Ovidiu Bagdasar

Ovidiu Bagdasar
University of Derby · Electronics, Computing and Mathematics

PhD FIMA SFHEA

About

120
Publications
72,651
Reads
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665
Citations
Citations since 2017
78 Research Items
605 Citations
2017201820192020202120222023050100150200
2017201820192020202120222023050100150200
2017201820192020202120222023050100150200
2017201820192020202120222023050100150200
Introduction
My research focuses on Optimization, Computational Mathematics, Recurrence sequences and Mathematical Modelling, Mathematical Education and Mathematical Anxiety.
Additional affiliations
January 2019 - present
University of Derby
Position
  • Professor (Associate)
Description
  • Erasmus departmental coordinator. PL Big Data Analytics.
August 2015 - present
University of Derby
Position
  • Lecturer
Description
  • Erasmus coordinator for Computing and Mathematics. Programme Leader for MSc Computational Mathematics and MSc Big Data Analytics.
January 2012 - September 2015
University of Derby
Position
  • Lecturer
Description
  • I am teaching Computational Mathematics, Calculus and Modelling with Differential Equations (BSc), and Optimization for MSc. I seek to inspire students through research informed lectures.
Education
September 2012 - July 2016
September 2007 - September 2015
Babeş-Bolyai University
Field of study
  • Mathematics (Pure)
May 2007 - December 2011
University of Nottingham
Field of study
  • Mathematics (Applied)

Publications

Publications (120)
Article
Full-text available
In this paper an explicit formula for the number of tuples of positive integers having the same lowest common multiple n is derived, and some of the properties of the resulting arithmetic function are analyzed. The tuples having also the same greatest common divisor are investigated, while some novel or existing integer sequences are recovered as p...
Conference Paper
Full-text available
Uniformly distributed pseudo-random number generators are commonly used in certain numerical algorithms and simulations. In this article a random number generation algorithm based on the geometric properties of complex Ho-radam sequences was investigated. For certain parameters, the sequence exhibited uniformity in the distribution of arguments. Th...
Article
Full-text available
Some arithmetic properties of the generalized Lucas sequences are studied, extending a number of recent results obtained for Fibonacci, Lucas, Pell, and Pell–Lucas sequences. These properties are then applied to investigate certain notions of Fibonacci, Lucas, Pell, and Pell–Lucas pseudoprimality, for which we formulate some conjectures.
Article
Full-text available
Compared to other types of social networks, criminal networks present particularly hard challenges, due to their strong resilience to disruption, which poses severe hurdles to Law-Enforcement Agencies (LEAs). Herein, we borrow methods and tools from Social Network Analysis (SNA) to (i) unveil the structure and organization of Sicilian Mafia gangs,...
Article
Full-text available
We deduce exact integral formulae for the coefficients of Gaussian, multinomial and Catalan polynomials. The method used by the authors in the papers [2, 3, 4] to prove some new results concerning cyclotomic and polygonal polynomials, as well as some of their extensions is applied.
Article
In the present paper we establish a few equivalent conditions of a Hilbert-type integral inequality with a non-homogeneous kernel in the whole plane. A few equivalent conditions of a Hilbert-type integral inequality with the homogeneous kernel in the whole plane are deduced, in the form of applications. We additionally consider operator expressions...
Article
Full-text available
We explore the dynamics of the sequence of Kasner quadrilaterals (AnBnCnDn)n≥0 defined via a complex parameter α. We extend the results concerning Kasner triangles with a fixed complex parameter obtained in earlier works and determine the values of α for which the generated dynamics are convergent, divergent, periodic, or dense.
Article
This article explores the O(t −β) synchronization and asymptotic synchronization for fractional order BAM neural networks (FBAMNNs) with discrete delays, distributed delays and non-identical perturbations. By designing a state feedback control law and a * new kind of fractional order Lyapunov functional, a new set of algebraic sufficient conditions...
Chapter
Full-text available
The advances within the Internet of Things and sensor systems put the focus on the improvement of the data reliability as close to the edge as possible. This work investigates how well-established techniques can be used for the imputation of contaminated data. We look at the performance of four algorithms for different contamination rates and error...
Article
Full-text available
In this manuscript, we are concerned with mixed (discrete and distributed) time-delayed both stability and non-fragile synchronization of nonlinear multi-agent systems (MASs). We shall find stability criteria for the unknown parameter value of nonlinear multi-agent systems using the Lyapunov–Krasovskii functions, Lemma, the analytical techniques, t...
