Articles et Chaps publiés en externe

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An Innovative Predictive Quantum Computer Modeling ;The Power of R2022A+ Cryptography Technology
(Contemporary Engineering Sciences, Vol. 16, 2023) Ndagijimana, P.; Shabani, J.; Nahayo, F.; Et al.
Due to the revolution of technology since the beginning of the 20th century, it is considerable to develop e cient tools on the quantum level in order to improve con dentiality and interoperability of data. The Quantum computer, with Quantum mechanics as its basic principle, still promises to bring great surprises even though we are at the beginning of its development. Quantum Computer is the only known model for computing that could o er exponential speedup classic computer. The current major challenges of the Quantum Computer include increasing or reducing the number of qubits for a given system, coherence management to preserve the properties of the superposition and entanglement state of a quantum system to perform data operation, of course through appropriate quantum algorithms. In this paper, we will give an overview of a quantum computer, will describe the evolution of cryptography and the theory related to computational performance, e ciency and predictive modeling of Quantum Computers. Prototype and Quantum simulation algorithm will be proposed to improve the life of new quantum universe.
La Recherche-Développement à l’Université du Burundi : bilan, défis et perspectives
(RUFORUM Working Document Series, 2018) Masharabu, Tatien; Nahayo, F.; Bogaert, J.; Et al.
Créée en 1964, l’Université du Burundi est la principale université publique du pays. En 2017, elle compte 9300 étudiants reparties à travers huit facultés et trois instituts, avec un effectif de l’ordre de 237 enseignants-chercheurs détenteurs d’un doctorat (PhD) et de 275 assistants toutes catégories, opérant dans 13 centres de recherche sur diverses thématiques pluridisciplinaires du pôle des Sciences Naturelles, de la Vie et de l’Ingénieur, et du pôle des Sciences Humaines et Sociales. Après plus d’un demi-siècle d’enseignement, de recherche et de services à la communauté, quel serait le bilan de sa production scientifique? Malgré les défis auxquels font face le Burundi et l’Afrique, l’Université du Burundi occupe la première place à l’échelle nationale, la 91ème place à l’échelle continentale, et la 5225 ème place à l’échelle planétaire sur base des indicateurs établis par Ranking Web ofUniversities dans le cadre du classement mondial des universités. Alors que la Recherche-Développement (R-D) peut et doit contribuer à trouver des solutions aux différents défis de la société (l’insécurité alimentaire, la crise énergétique, les problèmes de financement, les changements climatiques, la santé publique, etc.), il faudrait que le secteur de la R-D soit doté de bons indicateurs et instruments. Et tout laisse entendre qu’il est possible de transformer ces défis en opportunités de collaboration et/ou d’affaires à l’échelle locale, régionale et internationale. Burundi, Indicateurs, Innovation, Recherche-Développement
Mathematical Modeling and Stability Analysis of Systemic Risk in the Banking Ecosystem
(Hindawi Journal of Applied Mathematics, 2023) Irakoze,Irène; Nahayo, Fulgence; Ikpe, Dennis; Et al.
This paper investigates the dynamics of systemic risk in banking networks by analyzing equilibrium points and stability conditions. The focus is on a model that incorporates interactions among distressed and undistressed banks. The equilibrium points are determined by solving a reduced system of equations, considering both homogeneous and heterogeneous scenarios. Local and global stability analyses reveal conditions under which equilibrium points are stable or unstable. Numerical simulations further illustrate the dynamics of systemic risk, while the theoretical findings offer insights into the behavior of distressed banks under varying conditions. Overall, the model enhances our understanding of systemic financial risk and offers valuable insights for risk management and policymaking in the banking sector
Predictive Mathematical and Statistical Modeling of the Dynamic Poverty Problem in Burundi: Case of an Innovative Economic Optimization System
(Open Journal of Optimization, 2021) Nahayo, Fulgence; Bagorizamba, Ancille; Bigirimana, Marc; Et al.
