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Data Structures and Algorithms

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Algorithms and Data Structures

14th International Symposium, WADS 2015, Victoria, BC, Canada, August 5-7, 2015. Proceedings

• Conference proceedings
• © 2015
• Frank Dehne 0 ,
• Jörg-Rüdiger Sack 1 ,
• Ulrike Stege 2

Carleton University, Ottawa, Canada

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University of Victoria, Victoria, Canada

Part of the book series: Lecture Notes in Computer Science (LNCS, volume 9214)

Part of the book sub series: Theoretical Computer Science and General Issues (LNTCS)

Included in the following conference series:

• WADS: Algorithms and Data Structures Symposium

Conference proceedings info: WADS 2015.

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Table of contents (52 papers)

Front matter, contact graphs of circular arcs.

• Md. Jawaherul Alam, David Eppstein, Michael Kaufmann, Stephen G. Kobourov, Sergey Pupyrev, André Schulz et al.

Contact Representations of Graphs in 3D

• Jawaherul Alam, William Evans, Stephen Kobourov, Sergey Pupyrev, Jackson Toeniskoetter, Torsten Ueckerdt

Minimizing the Aggregate Movements for Interval Coverage

• Aaron M. Andrews, Haitao Wang

Online Bin Packing with Advice of Small Size

• Spyros Angelopoulos, Christoph Dürr, Shahin Kamali, Marc Renault, Adi Rosén

On the Approximability of Orthogonal Order Preserving Layout Adjustment

• Sayan Bandyapadhyay, Santanu Bhowmick, Kasturi Varadarajan

An Optimal Algorithm for Plane Matchings in Multipartite Geometric Graphs

• Ahmad Biniaz, Anil Maheshwari, Subhas C. Nandy, Michiel Smid

Generation of Colourings and Distinguishing Colourings of Graphs

• William Bird, Wendy Myrvold

Strictly Implicit Priority Queues: On the Number of Moves and Worst-Case Time

• Gerth Stølting Brodal, Jesper Sindahl Nielsen, Jakob Truelsen

On Conflict-Free Multi-coloring

• Andreas Bärtschi, Fabrizio Grandoni

Semi-dynamic Connectivity in the Plane

• Sergio Cabello, Michael Kerber

Interval Selection in the Streaming Model

• Sergio Cabello, Pablo Pérez-Lantero

On the Bounded-Hop Range Assignment Problem

• Paz Carmi, Lilach Chaitman-Yerushalmi, Ohad Trabelsi

Greedy Is an Almost Optimal Deque

• Parinya Chalermsook, Mayank Goswami, László Kozma, Kurt Mehlhorn, Thatchaphol Saranurak

A New Approach for Contact Graph Representations and Its Applications

• Yi-Jun Chang, Hsu-Chun Yen

Dealing with 4-Variables by Resolution: An Improved MaxSAT Algorithm

• Jianer Chen, Chao Xu, Jianxin Wang

Select with Groups of 3 or 4

• Ke Chen, Adrian Dumitrescu

Approximating Nearest Neighbor Distances

• Michael B. Cohen, Brittany Terese Fasy, Gary L. Miller, Amir Nayyeri, Donald R. Sheehy, Ameya Velingker

Linearity Is Strictly More Powerful Than Contiguity for Encoding Graphs

• Christophe Crespelle, Tien-Nam Le, Kevin Perrot, Thi Ha Duong Phan

On the Complexity of an Unregulated Traffic Crossing

• Philip Dasler, David M. Mount

Other volumes

• Algorithm Analysis
• Algorithm Design
• Algorithm Design Techniques
• Approximation algorithms analysis
• Concurrent Algorithms
• Data Structures Analysis
• Data Structures Design
• Data structures design and analysis
• Design and analysis of algorithms
• Distributed Algorithms
• Exact Algorithms
• Graph Agorithms
• Graph algorithms analysis
• Near Linear Time Algorithms
• Online algorithms
• Parallel Algorithms
• Parameterized Complexity
• Streaming, Sublinear and near linear time Algorithms
• Sublinear Algorithms
• algorithm analysis and problem complexity
• data structures

About this book

Editors and affiliations.

