Oscillations and periodic solutions in a two-dimensional differential delay model
- Authors: Ivanov, Anatoli , Dzalilov, Zari
- Date: 2021
- Type: Text , Conference paper
- Relation: International Conference on Applied Mathematics, Modeling and Computational Science, AMMCS 2019 Vol. 343, p. 59-70
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- Description: A class of two-dimensional differential systems with delay and overall negative feedback is considered. Sufficient conditions for the existence of periodic solutions are established. The instability of the unique equilibrium together with the one-sided boundedness of one of the two nonlinearities lead to the existence of periodic solutions. Systems of this type appear in various applications in engineering and natural sciences, in particular in mathematical biology and physiology as models of circadian rhythm generator and glucose-insulin regulation models in humans. © 2021, Springer Nature Switzerland AG.
Oscillations in low-dimensional cyclic differential delay systems
- Authors: Ivanov, Anatoli, , Dzalilov, Zari
- Date: 2018
- Type: Text , Conference paper
- Relation: International conference on Applied Mathematics, Modeling and Computational Science, AMMCS 2017, Waterloo, Canada, August 20–25, 2017 Vol. 259, p. 603-613
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- Description: Nonlinear autonomous N-dimensional systems of cyclic differential equations with delays and overall negative feedback are considered. Such systems serve as mathematical models of numerous real world phenomena in physics and laser optics, physiology and mathematical biology, economics and life sciences among others. In the case of lower dimensions and sufficient conditions are derived for the oscillation of all solutions about the unique equilibrium. Open problems and conjectures are discussed for the higher dimensional case and for more convoluted sign feedbacks. © 2018, Springer Nature Switzerland AG.
An extended lifetime measure for telecommunications networks : Improvements and implementations
- Authors: Dzalilov, Zari , Ouveysi, Iradj , Bektas, Tolga
- Date: 2012
- Type: Text , Journal article
- Relation: Journal of Industrial and Management Optimization Vol. 8, no. 3 (2012), p. 639-649
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- Description: Predicting the lifetime of a network is a stochastic and very hard task. Sensitivity analysis of a network in order to identify the weakest points in the network, provides valuable knowledge to draw an optimum investment strategy for the expansion of the networks for the network carriers. To achieve this goal, a new measure, called topology lifetime, was recently proposed for measuring the performance of a telecommunication network. This measure not only allows to perform a sensitivity analysis of the networks, but also it provides the means to compare the different topologies with respect to the ability of the network in supporting growth in network traffic before new capacity/facility is installed. This paper addresses some improvements upon the previously defined measures and presents the implementation results of the various lifetime measure methodologies. Computational analysis on some commonly used topologies show how the new measure can be utilized in assessing network performance.
- Description: 2003010401
Application of optimisation-based data mining techniques to medical data sets: A comparative analysis
- Authors: Dzalilov, Zari , Bagirov, Adil , Mammadov, Musa
- Date: 2012
- Type: Text , Conference paper
- Relation: IMMM 2102: The Second International Conference on Advances in Information Mining and Management p. 41-46
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- Description: Abstract - Computational methods have become an important tool in the analysis of medical data sets. In this paper, we apply three optimisation-based data mining methods to the following data sets: (i) a cystic fibrosis data set and (ii) a tobacco control data set. Three algorithms used in the analysis of these data sets include: the modified linear least square fit, an optimization based heuristic algorithm for feature selection and an optimization based clustering algorithm. All these methods explore the relationship between features and classes, with the aim of determining contribution of specific features to the class outcome. However, the three algorithms are based on completely different approaches. We apply these methods to solve feature selection and classification problems. We also present comparative analysis of the algorithms using computational results. Results obtained confirm that these algorithms may be effectively applied to the analysis of other (bio)medical data sets
Periodic solutions in a discrete model with delay
- Authors: Dzalilov, Zari , Ivanov, Anatoli
- Date: 2011
- Type: Text , Journal article
- Relation: Dynamics of Continuous, Discrete and Impulsive Systems Series B: Applications and Algorithms Vol. 18, no. 6 (2011), p. 799-810
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- Description: An essentially nonlinear difference equation with delay serving as a mathematical model of several applied problems is considered. Sufficient conditions for the existence of periodic solutions are derived. Copyright © 2011 Watam Press.
