Nicholas J . Daras | Hellenic Army Academy (original) (raw)

Papers by Nicholas J . Daras

Springer optimization and its applications, 2012

Aims and Scope Optimization has been expanding in all directions at an astonishing rate during th... more Aims and Scope Optimization has been expanding in all directions at an astonishing rate during the last few decades. New algorithmic and theoretical techniques have been developed, the diffusion into other disciplines has proceeded at a rapid pace, and our knowledge of all aspects of the field has grown even more profound. At the same time, one of the most striking trends in optimization is the constantly increasing emphasis on the interdisciplinary nature of the field. Optimization has been a basic tool in all areas of applied mathematics, engineering, medicine, economics, and other sciences. The series Springer Optimization and Its Applications publishes undergraduate and graduate textbooks, monographs and state-of-the-art expository work that focus on algorithms for solving optimization problems and also study applications involving such problems. Some of the topics covered include nonlinear optimization (convex and nonconvex), network flow problems, stochastic optimization, optimal control, discrete optimization, multiobjective programming, description of software packages, approximation techniques and heuristic approaches.

WORLD SCIENTIFIC eBooks, Dec 7, 2022

Clustering is one of the most common tasks of Machine Learning. In this chapter we examine how id... more Clustering is one of the most common tasks of Machine Learning. In this chapter we examine how ideas from topology can be used to improve clustering techniques. 1 Introduction With the advent of Big Data, algorithms that try to extract information from them are ubiquitous. Clustering algorithms are a subcategory of Machine Learning algorithms with a wide range of applications. Notions like closeness, distance and shape are central to clustering. It is then natural to try to use ideas and techniques from topology to improve clustering algorithms. This chapter examines some ways on how this could happen. In Section 2 a brief introduction to the clustering task is presented. In Subsection 2.1 a definition is presented along with notation. k-means algorithm will be one of our focus areas and is examined in more detail in Subsection 2.2. In Section 3 Topological Data Analysis is presented. We will be using Persistent Homology and the Mapper algorithm which are presented in Subsections 3.1 and 3.2 respectively. Ways of applying topology to clustering are examined in Section 4. Finally, Section 5 has some concluding remarks. All figures in this article were created using Scikit-TDA package [26] in Python. The relative code can be found in https://github.com/dpanagop/data_analytics_exampl 2 Clustering 2.1 Definition Clustering is the task of grouping a set of objects in such a way that objects in the same group (called a cluster) are more similar (in some sense) to each other than to those in other groups [32]. Clustering is a major task of Machine Learning with diverse applications from medicine [29] to sports [1].

Springer optimization and its applications, 2018

This paper documents a holistic mathematical modeling theory to provide a rigorous description of... more This paper documents a holistic mathematical modeling theory to provide a rigorous description of cyber-attacks and cyber-security. After determining valuations and vulnerabilities of parts of a node constituent, we recall the definitions of cyber-effect and cyber-interaction. Based on these concepts, we give the mathematical definitions of cyber navigation and infected node and we explain what is meant by dangerous cyber navigation and protection of cyber nodes from unplanned attacks. Our discussion proceeds to a rigorous description of passive and active cyber-attacks, as well as the relevant protections.

Springer optimization and its applications, 2018

This paper investigates the method of selective priorities for the data amounts in the processing... more This paper investigates the method of selective priorities for the data amounts in the processing of big data. After defining the focal data sets, it is introduced the concept of program of data selection which specifies the data amount that a processor may take into account. Then, they are determined the relations of data selection preference and of rational choice for the data amounts. Subsequently, it is considered the case of several data processors and it is shown that there are cores and equilibriums of contrasts, the study of which may provide useful information.

Springer optimization and its applications, 2017

First, we investigate the possibility of destruction of a passive point target. Subsequently, we ... more First, we investigate the possibility of destruction of a passive point target. Subsequently, we study the problem of determination of best targeting points in an area within which stationary or mobile targets are distributed uniformly or normally. Partial results are given in the case in which the number of targeting points is less than seven or four, respectively. Thereafter, we study the case where there is no information on the enemy distribution. Then, the targeting should be organized in such a way that the surface defined by the kill radii of the missiles fully covers each point within a desired region of space-time. The problem is equivalent to the problem of packing ellipsoids of different sizes and shapes into an ellipsoidal container in \(\mathbb{R}^{4}\) so as to minimize a measure of overlap between ellipsoids is considered.

Springer optimization and its applications, 2017

Springer eBooks, 2015

After giving definitions and background information of key terms, we report and analyze the multi... more After giving definitions and background information of key terms, we report and analyze the multi-layer graph model of network centric operations (NCOs), and we mention its advantages. Moreover, we investigate security problem of NCOs by applying methods of vertex pursuit games. Finally, in Sect. 6 we take up with the problem of network centric warfare strategic formation.