Chapter
Training Artificial Neural Networks (ANNs) is a non-trivial task. In the last years, there has been a growing interest in the academic community in understanding how those structures work and what strategies can be adopted to improve the efficiency of the trained models. Thus, the novel approach proposed in this paper is the inclusion of the entrop...
Article
Full-text available
Making use of complex analytic techniques as well as methods involving weight functions, we study a few equivalent conditions of a Hilbert-type integral inequality with nonhomogeneous kernel and parameters. In the form of applications we deduce a few equivalent conditions of a Hilbert-type integral inequality with homogeneous kernel, and we additio...
Article
Full-text available
Recent developments in cloud computing and the Internet of Things have enabled smart environments, in terms of both monitoring and actuation. Unfortunately, this often results in unsustainable cloud-based solutions, whereby, in the interest of simplicity, a wealth of raw (unprocessed) data are pushed from sensor nodes to the cloud. Herein, we advoc...
Article
Full-text available
In this paper, we examine a sampled-data Nash equilibrium strategy for a stochastic linear quadratic (LQ) differential game, in which admissible strategies are assumed to be constant on the interval between consecutive measurements. Our solution first involves transforming the problem into a linear stochastic system with finite jumps. This allows u...
Article
Given the considerable complexity of process plants, there has been a great deal of research focused on aiding the design of plant layout through mathematical optimisation, i.e. optimising the positioning of the equipment in the plant for space and cost efficiency. Recently, the use of modular approaches within the construction industry, whereby wo...
Article
Full-text available
Aim: Italian criminal groups become more and more dangerous spreading their activities into new sectors. A criminal group is made up of networks of hundreds of family gangs which extended their influence across the world, raking in billions from drug trafficking, extortion and money laundering. We focus in particular on the analysis of the social s...
Article
Full-text available
Data collected in criminal investigations may suffer from issues like: (i) incompleteness, due to the covert nature of criminal organizations; (ii) incorrectness, caused by either unintentional data collection errors or intentional deception by criminals; (iii) inconsistency, when the same information is collected into law enforcement databases mul...
Article
Full-text available
We study the number of ordered k-partitions of a multiset with equal sums, having elements α1,…,αn and multiplicities m1,…,mn. Denoting this number by Sk(α1,…,αn;m1,…,mn), we find the generating function, derive an integral formula, and illustrate the results by numerical examples. The special case involving the set {1,⋯,n} presents particular inte...
Article
The selfish routing of network flow often considers a single objective, namely travel time or travel distance, and optimisation models are often guided by the principle of user equilibrium (UE). A more challenging approach is to consider multiple objectives simultaneously, for example, distance, travel time and pollution. In this paper we present a...
Article
Internet of Planets (IoP) is a concept that enables solar planets to communicate with each other using the Internet. While there is a plethora of research on IoP, the delay-tolerant network (DTN) has emerged as the most advanced technology in recent years. DTN is an asynchronous networking technology that has been deployed for the networking enviro...
Article
Full-text available
We investigate the Fibonacci pseudoprimes of level k, and we disprove a statement concerning the relationship between the sets of different levels, and also discuss a counterpart of this result for the Lucas pseudoprimes of level k. We then use some recent arithmetic properties of the generalized Lucas, and generalized Pell–Lucas sequences, to defi...
Article
Full-text available
In this paper, a novel age-structured delayed mathematical model to control Aedes aegypti mosquitoes via Wolbachia-infected mosquitoes is introduced. To eliminate the deadly mosquito-borne diseases such as dengue, chikungunya, yellow fever, and Zika virus, the Wolbachia infection is introduced into the wild mosquito population at every stage. This...
Article
Full-text available
This work is devoted to analyzing an impulsive control synthesis to maintain the self-sustainability of Wolbachia among Aedes Aegypti mosquitoes. The present paper provides a fractional order Wolbachia invasive model. Through fixed point theory, this work derives the existence and uniqueness results for the proposed model. Also, we performed a glob...
Preprint
Full-text available
Social Network Analysis is the use of Network and Graph Theory to study social phenomena, which was found to be highly relevant in areas like Criminology. This chapter provides an overview of key methods and tools that may be used for the analysis of criminal networks, which are presented in a real-world case study. Starting from available juridica...
Article
Some arithmetic properties and new pseudoprimality results concerning generalized Lucas sequences are presented. The findings are connected to the classical Fibonacci, Lucas, Pell, and Pell-Lucas pseudoprimality. During the process new integer sequences are found and some conjectures are formulated.