Application of optimisation-based data mining techniques to tobacco control dataset
- Authors: Dzalilov, Zari , Zhang, J , Bagirov, Adil , Mammadov, Musa
- Date: 2010
- Type: Text , Journal article
- Relation: International Journal of Lean Thinking Vol. 1, no. 1 (2010), p. 27-41
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- Description: Tobacco smoking is one of the leading causes of death around the world. Consequently, control of tobacco use is an important global public health issue. Tobacco control may be aided by development of theoretical and methodological frameworks for describing and understanding complex tobacco control systems. Linear regression and logistic regression are currently very popular statistical techniques for modeling and analyzing complex data in tobacco control systems. However, in tobacco markets, numerous interrelated factors nontrivially interact with tobacco control policies, such that policies and control outcomes are nonlinearly related.
Cluster analysis of a tobacco control data set
- Authors: Dzalilov, Zari , Bagirov, Adil
- Date: 2010
- Type: Text , Journal article
- Relation: International Journal of Lean Thinking Vol. 1, no. 2 (2010), p.
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- Description: Development of theoretical and methodological frameworks in data analysis is fundamental for modeling complex tobacco control systems. Following this idea, a new optimization based approach was introduced in the paper through two distinct methods: the modified linear least square fit and a heuristic algorithm for feature slection based on optimization-based methods have the potential to detect nonlinearity, and therefore to be more effective analysis tools of complex data set. In this study we evaluate the modified global k-means clustering algorithm by applying it to a massive set of real-time tobacco control survey data. Cluster analysis identified fixed and stable clusters in the studied data. These clusters correspond to groups of smokers with similar behaviour and the identification of these clusters may allow us to give recommendations on modification of existing tobacco control systems and on the design of future data acquistion surveys.
Global attractors for discrete disperse dynamical systems
- Authors: Dzalilov, Zari , Zaslavski, Alexander
- Date: 2009
- Type: Text , Journal article
- Relation: Journal of nonlinear and convex analysis Vol. 10, no. 2 (2009), p. 191-198
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- Description: In this paper we discuss the asymptotic behavior of trajectories of discrete disperse dynamical systems generated by set-valued mappings.
Mathematical models for failure reconfiguration of telecommunication networks : Part 1
- Authors: Dzalilov, Zari , Ouveysi, Iradj
- Date: 2009
- Type: Text , Journal article
- Relation: Optimization Vol. 58, no. 5 (2009), p. 483-504
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- Description: This article proposes various mathematical modelling of networks for failure recovery. We consider a survivable communication network which is designed to carry different types of services under service level agreements (SLAs) between the network provider and the network users. Two different approaches for dynamical reconfiguration of networks are presented: with and without penalization. The approach without penalization does not require to consider the status of SLAs during the process of network reconfiguration. The second approach considers the status of the SLAs in the network and the corresponding re-optimization model for network reconfiguration is more complicated as the dimension of the linear programming problem in this case is higher than one for the problem of optimization without penalization. Some mathematical models and solution methodologies for this network operation problem are presented and an extensive implementation result has been provided.
Mathematical models for failure reconfiguration of telecommunication networks : Part 2
- Authors: Dzalilov, Zari , Ouveysi, Iradj
- Date: 2009
- Type: Text , Journal article
- Relation: Optimization Vol. 58, no. 5 (2009), p. 505-520
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- Description: This article proposes an efficient network reconfiguration model for failure recovery of a communication network. The novelty of our methodology is that, it considers a small neighbourhood of failed component(s) in the network in order to perform network reconfiguration. This approach significantly reduces the size of proposed linear programming problem, making our reconfiguration procedure theoretically scalable and practically implementable. Targeting a small neighbourhood of failed area in the network also minimizes the amount of traffic rerouting in the network. This is ideal in the management of a communication network.
Optimization of back-propagation neural networks architecture and parameters with a hybrid PSO/SA approach
- Authors: Zarei, Mahdi , Dzalilov, Zari
- Date: 2009
- Type: Text , Conference paper
- Relation: Paper presented at Fifth International Conference on Soft Computing, Computing with Words and Perceptions in System Analysis, Decision and Control, ICSCCW 2009, Famagusta, North Cyprus : 2nd-4th September 2009
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- Description: Determining the architecture and parameters of neural networks is an important scientific challenge. This paper reports a new hybrid optimization method for optimization of back-propagation neural networks architecture and parameters with a high accuracy. We use particle swarm optimization that has proven to be very effective and fast and has shown to increase the efficiency of simulated annealing when applied to a diverse set of optimization problems. To evaluate the proposed method, we employ the PIMA dataset from the University of California machine learning database. Compared with previous work, we show superior classification accuracy rates of the developed approach.
- Description: 2003007878
A new scoring system in Cystic Fibrosis : Statistical tools for database analysis - A preliminary report
- Authors: Hafen, Gaudenz , Hurst, Cameron , Yearwood, John , Smith, Julie , Dzalilov, Zari , Robinson, P. J.
