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Though gait asymmetry is used as a metric of functional recovery in clinical rehabilitation, there is no consensus on an ideal method for its evaluation. Various methods have been proposed but are limited in scope, as they can often use only positive signals or discrete values extracted from time-scale data as input. By defining five symmetry axioms, a framework for benchmarking existing methods was established and a new method was described here for the first time: the weighted universal symmetry index (wUSI), which overcomes limitations of other methods. Both existing methods and the wUSI were mathematically compared to each other and in respect to their ability to fulfill the proposed symmetry axioms. Eligible methods that fulfilled these axioms were then applied using both discrete and continuous approaches to ground reaction force (GRF) data collected from healthy gait, both with and without artificially induced asymmetry using a single instrumented elbow crutch. The wUSI with a continuous approach was the only symmetry method capable of determining GRF asymmetries in different walking conditions in all three planes of motion. When used with a continuous approach, the wUSI method was able to detect asymmetries while avoiding artificial inflation, a common problem reported in other methods. In conclusion, the wUSI is proposed as a universal method to quantify three-dimensional GRF asymmetries, which may also be expanded to other biomechanical signals.
Research software has become a central asset in academic research. It optimizes existing and enables new research methods, implements and embeds research knowledge, and constitutes an essential research product in itself. Research software must be sustainable in order to understand, replicate, reproduce, and build upon existing research or conduct new research effectively. In other words, software must be available, discoverable, usable, and adaptable to new needs, both now and in the future. Research software therefore requires an environment that supports sustainability. Hence, a change is needed in the way research software development and maintenance are currently motivated, incentivized, funded, structurally and infrastructurally supported, and legally treated. Failing to do so will threaten the quality and validity of research. In this paper, we identify challenges for research software sustainability in Germany and beyond, in terms of motivation, selection, research software engineering personnel, funding, infrastructure, and legal aspects. Besides researchers, we specifically address political and academic decision-makers to increase awareness of the importance and needs of sustainable research software practices. In particular, we recommend strategies and measures to create an environment for sustainable research software, with the ultimate goal to ensure that software-driven research is valid, reproducible and sustainable, and that software is recognized as a first class citizen in research. This paper is the outcome of two workshops run in Germany in 2019, at deRSE19 - the first International Conference of Research Software Engineers in Germany - and a dedicated DFG-supported follow-up workshop in Berlin.
We present time-space trade-offs for computing the Euclidean minimum spanning tree of a set S of n point-sites in the plane. More precisely, we assume that S resides in a random-access memory that can only be read. The edges of the Euclidean minimum spanning tree EMST(S) have to be reported sequentially, and they cannot be accessed or modified afterwards. There is a parameter s in {1, ..., n} so that the algorithm may use O(s) cells of read-write memory (called the workspace) for its computations. Our goal is to find an algorithm that has the best possible running time for any given s between 1 and n.
We show how to compute EMST(S) in O(((n^3)/(s^2)) log s) time with O(s) cells of workspace, giving a smooth trade-off between the two best-known bounds O(n^3) for s = 1 and O(n log n) for s = n. For this, we run Kruskal's algorithm on the "relative neighborhood graph" (RNG) of S. It is a classic fact that the minimum spanning tree of RNG(S) is exactly EMST(S). To implement Kruskal's algorithm with O(s)
cells of workspace, we define s-nets, a compact representation of planar graphs. This allows us to efficiently maintain and update the components of the current minimum spanning forest as the edges are being inserted.
Von Graphen zu Hypergraphen
(2020)
Motivated by the desire to numerically calculate rigorous upper and lower bounds on deviation probabilities over large classes of probability distributions, we present an adaptive algorithm for the reconstruction of increasing real-valued functions. While this problem is similar to the classical statistical problem of isotonic regression, the optimisation setting alters several characteristics of the problem and opens natural algorithmic possibilities. We present our algorithm, establish sufficient conditions for convergence of the reconstruction to the ground truth, and apply the method to synthetic test cases and a real-world example of uncertainty quantification for aerodynamic design.
Cycle inequalities play an important role in the polyhedral study of the periodic timetabling problem in public transport. We give the first pseudo-polynomial time separation algorithm for cycle inequalities, and we contribute a rigorous proof for the pseudo-polynomial time separability of the change-cycle inequalities. Moreover, we provide several NP-completeness results, indicating that pseudo-polynomial time is best possible. The efficiency of these cutting planes is demonstrated on real-world instances of the periodic timetabling problem.