New complex-valued activation functions

Özgür, Nihal Yılmaz; Taş, Ni̇hal; Peters, James F.

doi:10.11121/ijocta.01.2020.00756

Cited by 6 publications

(4 citation statements)

References 19 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The essential problem in a CVNN is selecting the nodes activation function. Özgür [23] et al introduced a new type of activation function for complex valued Hopfield neural network (CVHNN). This type of transformation is defined by…”

Section: An Application To Discontinuous Maps As Activation Functions...mentioning

confidence: 99%

{M}_{\alpha }(z)&amp;amp;amp;amp;#x0003D;\frac{1-\alpha {\overline{z}}&amp;amp;amp;amp;#x0005E;2}{\alpha z&amp;amp;amp;amp;#x0002B;\left(2\alpha &amp;amp;amp;amp;#x0002B;1\right)\overline{z}},

where

$$ \alpha \ge 0.

…”

Section: An Application To Discontinuous Maps As Activation Functions...mentioning

confidence: 99%

See 1 more Smart Citation

Fixed ellipse theorems in metric spaces and an application of discontinuous activation function in neural networks

Ermiş,

Zaim Erçınar,

Gelişgen

2023

Math Methods in App Sciences

View full text Add to dashboard Cite

In this article, we establish new fixed ellipse theorems that will provide a geometrical perspective to the classical metric fixed point theory. Also, we provide novel fixed ellipse consequences as the expanding of some existing and known fixed circle theorems in literature to ellipse case, and give non‐trivial illuminating examples, which show the impressiveness of our results. On the other hand, using the given fixed ellipse, we give some solutions for the open question which is posed by Rhoades with respect to the presence of contractive mappings that permissive discontinuity at the fixed point. Furthermore, we give an application to usage respecting activation functions handled at neural networks via the discontinuity and the obtained results of fixed ellipse.

show abstract

Section: An Application To Discontinuous Maps As Activation Functions...mentioning

confidence: 99%

{M}_{\alpha }(z)&amp;amp;amp;amp;#x0003D;\frac{1-\alpha {\overline{z}}&amp;amp;amp;amp;#x0005E;2}{\alpha z&amp;amp;amp;amp;#x0002B;\left(2\alpha &amp;amp;amp;amp;#x0002B;1\right)\overline{z}},

where

$$ \alpha \ge 0.

…”

Section: An Application To Discontinuous Maps As Activation Functions...mentioning

confidence: 99%

Fixed ellipse theorems in metric spaces and an application of discontinuous activation function in neural networks

Ermiş,

Zaim Erçınar,

Gelişgen

2023

Math Methods in App Sciences

View full text Add to dashboard Cite

show abstract

“…In addition to the sigmoid function, the unit step function, part by part linear, Gaussian function ie. normal distribution, as well as many others [1,12,16,18]. To develop the neural network model, a database with variables was created containing: records of student status, the average grade of students during current and past school years, number of subjects, the average grade of students per academic subjects.…”

Section: Figure 1: Model Of a Neuronmentioning

confidence: 99%

Personalization of Teaching in E-learning Systems

Ribarić

Avramović

2020

JITA

View full text Add to dashboard Cite

Personalized teaching offers students the opportunity to study independently, with a focus towards fostering and developing their research traits, to intensively develop students’ abilities and competencies. Traditional teaching is a common mode of education through which tutors use the same teaching method, regardless of the differences and complex personalities of students in a single class or group. Such an approach to teaching has the effect of slowing down the progression of talented students on one hand while making it harder for less successful students to follow classes on the other. The consequences of this approach to teaching are a rapid loss of learning motivation and perception of classes and learning as unpleasant obligations. Contemporary e-learning systems offer personalized learning, by tailoring it to the needs and unique traits of each student. Usage of neural networks in data processing for personalized learning will ensure the formation of adequate classes, full understanding, and adoption of the material prescribed by the curriculum, compliance with the general curriculum, and constant insight into the students’ progress.

show abstract

“…For example, the differential geometry of a normal red blood cell was investigated using the Cassinian oval for modelling its profile [1]. In [17], by using of a special activation function whose fixed point set is an ellipse, an application to a complex-valued Hopfield neural network (CVHNN) was given.…”

Section: Introductionmentioning

confidence: 99%

Suzuki type $\mathcal{Z}_{c}$-contraction mappings and the fixed-figure problem

Gopal,

Özgür,

Savaliya

et al. 2024

Hacettepe Journal of Mathematics and Statistics

Self Cite

View full text Add to dashboard Cite

Geometric approaches are important for the study of some real-life problems. In metric fixed point theory, a recent problem called \textquotedblleft \textit{fixed-figure problem}\textquotedblright\ is the investigation of the existence of self-mapping which remain invariant at each points of a certain geometric figure (e.g. a circle, an ellipse and a Cassini curve) in the space. This problem is well studied in the domain of the extension of this line of research in the context of fixed circle, fixed disc, fixed ellipse, fixed Cassini curve and so on. In this paper, we introduce the concept of a Suzuki type $\mathcal{Z}_c$-contraction. We deal with the fixed-figure problem by means of the notions of a $\mathcal{Z}_c$-contraction and a Suzuki type $\mathcal{Z}_c$-contraction. We derive new fixed-figure results for the fixed ellipse and fixed Cassini curve cases by means of these notions. Also fixed disc and fixed circle results given for Suzuki type $\mathcal{Z}_c$-contraction. There are couple of illustration related to the obtained theoretical results.

show abstract

New complex-valued activation functions

Cited by 6 publications

References 19 publications

Fixed ellipse theorems in metric spaces and an application of discontinuous activation function in neural networks

Fixed ellipse theorems in metric spaces and an application of discontinuous activation function in neural networks

Personalization of Teaching in E-learning Systems

Suzuki type $\mathcal{Z}_{c}$-contraction mappings and the fixed-figure problem

Contact Info

Product

Resources

About