Irem Kucukoglu

The road to dynamic Future Internet via content characterization

The Internet evolved from a network with a few terminals to an intractable network of millions of nodes. Recent interest in information-centric networks (ICNs) is gaining significant momentum as a Future Internet paradigm. The key question is, hence, how to model the massive amount of connected nodes with their content requests in dynamic paradigm. In this paper, we present a novel method to characterize data requests based on content demand ellipse (CDE), focusing on efficient content access and distribution as opposed to mere communication between data consumers and publishers. We employ an approach of a promising eminence, where requests are characterized by type and popularity. Significant case studies are used to demonstrate that critical properties of ellipses may be used to characterize the content request irregularity during peak times. Depending on the degree of irregularity, the curve we plot becomes elliptic with a positive eccentricity less than one and an orientation centered with a bias. Real traffic data have been used to demonstrate how various data demand/request types affect eccentricity, orientation, and bias. Through simulations, we propose a dynamic resource allocation framework for Virtual Data Repeaters (VDRs) by correlating the resource allocation schema with the factors that affect the CDE in ICN.

On k-ary Lyndon words and their generating functions

The main aim of this paper is to construct ordinary generating functions for the numbers of k-ary Lyndon words of length prime. We give combinatorial aspect of the generating functions for these numbers. Finally, we investigate relations between the k-ary de Bruijn sequences and a family of new numbers.The main aim of this paper is to construct ordinary generating functions for the numbers of k-ary Lyndon words of length prime. We give combinatorial aspect of the generating functions for these numbers. Finally, we investigate relations between the k-ary de Bruijn sequences and a family of new numbers.

Multidimensional Bernstein polynomials and Bezier curves: Analysis of machine learning algorithm for facial expression recognition based on curvature

Abstract In this paper, by using partial derivative formulas of generating functions for the multidimensional unification of the Bernstein basis functions and their functional equations, we derive derivative formulas and identities for these basis functions and their generating functions. We also give a conjecture and some open questions related to not only subdivision property of these basis functions, but also solutions of a higher-order special differential equations. Moreover, we provide an implementation for a real world problem of human facial expression recognition with the help of curvature of Bezier curves whose machine learning supported by statistical evaluations on feature vectors using in the aforementioned machine learning algorithm.

A new family of Lerch-type zeta functions interpolating a certain class of higher-order Apostol-type numbers and Apostol-type polynomials

Abstract The aim of this paper is to investigate some classes of higher-order Apostol-type numbers and Apostol-type polynomials. We construct Lerch-type zeta functions which interpolate these numbers and polynomials at negative integers. Moreover, by combining some well-known identities such as the Chu-Vandermonde identity with the Lerch-type zeta functions and generating functions for the higher- order Apostol-type numbers and Apostol-type polynomials, we derive some relations and identities including functional equation for these Lerch-type zeta functions with other zeta type functions, Raabe-type multiplication formula for the higher-order Apostol-type polynomials and the Stirling numbers. Finally, we give some remarks and observations on Lerch-type zeta functions and their functional equations.

Relations arising from a family of combinatorial numbers and Bernstein type basis functions

The aim of this paper is to give some combinatorial sums, identities and relations related to a family of combinatorial numbers and the Bernstein type basis functions. With the help of generating functions for the combinatorial numbers from this aforementioned family, we give some functional equations. By using these functional equations, we obtain several relationships including these combinatorial numbers and the Bernstein type basis functions. Moreover, we provide not only some identities, but also applications including combinatorial sums, integrals, the combinatorial numbers, the extended Bersntein basis functions, and the beta function.The aim of this paper is to give some combinatorial sums, identities and relations related to a family of combinatorial numbers and the Bernstein type basis functions. With the help of generating functions for the combinatorial numbers from this aforementioned family, we give some functional equations. By using these functional equations, we obtain several relationships including these combinatorial numbers and the Bernstein type basis functions. Moreover, we provide not only some identities, but also applications including combinatorial sums, integrals, the combinatorial numbers, the extended Bersntein basis functions, and the beta function.