- Date: 2008
- Type: Text , Journal article
- Relation: BMC Medical Informatics and Decision Making Vol. 8, no. 44 (2008), p.1-11
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- Description: Background. Cystic fibrosis is the most common fatal genetic disorder in the Caucasian population. Scoring systems for assessment of Cystic fibrosis disease severity have been used for almost 50 years, without being adapted to the milder phenotype of the disease in the 21st century. The aim of this current project is to develop a new scoring system using a database and employing various statistical tools. This study protocol reports the development of the statistical tools in order to create such a scoring system. Methods. The evaluation is based on the Cystic Fibrosis database from the cohort at the Royal Children's Hospital in Melbourne. Initially, unsupervised clustering of the all data records was performed using a range of clustering algorithms. In particular incremental clustering algorithms were used. The clusters obtained were characterised using rules from decision trees and the results examined by clinicians. In order to obtain a clearer definition of classes expert opinion of each individual's clinical severity was sought. After data preparation including expert-opinion of an individual's clinical severity on a 3 point-scale (mild, moderate and severe disease), two multivariate techniques were used throughout the analysis to establish a method that would have a better success in feature selection and model derivation: 'Canonical Analysis of Principal Coordinates' and 'Linear Discriminant Analysis'. A 3-step procedure was performed with (1) selection of features, (2) extracting 5 severity classes out of a 3 severity class as defined per expert-opinion and (3) establishment of calibration datasets. Results. (1) Feature selection: CAP has a more effective "modelling" focus than DA. (2) Extraction of 5 severity classes: after variables were identified as important in discriminating contiguous CF severity groups on the 3-point scale as mild/moderate and moderate/severe, Discriminant Function (DF) was used to determine the new groups mild, intermediate moderate, moderate, intermediate severe and severe disease. (3) Generated confusion tables showed a misclassification rate of 19.1% for males and 16.5% for females, with a majority of misallocations into adjacent severity classes particularly for males. Conclusion. Our preliminary data show that using CAP for detection of selection features and Linear DA to derive the actual model in a CF database might be helpful in developing a scoring system. However, there are several limitations, particularly more data entry points are needed to finalize a score and the statistical tools have further to be refined and validated, with re-running the statistical methods in the larger dataset. © 2008 Hafen et al; licensee BioMed Central Ltd.
An extended lifetime measure for telecommunication network
- Authors: Dzalilov, Zari , Ouveysi, Iradj , Rubinov, Alex
- Date: 2008
- Type: Text , Journal article
- Relation: Journal of Industrial and Management Optimization Vol. 4, no. 2 (2008), p. 329-337
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- Description: A new measure for network performance evaluation called topology lifetime was introduced in [4, 5]. This measure is based on the notion of unexpected traffic growth and can be used for comparison of topologies. We discuss some advantages and disadvantages of the approach of [4] and suggest some modifications to this approach. In particular we discuss how to evaluate the influence of a subgraph to the lifetime measure and introduce the notion of the order of a path. This notion is useful if we consider a possible extension to the set of working paths in order to support the traffic for the time that is needed for installation of new facilities.
Challenging issues in dynamic reconfiguration of telecommunication networks
- Authors: Dzalilov, Zari , Ouveysi, Iradj
- Date: 2008
- Type: Text , Conference paper
- Relation: Paper presented at Second International Conference: Problems of Cybernetics and Informatics, PCI 2008, Baku, Azerbaijan : 10th-12th September 2008 p. 48-51
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- Description: For the last quarter of a century understanding of the nature of telecommunication network traffic has been considered as an important research topic. Any well-designed recovery strategy has to take into account the different resilience requirements of the single traffic flows in order to avoid excessive usage of bandwidth for standby links. Here we discuss the issues of a reconfiguration procedure in order to perform network recovery in the case of any failure scenario in the telecommunication networks. We explain the complexities arising in the real life application and propose an optimization technique in order to minimize the size of the optimization problem in the process of reconfiguration. Our suggestion to achieve this is to find the minimal sub-graph surrounding the failure region that contains the required unused capacity to perform network recovery task.
