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Permanent URI for this collectionhttps://ada.atilim.edu.tr/handle/123456789/19

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Citation Count: 1
Cyclicity of Elliptic Curves Modulo Primes in Arithmetic Progressions
(Cambridge University Press, 2022) Akbal,Y.; Güloǧlu,A.M.; Mathematics
We consider the reduction of an elliptic curve defined over the rational numbers modulo primes in a given arithmetic progression and investigate how often the subgroup of rational points of this reduced curve is cyclic. ©
Citation Count: 0
A hybrid deep learning methodology for wind power forecasting based on attention
(Taylor & Francis inc, 2024) Akbal, Yildirim; Unlu, Kamil Demirberk; Industrial Engineering; Mathematics
Wind energy, as a sustainable energy source, poses challenges in terms of storage. Therefore, careful planning is crucial to utilize it efficiently. Deep learning algorithms are gaining popularity for analyzing complex time series data. However, as the "no free lunch" theorem suggests, the trade-off is: they need a lot of data to achieve the benefits. This even brings up a severe challenge for time series analysis, as the availability of historical data is often limited. This study aims to address this issue by proposing a novel shallow deep learning approach for wind power forecasting. The proposed model utilizes a fusion of transformers, convolutional and recurrent neural networks to efficiently handle several time series simultaneously. The empirical evidence demonstrates that the suggested innovative method exhibits exceptional forecasting performance, as indicated by a coefficient of determination (R2) of 0.99. When the forecasting horizon reaches 48, the model's performance declines significantly. However, when dealing with long ranges, utilizing the mean as a metric rather than individual point estimates would yield superior results. Even when forecasting up to 96 hrs in advance, obtaining an R2 value of 0.50 is considered a noteworthy accomplishment in the context of average forecasting.
Citation Count: 1
A short note on permutation trinomials of prescribed type
(Taylor & Francis inc, 2020) Akbal, Yildirim; Temur, Burcu Gulmez; Ongan, Pinar; Mathematics
We show that there are no permutation trinomials of the form hox 1/4 x5 ox5oq1 xq1 1 over Fq2 where q is not a power of 2. Together with a result of Zha, Z., Hu, L., Fan, S., hox permutes Fq2 if q 1/4 2k where k 2 omod 4, this gives a complete classification of those q's such that hox permutes F-q(2).
Citation Count: 14
A univariate time series methodology based on sequence-to-sequence learning for short to midterm wind power production
(Pergamon-elsevier Science Ltd, 2022) Akbal, Yildirim; Unlu, Kamil Demirberk; Industrial Engineering; Mathematics
The biggest wind farm of Turkey is placed at Manisa which is located in the Aegean Region. Electricity is a nonstorable commodity for that reason, it is very important to have a strong forecast and model of the potential electricity production to plan the electricity loads. In this study, the aim is to model and forecast electricity production of the wind farms located at Manisa by using a univariate model based on sequence-to-sequence learning. The forecasting range of the study is from short term to midterm. The strength of the proposed model is that; it only needs its own lagged value to make forecasts. The empirical evidences show that the model has high coefficient of variation (R-2) in short term and moderate R-2 in the midterm forecast. Although in the midrange forecasts R-2 slightly decreases mean squared error and mean absolute error shows that the model is accurate also in the midterm forecasts. The proposed model is not only strong in hourly electricity production forecasts but with a slight modification also in forecasting the minimum, maximum and average electricity production for a fixed range. This study concludes with two fresh and intriguing future research ideas.
Citation Count: 0
Variations on a Theme of Mirsky
(World Scientific, 2023) Akbal,Y.; Güloǧlu,A.M.; Mathematics
Let k and r be non-zero integers with r ≥ 2. An integer is called r-free if it is not divisible by the rth power of a prime. A result of Mirsky states that there are infinitely many primes p such that p + k is r-free. In this paper, we study an additive Goldbach-type problem and prove two uniform distribution results using these primes. We also study certain properties of primes p such that p + a1,...,p + aℓ are simultaneously r-free, where a1,...,aℓ are non-zero integers and ℓ ≥ 1. © 2023 World Scientific Publishing Company.

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