Browsing by Author "Polat, Refet"

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Citation - WoS: 1
Citation - Scopus: 1
A Feature Selection Application Using Particle Swarm Optimization for Learning Concept Detection
(SPRINGER-VERLAG BERLIN, 2017) Korhan Gunel; Kazim Erdogdu; Refet Polat; Yasin Ozarslan; Polat, Refet; Erdogdu, Kazim; Ozarslan, Yasin; Gunel, Korhan; A Rocha; AM Correia; H Adeli; LP Reis; S Costanzo
Recent developments of computational intelligence on educational technology yield concept map mining as a new research area. Concept map mining covers the extraction of learning concepts specifying relations among them and generating a concept map from educational contents. In this study we focused on determining the features that characterize a learning concept extracted from an educational text as raw data. The first three features are detected by using a hybrid system of Multi Layer Perceptron (MLP) and Particle Swarm Optimization (PSO) and the performance of the applied method is gauged in the viewpoint of a typical classification problem.
Adi diferansiyel denklemlerin uygulamaları
(2014) Nisa, Melis Buse; Tacar, Emine; Meherrem, Şahlar; Polat, Refet
Bu tez birinci mertebeden adi diferansiyel denklemler için analitik ve nümerik çözüm yöntemlerini içerir. Diferansiyel denklemler hakkında tarihsel bilgilerle başlayarak, diferansiyel denklemlerin temel kavramlarını tanıtır. Bu çalışmada analitik yöntemler adına değişkenlerine ayrılabilen, homojen, tam, doğrusal ve özel denklem tiplerinden bahsediyoruz. Öte yandan nümerik yöntem olarak, Euler, Geliştirilmiş Euler, İkinci Mertebeden Runge-Kutta ve Dördüncü Mertebeden Runge-Kutta Yöntemlerini çalışıyoruz. Yöntemleri tanıttıktan sonra uygulamaların matematiksel modellerini tanıtıyoruz. Modellemeleri geliştirdikten sonra birinci mertebeden adi diferansiyel denklemlerin problemlerini sunuyoruz. Bu problemler mühendislik, kimya, fizik, ekonomi ve sosyoloji gibi çeşitli alanlardan seçilerek sınıflandırıldı. Mekanik problemlerden başlayıp ikinci olarak karışım problemlerini sunuyoruz. Isınma- soğuma problemlerini, finans problemleri takip ediyor. Son olarak büyüme ve çürüme problemlerini sunuyoruz. Her alanda üç problem çalışıyoruz ve problemleri analitik ve nümerik olarak çözüyoruz. Nümerik çözümler için nümerik yakınsamalar elde ediyoruz. Böylece verilen nümerik yöntemler arasından daha iyi yakınsayanını belirlemeye odaklanıyoruz. Yakınsama adım büyüklüğüyle ilişkili olduğundan, farklı adım büyüklükleriyle çalışıyoruz. Son olarak yakınsamaları kıyaslıyoruz.
ALGORITHMIC APPROACH TO BITONIC ALGEBRAS AND THEIR GRAPHS
(Bayram Sahin, 2024) Şule Ayar Özbal; Refet Polat; Saadet Eskiizmirliler; Mehmet Kurt; Kurt, Mehmet; Polat, Refet; Ozbal, Sule Ayar; Eskiizmirliler, Saadet
Under the aim of this paper we establish the terms of graphs related with bitonic-algebras which is a bitonic-graph where the vertices are the elements of bitonic algebra and where the edges are the companian of two vertices that is two elements from bitonic algebra. We designate the upper sets of elements in a bitonic algebra and studied properties of these sets. We state algorithms to check whether the given set is a bitonic algebra or a commutative bitonic algebra or not. Additionally we mention the codes of these algorithms. Moreover we associate the algorithms of graphs of a bitonic algebra and state properties of these graphs obtained. © 2024 Elsevier B.V. All rights reserved.