- Description: 2003006857
On the implementation of dynamic reconfiguration in telecommunication networks
- Authors: Dzalilov, Zari , Ouveysi, Iradj
- Date: 2008
- Type: Text , Conference paper
- Relation: Paper presented at Second International Conference: Problems of Cybernetics and Informatics, PCI 2008, Baku, Azerbaijan : 10th-12th September 2008 p. 44-47
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- Description: In this paper we summarize our proposed methodology for dynamic reconfiguration of telecommunication networks. This procedure is implemented to achieve network recovery in the case of any failure in the network. We also outline a brief description of path analysis techniques that are considered in the rerouting of Origin-Destination traffic flows and address how these methods are used in the implementation of proposed algorithm
- Description: 2003006858
Dynamic reconfiguration and graph theory approaches to failures in IT based telecommunication networks
- Authors: Patel, Keyurkumar , Dzalilov, Zari
- Date: 2004
- Type: Text , Conference paper
- Relation: Paper presented at 4th IASTED International Conference on Modelling, Simulation, and Optimisation, Marbella, Spain : 17-19th August, 2004 p. 219-244
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- Description: For the last quarter of a century understanding of the nature of telecommunication network traffic has been considered as an important research topic. Any well designed recovery strategy has to take into account the different resilience requirements of the single traffic flows in order to avoid excessive usage of bandwidth for standby links. Faced with multiple recovery options, an internet service provider (ISP) must decide which flows to protect to what extent against networks. Traditional techniques and models used to determine the availability and failure rates of telecommunications networks are based on classic failure models such as Mean-time between failure and Mean-time between service outage predictors. Network failures occur for many different reasons and occur in many different forms. These classic models only assume that the failure is caused by a hardware component of the network. With the widespread deployment of Internet technologies other factors that cause or contribute to failure in a telecommunications network must be explored. Two additional failure modes to existing published failure models, failure from Denial of Service attacks, and failures due to catastrophic events have been identified and defined along with an initial outline of a generalized prediction model based on Dynamic System Theory. Discussion is done on the effects of failures and survivability issues in network failures and how to overcome failures in IT based telecommunication network
- Description: E1
- Description: 2003002567
Mathematical models of dynamic reconfiguration of telecommunication networks
- Authors: Dzalilov, Zari
- Date: 2004
- Type: Text , Thesis , PhD
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- Description: In this thesis we examine mathematical models for dynamical reconfiguration of telecommunication networks. Dynamical configuration is one of the most important problems in the field of network management. In the case of some part of the network being damaged the system should maintain its operations, taking into account the new conditions. This can be achieved by using the residual capacity of the system if it is available. If there were not enough residual capacity, the managers of the system need to involve some of the unaffected traffic in order to reorganize traffic. A prolonged breakdown will push some customers to change their provider; there is also a lost [sic] of profit because of breakdowns, that can be considered as a certain implicit penalty. To reorganize traffic by using new routes we should have a flexible routing system.
- Description: Doctor of Philosophy
A lifetime measure for telecommunication network : Theoretical aspects
- Authors: Dzalilov, Zari , Rubinov, Alex , Ouveysi, Iradj
- Date: 2003
- Type: Text , Conference paper
- Relation: Paper presented at ICON 2003 - 2003 11th IEEE International Conference on Networks, Sydney : 28th September, 2003
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- Description: A new measure for network performance evaluation called topology lifetime was introduced in [Maxemchuk, N et al., May 2002], see also [Maxemchuk, N et al.]. This measure is based on the notion of unexpected traffic growth and can be used for comparison of topologies. We discuss some advantages and disadvantages of the approach from [Maxemchuk, N et al., May 2002] and suggest some modifications to this approach. In particular we discuss how to evaluate the influence of a subgraph to the lifetime measure and introduce the notion of the order of a path. This notion is useful if we consider a possible extension to the set of working paths in order to support the traffic for the time that is needed for installation of new facilities.
- Description: E1
- Description: 2003000361
Dynamic reconfiguration of telecommunication networks
- Authors: Dzalilov, Zari , Ouveysi, Iradj , Rubinov, Alex
- Date: 2003
- Type: Text , Conference paper
- Relation: Paper presented at the Industrial Optimisation 2003 Conference, Perth : 30th October, 2002
- Full Text: false
- Reviewed:
- Description: E1
- Description: 2003000451
Abstract convexity of positive homogenous functions
- Authors: Rubinov, Alex , Dzalilov, Zari
- Date: 2002
- Type: Text , Journal article
- Relation: Journal of Statistics and Management Systems Vol. 5, no. 1 (2002), p. 1-19
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- Description: This paper is a survey of recent results to abstract convexity of positively homogeneous functions, that is, to a representation of such functions as the upper (lower) envelope of sets of fairly simple functions. In particular, we study sup-min and max-min representations of positively homogeneous of degree one functions through linear functions and various kinds of the so-called exhausters.
- Description: C1
- Description: 2003003353