On the computation of confluent hypergeometric functions for large imaginary part of parameters b and z

The final publication is available at http://link.springer.com/chapter/10.1007%2F978-3-319-42432-3_30We present an efficient algorithm for the confluent hypergeometric functions when the imaginary part of b and z is large. The algorithm is based on the steepest descent method, applied to a suitable representation of the confluent hypergeometric functions as a highly oscillatory integral, which is then integrated by using various quadrature methods. The performance of the algorithm is compared with open-source and commercial software solutions with arbitrary precision, and for many cases the algorithm achieves high accuracy in both the real and imaginary parts. Our motivation comes from the need for accurate computation of the characteristic function of the Arcsine distribution or the Beta distribution; the latter being required in several financial applications, for example, modeling the loss given default in the context of portfolio credit risk.Peer ReviewedPostprint (author's final draft

Model pathway diagrams for the representation of mathematical models

Mathematical models are the foundation of numerical simulation of optoelectronic devices. We present a concept for a machine-actionable as well as human-understandable representation of the mathematical knowledge they contain and the domain-specific knowledge they are based on. We propose to use theory graphs to formalize mathematical models and model pathway diagrams to visualize them. We illustrate our approach by application to the van Roosbroeck system describing the carrier transport in semiconductors by drift and diffusion. We introduce an approach for the block-based composition of models from simpler components

Mathematical models as research data via flexiformal theory graphs

Mathematical modeling and simulation (MMS) has now been established as an essential part of the scientific work in many disciplines. It is common to categorize the involved numerical data and to some extent the corresponding scientific software as research data. But both have their origin in mathematical models, therefore any holistic approach to research data in MMS should cover all three aspects: data, software, and models. While the problems of classifying, archiving and making accessible are largely solved for data and first frameworks and systems are emerging for software, the question of how to deal with mathematical models is completely open. In this paper we propose a solution -- to cover all aspects of mathematical models: the underlying mathematical knowledge, the equations, boundary conditions, numeric approximations, and documents in a flexi\-formal framework, which has enough structure to support the various uses of models in scientific and technology workflows. Concretely we propose to use the OMDoc/MMT framework to formalize mathematical models and show the adequacy of this approach by modeling a simple, but non-trivial model: van Roosbroeck's drift-diffusion model for one-dimensional devices. This formalization -- and future extensions -- allows us to support the modeler by e.g. flexibly composing models, visualizing Model Pathway Diagrams, and annotating model equations in documents as induced from the formalized documents by flattening. This directly solves some of the problems in treating MMS as "research data'' and opens the way towards more MKM services for models

Ontologies for Models and Algorithms in Applied Mathematics and Related Disciplines

In applied mathematics and related disciplines, the modeling-simulation-optimization workflow is a prominent scheme, with mathematical models and numerical algorithms playing a crucial role. For these types of mathematical research data, the Mathematical Research Data Initiative has developed, merged and implemented ontologies and knowledge graphs. This contributes to making mathematical research data FAIR by introducing semantic technology and documenting the mathematical foundations accordingly. Using the concrete example of microfracture analysis of porous media, it is shown how the knowledge of the underlying mathematical model and the corresponding numerical algorithms for its solution can be represented by the ontologies.Comment: Preprint of a Conference Paper to appear in the Proceeding of the 17th International Conference on Metadata and Semantics Researc

Extensional Higher-Order Paramodulation in Leo-III

Leo-III is an automated theorem prover for extensional type theory with Henkin semantics and choice. Reasoning with primitive equality is enabled by adapting paramodulation-based proof search to higher-order logic. The prover may cooperate with multiple external specialist reasoning systems such as first-order provers and SMT solvers. Leo-III is compatible with the TPTP/TSTP framework for input formats, reporting results and proofs, and standardized communication between reasoning systems, enabling e.g. proof reconstruction from within proof assistants such as Isabelle/HOL. Leo-III supports reasoning in polymorphic first-order and higher-order logic, in all normal quantified modal logics, as well as in different deontic logics. Its development had initiated the ongoing extension of the TPTP infrastructure to reasoning within non-classical logics.Comment: 34 pages, 7 Figures, 1 Table; submitted articl