Frank Dehne, Jörg-Rüdiger Sack

Ulrike Stege

Bibliographic Information

Book Title : Algorithms and Data Structures

Book Subtitle : 14th International Symposium, WADS 2015, Victoria, BC, Canada, August 5-7, 2015. Proceedings

Editors : Frank Dehne, Jörg-Rüdiger Sack, Ulrike Stege

Series Title : Lecture Notes in Computer Science

DOI : https://doi.org/10.1007/978-3-319-21840-3

Publisher : Springer Cham

eBook Packages : Computer Science , Computer Science (R0)

Copyright Information : Springer International Publishing Switzerland 2015

Softcover ISBN : 978-3-319-21839-7 Published: 15 July 2015

eBook ISBN : 978-3-319-21840-3 Published: 27 July 2015

Series ISSN : 0302-9743

Series E-ISSN : 1611-3349

Edition Number : 1

Number of Pages : XIII, 646

Number of Illustrations : 125 b/w illustrations

Topics : Algorithm Analysis and Problem Complexity , Data Structures , Discrete Mathematics in Computer Science , Computer Graphics , Numeric Computing , Computer Communication Networks

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Analysis and Research of Sorting Algorithm in Data Structure Based on C Language

Zhi-Gang Zhu 1

Published under licence by IOP Publishing Ltd Journal of Physics: Conference Series , Volume 1544 , 2020 5th International Conference on Intelligent Computing and Signal Processing (ICSP) 2020 20-22 March 2020, Suzhou, China Citation Zhi-Gang Zhu 2020 J. Phys.: Conf. Ser. 1544 012002 DOI 10.1088/1742-6596/1544/1/012002

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1 City Institute Dalian University Of Technology, Liaoning Dalian, 116600, China

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In the process of learning the data structure, it is very necessary to master the sorting algorithm, and in the program design, the sorting algorithm is applied frequently. Based on the importance of sorting algorithms, this paper will carefully compare the characteristics of different algorithms, starting with the work efficiency, algorithm implementation, basic ideas, sorting methods and other aspects, and draw conclusions so as to better select sorting algorithms.

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A practical data structure and algorithm research on drawing and editing vector graphics

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Search anything:

Must read research papers on Data Structures

Data structures.

Open-Source Internship opportunity by OpenGenus for programmers. Apply now.

Data Structures are not seen to be as important as Algorithms but in reality, it is equally important to solve computational problems efficiently. The must read research papers on Data Structures are:

• Ordered Hash Table (1973)
• Randomized Search Trees (1989)
• EERTREE: An Efficient Data Structure for Processing Palindromes in Strings (2015)
• Making data structures persistent (1986)
• Design and implementation of an efficient priority queue (1976)
• Fractional cascading: A data structuring technique (1986)

Note that the above list has been prepared by OpenGenus and is very accuracy. We will now go through each in detail:

Ordered Hash Table

Basic details on the paper:

• Author: O. Amble and D. E. Knuth
• Affiliation: University of Oslo and Stanford University
• Date published: 1973
• Journal/ Conference: The Computer Journal
• Read this paper here: by Oxford Academia
• Read about Hash Tables

Hash table is a fundamental progress as it shows how a simple data structure like array can be used to improve common operations like searching to constant time. Today, hash map has a central place in algorithms but a lot of ideas goes into it for efficiency like:

• collision avoidance
• hash generation

This is a must read for anyone interested in Computer Science and specially, Algorithms and Data Structures.

Randomized Search Trees

• Author: Raimund Seidel and Cecilia Aragon
• Affiliation: UC Berkeley
• Date published: November 1989
• Journal/ Conference: 30th Annual Symposium on Foundations of Computer Science
• Read this paper here: Research Gate (PDF)
• Read about Randomized Search Trees

Balanced Search trees are a solution to a number of problems but when it comes to reality, trees keep changing and keeping it balanced is a difficult process. This paper presents how balanced trees can be modified using randomness and opens up a whole new category of algorithms.

For will need to understand Binary Search Tree to get the complete idea of this.

