In this paper, we present a comprehensive survey of continuous stochastic volatility models, discussing their historical development and the key stylized facts that have driven the field. Special attention is dedicated to fractional and rough methods: without advocating for either roughness or long memory, we outline the motivation behind them and characterize some landmark models. In addition, we briefly touch on the problem of VIX modeling and recent advances in the SPX-VIX joint calibration puzzle.
This paper explores the 3D printing of poly vinyl alcohol (PVA) using the fused deposition modeling (FDM) process by conducting statistical modeling and optimization. This study focuses on varying the infill percentage (10-50%) and patterns (Cubic, Gyroid, tri-hexagon and triangle, Grid) as input parameters for the response surface methodology (DOE) while measuring modulus, elongation at break, and weight as experimental responses. To determine the optimal parameters, a regression equation analysis was conducted to identify the most significant parameters. The results indicate that both input parameters significantly impact the output responses. The Design Expert software was utilized to create surface and residual plots, and the interaction between the two input parameters shows that increasing the infill percentage (IP) leads to printing heavier samples, while the patterns do not affect the weight of the parts due to close printing structures. On the contrary, the discrepancy between the predicted and actual responses for the optimal samples is below 15%. This level of error is deemed acceptable for the DOE experiments.
The value of verification of cyberphysical systems depends on the relationship between the state of the software and the state of the physical system. This relationship can be complex because of the real-time nature and different timelines of the physical plant, the sensors and actuators, and the software that is almost always concurrent and distributed. In this paper, we study different ways to construct a transition system model for the distributed and concurrent software components of a CPS. The purpose of the transition system model is to enable model checking, an established and widely used verification technique. We describe a logical-time-based transition system model, which is commonly used for verifying programs written in synchronous languages, and derive the conditions under which such a model faithfully reflects physical states. When these conditions are not met (a common situation), a finer-grained event-based transition system model may be required. We propose an approach for formal verification of cyberphysical systems using Lingua Franca, a language designed for programming cyberphysical systems, and Rebeca, an actor-based language designed for model checking distributed event-driven systems. We focus on the cyber part and model a faithful interface to the physical part. Our method relies on the assumption that the alignment of different timelines during the execution of the system is the responsibility of the underlying platforms. We make those assumptions explicit and clear.