Various neural network based methods are capable of anticipating human body motions from data for a short period of time. What these methods lack are the interpretability and explainability of the network and its results. We propose to use Dynamic Mode Decomposition with delays to represent and anticipate human body motions. Exploring the influence of the number of delays on the reconstruction and prediction of various motion classes, we show that the anticipation errors in our results are comparable to or even better for very short anticipation times (<0.4 s) than a recurrent neural network based method. We perceive our method as a first step towards the interpretability of the results by representing human body motions as linear combinations of previous states and delays. In addition, compared to the neural network based methods large training times are not needed. Actually, our methods do not even regress to any other motions than the one to be anticipated and hence it is of a generic nature.

Dataset supporting the paper: Russell Bradford, James H. Davenport, Matthew England, Hassan Errami, Vladimir Gerdt, Dima Grigoriev, Charles Hoyt, Marek Košta, Ovidiu Radulescu, Thomas Sturm, and Andreas Weber. Identifying the Parametric Occurrence of Multiple Steady States for some Biological Networks. To appear in the Journal of Symbolic Computation. We provide all the accompanying material for the main computations, split up into sections as presented in the paper. For Sections 3 and 9 the computations are introduced by a plain text ReadMe. For Sections 4 and 6 they are introduced by a Maple (also available ad pdf printout).

The key prerequisite for accessing the huge potential of current machine learning techniques is the availability of large databases that capture the complex relations of interest. Previous datasets are focused on either 3D scene representations with semantic information, tracking of multiple persons and recognition of their actions, or activity recognition of a single person in captured 3D environments. We present Bonn Activity Maps, a large-scale dataset for human tracking, activity recognition and anticipation of multiple persons. Our dataset comprises four different scenes that have been recorded by time-synchronized cameras each only capturing the scene partially, the reconstructed 3D models with semantic annotations, motion trajectories for individual people including 3D human poses as well as human activity annotations. We utilize the annotations to generate activity likelihoods on the 3D models called activity maps.

The estimation of soft biometrics of a subject, including age, through the gait analysis is a challenging area of research due to variations in individuals' gaits and the effect of ageing on gait patterns. In this paper, we present the results of age estimation based on the analysis of inertial data of human walk. We have recorded 6D accelerations and angular velocities of 86 subjects while performing standardized gait tasks using chest-mounted inertial measurement units. The recorded data were segmented to decompose the long sequences of signals into single steps. For each step, we compute a total of 50 spatio-spectral features from 6D components. We trained three different machine learning classifiers-random forests, support vector machines, and multi-layer perceptron-to estimate the human age. Two different types of cross validation strategies, i.e., tenfold and subjectwise cross validation were employed to gauge the performance of the estimators. The results reveal that it is possible to predict the age of a subject with higher accuracy. With a random forest regressor, when trained and validated on hybrid data, we achieved an average root mean square error of 3.32 years and a mean absolute error of 1.75 years under tenfold cross validation and average root mean square error of 8.22 years under subjectwise cross validation. Since our participants belong to two different demographical regions, i.e., Europe and South Asia, we confirm on broader empirical basis previous findings that age information is present in the human gait. Our proposed approach allows rather robust estimations of age based on the inertial data of a single step, as the used data consist of those collected on different ground surfaces, and the participants were also told to walk pretending different emotional states. The findings on the existing data point out the change of gait while aging, which will also imply that person identification using the gait depends on data that is not too old.

Novel mathematical models of three different repressilator topologies are introduced. As designable transcription factors have been shown to bind to DNA non-cooperatively, we have chosen models containing non-cooperative elements. The extended topologies involve three additional transcription regulatory elements—which can be easily implemented by synthetic biology—forming positive feedback loops. This increases the number of variables to six, and extends the complexity of the equations in the model. To perform our analysis we had to use combinations of modern symbolic algorithms of computer algebra systems Mathematica and Singular . The study shows that all the three models have simple dynamics that can also be called regular behaviour: they have a single asymptotically stable steady state with small amplitude damping oscillations in the 3D case and no oscillation in one of the 6D cases and damping oscillation in the second 6D case. Using the program QeHopf we were able to exclude the presence of Hopf bifurcation in the 3D system.

​This book constitutes the proceedings of the 19th International Workshop on Computer Algebra in Scientific Computing, CASC 2017, held

We consider the problem of determining multiple steady states for positive real values in models of biological networks. Investigating the potential for these in models of the mitogen-activated protein kinases (MAPK) network has consumed considerable effort using special insights into the structure of corresponding models. Here we apply combinations of symbolic computation methods for mixed equality/inequality systems, specifically virtual substitution, lazy real triangularization and cylindrical algebraic decomposition. We determine multistationarity of an 11-dimensional MAPK network when numeric values are known for all but potentially one parameter. More precisely, our considered model has 11 equations in 11 variables and 19 parameters, 3 of which are of interest for symbolic treatment, and furthermore positivity conditions on all variables and parameters.

We investigate models of the mitogenactivated protein kinases (MAPK) network, with the aim of determining where in parameter space there exist multiple positive steady states. We build on recent progress which combines various symbolic computation methods for mixed systems of equalities and inequalities. We demonstrate that those techniques benefit tremendously from a newly implemented graph theoretical symbolic preprocessing method. We compare computation times and quality of results of numerical continuation methods with our symbolic approach before and after the application of our preprocessing.

We present efficient algorithmic methods to detect Hopf bifurcation fixed points in chemical reaction networks with symbolic rate constants, thereby yielding information about the oscillatory behavior of the networks. Our methods use the representations of the systems on convex coordinates that arise from stoichiometric network analysis. One of our methods then reduces the problem of determining the existence of Hopf bifurcation fixed points to a first-order formula over the ordered field of the reals that can be solved using computational logic packages. The second method uses ideas from tropical geometry to formulate a more efficient method that is incomplete in theory but worked very well for the examples that we have attempted; we have shown it to be able to handle systems involving more than 20 species.

We build on our previous work to compute Hopf bifurcation fixed points for chemical reaction systems on the basis of reaction coordinates. For determining the existence of Hopf bifurcations the main algorithmic problem is to determine whether a single multivariate polynomial has a zero for positive coordinates. For this purpose we provide heuristics on the basis of the Newton polytope that ensure the existence of positive and negative values of the polynomial for positive coordinates. We apply our method to the example of the Methylene Blue Oscillator (MBO).

Given a bio-chemical reaction network, we discuss the different algebraic entities e.g. stoichiometric matrix, polynomial system, deficiency and flux cones which are prerequisite for the application of various algebraic methods to qualitatively analyse them. We compute these entities on the examples obtained from two publicly available bio-databases called Biomodels and KEGG. The computations involve the use of computer algebra tools (e.g. polco, polymake). The results consisting of mostly matrices are arranged in form of a derived database called PoCaB (Platform of Chemical and Biological data). We also present a visualization program to visualize the extreme currents of the flux cone. We hope this will aid in the development of methods relevant for computational systems biology involving computer algebra. The database is publicly available at http://pocab.cg.cs.uni-bonn.de/

We study Muldowney's extension of the classical Bendixson-Dulac criterion for excluding periodic orbits to higher dimensions for polynomial vector fields. Using the formulation of Muldowney's sufficient criteria for excluding periodic orbits of the parameterized vector field on a convex set as a quantifier elimination problem over the ordered field of the reals we provide case studies of some systems arising in the life sciences. We discuss the use of simple conservation constraints and the use of parametric constraints for describing simple convex polytopes on which periodic orbits can be excluded by Muldowney's criteria.