An Overview of Probabilistic Dimensioning of Frequency Restoration Reserves with a Focus on the Greek Electricity Market

The dynamic dimensioning of frequency restoration reserves based on probabilistic criteria is becoming increasingly relevant in European power grid operations, following the guidelines of European legislation. This article compares dynamic dimensioning based on k-means clustering to static dimensioning on a case study of the Greek electricity market. It presents a model of system imbalances which aims to capture various realistic features of the stochastic behavior of imbalances, including skewed distributions, the dependencies of the imbalance distribution on various imbalance drivers, and the contributions of idiosyncratic noise to system imbalances. The imbalance model was calibrated in order to be consistent with historical reserve requirements in the Greek electricity market. The imbalance model was then employed in order to compare dynamic dimensioning based on probabilistic criteria to static dimensioning. The analysis revealed potential benefits of dynamic dimensioning for the Greek electricity market, which include a reduction in average reserve requirements and the preservation of a constant risk profile due to the adaptive nature of probabilistic dimensioning.

Extremal Copulas and Tail Dependence in Modeling Stochastic Financial Risk

These last years the stochastic modeling became essential in financial risk management related to the ownership and valuation of financial products such as assets, options and bonds. This paper presents a contribution to the modeling of stochastic risks in finance by using both extensions of tail dependence coefficients and extremal dependance structures based on copulas. In particular, we show that when the stochastic behavior of a set of risks can be modeled by a multivariate extremal process a corresponding form of the underlying copula describing theirdependence is determined. Moreover a new tail dependence measure is proposed and properties of this measure are established.

Modeling the Dependence of Losses of a Financial Portfolio Using Nested Archimedean Copulas

In financial analysis, stochastic models are more and more used to estimate potential outcomes in a risky framework. This paper proposes an approach of modeling the dependence of losses on securities, and the potential loss of the portfolio is divided into sectors each including two subsectors. The Weibull model is used to describe the stochastic behavior of the default time while a nested class of Archimedean copulas at three levels is used to model the maximum of the value at risk of the portfolio.

Exact Probability Landscapes of Stochastic Phenotype Switching in Feed-Forward Loops: Phase Diagrams of Multimodality

Feed-forward loops (FFLs) are among the most ubiquitously found motifs of reaction networks in nature. However, little is known about their stochastic behavior and the variety of network phenotypes they can exhibit. In this study, we provide full characterizations of the properties of stochastic multimodality of FFLs, and how switching between different network phenotypes are controlled. We have computed the exact steady-state probability landscapes of all eight types of coherent and incoherent FFLs using the finite-butter Accurate Chemical Master Equation (ACME) algorithm, and quantified the exact topological features of their high-dimensional probability landscapes using persistent homology. Through analysis of the degree of multimodality for each of a set of 10,812 probability landscapes, where each landscape resides over 105–106 microstates, we have constructed comprehensive phase diagrams of all relevant behavior of FFL multimodality over broad ranges of input and regulation intensities, as well as different regimes of promoter binding dynamics. In addition, we have quantified the topological sensitivity of the multimodality of the landscapes to regulation intensities. Our results show that with slow binding and unbinding dynamics of transcription factor to promoter, FFLs exhibit strong stochastic behavior that is very different from what would be inferred from deterministic models. In addition, input intensity play major roles in the phenotypes of FFLs: At weak input intensity, FFL exhibit monomodality, but strong input intensity may result in up to 6 stable phenotypes. Furthermore, we found that gene duplication can enlarge stable regions of specific multimodalities and enrich the phenotypic diversity of FFL networks, providing means for cells toward better adaptation to changing environment. Our results are directly applicable to analysis of behavior of FFLs in biological processes such as stem cell differentiation and for design of synthetic networks when certain phenotypic behavior is desired.

Autonomous Navigation Using Deep Reinforcement Learning in ROS

For an autonomous robot to move safely in an environment where people are around and moving dynamically without knowing their goal position, it is required to set navigation rules and human behaviors. This problem is challenging with the highly stochastic behavior of people. Previous methods believe to provide features of human behavior, but these features vary from person to person. The method focuses on setting social norms that are telling the robot what not to do. With deep reinforcement learning, it has become possible to set a time-efficient navigation scheme that regulates social norms. The solution enables mobile robot full autonomy along with collision avoidance in people rich environment.

On inactivity times of failed components of coherent system under double monitoring

This article discusses the stochastic behavior and reliability properties for the inactivity times of failed components in coherent systems under double monitoring. A mixture representation of reliability function is obtained for the inactivity times of failed components, and some stochastic comparison results are also established. Furthermore, some sufficient conditions are developed in terms of the aging properties of the inactivity times of failed components. Finally, some numerical examples are presented to illustrate the theoretical results.