The emergence of oscillatory behaviour represents fundamental information about the interactions of the underlying system. In biological systems, oscillations have been observed in experimental data, but due to the significant level of noise, it is difficult to characterize whether observed...

Solving non-linear parabolic partial differential equations (PDEs) in high dimension becomes an interest for its curse of dimensionality problem. Recently, a deep learning method associated with a backward stochastic differential equation (deep-BSDE) to solve the PDEs draws intensive discussions...

We formulate a decision model that accommodates correlation ambiguity between the insurer’s surplus and stock return processes and study its implications for the insurer’s asset allocation rule. The ambiguity-averse insurer invests more conservatively in the stock compared to an otherwise...

This paper presents analytical expressions for the mobility ( [[EQUATION]] ) and diffusion coefficient ( [[EQUATION]] ) of a chemical compound [[EQUATION]] that react with a carrier [[EQUATION]] giving a product [[EQUATION]] in the presence of drift. A one-dimensional lattice gas of [[EQUATION]]...

In the context of smart markets’ popularization, day-ahead pricing of electricity has been deployed more commonly as an attempt to improve the grid’s operation and maximize the socioeconomic welfare. However, estimating the utility function is necessary to maximize the socioeconomic welfare,...

In this paper, the theoretic analysis by stochastic dynamics and numerical simulation by ANN algorithm for tumor-immune models driven by random noises are studied. Firstly, a mathematical model about the competition between tumor cells and immune system is established based on the...

Understanding the statistical dynamics of growth and inequality is a fun- damental challenge to ecology and society. Recent analyses of wealth and income dynamics in contemporary societies show that economic inequality is very dynamic and that individuals experience substantially different...

Distribution system state estimation provides essential data for the system monitoring and control, which some uncertain parameters such as the intermittent and varying output of distributed generation (DG), random meter errors, and inaccurate network parameters make situational awareness of...

The inner part of dense clusters of primordial black holes is an active environment where multiple scattering processes take place. Some of them give rise from time to time to bounded pairs, and the rest ends up with a single scattering event. The former eventually evolves to a binary black hole...