EERTREE: An Efficient Data Structure for Processing Palindromes in Strings

• Author: Mikhail Rubinchik and Arseny M. Shur
• Affiliation: Ural Federal University, Ekaterinburg, Russia
• Date published: June 2015
• Journal/ Conference: European Journal of Combinatorics
• Read this paper here: ArXiv
• Read about EerTree

This is a must read because this data structure shows that some problems like string related problems may seem to be pruely algorithmic problems but a clever use of a data structure can improve the performance significantly.

This paper bridges the gap between algorithms and data structures with respect to strings.

Making data structures persistent

• Author: Driscoll, J.R., Sarnak, N., Sleator, D.D., Tarjan, R.E
• Affiliation: Carnegie-Mellon University, IBM, AT&T Bell Laboratories, Princeton University
• Date published: 5th August 1986
• Journal/ Conference: Journal of Computer and System Sciences
• Read this paper here: ACM
• Read about Persistent Segment Tree

Usually, data structures need not remember previous structures but as we went on to solve complex problems in time domain, need of persistent data structures that is data structures maintaining its previous structures rose. This paper is a must read as it shows what it means for a data structure to be persistent and how we can do so.

This opens up the path to a whole new domain of persistent data structures.

Design and implementation of an efficient priority queue

• Author: P. van Emde Boas, R. KaasE. Zijlstra
• Affiliation: Mathematical Centre, Amsterdam, Netherlands
• Date published: December 1976
• Journal/ Conference: Mathematical systems theory
• Read this paper here: Springer
• Read about Priority Queue

This is an old paper but is a good read as it shows how a data structure should be implemented depending on the system architecture and programming language used to get the most performance out of it.

This will open up your mind to look at algorithms and data structures differently.

Fractional cascading: A data structuring technique

• Author: Bernard Chazelle, Leonidas J. Guibas
• Affiliation: Brown University, Ecole Normale Supérieure, DEC/SRC and Stanford University, USA
• Date published: November 1986
• Journal/ Conference: Algorithmica

This is an important paper as it shows how particular data structure can perform less for the first few tries and then, show superior performance as it gets warmed up. This is a must read to understand the true potential of data structures.

Learn more about Data Structures

With this, you will have a good understanding of the wide variety of data structures and what can be done using them.

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Book description

Part I: Object-Oriented Programming Part II: Linear Structures Part III: Algorithms Part IV: Trees and Sets Part V: Advanced Topics Part VI: Appendices

