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For the first time, we enable the execution of hybrid machine learning methods on real quantum computers with 100 data samples and real-device-based simulations with 5,000 data samples, thereby outperforming the current state of research of Suryotrisongko and Musashi from 2022 who were dealing with 1,000 data samples and quantum simulators (pure software-based emulators) only. Additionally, we beat their reported accuracy of $76.8\%$ by an average accuracy of $89.0\%$, all within a total execution time of 382 seconds. %They did not report their execution time. We achieve this significant progress through two-step strategy: Firstly, we establish a stable quantum architecture that enables us to execute HQML algorithms on real quantum devices. Secondly, we introduce new hybrid quantum binary classification algorithms based on Hoeffding decision tree algorithms. These algorithms speed up the process via batch-wise execution, reducing the number of shots required on real quantum devices compared to conventional loop-based optimizers. Their incremental nature serves the purpose of online large-scale data streaming for DGA botnet detection, and allows us to apply hybrid quantum machine learning to the field of cybersecurity analytics. We conduct our experiments using the Qiskit library with the Aer quantum simulator, and on three different real quantum devices from MS Azure Quantum: IonQ, Rigetti, and Quantinuum. This is the first time these tools are combined in this manner., 29 pages, 3 figures, 5 tables

We implement and interpret various supervised learning experiments involving real quadratic fields with class numbers 1, 2 and 3. We quantify the relative difficulties in separating class numbers of matching/different parity from a data-scientific perspective, apply the methodology of feature analysis and principal component analysis, and use symbolic classification to develop machine-learned formulas for class numbers 1, 2 and 3 that apply to our dataset., 26 pages, 20 figures

Over the past decade, machine learning revolutionized vision-based quality assessment for which convolutional neural networks (CNNs) have now become the standard. In this paper, we consider a potential next step in this development and describe a quanvolutional neural network (QNN) algorithm that efficiently maps classical image data to quantum states and allows for reliable image analysis. We practically demonstrate how to leverage quantum devices in computer vision and how to introduce quantum convolutions into classical CNNs. Dealing with a real world use case in industrial quality control, we implement our hybrid QNN model within the PennyLane framework and empirically observe it to achieve better predictions using much fewer training data than classical CNNs. In other words, we empirically observe a genuine quantum advantage for an industrial application where the advantage is due to superior data encoding., 23 pages, 15 figures

In prior research we explored the use of time series analysis methods to detect one class of information technology (IT) infrastructure anomalies - Distributed Denial of Service (DDoS) attacks. The results of this prior work were a mathematical model and a prototype implementation that were concretely trialed and operated in the data centers of Germany's Federal Employment Agency (FEA). With this paper, we go one step further and generalize as well as optimize the mathematical model and create higher performance and scalability for an updated prototype through targeted use of cloud technologies. The starting point of our generalization is the Exponential Smoothing (E-S) approach, which underlies, for example, the well-known Holt-Winters method. This method is used to predict univariate time series. To detect anomalies (such as DDoS attacks) in infrastructure data, we extend the E-S approach to enable it to forecast multivariate time series. In this optimization of our method and our prototype, we take an exploratory, agile approach. Furthermore, we present a cloud-native architecture stack which we pilot in Azure.

The Mobius function is commonly used to define Euler’s totient function and the Mangoldt function. Similarly, the summatory Mobius function (the Mertens function) is used to define the summatory totient function and the summatory Mangoldt function (the second Chebyshev function). Analogues of the product formula for the totient function are introduced. An analogue of the summatory totient function with many additive properties is introduced.

The Collatz dynamic is known to generate a complex quiver of sequences over natural numbers which inflation propensity remains so unpredictable it could be used to generate reliable proof of work algorithms for the cryptocurrency industry; it has so far resisted every attempt at linearizing its behavior. Here we establish an ad hoc equivalent of modular arithmetic for Collatz sequences, based on five arithmetic rules we prove apply on the entire Collatz dynamical system and which iteration exactly define the full basin of attraction leading to any odd number. We further simulate these rules to gain insight on their quiver geometry and computational properties, and observe they allow to linearize the proof of convergence of the full rows of the binary tree over odd numbers in their natural order, a result which, along with the full description of the basin of any odd number, has never been achieved before. We then provide two theoretical programs to explain why the five rules allow to linearize Collatz convergence, one in ZFC and one in Peano arithmetic.