Integration of Cost andWork Breakdown Structures in the Management of Construction Projects

Scope management allows project managers to react when a project underperforms regarding schedule, budget, and/or quality at the execution stage. Scope management can also minimize project changes and budget omissions, as well as improve the accuracy of project cost estimates and risk responses. For scope management to be effective, though, it needs to rely on a robust work breakdown structure (WBS). A robust WBS hierarchically and faithfully reflects all project tasks and work packages so that projects are easier to manage. If done properly, the WBS also allows meeting the project objectives while delivering the project on time, on budget, and with the required quality. This paper analyzes whether the integration of a cost breakdown structure (CBS) can lead to the generation of more robust WBSs in construction projects. Over the last years, some international organizations have standardized and harmonized different cost classification systems (e.g., ISO 12006-2, ISO 81346-12, OmniClass, CoClass, UniClass). These cost databases have also been introduced into building information modeling (BIM) frameworks. We hypothesize that in BIM environments, if these CBSs are used to generate the project WBS, several advantages are gained such as sharper project definition. This enhanced project definition reduces project contradictions at both planning and execution stages, anticipates potential schedule and budget deviations, improves resource allocation, and overall it allows a better response to potential project risks. The hypothesis that the use of CBSs can generate more robust WBSs is tested by the response analysis of a questionnaire survey distributed among construction practitioners and project managers. By means of structural equation modeling (SEM), the correlation (agreement) and perception differences between two 250-respondent subsamples (technical project staff vs. project management staff) are also discussed. Results of this research support the use of CBSs by construction professionals as a basis to generate WBSs for enhanced project management (PM)

Design concept towards a human-centered learning factory

Learning factories play an important role when studying multi-disciplinary problems. Such a problem is to support operators in multi-variant assembly. Multi-variants cause problems with product quality, production time as well as cognitive load and therefore it is important to find ways to support operators in this context. To assess the effects of multi variants, a design concept were developed in a learning factory environment (SIILab, CPPS-testbed). The concept was constructed at a conveyer belt with three assembly stations using Casat software for instruction presentations. The following aspects were included in the human-centered learning factory: studying the introduction of advanced automation, managing product variety, supporting operators in finding information and supporting existing human-automation interactions

Lobachevskii DML: Towards a semantic digital mathematical library of Kazan University

The digital mathematical library Lobachevskii DML is one of the national initiatives that have emerged in the past decade in different countries of the world. During this time, the formed technical and organizational conditions allowed making mathematicians' dreams of a global World Digital Mathematical Library (WDML) a reality. Following the vision approved by the International Mathematical Union, we started the Lobachevskii DML project in 2017 - the year of the 225-th anniversary of the birth of the brilliant mathematician Nikolai Ivanovich Lobachevskii, the founder of non-Euclidean geometry, the rector of the Kazan University. The main task of Lobachevskii DML project is the development of tools for managing mathematical content, which take into account not only the specifics of mathematical texts, but also the features of processing Russian-language texts. A particular task of creating this digital library is the integration of mathematical resources of Kazan University. Therefore, the original goal of the project was to build up a sound basis for a digital archive comprising the relevant mathematical literature published for 213 years of the existence of Kazan University and stored in the libraries of the University and Kazan. According to our assumption, the digital library Lobachevskii DML should be endowed with all conceivable necessary functions and services, making it a comprehensive and up-to-date live DML, generally respected and used by the local as well as the global mathematical community. From the very beginning, we had in mind that the Lobachevskii DML should constitute a building block for the envisioned global WDML. In this paper, the results of the implementation of the digital mathematical library Lobachevsky-DML are presented. We describe the purpose of creating this digital library, methods of managing mathematical content based on semantic technologies. The following show how Lobachevskii DML interacts with the information systems of scientific journals. We also present a system of services to support the life cycle of a mathematical document and highlight technologies for supporting new forms of scientific publications and providing integration services with other digital mathematical archives and libraries