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Biotic stress and crop improvement

- Huseynova, Irada, Sultanova, Nargiz, Mammadov, Almadar, Suleymanov, Saftar, Aliyev, Jalal

  • Authors: Huseynova, Irada , Sultanova, Nargiz , Mammadov, Almadar , Suleymanov, Saftar , Aliyev, Jalal
  • Date: 2014
  • Type: Text , Book chapter
  • Relation: Improvement of Crops in the Era of Climatic Changes p. 91-120
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  • Description: Biotic stress is one of the major environmental factors affecting plants. Viruses, fungi, bacteria, weeds, insects, and other pests and pathogens represent a major constraint to agricultural productivity and a serious threat to vegetable and grain crops. Plant protection against pathogens and pests is a commercially important issue and one of the main directions of researches. Almost half of new infectious diseases identified in plants during the past 10 years have a viral nature. The number and distribution areas of some plant viruses in Europe have been increasing rapidly during the past 35 years that caused big problems from an economic point of view. Viral diseases have also become a real threat for different cultivars of vegetables, grains, and other agricultural crops in our country. It causes extensive leaf yellowing, stem and leaf deformation, reducing the fruit quality, substantial yield loss, and shortening the lifecycle of crops. The probable cause of decay of virus-infected plants is not only the virus activity itself but also reduced tolerance to unfavorable environmental conditions. The identification of the viruses affecting plants and the study of the plant responses are very important for the better understanding of the plant–virus interactions and for developing the tendency to reduce the plant virus-associated risks in Azerbaijan. Therefore, the main goal of the present study is to identify the most widespread plant viruses in Azerbaijan using different molecular techniques and to evaluate some characteristics of plant response to viral stress

Matching algorithms : fundamentals, applications and challenges

- Ren, Jing, Xia, Feng, Chen, Xiangtai, Liu, Jiaying, Sultanova, Nargiz

  • Authors: Ren, Jing , Xia, Feng , Chen, Xiangtai , Liu, Jiaying , Sultanova, Nargiz
  • Date: 2021
  • Type: Text , Journal article , Review
  • Relation: IEEE Transactions on Emerging Topics in Computational Intelligence Vol. 5, no. 3 (2021), p. 332-350
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  • Description: Matching plays a vital role in the rational allocation of resources in many areas, ranging from market operation to people's daily lives. In economics, the term matching theory is coined for pairing two agents in a specific market to reach a stable or optimal state. In computer science, all branches of matching problems have emerged, such as the question-answer matching in information retrieval, user-item matching in a recommender system, and entity-relation matching in the knowledge graph. A preference list is the core element during a matching process, which can either be obtained directly from the agents or generated indirectly by prediction. Based on the preference list access, matching problems are divided into two categories, i.e., explicit matching and implicit matching. In this paper, we first introduce the matching theory's basic models and algorithms in explicit matching. The existing methods for coping with various matching problems in implicit matching are reviewed, such as retrieval matching, user-item matching, entity-relation matching, and image matching. Furthermore, we look into representative applications in these areas, including marriage and labor markets in explicit matching and several similarity-based matching problems in implicit matching. Finally, this survey paper concludes with a discussion of open issues and promising future directions in the field of matching. © 2017 IEEE. **Please note that there are multiple authors for this article therefore only the name of the first 5 including Federation University Australia affiliate “Jing Ren, Xia Feng, Nargiz Sultanova" is provided in this record**

Lost in optimisation of water distribution systems? A literature review of system operation