Franel and Landau derived an arithmetic statement involving the Farey sequence that is equivalent to the Riemann hypothesis. Since there is a relationship between the Mertens function and the Riemann hypothesis, there should be a relationship between the Mertens function and the Farey sequence. Functions of subsets of the fractions in Farey sequences that are analogous to the Mertens function are introduced. Mikolas proved that the sum of certain Mertens function values is 1. Results analogous to Mikolas theorem are the defining property of these functions. A relationship between the Farey sequence and the Riemann hypothesis other than the Franel-Landau theorem is postulated. This conjecture involves a theorem of Mertens and the second Chebyshev function., 9 Pages, 4 Figures, 8 References

The Collatz dynamic is known to generate a complex quiver of sequences over natural numbers which inflation propensity remains so unpredictable it could be used to generate reliable proof of work algorithms for the cryptocurrency industry. Here we establish an ad hoc equivalent of modular arithmetic for Collatz sequences to automatically demonstrate the convergence of infinite quivers of numbers, based on five arithmetic rules we prove apply on the entire Collatz dynamic and which we further simulate to gain insight on their graph geometry and computational properties. We then formally demonstrate these rules define an automaton that is playing a Hydra game on the graph of undecided numbers we also prove is embedded in 24N-7, proving that in ZFC the Collatz conjecture is true, before giving a promising direction to also prove it in Peano arithmetic.

Chatbots have the potential to significantly increase the efficiency of banks and public institutions. Both sectors, however, are subject to special regulations and restrictions in areas such as information security and data protection. The policies of these organizations therefore, in some cases, reject the use of cloud and proprietary products because in their view they lack transparency. As a result, the implementation of chatbots in banks and public institutions often focuses on open-source and on-premises solutions; however, there are hardly any scientific guidelines on how to implement these systems. Our paper aims to close this research gap. The article proposes a reference architecture for chatbots in banks and public institutions that are a.) based on open-source software and b.) are hosted on-premises. The framework is validated by case studies at TeamBank AG and the German Federal Employment Agency. Even if our architecture is designed for these specific industries, it may also add value in other sectors ��� as chatbots are expected to become increasingly important for the practical application of artificial intelligence in enterprises.

AI systems are increasingly evolving from laboratory experiments in data analysis to increments of productive software products. A professional AI platform must therefore not only function as a laboratory environment but must be designed and procured as a workbench for the development, productive implementation, operation and maintenance of ML models. Subsequently, it needs to integrate within a global software engineering approach. This way, Enterprise Architecture Management (EAM) must implement efficient governance of the development cycle, to enable organization-wide collaboration, to accelerate the go-live and to standardize operations. In this paper we highlight obstacles and show best practices on how architects can integrate data science and AI in their environment. Additionally, we suggest an integrated approach adapting the best practices from both the data science and DevOps.

In this paper we argue that the Enterprise Architect (EA) should be considered as a crisis manager. In times of a crisis organizations must create a holistic view on the situation and evaluate the proposed measures. Evaluation will be based on experience, data, upfront-created scenarios and assessments of risks, cost and benefits. The EA is already engaged in processes such as Continuity Management, Risk Management, IT Security, Business Process Management, IT Strategy, and others. Therefore, we propose that the EA is one good candidate (not the only one) for handling organizational crises. This paper presents a model of overall crisis management that incorporates an enterprise architecture view as well as related dimensions of crisis management: the ability to control a crisis, the level of communication during and after a crisis, the type of change brought by a crisis, the crisis' outcomes, its distribution within an enterprise, and an organization's criticality of business functions. Finally, we highlight how the EA role supports crisis management at Lufthansa, a top German aviation company.

The Collatz conjecture is an unsolved number theory problem. We approach the question by examining the divisions by two that are performed within Collatz sequences. Aside from classical mathematical methods, we use techniques of data science. Based on the analysis of 10,000 sequences we show that the number of divisions by two lies within clear boundaries. Building on the results, we develop and prove an equation to calculate the maximum possible number of divisions by two for any given a Collatz sequence. Whenever this maximum is reached, a sequence leads to the result one, as conjectured by Lothar Collatz. Furthermore, we show how many divisions by two are required for a cycle of a specific length. The findings are valuable for further investigations and could form the basis for a comprehensive proof of the conjecture.

The Collatz conjecture is an unsolved number theory problem. We approach the question by examining the divisions by two that are performed within Collatz sequences. Aside from classical mathematical methods, we use techniques of data science. Based on the analysis of 10,000 sequences we show that the number of divisions by two lies within clear boundaries. Building on the results, we formulate and prove several theorems on the occurrence of cycles and the termination of Collatz sequences. The findings are useful for further investigations and could form the basis for a comprehensive proof of the conjecture.

In this paper, we present a novel tool for data center management that incorporates data visualization and machine learning capabilities. We developed the tool in the context of an action design research project conducted at a large government agency in Germany, which hosts three highly available data centers containing more than 10,000 servers. We derived the requirements for the tool from qualitative interviews with agency employees who are familiar with monitoring the data center infrastructure as well as from a review of existing data center and other large infrastructure monitoring solutions. We implemented a web-based 3D prototype for the tool as an Angular 6 application running on Node.js, and evaluated it with the same employees. Most participants preferred the new tool, which provided a significantly better option and enabled visualization of historical data for all server instances at the same time, as well as real-time charts. Planned improvements will take advantage of the full potential of machine learning for time series forecasting.

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.

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.