AN ARTIFICIAL NEURAL NETWORK SOLUTION TO THE SPACE-TIME FRACTIONAL PARTIAL DIFFERENTIAL-DIFFERENCE TODA LATTICE EQUATION
(Jomard Publishing, 2025) Refet Polat; Burhan Pektas; Pektas, Burhan; Polat, Refet
In this paper the solution of the fractional partial differential-difference Toda Lattice Equation by Artificial Neural Networks is examined. According to the method we approximate the unknown values un = u(. tn) of the desired function by the artificial neural networks. As an application we demonstrate the capabilities of this method for identification of various values of order of fractional derivative α. Thereafter the artificial neural networks algorithm is used in order to identify the unknown values un. Comparing the results with the finite difference solution the algorithm can identify the function u(x t) better than the other method. © 2025 Elsevier B.V. All rights reserved.
Citation - WoS: 8
Citation - Scopus: 10
An empirical study on evolutionary feature selection in intelligent tutors for learning concept detection
(WILEY, 2019) Korhan Gunel; Kazim Erdogdu; Refet Polat; Yasin Ozarslan; Polat, Refet; Erdogdu, Kazim; Ozarslan, Yasin; Gunel, Korhan
Concept map mining (CMM) has emerged as a new research area with recent developments in computational intelligence in educational technology. CMM includes the following steps: extracting the learning concepts from educational content specifying relations among them and generating a concept map as a result. The purpose of this study was to develop a mechanism using data mining technique to determine the features that characterize a learning concept extracted automatically from a single educational text. The 3 major features that distinguish the real learning concepts from other sequences of strings are detected by using a hybrid system of a feed-forward neural network and some evolutionary algorithms. Ant colony optimization and genetic algorithm and particle swarm optimization are used as a binary feature selection method. In addition the aforementioned methods are hybridized to get better accuracy and precision. The performance comparisons with two different state-of-the-art algorithms have been made from the viewpoint of a typical classification problem.
Citation - WoS: 3
Citation - Scopus: 3
Analyzing Learning Concepts in Intelligent Tutoring Systems
(ZARKA PRIVATE UNIV, 2016) Korhan Gunel; Refet Polat; Mehmet Kurt; Kurt, Mehmet; Polat, Refet; Gunel, Korhan
The information that is increasing and changing rapidly at the present day and the usage of computers in educational and instructional processes has become inevitable. With the rapid progress in technology research gives more importance to integrate intelligent issues with educational support systems such as distance learning and learning management systems. Such studies are considered as applications of the artificial intelligence on educational processes. Regarding this viewpoint some supervised learning models which is able to recognize the learning concepts from a given educational content presented to a tutoring system has been designed in this study. For this aim firstly three different corpora constructed from educational contents related to the subject titles such as calculus abstract algebra and computer science have been composed. For each candidate learning concepts the feature vectors have been generated using a relation factor in addition to tf-idf values. The relation factor is defined as the ratio of the total number of the most frequent substrings in the corpus that appear with a candidate concept in the same sentence within an educational content to most frequent substring in the corpus. The achievement of this system is measured according to the F-measure.
Black-Scholes kısmi diferansiyel denkleminin yapay sinir ağları ile çözümü üzerine
(2019) Eskiizmirliler, Saadet; Polat, Refet; Günel, Korhan
Black-Scholes modeli temettü ödemesi yapmayan Avrupa tipi opsiyonların fiyatlarını hesaplamak üzere 1973 yılında Fisher Black ve Myran Scholes tarafından geliştirilmiştir. Robert C. Merton'un yeni bir çözüm önerisi ile model literatürde Black-Scholes-Merton olarak isimlendirilmeye başlanmıştır. 1997 yılında bu çalışmaları sayesinde, Merton ve Scholes, Ekonomi alanında Nobel Ödülü almışlardır. Yapay sinir ağları (YSA) biyolojik sinir sistemlerinden esinlenerek oluşturulan matematiksel modellerdir. Bu ağlar beyin yeteneklerine adaptif olmuştur ve bu durum makineler beyin gibi öğrenir olarak açıklanabilir. Yapay sinir ağları kullanılarak diferansiyel denklemlerin çözülmesi 1990'lı yıllarda başlamış ve son dönemlerde artmıştır. Bu çalışmadaki amaç, Black-Scholes Probleminin YSA yöntemi ile yaklaşık çözümünü bulmak ve literatürde yer alan yaklaşık analitik çözümü ile karşılaştırmaktır.
