@techreport{SultanowKochCox2019, author = {Sultanow, Eldar and Koch, Christian and Cox, Sean}, title = {Collatz Sequences in the Light of Graph Theory}, edition = {2nd version}, doi = {10.25932/publishup-43741}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-437416}, pages = {21}, year = {2019}, abstract = {The Collatz conjecture is a number theoretical problem, which has puzzled countless researchers using myriad approaches. Presently, there are scarcely any methodologies to describe and treat the problem from the perspective of the Algebraic Theory of Automata. Such an approach is promising with respect to facilitating the comprehension of the Collatz sequence's "mechanics". The systematic technique of a state machine is both simpler and can fully be described by the use of algebraic means. The current gap in research forms the motivation behind the present contribution. The present authors are convinced that exploring the Collatz conjecture in an algebraic manner, relying on findings and fundamentals of Graph Theory and Automata Theory, will simplify the problem as a whole.}, language = {en} } @techreport{SultanowKochCox2019, author = {Sultanow, Eldar and Koch, Christian and Cox, Sean}, title = {Collatz Sequences in the Light of Graph Theory}, doi = {10.25932/publishup-43008}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-430089}, pages = {15}, year = {2019}, abstract = {The Collatz conjecture is a number theoretical problem, which has puzzled countless researchers using myriad approaches. Presently, there are scarcely any methodologies to describe and treat the problem from the perspective of the Algebraic Theory of Automata. Such an approach is promising with respect to facilitating the comprehension of the Collatz sequences "mechanics". The systematic technique of a state machine is both simpler and can fully be described by the use of algebraic means. The current gap in research forms the motivation behind the present contribution. The present authors are convinced that exploring the Collatz conjecture in an algebraic manner, relying on findings and fundamentals of Graph Theory and Automata Theory, will simplify the problem as a whole.}, language = {en} } @techreport{SultanowKochCox2020, author = {Sultanow, Eldar and Koch, Christian and Cox, Sean}, title = {Collatz Sequences in the Light of Graph Theory}, edition = {3rd version}, doi = {10.25932/publishup-44185}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-441859}, pages = {29}, year = {2020}, abstract = {It is well known that the inverted Collatz sequence can be represented as a graph or a tree. Similarly, it is acknowledged that in order to prove the Collatz conjecture, one must demonstrate that this tree covers all (odd) natural numbers. A structured reachability analysis is hitherto not available. This paper investigates the problem from a graph theory perspective. We define a tree that consists of nodes labeled with Collatz sequence numbers. This tree will be transformed into a sub-tree that only contains odd labeled nodes. The analysis of this tree will provide new insights into the structure of Collatz sequences. The findings are of special interest to possible cycles within a sequence. Next, we describe the conditions which must be fulfilled by a cycle. Finally, we demonstrate how these conditions could be used to prove that the only possible cycle within a Collatz sequence is the trivial cycle, starting with the number 1, as conjectured by Lothar Collatz.}, language = {en} } @techreport{SultanowKochCox2020, author = {Sultanow, Eldar and Koch, Christian and Cox, Sean}, title = {Collatz Sequences in the Light of Graph Theory}, edition = {4th version}, doi = {10.25932/publishup-44325}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-443254}, pages = {31}, year = {2020}, abstract = {It is well known that the inverted Collatz sequence can be represented as a graph or a tree. Similarly, it is acknowledged that in order to prove the Collatz conjecture, one must demonstrate that this tree covers all odd natural numbers. A structured reachability analysis is hitherto not available. This paper investigates the problem from a graph theory perspective. We define a tree that consists of nodes labeled with Collatz sequence numbers. This tree will be transformed into a sub-tree that only contains odd labeled nodes. The analysis of this tree will provide new insights into the structure of Collatz sequences. The findings are of special interest to possible cycles within a sequence. Next, we describe the conditions which must be fulfilled by a cycle. Finally, we demonstrate how these conditions could be used to prove that the only possible cycle within a Collatz sequence is the trivial cycle, starting with the number one, as conjectured by Lothar Collatz.