Digital transformation (also called digitalization or, to a lesser extent, digitization) can enhance the customer experience, streamline operations, revolutionize existing business models, and disrupt entire industries. In this paper, we explore the opportunities for digital transformation in the pharmaceutical industry and develop a pharma-specific reference architecture for digitalization. We build on a model initially developed internally at Capgemini and show how it can be used to describe the use of several emerging digital transformation technologies: Internet of Things (IoT), Cognitive Computing (CC) and Augmented Reality (AR). Our analysis presents the architectural implications of each of these technologies for the pharma industry from the perspectives of four standard TOGAF domains (covering the technology, application, data and business architecture) and of four digitalization steps (Sense, Tag and Connect, Ingest, Analyze and Prepare, and Utilize). We also present an integrated view of the business capabilities all three technologies offer to organizations.

Many studies have shown that parallelization decreases efficiency [1], [2]. There are many reasons for these decrements. This paper investigates those which appear in the context of parallel data integration. Integration processes generally cannot be allocated to packages of identical size (i. e. tasks of identical complexity). The reason for this is unknown heterogeneous input data which result in variable task lengths. Process delay is defined by the slowest processing node. It leads to a detrimental effect on the total processing time. With a real world example, this study will show that while process delay does initially increase with the introduction of more nodes it ultimately decreases again after a certain point. The example will make use of the cloud computing platform Hadoop and be run inside Amazon-s EC2 compute cloud. A stochastic model will be set up which can explain this effect., {"references":["Kumar, V.: Introduction to Parallel Computing, 2nd edition. Addison-\nWesley Longman Publishing Co., Inc., (2002)","Eager, D. L., Zahorjan, J., Lozowska, E. D.: Speedup Versus Efficiency\nin Parallel Systems. IEEE Transactions on Computers, Vol. 38, No. 3,\npp. 408--423 (1989)","Cutting, D.: Nutch: an Open-Source Platform for Web Search. In:\nBeigbeder, M., Yee, W. G. (eds.) Workshop on Open Source Web\nInformation Retrieval (OSWIR), pp. 31--33 (2005)","Khare, R., Cutting, D., Sitaker, K., Rifkin, A.: Nutch: A Flexible and\nScalable Open-Source Web Search Engine (2004)","Ghemawat, S., Gobioff, H., Leung, S.-T.: The Google File System.\nSOSP '03: Proceedings of 19th ACM symposium on Operating systems\nprinciples, ACM Press, pp. 29--43, NY (2003)","Dean, J., Ghemawat, S.: MapReduce: Simplified Data Processing on\nLarge Clusters, OSDI'04: Sixth Symposium on Operating System\nDesign and Implementation, San Francisco, CA (2004)","Cafarella, M. J., Etzioni, O.: A Search Engine for Natural Language\nApplications. WWW '05: Proceedings of the 14th international\nconference on World Wide Web, pp. 442--452. ACM Press, NY (2005)","Drost, I., Scheffer, T.: Thwarting the Nigritude Ultramarine: Learning to\nIdentify Link Spam. ECML, pp. 96--107 (2005)","Kimball, A., Michels-Slettvet, S., Bisciglia, C.: Cluster Computing for\nWeb-Scale Data Processing. SIGCSE '08: Proceedings of the 39th\nSIGCSE technical symposium on Computer science education, ACM,\npp. 116--120 (2008)\n[10] Butler, M. H., Rutherford, J.: Distributed Lucene : A distributed free\ntext index for Hadoop. HP Laboratories (2008)\n[11] Hasan, W., Motwani, R.: Optimization Algorithms for Exploiting the\nParallelism-Communication Tradeoff in Pipelined Parallelism. VLDB\n'94: Proceedings of the 20th International Conference on Very Large\nData Bases, Morgan Kaufmann Publishers Inc., pp. 36--47 (1994)\n[12] Ahn, J. H., Erez, M., Dally, W. J.: Tradeoff between Data-, Instruction-,\nand Thread-Level Parallelism in Stream Processors. ICS '07:\nProceedings of the 21st annual international conference on\nSupercomputing, ACM, pp. 126--137 (2007)\n[13] Amini, H., Kazakov D., Ridge, E.: Parallelism vs Communication\nOverhead Trade-off in a JADE Multi-Agent Implementation of Cellular\nAutomata. The First International Symposium on Nature-Inspired\nSystems for Parallel, Asynchronous and Decentralised Environments\n(NISPADE), AISB convention, Bristol (2006)\n[14] Balasubramonian, R., Dwarkadas, S., Albonesi, D. H.: Dynamically\nmanaging the communication-parallelism trade-off in future clustered\nprocessors. SIGARCH Comput. Archit. News, ACM, pp. 275--287\n(2003)\n[15] Zaharia, M., Konwinski, A., Joseph, A. D., Katz, R. H., Stoica, I.:\nImproving MapReduce Performance in Heterogeneous Environments.\n8th Symposium on Operating Systems Design and Implementation, pp.\n29--42 (2008)\n[16] Ukkonen, E.: Approximate string-matching with q-grams and maximal\nmatches. Theor. Comput. Sci., Elsevier Science Publishers Ltd., 92, pp.\n191--211 (1992)"]}