Multivariate signal processing is often based on dimensionality reduction techniques. We propose a new method, Dynamical Component Analysis (DyCA), leading to a classification of the underlying dynamics and -for a certain type of dynamics -to a signal subspace representing the dynamics of the data. In this paper the algorithm is derived leading to a generalized eigenvalue problem of correlation matrices. The application of the DyCA on high-dimensional chaotic signals is presented both for simulated data as well as real EEG data of epileptic seizures.

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Dynamical Component Analysis (DyCA) is a recentlyproposed method to detect projection vectors to reduce the dimensionality of multi-variate deterministic datasets. It is based on the solution of a generalized eigenvalue problem and therefore straight forward to implement. DyCA is introduced and applied to EEG data of epileptic seizures. The obtained eigenvectors are used to project the signal and the corresponding trajectories in phase space are compared with PCA and ICA-projections. The eigenvalues of DyCA are utilized for seizure detection and the obtained results in terms of specificity, false discovery rate and miss rate are compared to other seizure detection algorithms.

COVID-19 poses a major challenge to individuals and societies around the world. Yet, it is difficult to obtain a good overview of studies across different medical fields of research such as clinical trials, epidemiology, and public health. Here, we describe a consensus metadata model to facilitate structured searches of COVID-19 studies and resources along with its implementation in three linked complementary web-based platforms. A relational database serves as central study metadata hub that secures compatibilities with common trials registries (e.g. ICTRP and standards like HL7 FHIR, CDISC ODM, and DataCite). The Central Search Hub was developed as a single-page application, the other two components with additional frontends are based on the SEEK platform and MICA, respectively. These platforms have different features concerning cohort browsing, item browsing, and access to documents and other study resources to meet divergent user needs. By this we want to promote transparent and harmonized COVID-19 research.

A lattice is a partially ordered set supporting a meet (or join) operation that returns the largest lower bound (smallest upper bound) of two elements. Just like graphs, lattices are a fundamental structure that occurs across domains including social data analysis, natural language processing, computational chemistry and biology, and database theory. In this paper we introduce discretelattice signal processing (DLSP), an SP framework for data, or signals, indexed by such lattices. We use the meet (or join) to define a shift operation and derive associated notions of filtering, Fourier basis and transform, and frequency response. We show that the spectrum of a lattice signal inherits the lattice structure of the signal domain and derive a sampling theorem. Finally, we show two prototypical applications: spectral analysis of formal concept lattices in social science and sampling and Wiener filtering of multiset lattices in combinatorial auctions. Formal concept lattices are a compressed representation of relations between objects and attributes. Since relations are equivalent to bipartite graphs and hypergraphs, DLSP offers a form of Fourier analysis for these structures.