Ferromagnetism and the Kondo effect are crucial for 3d electrons to become spin-separated and heavy at the same time.

Simulation optimisation offers great opportunities in the design and optimisation of complex systems. In the presence of multiple objectives, there is usually no single solution that performs best on all objectives. Instead, there are several Pareto-optimal (efficient) solutions with different trade-offs which cannot be improved in any objective without sacrificing performance in another objective. For the case where alternatives are evaluated on multiple stochastic criteria, and the performance of an alternative can only be estimated via simulation, we consider the problem of efficiently identifying the Pareto-optimal designs out of a (small) given set of alternatives. We present a simple myopic budget allocation algorithm for multi-objective problems and propose several variants for different settings. In particular, this myopic method only allocates one simulation sample to one alternative in each iteration. This paper shows how the algorithm works in bi-objective problems under different settings. Empirical tests show that our algorithm can significantly reduce the necessary simulation budget.

We propose a novel probabilistic model to facilitate the learning of multivariate tail dependence of multiple financial assets. Our method allows one to construct from known random vectors, e.g., standard normal, sophisticated joint heavy-tailed random vectors featuring not only distinct marginal tail heaviness, but also flexible tail dependence structure. The novelty lies in that pairwise tail dependence between any two dimensions is modeled separately from their correlation, and can vary respectively according to its own parameter rather than the correlation parameter, which is an essential advantage over many commonly used methods such as multivariate t or elliptical distribution. It is also intuitive to interpret, easy to track, and simple to sample comparing to the copula approach. We show its flexible tail dependence structure through simulation. Coupled with a GARCH model to eliminate serial dependence of each individual asset return series, we use this novel method to model and forecast multivariate conditional distribution of stock returns, and obtain notable performance improvements in multi-dimensional coverage tests.Besides, our empirical finding about the asymmetry of tails of the idiosyncratic component as well as the whole market is interesting and worth to be well studied in the future.

Responses of crop growth to climate warming are fundamental to future food security. The response of crops to climate change may be subtly different at their growing stages. Close insights into the differentiated stage-dependent responses of crops are significantly important in making adaptive adjustments of crops’ phenological optimization and cultivar improvement in diverse cropping systems. Using the Agro-C model, we studied the influence of past climate warming on crops in typical cropping systems in China. The results showed that while the temperature had increased distinctly from the 1960s to 2000s, the temperature frequency distributions in the growth season of crops moved to the high-temperature direction. The low temperature days during the crop growth periods that suppress crop growth decreased in the winter wheat area in North and East China, rice and maize areas in Northeast China, and the optimum temperature days increased significantly. As a result, the above ground biomass (AGB) of rice and maize in Northeast China and winter wheat in North and East China increased distinctly, while that of rice in South China had no significant change. A comparison of the key growth periods before and after heading (silking) showed that the warming before heading (silking) made a great contribution to the increase in the AGB, especially for winter wheat.

In this paper, we consider a ratio-dependent predator-prey system with multiple delays where the dynamics are logistic with the carrying capacity proportional to prey population. By choosing the sum τ of two delays as the bifurcation parameter, the stability of the positive equilibrium and the existence of Hopf bifurcation are investigated. Furthermore, the direction of Hopf bifurcation and the stability of the bifurcating periodic solutions are determined by the normal form theory and the center manifold theorem for functional differential equations. Finally, some numerical simulations are carried out for illustrating the theoretical results.