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- ItemAudio Ontologies for Intangible Cultural Heritage(Bramhall, Stockport ; EasyChair Ltd., 2022-04-12) Tan, Mary Ann; Posthumus, Etienne; Sack, HaraldCultural heritage portals often contain intangible objects digitized as audio files. This paper presents and discusses the adaptation of existing audio ontologies intended for non-cultural heritage applications. The resulting alignment of the German Digital Library-Europeana Data Model (DDB-EDM) with Music Ontology (MO) and Audio Commons Ontology (ACO) is presented.
- ItemFrom Floppy Disks to 5-Star LOD: FAIR Research Infrastructure for NFDI4Culture(Köln : ZB MED, 2023) Tietz, Tabea; Bruns, Oleksandra; Söhn, Linnaea; Tolksdorf, Julia; Posthumus, Etienne; Steller, Jonatan Jalle; Fliegl, Heike; Norouzi, Ebrahim; Waitelonis, Jörg; Schrade, Torsten; Sack, HaraldNFDI4Culture is establishing an infrastructure for research data on material and immaterial cultural heritage in the context of the German National Research Data Infrastructure (NFDI) in compliance with the FAIR principles. The NFDI4Culture Knowledge Graph is developed and integrated with the Culture Information Portal to aggregate diverse and isolated data from the culture research landscape and thereby increase the discoverability, interoperability and reusability of cultural heritage data. This paper presents the research data management strategy in the long-term project NFDI4Culture, which combines a CMS and a Knowledge Graph-based infrastructure to enable an intuitive and meaningful interaction with research resources in the cultural heritage domain.
- ItemGenealogical properties of spatial models in Population Genetics(Hannover : Technische Informationsbibliothek, 2023-09) Wirtz, JohannesAt the interface between Phylo- and Population Genetics, and recently heavily inspired by Epidemonology, the discipline of Phylogeography comprises modelling techniques from classical theoretical biology and combines them with a spatial (2D or 3D) aspect, with the purpose of utilizing geographical information in the analysis to understand the evolutionary history of a biological system or aspects of virology such as directionality and seasonality in pandemic outbreaks [1, 2, 3, 4]. An prime example of this are datasets that take into account the sampling locations of its components (geo-referenced genomic data). In this project, we have focused on the model called "spatial Lambda-Fleming-Viot process" ( V [5, 6]) and analzed its statistical properties forward in time as well as in the ancestral (dual) process, with results that may be used for parameter inference. Of particlar interest was the spatial variance, denoted , a parameter controlling the speed at which genetic information is spread across space and therefore an analog of the reproduction number (R0) used in epidemonology e.g. to assess the infectiousness of differing viral strains. We explored the relation of this parameter to the time to coalescence between lineage pairs in this model and described methods of estimating it from sampled data under different circumstances. We have furthermore investigated similarities and differences between this model and classical models in Population Genetics, particularly Birth-Death processes, which are heavily used for all kinds of biological inference problems, but do not by themselves feature a spatial component. We compared the Vto a variant of the Birth-Death process where the location of a live individual changes over the course of its lifetime according to a Brownian motion. This process is not as easily viewed backward in time as the V, but the genalogical process is accessible by Markov-Chain Monte Carlosimulation, as the likelihoods of ancestral positions and branch lengths are easily calculated, making this model easily applicable to data. Our analysis highlights the analogy between the two processes forward in time as well as backward in time; on the other hand, we also observed a divergent behavior of the two models when no prior on the phylogenetic time scale was assumed. Lastly, this project has given rise to a study of combinatorial properties of tree shapes relevant to the V, the Birth-Death and other biological processes. In particular, we were able to identify the combinatorial class genealogical trees generated from these processes belong to and verify a conjecture regarding their enumeration. Preliminary versions of software tools for the aforementioned inference have also been provided.