- Mala-Jetmarova, Helena, Sultanova, Nargiz, Savic, Dragan

  • Authors: Mala-Jetmarova, Helena , Sultanova, Nargiz , Savic, Dragan
  • Date: 2017
  • Type: Text , Journal article , Review
  • Relation: Environmental Modelling and Software Vol. 93, no. (2017), p. 209-254
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  • Description: Optimisation of the operation of water distribution systems has been an active research field for almost half a century. It has focused mainly on optimal pump operation to minimise pumping costs and optimal water quality management to ensure that standards at customer nodes are met. This paper provides a systematic review by bringing together over two hundred publications from the past three decades, which are relevant to operational optimisation of water distribution systems, particularly optimal pump operation, valve control and system operation for water quality purposes of both urban drinking and regional multiquality water distribution systems. Uniquely, it also contains substantial and thorough information for over one hundred publications in a tabular form, which lists optimisation models inclusive of objectives, constraints, decision variables, solution methodologies used and other details. Research challenges in terms of simulation models, optimisation model formulation, selection of optimisation method and postprocessing needs have also been identified. © 2017

Subgradient Method for Nonconvex Nonsmooth Optimization

- Bagirov, Adil, Jin, L., Karmitsa, Napsu, Al Nuaimat, A., Sultanova, Nargiz

  • Authors: Bagirov, Adil , Jin, L. , Karmitsa, Napsu , Al Nuaimat, A. , Sultanova, Nargiz
  • Date: 2012
  • Type: Text , Journal article
  • Relation: Journal of Optimization Theory and Applications Vol.157, no.2 (2012), p.416–435
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  • Description: In this paper, we introduce a new method for solving nonconvex nonsmooth optimization problems. It uses quasisecants, which are subgradients computed in some neighborhood of a point. The proposed method contains simple procedures for finding descent directions and for solving line search subproblems. The convergence of the method is studied and preliminary results of numerical experiments are presented. The comparison of the proposed method with the subgradient and the proximal bundle methods is demonstrated using results of numerical experiments. © 2012 Springer Science+Business Media, LLC.

An algorithm for minimization of pumping costs in water distribution systems using a novel approach to pump scheduling

- Bagirov, Adil, Barton, Andrew, Mala-Jetmarova, Helena, Al Nuaimat, Alia, Ahmed, S. T., Sultanova, Nargiz, Yearwood, John

  • Authors: Bagirov, Adil , Barton, Andrew , Mala-Jetmarova, Helena , Al Nuaimat, Alia , Ahmed, S. T. , Sultanova, Nargiz , Yearwood, John
  • Date: 2013
  • Type: Text , Journal article
  • Relation: Mathematical and Computer Modelling Vol. 57, no. 3-4 (2013), p. 873-886
  • Relation: http://purl.org/au-research/grants/arc/LP0990908
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  • Description: The operation of a water distribution system is a complex task which involves scheduling of pumps, regulating water levels of storages, and providing satisfactory water quality to customers at required flow and pressure. Pump scheduling is one of the most important tasks of the operation of a water distribution system as it represents the major part of its operating costs. In this paper, a novel approach for modeling of explicit pump scheduling to minimize energy consumption by pumps is introduced which uses the pump start/end run times as continuous variables, and binary integer variables to describe the pump status at the beginning of the scheduling period. This is different from other approaches where binary integer variables for each hour are typically used, which is considered very impractical from an operational perspective. The problem is formulated as a mixed integer nonlinear programming problem, and a new algorithm is developed for its solution. This algorithm is based on the combination of the grid search with the Hooke-Jeeves pattern search method. The performance of the algorithm is evaluated using literature test problems applying the hydraulic simulation model EPANet. © 2012 Elsevier Ltd.
  • Description: 2003010583