Citation - Scopus: 3
Dealing with learning concepts via support vector machines
(Springer Verlag service@springer.de, 2014) Korhan Günel; Rifat Aşliyan; Mehmet Kurt; Refet Polat; Turgut Ozis; Özis, Turgut; Kurt, Mehmet; Aşliyan, Rifat; Polat, Refet; Günel, Korhan
Extracting learning concepts is one of the major problems of artificial intelligence on education. Essentially the determination of learning concepts within an educational content has some differences as compared with keyword or technical term extraction process. However the problem can still taught as a classification problem notwithstanding. In this paper we examine how to handle the extraction of learning concepts using support vector machines as a supervised learning algorithm and we evaluate the performance of the proposed approach using f-measure. © Springer-Verlag Berlin Heidelberg 2014. © 2016 Elsevier B.V. All rights reserved.
EDGE-NEIGHBOR-RUPTURE DEGREE OF GRAPHS AND EXAMINED ON THORNY GRAPH
(BAKU STATE UNIV INST APPLIED MATHEMATICS, 2018) Saadet Eskiizmirliler; Zeynep Ors Yorgancioglu; Refet Polat; Mehmet Umit Gursoy; Yorgancioglu, Zeynep Ors; Gursoy, Mehmet Umit; Polat, Refet; Eskiizmirliler, Saadet; A Fikret; B Tamer
Finans piyasalarında kullanılan black-scholes kısmi diferansiyel denkleminin nümerik çözümleri
(2016) Özbal, Kemal; Polat, Refet
In this thesis we defined some of the risk management techniques of which need for use is recently increasing in Turkey. These are forward, future and swap operations which are explained in general and American option problems which are explained in full details. We studied in general comparing forward, future and swap operations and Black–Scholes Option Valuing Models for Valuing and Pricing of Commodity Contract. Some of the recent articles on Numerical Solutions of Black-Scholes Partial Differential Equations are examined and compared the results of given solutions. Key words:Black-Scholes Equation, Options, Partial Differential Equations, Derivative Securities
Graf işlemleri üzerinde zedelenebilirlik parametreleri
(2012) Eskiizmirliler, Saadet; Turan, Gökşen Bacak; Polat, Refet
Bir iletişim ağında, belli merkezlerin ya da bağlantıların zarar görmesinden sonra, iletişim kesilene kadar geçen süredeki ağın dayanma gücünün ölçümüne, zedelenebilirlik değeri denir. Bir iletişim ağı, zedelenebilirlik değerinin belirlenebilmesi için, merkezleri bir grafın tepelerine, bağlantıları grafın ayrıtlarına karşılık gelecek şekilde bir graf ile modellenir. Bilinen zedelenebilirlik parametrelerinden bazıları Connectivity (Bağlantılılık), Integrity (Bütünlük), Neighbor Integrity (Komşu Bütünlük), Rupture Degree, Neighbor Rupture Degree, Toughness, Tenacity, Scattering Sayısı?dır. Bu tezde komşu rupture dereceleri üzerine çalışılmıştır. Bazı özel graflara graf işlemleri uygulanmış ve komşu rupture dereceleri hesaplanmıştır. Son olarak total graflar ve tümleyenleri incelenmiş neighbor rupture dereceleri hesaplanmıştır. Anahtar Sözcükler: Zedelenebilirlik, Rupture Derecesi, Komşu Rupture Derecesi, Graf İşlemleri, Total Graflar.
