Hyung Ju Hwang

As the amount of data increases, it is more likely that the assumptions in the existing economic analysis model are unsatisfied or make it difficult to establish a new analysis model. Therefore, there has been increased demand for applying the machine learning methodology to bankruptcy prediction due to its high performance. By contrast, machine learning models usually operate as black-boxes but credit rating regulatory systems require the provisioning of appropriate information regarding credit

A widespread phenomenon in moving microorganisms and cells is their ability to reorient themselves depending on changes of concentrations of certain chemical signals. In this paper we discuss kinetic models for chemosensitive movement, which also takes into account evaluations of gradient fields of chemical stimuli which subsequently influence the motion of the respective microbiological species. The basic type of model was discussed by Alt [J. Math. Biol., 9 (1980), pp. 147--177], [J. Reine Ang

Abstract Mathematical modeling is a process aimed at finding a mathematical description of a system and translating it into a relational expression. When a system is continuously changing over time (e.g., infectious diseases) differential equations, which may include parameters, are used for modeling the system. The process of finding those parameters that best fit the given data from the system is called an inverse problem. This study aims at analyzing the novel coronavirus infection (COVID-19)

In this paper we prove the existence of a large class of periodic solutions of the Vlasov-Poisson in one space dimension that decay exponentially as t -> infinity. The exponential decay is well known for the linearized version of the Landau damping problem and it has been proved in [4] for a class Of solutions of the Vlasov-Poisson system that behaves asymptotically as free streaming solutions and are sufficiently flat in the space of velocities. The results in this paper enlarge the class of

We study a kinetic model for chemotaxis introduced by Othmer, Dunbar, and Alt [23], which was motivated by earlier results of Alt, presented in [1], [2]. In two papers by Chalub, Markowich, Perthame and Schmeiser, it was rigorously shown that, in three dimensions, this kinetic model leads to the classical Keller-Segel model as its drift-diffusion limit when the equation of the chemo-attractant is of elliptic type [4], [5]. As an extension of these works we prove that such kinetic models have a m

We consider the initial-boundary value problem in a convex domain for the Vlasov--Poisson system. Boundary effects play an important role in such physical problems that are modeled by the Vlasov--Poisson system. We establish the global existence of classical solutions with regular initial boundary data under the absorbing boundary condition. We also prove that regular symmetric initial data lead to unique classical solutions for all time in the specular reflection case.

We establish the exponential time decay rate of smooth solutions of smallamplitude to the Vlasov-Poisson-Fokker-Planck equations to the Maxwellian bothin the whole space and in the periodic box via the uniform-in-time energyestimates and also the macroscopic equations.

The methodology and new model of this study could be employed for short-term prediction of COVID-19, which could help the government prepare for a new outbreak. In addition, from the perspective of measuring medical resources, our model has powerful strength because it assumes all the parameters as time-dependent, which reflects the exact status of viral spread.