Subgradient smoothing method for nonsmooth nonconvex optimization

- Bagirov, Adil, Sultanova, Nargiz, Taheri, Sona, Ozturk, Gurkan

  • Authors: Bagirov, Adil , Sultanova, Nargiz , Taheri, Sona , Ozturk, Gurkan
  • Date: 2021
  • Type: Text , Conference paper
  • Relation: 5th International Conference on Numerical Analysis and Optimization: Theory, Methods, Applications and Technology Transfer, NAOV, Muscan, 6-9 January 2020 Vol. 354, p. 57-79
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  • Description: In this chapter an unconstrained nonsmooth nonconvex optimization problem is considered and a method for solving this problem is developed. In this method the subproblem for finding search directions is reduced to the unconstrained minimization of a smooth function. This is achieved by using subgradients computed in some neighborhood of a current iteration point and by formulating the search direction finding problem to the minimization of the convex piecewise linear function over the unit ball. The hyperbolic smoothing technique is applied to approximate the minimization problem by a sequence of smooth problems. The convergence of the proposed method is studied and its performance is evaluated using a set of nonsmooth optimization academic test problems. In addition, the method is implemented in GAMS and numerical results using different solvers from GAMS are reported. The proposed method is compared with a number of nonsmooth optimization methods. © 2021, The Author(s), under exclusive license to Springer Nature Switzerland AG.

Reconstruction of tropical cyclone and depression proxies for the South Pacific since the 1850s

- Yeasmin, Alea, Chand, Savin, Sultanova, Nargiz

  • Authors: Yeasmin, Alea , Chand, Savin , Sultanova, Nargiz
  • Date: 2023
  • Type: Text , Journal article
  • Relation: Weather and Climate Extremes Vol. 39, no. (2023), p.
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  • Description: Southwest Pacific nations are highly vulnerable to extreme weather and climate events, particularly those associated with synoptic-scale systems such as tropical cyclones (TCs) and depressions (TDs). This study utilises the Okubo–Weiss–Zeta parameter (OWZP) method to reconstruct historical records of both TCs and TDs for the South Pacific basin using state-of-the-art NOAA-CIRES Twentieth Century Reanalysis (20CR) product. Extensive statistical assessments of these reconstructions are carried out using observational records for the satellite period (i.e., 1979–2014) as ‘ground-truths’. Results show that 20CR-derived TCs and TDs resemble several key characteristics of the observational records, including spatial distribution of genesis locations and track shapes. This gives us confidence that the 20CR-derived long-term records of TCs and TDs can serve as an effective tool for examining historical changes in various characteristics of TCs and TDs, particularly in the context of anthropogenic climate change. © 2022

Finding compact and well-separated clusters : clustering using silhouette coefficients

- Bagirov, Adil, Aliguliyev, Ramiz, Sultanova, Nargiz

  • Authors: Bagirov, Adil , Aliguliyev, Ramiz , Sultanova, Nargiz
  • Date: 2023
  • Type: Text , Journal article
  • Relation: Pattern Recognition Vol. 135, no. (2023), p.
  • Relation: http://purl.org/au-research/grants/arc/DP190100580
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  • Description: Finding compact and well-separated clusters in data sets is a challenging task. Most clustering algorithms try to minimize certain clustering objective functions. These functions usually reflect the intra-cluster similarity and inter-cluster dissimilarity. However, the use of such functions alone may not lead to the finding of well-separated and, in some cases, compact clusters. Therefore additional measures, called cluster validity indices, are used to estimate the true number of well-separated and compact clusters. Some of these indices are well-suited to be included into the optimization model of the clustering problem. Silhouette coefficients are among such indices. In this paper, a new optimization model of the clustering problem is developed where the clustering function is used as an objective and silhouette coefficients are used to formulate constraints. Then an algorithm, called CLUSCO (CLustering Using Silhouette COefficients), is designed to construct clusters incrementally. Three schemes are discussed to reduce the computational complexity of the algorithm. Its performance is evaluated using fourteen real-world data sets and compared with that of three state-of-the-art clustering algorithms. Results show that the CLUSCO is able to compute compact clusters which are significantly better separable in comparison with those obtained by other algorithms. © 2022 Elsevier Ltd

Robust piecewise linear L 1-regression via nonsmooth DC optimization

- Bagirov, Adil, Taheri, Sona, Karmitsa, Napsu, Sultanova, Nargiz, Asadi, Soodabeh