}, language = {en} } @techreport{SultanowKochCox2020, author = {Sultanow, Eldar and Koch, Christian and Cox, Sean}, title = {Collatz Sequences in the Light of Graph Theory}, edition = {Fifth version}, doi = {10.25932/publishup-48214}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-482140}, pages = {47}, year = {2020}, abstract = {It is well known that the inverted Collatz sequence can be represented as a graph or a tree. Similarly, it is acknowledged that in order to prove the Collatz conjecture, one must demonstrate that this tree covers all odd natural numbers. A structured reachability analysis is hitherto unavailable. This paper investigates the problem from a graph theory perspective. We define a tree that consists of nodes labeled with Collatz sequence numbers. This tree will be transformed into a sub-tree that only contains odd labeled nodes. Furthermore, we derive and prove several formulas that can be used to traverse the graph. The analysis covers the Collatz problem both in it's original form 3x + 1 as well as in the generalized variant kx + 1. Finally, we transform the Collatz graph into a binary tree, following the approach of Kleinnijenhuis, which could form the basis for a comprehensive proof of the conjecture.}, language = {en} } @techreport{SultanowVolkovCox2017, author = {Sultanow, Eldar and Volkov, Denis and Cox, Sean}, title = {Introducing a Finite State Machine for processing Collatz Sequences}, edition = {1st version}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-399223}, year = {2017}, abstract = {The present work will introduce a Finite State Machine (FSM) that processes any Collatz Sequence; further, we will endeavor to investigate its behavior in relationship to transformations of a special infinite input. Moreover, we will prove that the machine's word transformation is equivalent to the standard Collatz number transformation and subsequently discuss the possibilities for use of this approach at solving similar problems. The benefit of this approach is that the investigation of the word transformation performed by the Finite State Machine is less complicated than the traditional number-theoretical transformation.}, language = {en} } @techreport{SultanowVolkovCox2017, author = {Sultanow, Eldar and Volkov, Denis and Cox, Sean}, title = {Introducing a Finite State Machine for processing Collatz Sequences}, edition = {2nd version}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-404738}, pages = {17}, year = {2017}, abstract = {The present work will introduce a Finite State Machine (FSM) that processes any Collatz Sequence; further, we will endeavor to investigate its behavior in relationship to transformations of a special infinite input. Moreover, we will prove that the machine's word transformation is equivalent to the standard Collatz number transformation and subsequently discuss the possibilities for use of this approach at solving similar problems. The benefit of this approach is that the investigation of the word transformation performed by the Finite State Machine is less complicated than the traditional number-theoretical transformation.}, language = {en} } @inproceedings{SultanowChircuWuestemannetal.2022, author = {Sultanow, Eldar and Chircu, Alina and W{\"u}stemann, Stefanie and Schwan, Andr{\´e} and Lehmann, Andreas and Sept, Andr{\´e} and Szymaski, Oliver and Venkatesan, Sripriya and Ritterbusch, Georg David and Teichmann, Malte Rolf}, title = {Metaverse opportunities for the public sector}, series = {International Conference on Information Systems 2022 : Special Interest Group on Big Data : Proceedings}, booktitle = {International Conference on Information Systems 2022 : Special Interest Group on Big Data : Proceedings}, publisher = {AIS}, address = {Atlanta}, year = {2022}, abstract = {The metaverse is envisioned as a virtual shared space facilitated by emerging technologies such as virtual reality (VR), augmented reality (AR), the Internet of Things (IoT), 5G, artificial intelligence (AI), big data, spatial computing, and digital twins (Allam et al., 2022; Dwivedi et al., 2022; Ravenscraft, 2022; Wiles, 2022). While still a nascent concept, the metaverse has the potential to "transform the physical world, as well as transport or extend physical activities to a virtual world" (Wiles, 2022). Big data technologies will also be essential in managing the enormous amounts of data created in the metaverse (Sun et al., 2022). Metaverse technologies can offer the public sector a host of benefits, such as simplified information exchange, stronger communication with citizens, better access to public services, or benefiting from a new virtual economy. Implementations are underway in several cities around the world (Geraghty et al., 2022). In this paper, we analyze metaverse opportunities for the public sector and explore their application in the context of Germany's Federal Employment Agency. Based on an analysis of academic literature and practical examples, we create a capability map for potential metaverse business capabilities for different areas of the public sector (broadly defined). These include education (virtual training and simulation, digital campuses that offer not just online instruction but a holistic university campus experience, etc.), tourism (virtual travel to remote locations and museums, virtual festival participation, etc.), health (employee training - as for emergency situations, virtual simulations for patient treatment - for example, for depression or anxiety, etc.), military (virtual training to experience operational scenarios without being exposed to a real-world threats, practice strategic decision-making, or gain technical knowledge for operating and repairing equipment, etc.), administrative services (document processing, virtual consultations for citizens, etc.), judiciary (AI decision-making aids, virtual proceedings, etc.), public safety (virtual training for procedural issues, special operations, or unusual situations, etc.), emergency management (training for natural disasters, etc.), and city planning (visualization of future development projects and interactive feedback, traffic management, attraction gamification, etc.), among others. We further identify several metaverse application areas for Germany's Federal Employment Agency. These applications can help it realize the goals of the German government for digital transformation that enables faster, more effective, and innovative government services. They include training of employees, training of customers, and career coaching for customers. These applications can be implemented using interactive learning games with AI agents, virtual representations of the organizational spaces, and avatars interacting with each other in these spaces. Metaverse applications will both use big data (to design the virtual environments) and generate big data (from virtual interactions). Issues related to data availability, quality, storage, processing (and related computing power requirements), interoperability, sharing, privacy and security will need to be addressed in these emerging metaverse applications (Sun et al., 2022). Special attention is needed to understand the potential for power inequities (wealth inequity, algorithmic bias, digital exclusion) due to technologies such as VR (Egliston \& Carter, 2021), harmful surveillance practices (Bibri \& Allam, 2022), and undesirable user behavior or negative psychological impacts (Dwivedi et al., 2022). The results of this exploratory study can inform public sector organizations of emerging metaverse opportunities and enable them to develop plans for action as more of the metaverse technologies become a reality. While the metaverse body of research is still small and research agendas are only now starting to emerge (Dwivedi et al., 2022), this study offers a building block for future development and analysis of metaverse applications.}, language = {en} } @article{SultanowVladovaWeber2009, author = {Sultanow, Eldar and Vladova, Gergana and Weber, Edzard}, title = {Overcoming communication barriers for CMC in enterprises}, isbn = {978-0-615-30358-1}, year = {2009}, language = {en} } @article{UllrichBertheauWiedmannetal.2021, author = {Ullrich, Andre and Bertheau, Clementine and Wiedmann, Miriam and Sultanow, Eldar and K{\"o}rppen, Tim and Bente, Stefan}, title = {Roles, tasks and skills of the enterprise architect in the VUCA world}, series = {2021 IEEE 25th International Enterprise Distributed Object Computing Conference Workshops : EDOCW 2021 : 25-29 October 2021, Gold Coast, Australia : proceedings}, journal = {2021 IEEE 25th International Enterprise Distributed Object Computing Conference Workshops : EDOCW 2021 : 25-29 October 2021, Gold Coast, Australia : proceedings}, publisher = {IEEE}, address = {Piscataway}, isbn = {978-1-6654-4488-0}, doi = {10.1109/EDOCW52865.2021.00057}, pages = {261 -- 270}, year = {2021}, abstract = {For the last 20 years, enterprise architecture management (EAM) was primarily an instrument for harmonizing and consolidating IT landscapes and is lived as a transformation and governance discipline. It, however, is rather related to IT strategy than aligned to the actual corporate strategy and the work of the enterprise architect is characterized by tasks like prescribing, monitoring, documenting, and controlling. As digital transformation continues apace, companies are facing new challenges that lead to a volatile, uncertain, complex, and ambiguous (VUCA) world. To face these challenges, vision, understanding, clarity and agility allow to anticipative and implement necessary changes. This, of course, has implications for the role of the enterprise architect. S/he needs to start actively supporting innovation and taking more of an advisory role instead of just being driven by the current state of the enterprise architecture. This paper investigates the role of the enterprise architect in the VUCA world. Based on current literature and expert interviews, a survey was conducted among consultants who work as (or with) enterprise architects. Survey results include the evaluation of statements on current tasks of enterprise architects, their influence on projects and companies as well as future requirements on the roles of the enterprise architect. The results from the survey were synthesized with the findings from literature to derive the roles, tasks and skills of enterprise architect in the VUCA world.}, language = {en} }