Article
Full-text available
In this paper we introduce the functions which count the number of generalized Lucas and Pell-Lucas sequence terms not exceeding a given value x and, under certain conditions, we derive exact formulae (Theorems 3 and 4) and establish asymptotic limits for them (Theorem 6). We formulate necessary and sufficient arithmetic conditions which can identi...
Preprint
Full-text available
Data collected in criminal investigations may suffer from: (i) incompleteness, due to the covert nature of criminal organisations; (ii) incorrectness, caused by either unintentional data collection errors and intentional deception by criminals; (iii) inconsistency, when the same information is collected into law enforcement databases multiple times...
Chapter
Social Network Analysis is the use of Network and Graph Theory to study social phenomena, which was found to be highly relevant in areas like Criminology. This chapter provides an overview of key methods and tools that may be used for the analysis of criminal networks, which are presented in a real-world case study. Starting from available juridica...
Article
The aim of this paper is to establish the stability results based on the approach of Linear Matrix Inequality (LMI) for the addressed mathematical model using Caputo-Fabrizio operator (CF operator). Firstly, we extend some existing results of Caputo fractional derivative in the literature to a new fractional order operator without using singular ke...
Article
Full-text available
Dynamics of discrete‐time neural networks have not been well documented yet in fractional‐order cases, which is the first time documented in this manuscript. This manuscript is mainly considered on the stability criterion of discrete‐time fractional‐order complex‐valued neural networks with time delays. When the fractional‐order β holds 1 < β < 2,...
Chapter
Network Science is an active research field, with numerous applications in areas like computer science, economics, or sociology. Criminal networks, in particular, possess specific topologies which allow them to exhibit strong resilience to disruption. Starting from a dataset related to meetings between members of a Mafia organization which operated...
Chapter
By the use of weight functions, a few equivalent conditions of two kinds of Hardy-type integral inequalities with multi-parameters in the whole plane are obtained. The constant factors related to the extended Riemann-zeta function are proved to be the best possible. Applying our results, we deduce a few equivalent conditions of two kinds of Hardy-t...
Article
Full-text available
The development of deep learning has led to a dramatic increase in the number of applications of artificial intelligence. However, the training of deeper neural networks for stable and accurate models translates into artificial neural networks (ANNs) that become unmanageable as the number of features increases. This work extends our earlier study w...
Chapter
In this chapter we start by presenting some key results concerning the number of ordered k-partitions of multisets with equal sums. For these we give generating functions, recurrences and numerical examples. The coefficients arising from these formulae are then linked to certain elliptic and superelliptic Diophantine equations, which are investigat...
Preprint
Full-text available
Anomaly detection is concerned with identifying data patterns that deviate remarkably from the expected behaviour. This is an important research problem, due to its broad set of application domains, from data analysis to e-health, cybersecurity, predictive maintenance, fault prevention, and industrial automation. Herein, we review state-of-the-art...
Conference Paper
Full-text available
To improve city services, local administrators need to have a deep understanding of how the citizens explore the city, use the relevant services, interact and move. This is a challenging task, which has triggered extensive research in the last decade, with major solutions that rely on analysing traces of network traffic generated by citizens WiFi d...
Chapter
The sequence (xn)n≥0 = (xn(a, b;p, q))n≥0 defined by xn+2=pxn+1+qxn,x0=a,x1=b, with a, b, p, and q arbitrary complex numbers is called a Horadam sequence. For simplicity, we shall denote (xn(a, b;p, q))n≥0 by (xn)n≥0 hereafter.
Chapter
In this chapter we present fundamental concepts and motivating examples of recurrent sequences, and show connections of recurrence relations to mathematical modeling, algebra, combinatorics, and analysis. There are numerous sources presenting the classical theory.
Chapter
The classical second-order recurrent sequences discussed in Chapter 2 have many interesting properties. In Section 3.1 we present arithmetic properties of the Fibonacci and Lucas sequences first found in [23]. Section 3.2 studies properties of Pell and Pell–Lucas sequences. We also discuss about certain notions of Fibonacci, Lucas, Pell, or Pell–Lu...
Chapter
In this chapter we present a thematic collection of 123 olympiad training problems, involving recurrences in various contexts. We have chosen 123 as it represents the 10th Lucas number L10. The problems relate to topics such as linear recurrence sequences of first, second, and higher orders, classical sequences, homographic recurrent sequences, sys...
Chapter
This chapter presents key properties of the complex linear recurrent sequences of arbitrary order, including general term formulae, periodicity, or the asymptotic behavior in some particular cases. We also give results for systems of linear recurrent sequences.