  • Authors: Bagirov, Adil , Taheri, Sona , Karmitsa, Napsu , Sultanova, Nargiz , Asadi, Soodabeh
  • Date: 2022
  • Type: Text , Journal article
  • Relation: Optimization Methods and Software Vol. 37, no. 4 (2022), p. 1289-1309
  • Relation: http://purl.org/au-research/grants/arc/DP190100580
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  • Description: Piecewise linear (Formula presented.) -regression problem is formulated as an unconstrained difference of convex (DC) optimization problem and an algorithm for solving this problem is developed. Auxiliary problems are introduced to design an adaptive approach to generate a suitable piecewise linear regression model and starting points for solving the underlying DC optimization problems. The performance of the proposed algorithm as both approximation and prediction tool is evaluated using synthetic and real-world data sets containing outliers. It is also compared with mainstream machine learning regression algorithms using various performance measures. Results demonstrate that the new algorithm is robust to outliers and in general, provides better predictions than the other alternative regression algorithms for most data sets used in the numerical experiments. © 2020 Informa UK Limited, trading as Taylor & Francis Group.

Subseasonal prediction framework for tropical cyclone activity in the Solomon Islands region

- Haruhiru, Alick, Chand, Savin, Sultanova, Nargiz, Ramsay, Hamish, Sharma, Krishneel, Tahani, Lloyd

  • Authors: Haruhiru, Alick , Chand, Savin , Sultanova, Nargiz , Ramsay, Hamish , Sharma, Krishneel , Tahani, Lloyd
  • Date: 2023
  • Type: Text , Journal article
  • Relation: International Journal of Climatology Vol. 43, no. 12 (2023), p. 5763-5777
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  • Description: Recently, we developed seasonal prediction schemes with improved skill to predict tropical cyclone (TC) activity up to 3 months in advance for the Solomon Islands (SI) region (5°–15°S, 155°–170°E) using sophisticated Bayesian regression techniques. However, TC prediction at subseasonal timescale (i.e., 1–4 weeks in advance) is not being researched for that region despite growing demands from decision makers at sectoral level. In this paper, we first assess the feasibility of developing subseasonal prediction frameworks for the SI region using a pool of predictors that are known to affect TC activity in the region. We then evaluate multiple predictor combinations to develop the most appropriate models using a statistical approach to forecast weekly TC activity up to 4 weeks in advance. Predictors used include indices of various natural climate variability modes, namely the Madden–Julian Oscillation (MJO), the El Niño–Southern Oscillation (ENSO), the Indian Ocean Dipole (IOD) and the Interdecadal Pacific Oscillation (IPO). These modes often have robust physical and statistical relationships with TC occurrences in the SI region and the broader southwest Pacific territory as shown by preceding studies. Additionally, we incorporate TC seasonality as a potential predictor given the persistence of TCs occurring more in certain months than others. Note that a model with seasonality predictor alone (hereafter called the “climatology” model) forms a baseline for comparisons. The hindcast verifications of the forecasts using leave-one-out cross-validation procedure over the study period 1975–2019 indicate considerable improvements in prediction skill of our logistic regression models over climatology, even up to 4 weeks in advance. This study sets the foundation for introducing subseasonal prediction services, which is a national priority for improved decision making in sectors like agriculture and food security, water, health and disaster risk mitigation in the Solomon Islands. © 2023 The Authors. International Journal of Climatology published by John Wiley & Sons Ltd on behalf of Royal Meteorological Society.

Detection and verification of tropical cyclones and depressions over the South Pacific Ocean basin using ERA-5 reanalysis dataset