We give a short overview of the recent research perspectives and mathematical foundations in topo... more We give a short overview of the recent research perspectives and mathematical foundations in topological quantum computation theory. In particular, we will be interested in braid representation theory, topological invariants of braids, approximation with braiding generators and quantum hashing with the icosahedral group.

Springer optimization and its applications, 2014

In this paper we study the positioning of defender forces in order to handle in an efficient way ... more In this paper we study the positioning of defender forces in order to handle in an efficient way the forces of the attacker. The scope is to determine the minimum amplitude of territories which the invader will occupy. The defender’s forces should swoop rapidly to any point of the defence locus in order to protect their territories. The selection of the “optimal” position in which the defender’s forces should be placed is a difficult problem and it aims at the minimization of enemy’s penetration. The minimization methods result to non-linear equations and there are many classical numerical algorithms for solving such equations. The most known one is Newton’s method. Since the selection of a suitable initial point is not a trivial task, we will study the behaviour of these numerical procedures for various initial points and small perturbations of the data in order to present stable procedures which compute efficiently the solution of non-linear equations, leading to the optimal selection of the position, on which the forces of the defender should be placed. All the proposed methods are tested for various sets of data and useful conclusions arise. The algorithms are compared as to the computational complexity and stability through error analysis yielding useful results.

Journal of Computational and Applied Mathematics, Sep 1, 2001

We introduce Padà e-type (and Padà e) approximation to complex-valued harmonic functions in the u... more We introduce Padà e-type (and Padà e) approximation to complex-valued harmonic functions in the unit disk D. This coordinate approximation is deÿned to be a composed Padà e-type approximation (respectively, a composed Padà e approximation). The basic properties of such an approximation are being studied and we are showing that any classical Padà e-type approximant to an analytic function on D coincides with a composed Padà e-type approximant to this function.

We show reflective arrangement of primes around natural numbers and, using this, we prove Goldbac... more We show reflective arrangement of primes around natural numbers and, using this, we prove Goldbach's conjecture.

We construct optimal multivariate vectors of rational approximation numbers with common denominat... more We construct optimal multivariate vectors of rational approximation numbers with common denominator and whose coordinate decimal expansion string of digits coincides with the decimal expansion digital string of a given sequence of mutually irrational numbers as far as possible. We investigate several numerical examples and we present an application in Nuclear Physics related to the beam stability problem of particle beams in high-energy hadron colliders.

Proceedings of Indian National Science Academy, 2015

CONTINUITY OF DISTRIBUTIONS AND GLOBAL CONVERGENCE OF PADÉ-TYPE APPROXIMANTS IN RUNGE DOMAINS

This book highlights recent advances in the development of effective modeling and solution approa... more This book highlights recent advances in the development of effective modeling and solution approaches to enhance the performance of military logistics. It seeks to further research in global defense-related topics, including military operations, governmental operations and security, as well as nation support. Additionally its purpose is to promote the global exchange of information and ideas amongst developers and users of military operations research tools and techniques. Over the course of its nine chapters, this edited volume addresses significant issues in military logistics including: a) Restructuring processes via OR methods aimed at improving the efficiency and effectiveness of the military logistics, b) Sense-and-Respond logistics prediction and coordination techniques that provide competitive advantage, spanning the full range of military operations across the strategic, operational and tactical levels of war, c) Procurement and auctioning, d) Inventory and stock control th...

Weprove that there is no non-trivial solution to the Diophantine equation Ax^p+By^q=Cz^r provided... more Weprove that there is no non-trivial solution to the Diophantine equation Ax^p+By^q=Cz^r provided that min{p,q,r}>2 and gcd(Ax, By,Cz)=1. In particular, we reaffirm Beal's

Confidentiality, Integrity, and Availability of Military information is a crucial and critical fa... more Confidentiality, Integrity, and Availability of Military information is a crucial and critical factor for a country's national security. The security of military information systems (MIS) and Networks (MNET) is a subject of continuous research and design, due to the fact that they manage, store, manipulate, and distribute the information. This study presents a bio-inspired hybrid artificial intelligence framework for cyber security (bioHAIFCS). This framework combines timely and bio-inspired Machine Learning methods suitable for the protection of critical network applications, namely military information systems, applications and networks. More specifically, it combines (a) the hybrid evolving spiking anomaly detection model (HESADM), which is used in order to prevent in time and accurately, cyber-attacks, which cannot be avoided by using passive security measures, namely: Firewalls, (b) the evolving computational intelligence system for malware detection (ECISMD) that spots and isolates malwares located in packed executables untraceable by antivirus, and (c) the evolutionary prevention system from SQL injection (ePSSQLI) attacks, which early and smartly forecasts the attacks using SQL Injections methods.