Table of contents

• Contents (1/2)
• Contents (2/2)
• 1.1 Software Development
• 1.2 Classes and Objects (1/2)
• 1.2 Classes and Objects (2/2)
• 1.3 Using Objects (1/3)
• 1.3 Using Objects (2/3)
• 1.3 Using Objects (3/3)
• 2.1 Reference Types
• 2.2 Arrays (1/3)
• 2.2 Arrays (2/3)
• 2.2 Arrays (3/3)
• 2.3 Interfaces
• 2.4 Overloading
• 3.1 Extending a Class
• 3.2 The Object Class
• 3.3 Packages and Access Levels
• 4.1 The Stack Interface
• 4.2 The Call Stack
• 4.3 Exceptions (1/2)
• 4.3 Exceptions (2/2)
• 4.4 The Queue Interface (1/2)
• 4.4 The Queue Interface (2/2)
• 5.1 Shrinking and Stretching Arrays
• 5.2 Implementing Stacks and Queues (1/2)
• 5.2 Implementing Stacks and Queues (2/2)
• 5.3 The List Interface (1/2)
• 5.3 The List Interface (2/2)
• 5.4 Iterators (1/3)
• 5.4 Iterators (2/3)
• 5.4 Iterators (3/3)
• 5.5 The Java Collections Framework: A First Look
• 6.1 List Nodes
• 6.2 Stacks and Queues (1/2)
• 6.2 Stacks and Queues (2/2)
• 6.3 The LinkedList Class (1/2)
• 6.3 The LinkedList Class (2/2)
• 6.4 The Java Collections Framework Revisited
• 7.2 Asymptotic Notation (1/2)
• 7.2 Asymptotic Notation (2/2)
• 7.3 Counting Steps
• 7.4 Best, Worst, and Average Case
• 7.5 Amortized Analysis
• 8.1 Linear Search
• 8.2 Binary Search
• 8.3 Insertion Sort
• 8.4 The Comparable Interface
• 8.5 Sorting Linked Lists
• 9.1 Thinking Recursively
• 9.2 Analyzing Recursive Algorithms
• 9.3 Merge Sort
• 9.4 Quicksort
• 9.5 Avoiding Recursion
• 10.1 Binary Trees
• 10.2 Tree Traversal
• 10.3 General Trees (1/2)
• 10.3 General Trees (2/2)
• 11.1 The Set Interface
• 11.2 Ordered Lists
• 11.3 Binary Search Trees (1/2)
• 11.3 Binary Search Trees (2/2)
• 11.4 Hash Tables (1/3)
• 11.4 Hash Tables (2/3)
• 11.4 Hash Tables (3/3)
• 11.5 The Java Collections Framework Again
• 12.1 Bit Vectors
• 12.2 Sparse Arrays
• 12.3 Contiguous Representation of Multidimensional Arrays (1/2)
• 12.3 Contiguous Representation of Multidimensional Arrays (2/2)
• 12.4 Advanced Searching and Sorting
• 13.1 Strings and StringBuilders
• 13.2 String Matching (1/3)
• 13.2 String Matching (2/3)
• 13.2 String Matching (3/3)
• 14.2 Disjoint Set Clusters (1/2)
• 14.2 Disjoint Set Clusters (2/2)
• 14.3 Digital Search Trees (1/2)
• 14.3 Digital Search Trees (2/2)
• 14.4 Red-Black Trees (1/3)
• 14.4 Red-Black Trees (2/3)
• 14.4 Red-Black Trees (3/3)
• 15.1 Terminology
• 15.2 Representation (1/2)
• 15.2 Representation (2/2)
• 15.3 Graph Traversal
• 15.4 Topological Sorting
• 15.5 Shortest Paths
• 15.6 Minimum Spanning Trees
• 16.1 Explicit Memory Management
• 16.2 Automatic Memory Management (1/2)
• 16.2 Automatic Memory Management (2/2)
• 17.1 Interacting with Files
• 17.2 Compression (1/3)
• 17.2 Compression (2/3)
• 17.2 Compression (3/3)
• 17.3 External Sorting (1/2)
• 17.3 External Sorting (2/2)
• 17.4 B-Trees (1/4)
• 17.4 B-Trees (2/4)
• 17.4 B-Trees (3/4)
• 17.4 B-Trees (4/4)
• A.1 The First Program
• A.2 Variables and Types
• A.4 Interacting with the User
• A.5 Branching
• A.6 Methods and Breaking Out
• A.7 Constants
• A.8 Operators
• A.9 Debugging
• A.10 Coding Conventions
• B.1 Class Diagrams
• B.2 Instance Diagrams
• C.1 Sum Notation
• C.2 Sum of Constants
• C.3 Sum of First n Integers
• C.4 Sums of Halves and Doubles
• C.5 Upper Limit on Sum of a Function
• C.6 Constant Factors
• D.1 Data Structures and Algorithms

Product information

• Title: Data Structures and Algorithms in Java
• Author(s): Peter Drake
• Release date: May 2024
• Publisher(s): Pearson India
• ISBN: 9781282650404

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1. Introduction

• 2. Solving the phase problem for data expanded to space group P1

3. Using phases to find the origin shift and space group

4. assigning chemical elements to the electron-density peaks, 5. isotropic refinement and absolute structure determination, 6. building the structure, 7. examples, 8. program development and distribution.

research papers \(\def\hfill{\hskip 5em}\def\hfil{\hskip 3em}\def\eqno#1{\hfil {#1}}\)

SHELXT – Integrated space-group and crystal-structure determination

a Department of Structural Chemistry, Georg-August Universität Göttingen, Tammannstrasse 4, Göttingen, 37077, Germany * Correspondence e-mail: [email protected]

The new computer program SHELXT employs a novel dual-space algorithm to solve the phase problem for single-crystal reflection data expanded to the space group P 1. Missing data are taken into account and the resolution extended if necessary. All space groups in the specified Laue group are tested to find which are consistent with the P 1 phases. After applying the resulting origin shifts and space-group symmetry, the solutions are subject to further dual-space recycling followed by a peak search and summation of the electron density around each peak. Elements are assigned to give the best fit to the integrated peak densities and if necessary additional elements are considered. An isotropic refinement is followed for non-centrosymmetric space groups by the calculation of a Flack parameter and, if appropriate, inversion of the structure. The structure is assembled to maximize its connectivity and centred optimally in the unit cell. SHELXT has already solved many thousand structures with a high success rate, and is optimized for multiprocessor computers. It is, however, unsuitable for severely disordered and twinned structures because it is based on the assumption that the structure consists of atoms.