Graflarda zedelenebilirlik ve komşu ayrıt kopma derecesi
(2016) Polat, Dilek; Polat, Refet
This thesis is mainly consist of five sections. In the first part the graphs which are the subject of this thessis has been introdiced. In the second some fundemental desciriptions and properties have been presented to understand the thesis easily. In the thırd part, the description of the vulnarability of graphs has been introduced and the brief summary of the vulnarability of the parameters which has been studied so far has been presented. In the third par, the degree of the rupture and the descriptions of the degree of neighbour rupture and the properties of these parameters have been introduced. In the fourth part, the degree of the neighbour edge rupture and the descriptions and properities about neighbour edge rupture of the middle graphs have been examined. The middle graphs have been defined and the theories about neighbour edge rupture about middle graphs of spesific graphs have found and proved. Finally; in the fifth part, discussion and conclusion part is given.
Citation - WoS: 3
Citation - Scopus: 3
Graph Operations and Neighbor Rupture Degree
(HINDAWI LTD, 2013) Saadet Kandilci; Goksen Bacak-Turan; Refet Polat; Bacak-Turan, Goksen; Kandilci, Saadet; Polat, Refet
In a communication network the vulnerability parameters measure the resistance of the network to disruption of operation after the failure of certain stations or communication links. A vertex subversion strategy of a graph G say S is a set of vertices in G whose closed neighborhood is removed from G. The survival subgraph is denoted by G/S. The neighbor rupture degree of G Nr(G) is defined to be Nr(G) = max{w(G/S) - vertical bar S vertical bar - c(G/S) : S subset of V(G) w(G/S) > 1} where S is any vertex subversion strategy of G w(G/S) is the number of connected components in G/S and c(G/S) is the maximum order of the components of G/S (G. Bacak Turan 2010). In this paper we give some results for the neighbor rupture degree of the graphs obtained by some graph operations.
The Laplace Transformation Applied to Differential Equations and Their Applications
(2015) Dereli, Seçil; Polat, Refet
Bu tezin ilk bölümünde Matematik, Laplace dönüşümü ve diferansiyel denklem hakkında bir giriş verilmiştir. İkinci bölümünde Laplace dönüşümü ve ters Laplace dönüşümü hakkında temel bilgiler vardır. Üçüncü bölümde Laplace dönüşümü ile alakalı incelenen makaleler, karşılaştırmaları ve sonuçları verilmiştir. Dördüncü bölümde ise Laplace dönüşümünün uygulamaları verilmiştir.
Lie symmetries of the Black-Scholes equation
(2010) REFET POLAT; Polat, Refet
In this paper symmetry expansions for Black-Scholes equation are studied. Differently then the other studies in the literature for Black-Scholes equation we expanded the equation into a parametric form by adding a coefficient a. By using this expansion the dimension of the solution spaces is increased by one and symmetry reduction will be done with the deterministic equations in the new increased solution spaces.
Lineer adi diferensiyel denklemler çözüm yöntemlerinin karşılaştırılması ve uygulamaları
(2016) Ayvaz, Cansu; Polat, Refet
Bu tezin ilk bölümünde diferansiyel denklemlerin oluşumundan bahsedilmiş ve ilgili tanımlar verilmiştir. İkinci bölümünde çözüme ulaşmak için gerekli metotlar vardır. Uygulamalı matematikte yöntem farklı tipte operatörler için analitik ve yaklaşık çözümler elde etmede etkili bir prosedürdür. Üçüncü bölümde lineer adi diferansiyel denklemler ile ilgili incelenen makaleler, ve sentezi verilmiştir. Dördüncü bölümde ise lineer adi diferansiyel denklemlerin ekonomi, biyoloji, mekanik gibi çeşitli alanlarda uygulamaları verilmiştir. Son olarak beşinci bölümde sonuç verilmiştir.
