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Articles by Valeriu Beiu
Cyber Risk Quantification and Security Portfolio Optimisation via Calibrated Monte Carlo Simulation
You are already at the latest version The persistent growth of cybersecurity incidents and their escalating financial consequences impose a critical need for rigorous, quantitative approaches to security investment decision-making. This paper presents a Monte Carlo-based framework for cyber risk quantification and security portfolio optimisation, grounded in empirical calibration from publicly available incident and cost databases.
On the Construction of 3D Fibonacci Spirals
1. Introduction and Motivation This paper is a surprisingly long answer to a reasonably simple question raised in Spring 2017 while the authors were chatting about the classical two-dimensional (2D) Fibonacci spiral. The question was: “Are there 3D versions of the classical 2D Fibonacci spiral?” We were expecting to find answers quickly by conducting a few searches online.
The Roots of the Reliability Polynomials of Circular Consecutive-k-out-of-n:F Systems
This is an early access version, the complete PDF, HTML, and XML versions will be available soon. Open AccessArticle by 1,*, 1, 2 and 2 1 Department of Mathematics and Computer Science, Technical University of Civil Engineering Bucharest, 020396 Bucharest, Romania 2 Department of Mathematics and Computer Science, Faculty of Exact Sciences, “Aurel Vlaicu” University of Arad, 310330 Arad, Romania * Author to whom correspondence should be addressed.
Reliability polynomials of consecutive‐k‐out‐of‐n:F systems have unbounded roots
Abstract This article studies the roots of the reliability polynomials of linear consecutive-k-out-of-n:F systems. We prove that these roots are unbounded in the complex plane, for any fixed k ≥ 2 $$ k\ge 2 $$ . In the particular case k = 2 $$ k=2 $$ , we show that the reliability polynomials have only real roots and highlight the closure of these roots by establishing their explicit formulas.
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