Speakers

Richards’ equation for flow in an unsaturated soil is a nonlinear diffusion convection equation. In a cropped field, the web of plant roots leads to an additional nonlinear sink term. Before now, the only known exact solutions assumed a sink function that was proportional to the metric flux potential. This gives the wrong convexity for plant water uptake. Now there is a class of nonlinear reaction-diffusion-convection equations that allows a nonclassical symmetry reduction to a linear system. This requires two differential relations among the soil-water diffusivity, hydraulic conductivity and plant root uptake, each being a function of water content. That leaves one free function and a realistic model that can be solved.

Solutions are shown for crop uptake from periodic irrigation furrows and from a circular sprinkler.

One of the important problems in many branches of science and industry, e.g., pandemic, ecology, biology, engineering, finance, social science, is the specification of the stochastic process governing the behaviour of an underlying quantity. We here use the term it underlying quantity to describe any interested object whose value is known at present but is liable to change in the future. In this talk we will explain how the ordinary differential equations (ODEs) are not enough to model the underlying stochastic quantity and why stochastic differential equations (SDEs) appear naturally. Several well-known SDE models will be presented including the Nobel prize winning model in finance, stochastic SIS epidemic model, stochastic Lotka-Volterra model in population dynamics. We will then explain how SDE models differ significantly from ODE models and reveal the crucial role of  noise. We will see the use of SDE models depend on the estimation of system parameters. In the case when the model has only a few parameters, we show how they can be estimated by the classical statistical methods, e.g., the least-square one; while when there are lots of parameters, we will show how the deep learning plays its crucial role.

Risk management is a crucial component across all aspects of life, with market risk representing a significant area of focus, especially when utilizing publicly available data for analysis. In some instances, risks are isolated and can be managed individually; however, they are often interdependent, necessitating a comprehensive approach to understanding market risk dependencies. This study predominantly employs the Value-at-Risk (VaR) methodology for assessing individual risks, while Conditional VaR (CoVaR) through Quantile Regression (QR) is used to evaluate the causal relationships between multiple risks. The presence of nonlinear dependencies between risks calls for applying a nonlinear model. To this end, this research incorporates a Quantile Regression Neural Network (QRNN) to investigate potential nonlinear risk interactions among publicly listed companies. Utilizing the Least Absolute Shrinkage and Selection Operator (LASSO) regularization, the QRNN model efficiently identifies relevant risk factors. This process is implemented in two distinct strategies: hybrid and embedded. Moreover, the weighting parameter of LASSO serves as a tool for calculating a Financial Risk Meter (FRM) across various organizations or corporations. By applying these methodologies, the study analyzes market risk interdependencies among the selected Indonesian public companies, identifying a significant increase in systemic risk during the COVID-19 pandemic, underscoring the complex dynamics of market risks in global crises.

This presentation explores the intersection of talent mobility project and mathematical modeling processes to drive practical solutions in Industry, Business and Community. By integrating talent mobility strategies with systematic mathematical modeling processes, organizations can optimize workforce allocation, enhance risk management, and improve resource utilization. The journey begins with clear problem formulation, followed by meticulous data collection and preprocessing to inform model development. Model selection is guided by the complexities of each industry, with parameter estimation ensuring alignment with real-world dynamics. Validation tests the model’s predictive capabilities against independent datasets or observed outcomes, while sensitivity analysis identifies key factors influencing decision-making. Optimization techniques then enable the identification of optimal solutions, balancing objectives and constraints. Implementation integrates models into decision support systems, facilitating informed talent mobility decisions. Continuous monitoring and feedback ensure models evolve alongside changing conditions and stakeholder needs. By elucidating these processes, this presentation showcases how talent mobility and mathematical modeling synergize to drive innovation, foster workforce agility, and optimize organizational performance in finance, insurance, and water management sectors.

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