Keywords: Patterson superposition ; direct methods ; dual-space recycling ; space-group determination ; element assignment .

Before the phase problem can be solved, the usual procedure is to determine the space group of the crystal with the help of the Laue symmetry of the diffraction pattern, the presence or absence of certain reflections (the systematic absences) and statistical tests ( e.g. to distinguish between centrosymmetric and non-centrosymmetric structures). This space-group determination may be upset by the presence of dominant heavy atoms or by pseudo-symmetry affecting the intensities of certain classes of reflections, and in some cases the space group is ambiguous. For example, the space groups I 222 and I 2 1 2 1 2 1 have the same systematic absences, as do Pmmn and two different orientations of Pmn 2 1 .

2. Solving the phase problem for data expanded to space group P 1

SHELXT reads standard SHELX format . i n s and . h k l files. It extracts the unit cell, Laue group (but not space group) and the elements that are expected to be present (but not how many atoms of each). A number of options, e.g. that all trigonal and hexagonal Laue groups should be considered ( - L 15 ), may be specified by command-line switches. A summary of the possible options is output when no filename is given on the SHELXT command line and further details are available on the SHELX home page.

The data are first merged according to the specified Laue group and then expanded to P 1. In theory, SHELXT could also have been programmed to determine the Laue group, e.g. by calculating the R values or correlation coefficients when the equivalent reflections are merged. However, the Laue group has to be known to scale the data, which is an essential step for the highly focused beams now common for synchrotrons and laboratory microsources, because the effective volume of the crystal irradiated is different for different reflections and needs to be corrected for. So in practice it is best to determine the Laue group first anyway. Even though programs such as XPREP (Bruker AXS, Madison, WI 53711, USA) are no longer required to determine the space group, it is still necessary to identify the correct unit cell and metric symmetry.

2.1. Dual-space iteration starting from a Patterson superposition

2.2. the random omit procedure.

Omit maps are frequently used in macromolecular crystallography to reduce model bias. A small part of the structure is deleted and the rest is refined to reduce memory effects, then a new difference-density map is generated and interpreted. This concept plays an important role in SHELXT , but because no model is available at the P 1 dual-space stage, it is implemented differently. The following density modification is performed unless otherwise specified by the user. A mask M ( x ) is constructed consisting of Gaussian-shaped peaks of unit volume at the positions of the maxima in the electron-density map. A small number of these Gaussian peaks are then deleted from the mask at random, usually every third dual-space cycle, and the new density is obtained by multiplying the original density ρ ( x ) with the mask:

where X is 1.0 unless reset by the user. For organic or organo­metallic structures, especially for low resolution or incomplete data, the alternative,

is sometimes better, but this is not the default option because it is not appropriate for inorganic and mineral structures. If CFOM is less than a preset threshold, the program refines further sets of starting phases, increasing the number of iterations each time this is done.

The idea of trying all possible space groups in a specified Laue group is also sometimes used in macromolecular crystal structure determination. For example, if the crystal is ortho­rhombic P , Laue group mmm , and only the Sohncke space groups need to be considered, a molecular-replacement program can be asked to test all eight possibilities. If only one of the eight gives a solution with good figures of merit, both the crystal structure and the space group have been determined! For chemical problems the situation is more interesting, because there are 30 possible orthorhombic P space groups and a total of 120 possibilities when different orientations of the axes are taken into account (as in SHELXT ).

For the correct space group and the correct origin shift Δ x , η should be close to zero. To facilitate comparisons, the figure of merit α is defined as the F 2 -weighted sum of η 2 over all pairs of equivalents for all reflections, normalized so that it should be unity for random phases. α should be as small as possible for the correct combination of space group and origin shift.