Chapter
Generating functions play an important role in the study of recurrent sequences. In this chapter we present basic properties, operations, and examples involving ordinary generating functions (Section 4.1), or exponential generating functions (Section 4.2). Then we derive such generating functions for some classical polynomials and integer sequences...
Chapter
In this chapter we present basic results and examples of first-order and second-order linear recurrent sequences with arbitrary coefficients, some classical sequences, polynomials, and linear fractional transformations.
Chapter
In this chapter we present detailed solutions (sometimes two or three) for the proposed problems in Chapter 7.
Article
Full-text available
The explosion of the internet has resulted in various emerging technologies, as for example the Internet of Things (IoT). IoT is an intelligent technology and service connecting objects in the Internet. IoT facilitates the exchange of information between people and devices that communicate with each other. Beyond IoT, we are now studying a new para...
Article
Full-text available
For a positive integer n ≥ 1 the n-th cyclotomic polynomial is dened by Φn(z) = ζ n =1 (z − ζ), where ζ are the primitive n-th roots of unity. These polynomials are known to possess many interesting properties. In this article we establish an integral formula for the coecients of the cyclotomic polynomial, we then discuss the direct and alternate s...
Article
Full-text available
This sequel is concerned with the analysis of robust synchronization for a multi-weighted complex structure on fractional-order coupled neural networks (MWCFCNNs) with linear coupling delays via state feedback controller. Firstly, by means of fractional order comparison principle, suitable Lyapunov method, Kronecker product technique, some famous i...
Article
Full-text available
The dynamic travelling salesman problem (DTSP) is a natural extension of the standard travelling salesman problem, and it has attracted significant interest in recent years due to is practical applications. In this article, we propose an efficient solution for DTSP, based on a genetic algorithm (GA), and on the one-by-one revision of two sides (GOR...
Preprint
Full-text available
Compared to other types of social networks, criminal networks present hard challenges, due to their strong resilience to disruption, which poses severe hurdles to law-enforcement agencies. Herein, we borrow methods and tools from Social Network Analysis to (i) unveil the structure of Sicilian Mafia gangs, based on two real-world datasets, and (ii)...
Chapter
Congestion games possess the property of emitting at least one pure Nash equilibrium and have a rich history of practical use in transport modelling. In this paper we approach the problem of modelling equilibrium within congestion games using a decentralised multi-player probabilistic approach via stochastic bandit feedback. Restricting the strateg...
Chapter
Deep Learning opened artificial intelligence to an unprecedented number of new applications. A critical success factor is the ability to train deeper neural networks, striving for stable and accurate models. This translates into Artificial Neural Networks (ANN) that become unmanageable as the number of features increases. The novelty of our approac...
Article
Motorists often have to choose routes helping them to realize faster journey times. Route choices between an origin and a destination might involve direct main roads, shorter routes through narrow side streets, or longer but (potentially) faster journeys using motorways or ring-roads. In the absence of effective traffic control measures, an approxi...
Article
Full-text available
The novel delay-dependent asymptotic stability of a differential and Riemann-Liouvillefractional differential neutral system with constant delays and nonlinear perturbation is studied.We describe the new asymptotic stability criterion in the form of linear matrix inequalities (LMIs),using the application of zero equations, model transformation and...
Chapter
Full-text available
In this paper, we focus on the study of Sicilian Mafia organizations through Social Network Analysis. We analyse datasets reflecting two different Mafia Families, based on examinations of digital trails and judicial documents, respectively. The first dataset includes the phone calls logs among suspected individuals. The second one is based on polic...
Book
This self-contained text presents state-of-the-art results on recurrent sequences and their applications in algebra, number theory, geometry of the complex plane and discrete mathematics. It is designed to appeal to a wide readership, ranging from scholars and academics, to undergraduate students, or advanced high school and college students traini...
Article
Full-text available
The concept of generalized exponential trichotomy for linear time-varying systems is investigated in relationship with the classical notion of uniform exponential trichotomy. Some key properties of generalized exponential trichotomy are explored through supplementary projections. These results are also extended to the case of projection sequences,...
Article
This article, we explore the asymptotic stability and asymptotic synchronization analysis of fractional order delayed Cohen–Grossberg neural networks with discontinuous neuron activation functions (FCGNNDDs). First, under the framework of Filippov theory and differential inclusion theoretical analysis, the global existence of Filippov solution for...
Article
Full-text available
This paper addresses Master-Slave synchronization for some memristor-based fractional-order BAM neural networks (MFBNNs) with mixed time-varying delays and switching jumps mismatch. Firstly, considering the inherent characteristic of FMNNs, a new type of fractional-order differential inequality is proposed. Secondly, an adaptive switching control s...