Springer optimization and its applications, 2012

Aims and Scope Optimization has been expanding in all directions at an astonishing rate during th... more Aims and Scope Optimization has been expanding in all directions at an astonishing rate during the last few decades. New algorithmic and theoretical techniques have been developed, the diffusion into other disciplines has proceeded at a rapid pace, and our knowledge of all aspects of the field has grown even more profound. At the same time, one of the most striking trends in optimization is the constantly increasing emphasis on the interdisciplinary nature of the field. Optimization has been a basic tool in all areas of applied mathematics, engineering, medicine, economics, and other sciences. The series Springer Optimization and Its Applications publishes undergraduate and graduate textbooks, monographs and state-of-the-art expository work that focus on algorithms for solving optimization problems and also study applications involving such problems. Some of the topics covered include nonlinear optimization (convex and nonconvex), network flow problems, stochastic optimization, optimal control, discrete optimization, multiobjective programming, description of software packages, approximation techniques and heuristic approaches.

WORLD SCIENTIFIC eBooks, Dec 7, 2022

Clustering is one of the most common tasks of Machine Learning. In this chapter we examine how id... more Clustering is one of the most common tasks of Machine Learning. In this chapter we examine how ideas from topology can be used to improve clustering techniques. 1 Introduction With the advent of Big Data, algorithms that try to extract information from them are ubiquitous. Clustering algorithms are a subcategory of Machine Learning algorithms with a wide range of applications. Notions like closeness, distance and shape are central to clustering. It is then natural to try to use ideas and techniques from topology to improve clustering algorithms. This chapter examines some ways on how this could happen. In Section 2 a brief introduction to the clustering task is presented. In Subsection 2.1 a definition is presented along with notation. k-means algorithm will be one of our focus areas and is examined in more detail in Subsection 2.2. In Section 3 Topological Data Analysis is presented. We will be using Persistent Homology and the Mapper algorithm which are presented in Subsections 3.1 and 3.2 respectively. Ways of applying topology to clustering are examined in Section 4. Finally, Section 5 has some concluding remarks. All figures in this article were created using Scikit-TDA package [26] in Python. The relative code can be found in https://github.com/dpanagop/data_analytics_exampl 2 Clustering 2.1 Definition Clustering is the task of grouping a set of objects in such a way that objects in the same group (called a cluster) are more similar (in some sense) to each other than to those in other groups [32]. Clustering is a major task of Machine Learning with diverse applications from medicine [29] to sports [1].

Springer optimization and its applications, 2018

This paper documents a holistic mathematical modeling theory to provide a rigorous description of... more This paper documents a holistic mathematical modeling theory to provide a rigorous description of cyber-attacks and cyber-security. After determining valuations and vulnerabilities of parts of a node constituent, we recall the definitions of cyber-effect and cyber-interaction. Based on these concepts, we give the mathematical definitions of cyber navigation and infected node and we explain what is meant by dangerous cyber navigation and protection of cyber nodes from unplanned attacks. Our discussion proceeds to a rigorous description of passive and active cyber-attacks, as well as the relevant protections.

Springer optimization and its applications, 2018

This paper investigates the method of selective priorities for the data amounts in the processing... more This paper investigates the method of selective priorities for the data amounts in the processing of big data. After defining the focal data sets, it is introduced the concept of program of data selection which specifies the data amount that a processor may take into account. Then, they are determined the relations of data selection preference and of rational choice for the data amounts. Subsequently, it is considered the case of several data processors and it is shown that there are cores and equilibriums of contrasts, the study of which may provide useful information.

Springer optimization and its applications, 2017

First, we investigate the possibility of destruction of a passive point target. Subsequently, we ... more First, we investigate the possibility of destruction of a passive point target. Subsequently, we study the problem of determination of best targeting points in an area within which stationary or mobile targets are distributed uniformly or normally. Partial results are given in the case in which the number of targeting points is less than seven or four, respectively. Thereafter, we study the case where there is no information on the enemy distribution. Then, the targeting should be organized in such a way that the surface defined by the kill radii of the missiles fully covers each point within a desired region of space-time. The problem is equivalent to the problem of packing ellipsoids of different sizes and shapes into an ellipsoidal container in \(\mathbb{R}^{4}\) so as to minimize a measure of overlap between ellipsoids is considered.

Springer optimization and its applications, 2017

Springer eBooks, 2015

After giving definitions and background information of key terms, we report and analyze the multi... more After giving definitions and background information of key terms, we report and analyze the multi-layer graph model of network centric operations (NCOs), and we mention its advantages. Moreover, we investigate security problem of NCOs by applying methods of vertex pursuit games. Finally, in Sect. 6 we take up with the problem of network centric warfare strategic formation.