- Yeasmin, Alea, Chand, Savin, Turville, Christopher, Sultanova, Nargiz

  • Authors: Yeasmin, Alea , Chand, Savin , Turville, Christopher , Sultanova, Nargiz
  • Date: 2021
  • Type: Text , Journal article
  • Relation: International Journal of Climatology Vol. 41, no. 11 (2021), p. 5318-5330
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  • Description: Tropical cyclones (TCs) are one of the most destructive synoptic systems and can cause enormous loss of life and property damages in the South Pacific island nations. The impact of tropical depressions (TDs, i.e. weaker systems that do not develop into TCs) can also be staggering in the region in terms of heavy flooding and landslides, but a lack of complete records often hinders research involving TD impacts. A methodology has been developed here to detect TDs in the ERA-5 reanalysis dataset (the fifth generation ECMWF atmospheric reanalysis of the global climate) using the Okubo–Weiss–Zeta parameter (OWZP) detection scheme. The new South Pacific Enhanced Archive for Tropical Cyclones dataset (SPEArTC), the Dvorak analysis of satellite-based cloud patterns over the South Pacific Ocean basin, and a rainfall dataset for various stations and historical archives have been utilized to validate ERA5-derived TCs and TDs for the period between 1979 and 2019. Results indicate that the OWZP method shows substantial skill in capturing the realistic climatological distribution of TDs (as well as TCs) for the South Pacific Ocean in the ERA5 reanalysis, paving a way forward for future climatological studies involving the impacts of TCs and TDs over the island nations using longer-term reanalyses products such as the 20th-century reanalysis dataset that extends back to the 1850s. © 2021 Royal Meteorological Society

A novel approach to optimal pump scheduling in water distribution systems

- Bagirov, Adil, Barton, Andrew, Mala-Jetmarova, Helena, Al Nuaimat, Alia, Ahmed, S. T., Sultanova, Nargiz, Yearwood, John

  • Authors: Bagirov, Adil , Barton, Andrew , Mala-Jetmarova, Helena , Al Nuaimat, Alia , Ahmed, S. T. , Sultanova, Nargiz , Yearwood, John
  • Date: 2012
  • Type: Text , Conference paper
  • Relation: 14th Water Distribution Systems Analysis Conference 2012, WDSA 2012 Vol. 1; Adelaide, Australia; 24th-27th September; p. 618-631
  • Relation: http://purl.org/au-research/grants/arc/LP0990908
  • Full Text: false
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  • Description: The operation of a water distribution system is a complex task which involves scheduling of pumps, regulating water levels of storages, and providing satisfactory water quality to customers at required flow and pressure. Pump scheduling is one of the most important tasks of the operation of a water distribution system as it represents the major part of its operating costs. In this paper, a novel approach for modeling of pump scheduling to minimize energy consumption by pumps is introduced which uses pump's start/end run times as continuous variables. This is different from other approaches where binary integer variables for each hour are typically used which is considered very impractical from an operational perspective. The problem is formulated as a nonlinear programming problem and a new algorithm is developed for its solution. This algorithm is based on the combination of the grid search with the Hooke-Jeeves pattern search method. The performance of the algorithm is evaluated using literature test problems applying the hydraulic simulation model EPANet.
  • Description: E1

Aggregate subgradient smoothing mehtods for large scale nonsmooth nonconvex optimisation and applications

- Sultanova, Nargiz

  • Authors: Sultanova, Nargiz
  • Date: 2015
  • Type: Text , Journal article
  • Relation: Bulletin of the Australian Mathematical Society Vol. 91, no. 3 (2015), p. 523-524
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  • Description: Nonsmooth optimisation problems are problems which deal with minimisation or maximisation of functions that are not necessarily differentiable. They arise frequently in many practical applications, for example in engineering, machine learning and economics. In addition, some smooth problems can be reformulated as nonsmooth optimisation problems with a simpler structure or a smaller dimension. Despite the fact that there exist many algorithms for solving nonsmooth optimisation problems, the field is still very much in development. Nonsmooth nonconvex optimisation, in particular, is far from being considered a mature branch of optimisation.