Each solution with a reasonable α value is first subject to ten cycles of density modification in the chosen space group after applying the origin shift. This density modification consists only of averaging the phases of equivalent reflections taking the space-group symmetry into account and resetting negative density to zero. A peak search is then performed, and the density inside a sphere (default radius 0.7 Å) about each peak is summed. It is better to use integrated densities rather than peak heights because the atoms may have different atomic displacement parameters. However, these integrated densities are not on an absolute scale, so the problem is how to set the scale so that they correspond to atomic numbers and the elements can be assigned. SHELXT attempts to set the scale as follows, going on to the next test only if the previous tests are negative:

( a ) If carbon is specified as one of the elements present, the program searches for peaks with similar integrated densities separated from each other by typical C—C distances ( i.e. between 1.25 and 1.65 Å). If enough are found, the scale is set so that they will have average atomic numbers of 6.

( b ) If boron is expected, boron cages with distances between 1.65 and 1.8 Å are searched for.

( c ) A search is made for oxyanions. The oxygen atoms should have similar integrated densities to each other and similar distances to a central atom.

( d ) If the above tests are negative, it is assumed that the heaviest atom expected corresponds to the peak with the highest integrated density. This can run into trouble if, for example, there is an unexpected bromide or iodide ion in the structure and it has not been possible to fix the scale by one of the above methods.

When the density scale has been found, it is used to assign elements to the remaining atoms. If it then appears that there are high-density peaks that cannot be assigned because only light atoms were expected, chlorine, bromine or iodine atoms are added. Some rudimentary checks are made to ensure that the element assignments are chemically reasonable.

The following algorithm used to assemble the structure is diabolically simple but almost always builds and clusters the molecules in a way that is instantly recognizable. No covalent radii etc . are used, so the algorithm is independent of the element assignments.

( a ) Generate the SDM (shortest-distance matrix). This is a triangular matrix of the shortest distances between unique atoms, taking symmetry into account.

( b ) Set a flag to -1 for each unique atom, then change it to +1 for one atom (it does not matter which).

( c ) Search the SDM for the shortest distance for which the product of the two flags is -1 . If none, exit.

( d ) Symmetry transform the atom with flag -1 corresponding to this distance so that it is as near as possible to the atom with flag +1 , then set its flag to +1 .

( e ) Go to ( c ).

SHELXT is compiled with the Intel ifort Fortran compiler using the statically linked MKL library and is particularly suitable for multi-CPU computers. It is available free to academics for the 32- or 64-bit Windows, 32- or 64-bit Linux and 64-bit Mac OS X operating systems. The program may be downloaded as part of the SHELX system via the SHELX home page ( https://shelx.uni-ac.gwdg.de/SHELX/ ), which also provides documentation and other useful information. Users are recommended to view the `recent changes' section on the home page from time to time.

The initial development of SHELXT was based on a test databank of about 650 structures, mostly determined in Göttingen, covering a wide range of problems. It has also been tested by more than 200 beta-testers for up to three years, in the course of which several thousand structures were solved (and a few not solved). It is difficult to generalize, but the correct space group was identified in about 97% of cases, and for about half of the structures every atom was located and assigned to the correct element. Most of the remaining structures were basically correct, the most common errors being carbon assigned as nitrogen or vice versa . Poor solutions were sometimes obtained when the heavy atoms corresponded to a centrosymmetric substructure but the full structure possessed a lower symmetry. It is always essential to check the element assignments, especially if the program has added extra elements, and also to check for the presence of disordered solvent molecules that may have been missed. The biggest danger is that inexperienced users may assume that the program is always right!

Acknowledgements

The author is very grateful to the many SHELXT beta-testers for patiently reporting bugs, suggesting improvements and providing interesting data sets for testing. He is particularly grateful to Bruker AXS for their help with the logistics of the three-year beta-test, and for the use of their email list for rapid communication with the beta-testers. He thanks the Volkswagen-Stiftung and the state of Niedersachsen for the award of a Niedersachsen (emeritus) Professorship.

This is an open-access article distributed under the terms of the Creative Commons Attribution (CC-BY) Licence , which permits unrestricted use, distribution, and reproduction in any medium, provided the original authors and source are cited.