The mathematical and statistical modeling of the problem of poverty is a major challenge given Burundi’s economic development. Innovative economic optimization systems are widely needed to face the problem of the dynamic of the poverty in Burundi. The Burundian economy shows an inflation rate of −1.5% in 2018 for the Gross Domestic Product growth real rate of 2.8% in 2016. In this research, the aim is to find a model that contributes to solving the problem of poverty in Burundi. The results of this research fill the knowledge gap in the modeling and optimization of the Burundian economic system. The aim of this model is to solve an optimization problem combining the variables of production, consumption, budget, human resources and available raw materials. Scientific modeling and optimal solving of the poverty problem show the tools for measuring poverty rate and determining various countries’ poverty levels when considering advanced knowledge. In addition, investigating the aspects of poverty will properly orient development aid to developing countries and thus, achieve their objectives of growth and the fight against poverty. This paper provides a new and innovative framework for global scientific research regarding the multiple facets of this problem. An estimate of the poverty rate allows good progress with the theory and optimization methods in measuring the poverty rate and achieving sustainable development goals. By comparing the annual food production and the required annual consumption, there is an imbalance between different types of food. Proteins, minerals and vitamins produced in Burundi are sufficient when considering their consumption as required by the entire Burundian population. This positive contribution mains in deficit. The lipids, acids, calcium, fibers and carbohydrates produced in Burundi are insufficient for consumption. This negative contribution proves a Burundian food deficit. It is a decision-making indicator for the design and updating of agricultural policy and implementation programs as well as projects. Investment and economic growth are only possible when food security is mastered. The capital allocated to food investment must be revised upwards. Demographic control is also a relevant indicator to push forward Burundi among the emerging countries in 2040. Meanwhile, better understanding of the determinants of poverty by taking cultural and organizational aspects into account guides managers for poverty reduction projects and programs.
Réduction du bruit de deux avions commerciaux en approche par une technique de commande optimale
(Researchgate, 2010) Nahayo, Fulgence; Khardi, Salah; Hamadiche, Mahmoud; Et al.
L’objectif de ce travail est le d´eveloppement d’un mod`ele d’optimisation acoustique de trajectoires de vol minimisant les bruits per¸cus au sol pour deux avions. Il s’agit de minimiser le bruit tenant compte des contraintes de vol. La dynamique de vol, associ´ee au crit`ere `a minimiser g´en`ere un probl`eme de commande optimale r´egi par des ´equations diff´erentielles ordiniaires non-lin´eaires. Le probl`eme est resolu `a l’aide d’une m´ethode newtonienne consid´erant les conditions d’optimalit´e de Karush-Kuhn-Tucker et une m´ethode SQP. Les r´esultats obtenus montrent des r´eductions significatives des niveaux de bruit. En fonction de la distance s´eparant les deux avions en vol, la trajectoire optimale d’approche est obtenue.
Statistic Modeling for Understanding the Origin of the Random Effects in the Tax Revenues Panel Data System in DR-Congo : Case of North-Kivu Province
(Mathematical and Statistical Economics, 2021) Byamungu, Wanguwabo David; Nahayo, Fulgence; Fono, Louis Aimé; Et al.
Forecasting tax revenues, particularly in Democratic Republic of the Congo economy, is an uphill task. Recent past of the country has been dominated by economic uncertainty, precisely in mining and in agriculture sectors. This factor, alone, has greatly contributed to high volatility of tax revenues collected by customs officers. The fuzzy characteristic of tax revenues has made it quite impossible for researchers to detect or distinguish from randomness the three well known components of a classical time series, precisely trends, seasonality, and cyclical phenomena .What are the factors which explain the random effects in the tax revenues panel in DRC? Our purpose is to detect and understand the origin of the random effects in the tax revenues panel data in DR-Congo through statistics about citizen’s perceptions around tax operation. A quantitative questionnaire with scaled values, open and closed questions, consisting in collecting various perceptions of different economic operators in the import-export sector has been administered to 170 taxpayers randomly selected. Through Analysis of variance, t-test analysis and Pearson Chi-square results show that dissatisfaction of taxpayers, lack of legitimacy in political institutions and government policies, highest tax rate, non-compliance with tax rate for all taxpayers, low level of knowledge in tax matters and corruption, fraud and tax evasion perpetuated by customs officers are the most factors which explain the random effects in DRC’s tax revenues panel data. Marital status is not a source influencing taxation. Mind of counterpart of the taxes in terms of achievements for improving social conditions which is not visible involves broken contract between taxpayers and tax authorities for several reasons sources of random effects above developed.
Two-Aircraft optimal control problem. The in-flight noise reduction
(ResearchGate, 2012) Nahayo, Fulgence; Khardi, Salah; Haddou,Mounir; Et al.
The aim of this paper is to present and solve a mathematical model of a two-aircraft optimal control problem reducing the noise on the ground during the approach. The mathematical modelization of this problem is a non-convex optimal control governed by ordinary non-linear differential equations. To solve this problem, A direct method and a Runge-Kutta RK4 discretization schema are used. This discretization schema is chosed because it is a sufficiently high order and it does-not require computation of the partial derivatives of the aircraft dynamic. The Nonlinear Interior point Trust Region Optimization solver KNITRO is applied. A large set of numerical experiments is presented. The obtained results give feasible trajectories with a significant noise reduction.

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