ON A SOLUTION TO A NONLOCAL INVERSE COEFFICIENT PROBLEM USING FEED-FORWARD NEURAL NETWORKS
(INST MATHEMATICS & MECHANICS NATL ACAD SCIENCES AZERBAIJAN, 2022) Refet Polat; Polat, Refet
This study gives a determination of the diffusion coefficient D(x) from the equation ut = (D(x)u(x))(x) + nu (C(x)u(x))(x) + f (xt) using Neumann type boundary measurements. The nonlocal condition enables us to reduce the par-abolic problem to a boundary-value problem for ODE. The flux data can be used for the initial condition of the Cauchy problem obtained from the reduced problem. The feed-forward neural network is used to find the solution to the corresponding inverse problem for D(x). The presented approach is based on the solution of a nonlinear optimization problem using Particle Swarm Opti-mization. The efficiency and applicability of the method is demonstrated using various numerical examples with noisy free and noisy data.
Citation - WoS: 14
Citation - Scopus: 14
On the Solution of the Black-Scholes Equation Using Feed-Forward Neural Networks
(SPRINGER, 2021) Saadet Eskiizmirliler; Korhan Gunel; Refet Polat; Eskiizmirliler, Saadet; Polat, Refet; Gunel, Korhan
This paper deals with a comparative numerical analysis of the Black-Scholes equation for the value of a European call option. Artificial neural networks are used for the numerical solution to this problem. According to this method we approximate the unknown function of the option value using a trial function which depends on a neural network solution and satisfies the given boundary conditions of the Black-Scholes equation. We consider some optimization methods not examined in the standard literature such as particle swarm optimization and the gradient-type monotone iteration process to obtain the unknown parameters of the neural network. Numerical results show that this proposed version of neural network method obtains all data from the terminal value and boundary conditions with sufficient accuracy.
Citation - Scopus: 1
The travelling wave solutions of the active-dissipative dispersive media equation by (G′/G) -expansion method
(2014) Refet Polat; Turgut Ozis; Öziş, Turgut; Polat, Refet
Over the past decades a number of approximate methods for finding travelling wave solutions to nonlinear evolution equations have been proposed. Among these methods one of the current methods is so called (G′/G) -expansion method. In this paper we will examine the(G′/G) -expansion method for determining the solutions of the active-dissipative dispersive media equation. The active-dissipative dispersive media equation is given by μt+μμx+αμxx+βμ xxx+γμxxxx = 0 where for positive constants α and γ in equation are small-amplitude. This equation describe long waves on a viscous fluid flowing down along an inclined plane unstable drift waves in plasma and stress waves in fragmentated porous media. When β = 0 equation is reduced to the Kuramoto-Sivashinsky equation which is the simplest equations that appears in modelling the nonlinear behaviour of disturbances for a sufficiently large class of active dissipative media. It represents the evolution of concentration in chemical reactions hydrodynamic instabilities in laminar flame fronts and at the interface of two viscous fluids. © Springer-Verlag Berlin Heidelberg 2014. © 2014 Elsevier B.V. All rights reserved.
Citation - WoS: 3
Citation - Scopus: 3
Weak subdifferential in nonsmooth analysis and optimization
(Hindawi Publishing Corp, 2011) Shahlar Meherrem; Refet Polat; Meherrem, Sahlar F.; Meherrem, Ahlar F.; Polat, Refet
Some properties of the weak subdifferential are considered in this paper. By using the definition and properties of the weak subdifferential which are described in the papers (Azimov and Gasimov 1999, Kasimbeyli and Mammadov 2009, Kasimbeyli and Inceoglu 2010) the author proves some theorems connecting weak subdifferential in nonsmooth and nonconvex analysis. It is also obtained necessary optimality condition by using the weak subdifferential in this paper. Copyright © 2011 ahlar F. Meherrem and Refet Polat. © 2011 Elsevier B.V. All rights reserved.