell motility and directional guidance. In many cases, especially in developmental biology, growth of the domain also plays a large role in the distribution of cells and, in some cases, cell or signal distribution may actually drive domain growth. There is a ubiquitous use of partial differential equations (PDEs) for modelling the time evolution of cellular density and environmental cues. In the last twenty years, a lot of attention has been devoted to connecting macroscopic PDEs with more detailed microscopic models of cellular motility, including models of directional sensing and signal transduction pathways. However, domain growth is largely omitted in the literature. In this paper, individual-based models describing cell movement and domain growth are studied, and correspondence with a macroscopic-level PDE describing the evolution of cell density is demonstrated. The individual-based models are formulated in terms of random walkers on a lattice. Domain growth provides an extra mathematical challenge by making the lattice size variable over time. A reaction-diffusion master equation formalism is generalised to the case of growing lattices and used in the derivation of the macroscopic PDEs.
Hairsine-Rose (HR) model is the only multi sediment size soil erosion
model. The HR model is modifed by considering the effects of sediment bedload and
bed elevation. A two step composite Liska-Wendroff scheme (LwLf4) which
designed for solving the Shallow Water Equations is employed for solving the
modifed Hairsine-Rose model. The numerical approximations of LwLf4 are
compared with an independent MOL solution to test its validation. They
are also compared against a steady state analytical solution and experiment
data. Buffer strip is an effective way to reduce sediment transportation for
certain region. Modifed HR model is employed for solving a particular buffer
strip problem. The numerical approximations of buffer strip are compared
with some experiment data which shows good matches.
Much of group theory is concerned with whether one property entails another. When such a question is answered in the negative it is often via a pathological example. We will examine the Rips construction, an important tool for producing such pathologies, and touch upon a recent refinement of the construction and some applications. In the course of this we will introduce and consider the profinite topology on a group, various separability conditions, and decidability questions in groups.