Article
Full-text available
This paper deals with the extended design of Mittag‐Leffler state estimator and adaptive synchronization for fractional‐order bidirectional associative memory neural networks with time delays. By the aid of Lyapunov direct approach and Razumikhin‐type method, a suitable fractional‐order Lyapunov functional is constructed and a new set of novel suff...
Article
Full-text available
In this paper we define the nth polygonal polynomial Pn(z) = (z − 1)(z 2 − 1) · · · (z n − 1) and we investigate recurrence relations and exact integral formulae for the coefficients of Pn and for those of the Mahonian polynomials Qn(z) = (z + 1)(z 2 + z + 1) · · · (z n−1 + · · · + z + 1). We also explore numerical properties of these coefficients,...
Article
Full-text available
An online, cross-sectional approach was taken, including an opportunity sample of 160 undergraduate students from a university in the Midlands, UK. Exploratory factor analysis indicated a parsimonious, four-factor solution: abstract maths anxiety , statistics probability anxiety , statistics calculation anxiety , and numerical calculation anxiety ....
Article
Full-text available
Integral formulae for the coefficients of cyclotomic and polygonal polynomials were recently obtained in [2] and [3]. In this paper, we define and study a family of polynomials depending on an integer sequence m1, . . . , mn, . . . , and on a sequence of complex numbers z1, . . . , zn, . . . of modulus one. We investigate some particular instances...
Article
Integer division and perfect powers play a central role in numerous mathematical results, especially in number theory. Classical examples involve perfect squares like in Pythagora's theorem, or higher perfect powers as the conjectures of Fermat (solved in 1994 by A. Wiles [Wiles, A.J., Modular elliptic curves and Fermat's Last Theorem, Annals of Ma...
Article
Partitions play an important role in numerous combinatorial optimization problems. Here we introduce the number of ordered 3-partitions of a multiset M having equal sums denoted by S(m1,… mn; α1,… αn), for which we find the generating function and give a useful integral formula. Some recurrence formulae are then established and new integer sequence...
Article
Full-text available
The Cauchy integral formula has many applications in various areas of mathematics, having a long history in complex analysis, combinatorics, discrete mathematics, or number theory. Recently, it has been used to derive an exact integral formula for the coefficients of cyclotomic and other classes of polynomials. The aim of this work is twofold. We �...
Article
Full-text available
It is well-known that all local minimum points of a semistrictly quasiconvex real-valued function are global minimum points. Also, any local maximum point of an explicitly quasiconvex real-valued function is a global minimum point, provided that it belongs to the intrinsic core of the function’s domain. The aim of this paper is to show that these “...
Article
Motorists often face the dilemma of choosing the route enabling them to realise the fastest (i.e., shortest) journey time. In this paper we examine discrete and continuous optimisation and equilibrium-type problems for a simplified parallel link traffic model using a variance based approach. Various methodologies used for solving these problems (br...
Article
Full-text available
In this paper we present theoretical and computational results regarding generalized arithmetic m-triangles. The numerical values recover well-known number sequences, indexed in the OEIS including binomial coefficients and their extensions. Some combinatorial interpretations, generating functions and also asymptotic formulae for these triangles are...
Article
Full-text available
Horadam sequences are second-order linear recurrences in the complex plane which depend on two initial conditions and two recurrence coefficients which are complex numbers. Recently, numerous papers have been devoted to the periodicity of these sequences, as well as to generalizations and applications. In this paper we investigate aspects related t...
Article
Fractional order system is playing an increasingly important role in terms of both theory and applications. In this paper we investigate the global existence of Filippov solutions and the robust generalized Mittag-Leffler synchronization of fractional order neural networks with discontinuous activation and impulses. By means of growth conditions, d...
Article
Full-text available
The Horadam sequence is a general second order linear recurrence sequence, dependent on a family of four (possibly complex) parameters-two recurrence coefficients and two initial conditions. In this article we examine a phenomenon identified previously and referred to as 'masked' periodicity, which links the period of a self-repeating Horadam seque...
Chapter
The next section shows not only how a heuristic approach can be employed to solve hard problems but also how an investigation of the mathematical model can lead to a simpler solution technique.
Chapter
The aim of these case studies is to demonstrate how large and complex decision-making problems can be “solved” using heuristic methods.
Article
Any local maximizer of an explicitly quasiconvex real-valued function is actually a global minimizer, if it belongs to the intrinsic core of the function's domain. In this paper we show that similar properties hold for componentwise explicitly quasiconvex vector-valued functions, with respect to the concepts of ideal, strong and weak optimality. We...