We give a short overview of the recent research perspectives and mathematical foundations in topo... more We give a short overview of the recent research perspectives and mathematical foundations in topological quantum computation theory. In particular, we will be interested in braid representation theory, topological invariants of braids, approximation with braiding generators and quantum hashing with the icosahedral group.

Springer optimization and its applications, 2014

In this paper we study the positioning of defender forces in order to handle in an efficient way ... more In this paper we study the positioning of defender forces in order to handle in an efficient way the forces of the attacker. The scope is to determine the minimum amplitude of territories which the invader will occupy. The defender’s forces should swoop rapidly to any point of the defence locus in order to protect their territories. The selection of the “optimal” position in which the defender’s forces should be placed is a difficult problem and it aims at the minimization of enemy’s penetration. The minimization methods result to non-linear equations and there are many classical numerical algorithms for solving such equations. The most known one is Newton’s method. Since the selection of a suitable initial point is not a trivial task, we will study the behaviour of these numerical procedures for various initial points and small perturbations of the data in order to present stable procedures which compute efficiently the solution of non-linear equations, leading to the optimal selection of the position, on which the forces of the defender should be placed. All the proposed methods are tested for various sets of data and useful conclusions arise. The algorithms are compared as to the computational complexity and stability through error analysis yielding useful results.

Journal of Computational and Applied Mathematics, Sep 1, 2001

We introduce Padà e-type (and Padà e) approximation to complex-valued harmonic functions in the u... more We introduce Padà e-type (and Padà e) approximation to complex-valued harmonic functions in the unit disk D. This coordinate approximation is deÿned to be a composed Padà e-type approximation (respectively, a composed Padà e approximation). The basic properties of such an approximation are being studied and we are showing that any classical Padà e-type approximant to an analytic function on D coincides with a composed Padà e-type approximant to this function.

We show reflective arrangement of primes around natural numbers and, using this, we prove Goldbac... more We show reflective arrangement of primes around natural numbers and, using this, we prove Goldbach's conjecture.

We construct optimal multivariate vectors of rational approximation numbers with common denominat... more We construct optimal multivariate vectors of rational approximation numbers with common denominator and whose coordinate decimal expansion string of digits coincides with the decimal expansion digital string of a given sequence of mutually irrational numbers as far as possible. We investigate several numerical examples and we present an application in Nuclear Physics related to the beam stability problem of particle beams in high-energy hadron colliders.

Proceedings of Indian National Science Academy, 2015

CONTINUITY OF DISTRIBUTIONS AND GLOBAL CONVERGENCE OF PADÉ-TYPE APPROXIMANTS IN RUNGE DOMAINS

This book highlights recent advances in the development of effective modeling and solution approa... more This book highlights recent advances in the development of effective modeling and solution approaches to enhance the performance of military logistics. It seeks to further research in global defense-related topics, including military operations, governmental operations and security, as well as nation support. Additionally its purpose is to promote the global exchange of information and ideas amongst developers and users of military operations research tools and techniques. Over the course of its nine chapters, this edited volume addresses significant issues in military logistics including: a) Restructuring processes via OR methods aimed at improving the efficiency and effectiveness of the military logistics, b) Sense-and-Respond logistics prediction and coordination techniques that provide competitive advantage, spanning the full range of military operations across the strategic, operational and tactical levels of war, c) Procurement and auctioning, d) Inventory and stock control th...

Weprove that there is no non-trivial solution to the Diophantine equation Ax^p+By^q=Cz^r provided... more Weprove that there is no non-trivial solution to the Diophantine equation Ax^p+By^q=Cz^r provided that min{p,q,r}>2 and gcd(Ax, By,Cz)=1. In particular, we reaffirm Beal's

Confidentiality, Integrity, and Availability of Military information is a crucial and critical fa... more Confidentiality, Integrity, and Availability of Military information is a crucial and critical factor for a country's national security. The security of military information systems (MIS) and Networks (MNET) is a subject of continuous research and design, due to the fact that they manage, store, manipulate, and distribute the information. This study presents a bio-inspired hybrid artificial intelligence framework for cyber security (bioHAIFCS). This framework combines timely and bio-inspired Machine Learning methods suitable for the protection of critical network applications, namely military information systems, applications and networks. More specifically, it combines (a) the hybrid evolving spiking anomaly detection model (HESADM), which is used in order to prevent in time and accurately, cyber-attacks, which cannot be avoided by using passive security measures, namely: Firewalls, (b) the evolving computational intelligence system for malware detection (ECISMD) that spots and isolates malwares located in packed executables untraceable by antivirus, and (c) the evolutionary prevention system from SQL injection (ePSSQLI) attacks, which early and smartly forecasts the attacks using SQL Injections methods.