Hyperbolic smoothing function method for minimax problems

- Bagirov, Adil, Al Nuaimat, Alia, Sultanova, Nargiz

  • Authors: Bagirov, Adil , Al Nuaimat, Alia , Sultanova, Nargiz
  • Date: 2013
  • Type: Text , Journal article
  • Relation: Optimization Vol. 62, no. 6 (2013), p. 759-782
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  • Description: In this article, an approach for solving finite minimax problems is proposed. This approach is based on the use of hyperbolic smoothing functions. In order to apply the hyperbolic smoothing we reformulate the objective function in the minimax problem and study the relationship between the original minimax and reformulated problems. We also study main properties of the hyperbolic smoothing function. Based on these results an algorithm for solving the finite minimax problem is proposed and this algorithm is implemented in general algebraic modelling system. We present preliminary results of numerical experiments with well-known nonsmooth optimization test problems. We also compare the proposed algorithm with the algorithm that uses the exponential smoothing function as well as with the algorithm based on nonlinear programming reformulation of the finite minimax problem. © 2013 Copyright Taylor and Francis Group, LLC.
  • Description: 2003011099

Solving minimax problems : Local smoothing versus global smoothing

- Bagirov, Adil, Sultanova, Nargiz, Al Nuaimat, Alia, Taheri, Sona

A proximal subgradient algorithm with extrapolation for structured nonconvex nonsmooth problems

- Pham, Tan, Dao, Minh, Shah, Rakibuzzaman, Sultanova, Nargiz, Li, Guoyin, Islam, Syed

  • Authors: Pham, Tan , Dao, Minh , Shah, Rakibuzzaman , Sultanova, Nargiz , Li, Guoyin , Islam, Syed
  • Date: 2023
  • Type: Text , Journal article
  • Relation: Numerical Algorithms Vol. 94, no. 4 (2023), p. 1763-1795
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  • Description: In this paper, we consider a class of structured nonconvex nonsmooth optimization problems, in which the objective function is formed by the sum of a possibly nonsmooth nonconvex function and a differentiable function with Lipschitz continuous gradient, subtracted by a weakly convex function. This general framework allows us to tackle problems involving nonconvex loss functions and problems with specific nonconvex constraints, and it has many applications such as signal recovery, compressed sensing, and optimal power flow distribution. We develop a proximal subgradient algorithm with extrapolation for solving these problems with guaranteed subsequential convergence to a stationary point. The convergence of the whole sequence generated by our algorithm is also established under the widely used Kurdyka–Łojasiewicz property. To illustrate the promising numerical performance of the proposed algorithm, we conduct numerical experiments on two important nonconvex models. These include a compressed sensing problem with a nonconvex regularization and an optimal power flow problem with distributed energy resources. © 2023, The Author(s).

Comparison of metaheuristic algorithms for pump operation optimization

- Bagirov, Adil, Ahmed, S. T., Barton, Andrew, Mala-Jetmarova, Helena, Al Nuaimat, Alia, Sultanova, Nargiz

  • Authors: Bagirov, Adil , Ahmed, S. T. , Barton, Andrew , Mala-Jetmarova, Helena , Al Nuaimat, Alia , Sultanova, Nargiz
  • Date: 2012
  • Type: Text , Conference paper
  • Relation: 14th Water Distribution Systems Analysis Conference 2012, WDSA 2012 Vol. 2; Adelaide, Australia; 24th-27th September 2012; p. 886-896
  • Relation: http://purl.org/au-research/grants/arc/LP0990908
  • Full Text: false
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  • Description: Pumping cost constitutes the main part of the overall operating cost of water distribution systems. There are different optimization formulations of the pumping cost minimization problem including those with application of continuous and integer programming approaches. To date mainly various metaheuristics have been applied to solve this problem. However, the comprehensive comparison of those metaheuristics has not been done. Such a comparison is important to identify strengths and weaknesses of different algorithms which reflects on their performance. In this paper, we present a methodology for comparative analysis of widely used metaheuristics for solving the pumping cost minimization problem. This methodology includes the following comparison criteria: (a) the "optimal solution" obtained; (b) the efficiency; and (c) robustness. Algorithms applied are: particle swarm optimization, artificial bee colony and firefly algorithms. These algorithms were applied to one test problem available in the literature. The results obtained demonstrate that the artificial bee colony is the most robust and the firefly is the most efficient and accurate algorithm for this test problem. Funding :ARC

