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Article On the Notion of Discrete-Time Signature and Some Associated Properties and Results(Cambridge University Press, 2026) Balakrishnan, Narayanaswamy; Yi, He; Goroncy, AgnieszkaIn this work, by considering coherent systems comprising independent components with discrete lifetimes, we introduce the notion of discrete-time signature and then discuss some of its properties. With the use of the introduced signature, a stochastic ordering result is also established. We then introduce transformation formulas for the discrete-time signature to facilitate the comparison of systems of different sizes. Some examples are also presented to illustrate all the results developed here.Article Citation - WoS: 5Citation - Scopus: 4Cyclicity of Elliptic Curves Modulo Primes in Arithmetic Progressions(Cambridge University Press, 2022) Akbal,Y.; Güloǧlu,A.M.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. ©Conference Object Citation - Scopus: 1Systematic Generation of a 3d Dsm by Extracting Social Robot Behaviors From Literature(Cambridge University Press, 2019) Ozer,I.; Erden,Z.Social robots are in direct communication and interaction with people, thus it is important to design these robots for different needs of individuals or small groups. This has revealed the need to develop design methods for personalized or mass-individualized social robots, which are expected to respond to many different needs of people today and in the future. In this paper, a previously developed 3D DSM model is implemented in the systematic conceptual design of social robot families. The model is independent of any physical elements and based on behavioural elements as perception, cognition and motoric action. The data regarding 45 different social robots from 80 articles in the literature is used to identify these three behaviours of the existing social robots and the mutual relationships among these different behaviours are defined in order to develop a 3D DSM structure to be used as a basis for designing social robot families. The resulting novel 3D DSM is a general-purpose, basic model that can be used to identify behavioural modules to design social robot families. © 2019 Design Society. All rights reserved.