Tropical cyclones and depressions over the South Pacific Ocean since the late 19th century : assessing synergistic relationship between the El Niño Southern Oscillation and Interdecadal Pacific Oscillation

- Yeasmin, Alea, Chand, Savin, Sultanova, Nargiz

  • Authors: Yeasmin, Alea , Chand, Savin , Sultanova, Nargiz
  • Date: 2023
  • Type: Text , Journal article
  • Relation: International Journal of Climatology Vol. 43, no. 12 (2023), p. 5422-5443
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  • Description: Tropical cyclones (TCs) and tropical depressions (TDs), hereafter collectively referred to as tropical storms, often exhibit large year-to-year variability in the South Pacific Ocean basin. Many past studies have examined this variability in relation to the El Niño Southern Oscillation (ENSO) phenomenon, particularly using observational data from the post-satellite era (i.e., after the 1970s when TC observations became more consistent). However, less emphasis is placed on how tropical storms are modulated at interdecadal and decadal time scales such as due to Interdecadal Pacific Oscillation (IPO). This is because post-satellite data are available for relatively short time period (i.e., post-1970s), limiting our understanding of the IPO–TC relationship in the South Pacific. Here, using NOAA-CIRES 20th Century Reanalysis (20CR) dataset, we reconstruct historical records (1871–2014) of TC and depression proxies for the South Pacific Ocean basin, and then utilize these reconstructed proxies to first understand the connections between TC–ENSO and TC–IPO over the 20th century, and then investigate the combined effects of ENSO–IPO effects on TCs and depressions. Results show that La Niña (El Niño) is more dominant on TC activity than El Niño (La Niña) over the western subregion 140–170° E (eastern sub-region, 170–220° E) as expected. We also show that TC numbers are strongly modulated by the IPO phenomenon with, on average, more TCs occurring during the positive phase than during the negative phase of the IPO in both western and eastern sub-regions. We show for the first time (using a long-term reconstructed TC dataset) that the combined phases of El Niño and + IPO account for increased TC activity, as opposed to the combined phase of La Niña and

Methods and applications of clusterwise linear regression : a survey and comparison

- Long, Qiang, Bagirov, Adil, Taheri, Sona, Sultanova, Nargiz, Wu, Xue

A class of Increasing Positively Homogeneous functions for which global optimization problem is NP-hard

- Sultanova, Nargiz

  • Authors: Sultanova, Nargiz
  • Date: 2009
  • Type: Text , Thesis , Masters
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  • Description: It is well known that global optimization problems are, generally speaking, computationally infeasible, that is solving them would require an unreasonably large amount of time and/or space. In certain cases, for example, when objective functions and constraints are convex, it is possible to construct a feasible algorithm for solving global optimization problem successfully. Convexity, however, is not a phenomenon to be often expected in the applications. Nonconvex problems frequently arise in many industrial and scienti¯c areas. Therefore, it is only natural to try to replace convexity with some other structure at least for some classes of nonconvex optimization problems to render the global optimization problem feasible. A theory of abstract convexity has been developed as a result of the above considerations. Monotonic analysis, a branch of abstract convex analysis, is analogous in many ways to convex analysis, and sometimes is even simpler. It turned out that many problems of nonconvex optimization encountered in applications can be described in terms of monotonic functions. The analogies with convex analysis were considered to aid in solving some classes of nonconvex optimization problems. In this thesis we will focus on one of the elements of monotonic analysis - Increasing Positively Homogeneous functions of degree one or in short IPH functions. The aim of present research is to show that finding the solution and ²-approximation to the solution of the global optimization problem for IPH functions restricted to a unit simplex is an NP-hard problem. These results can be further extended to positively homogeneous functions of degree ´, ´ > 0.
  • Description: Master of Mathematical Sciences (Research)