- ItemAuditory cortex modelled as a dynamical network of oscillators: Understanding event-related fields and their adaptation(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2021) Hajizadeh, Aida; Matysiak, Artur; Wolfrum, Matthias; May, Patrick J. C.Adaptation, the reduction of neuronal responses by repetitive stimulation, is a ubiquitous feature of auditory cortex (AC). It is not clear what causes adaptation, but short-term synaptic depression (STSD) is a potential candidate for the underlying mechanism. We examined this hypothesis via a computational model based on AC anatomy, which includes serially connected core, belt, and parabelt areas. The model replicates the event-related field (ERF) of the magnetoencephalogram as well as ERF adaptation. The model dynamics are described by excitatory and inhibitory state variables of cell populations, with the excitatory connections modulated by STSD. We analysed the system dynamics by linearizing the firing rates and solving the STSD equation using time-scale separation. This allows for characterization of AC dynamics as a superposition of damped harmonic oscillators, so-called normal modes. We show that repetition suppression of the N1m is due to a mixture of causes, with stimulus repetition modifying both the amplitudes and the frequencies of the normal modes. In this view, adaptation results from a complete reorganization of AC dynamics rather than a reduction of activity in discrete sources. Further, both the network structure and the balance between excitation and inhibition contribute significantly to the rate with which AC recovers from adaptation. This lifetime of adaptation is longer in the belt and parabelt than in the core area, despite the time constants of STSD being spatially constant. Finally, we critically evaluate the use of a single exponential function to describe recovery from adaptation.
- ItemQuantum symmetry(Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach gGmbH, 2020) Caspers, MartijnThe symmetry of objects plays a crucial role in many branches of mathematics and physics. It allowed, for example, the early prediction of the existence of new small particles. “Quantum symmetry” concerns a generalized notion of symmetry. It is an abstract way of characterizing the symmetry of a much richer class of mathematical and physical objects. In this snapshot we explain how quantum symmetry emerges as matrix symmetries using a famous example: Mermin’s magic square. It shows that quantum symmetries can solve problems that lie beyond the reach of classical symmetries, showing that quantum symmetries play a central role in modern mathematics.
- ItemDeterminacy versus indeterminacy(Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach gGmbH, 2020) Berg, ChristianCan a continuous function on an interval be uniquely determined if we know all the integrals of the function against the natural powers of the variable? Following Weierstrass and Stieltjes, we show that the answer is yes if the interval is finite, and no if the interval is infinite.
- ItemEmergence in biology and social sciences(Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach gGmbH, 2022) Hoffmann, Franca; Merino-Aceituno, SaraMathematics is the key to linking scientific knowledge at different scales: from microscopic to macroscopic dynamics. This link gives us understanding on the emergence of observable patterns like flocking of birds, leaf venation, opinion dynamics, and network formation, to name a few. In this article, we explore how mathematics is able to traverse scales, and in particular its application in modelling collective motion of bacteria driven by chemical signalling.
- ItemWeak-strong uniqueness for energy-reaction-diffusion systems(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2021) Hopf, KatharinaWe establish weak-strong uniqueness and stability properties of renormalised solutions to a class of energy-reaction-diffusion systems, which genuinely feature cross-diffusion effects. The systems considered are motivated by thermodynamically consistent models, and their formal entropy structure allows us to use as a key tool a suitably adjusted relative entropy method. Weak-strong uniqueness is obtained for general entropy-dissipating reactions without growth restrictions, and certain models with a non-integrable diffusive flux. The results also apply to a class of (isoenergetic) reaction-cross-diffusion systems.
- ItemNumerical analysis for nematic electrolytes(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2020) Baňas, L'ubomír; Lasarzik, Robert; Prohl, AndreasWe consider a system of nonlinear PDEs modeling nematic electrolytes, and construct a dissipative solution with the help of its implementable, structure-inheriting space-time discretization. Computational studies are performed to study the mutual effects of electric, elastic, and viscous effects onto the molecules in a nematic electrolyte.
- ItemFast reaction limits via $Gamma$-convergence of the flux rate functional(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2020) Peletier, Mark A.; Renger, D. R. MichielWe study the convergence of a sequence of evolution equations for measures supported on the nodes of a graph. The evolution equations themselves can be interpreted as the forward Kolmogorov equations of Markov jump processes, or equivalently as the equations for the concentrations in a network of linear reactions. The jump rates or reaction rates are divided in two classes; `slow' rates are constant, and `fast' rates are scaled as 1/∈, and we prove the convergence in the fast-reaction limit ∈ → 0. We establish a Γ-convergence result for the rate functional in terms of both the concentration at each node and the flux over each edge (the level-2.5 rate function). The limiting system is again described by a functional, and characterizes both fast and slow fluxes in the system. This method of proof has three advantages. First, no condition of detailed balance is required. Secondly, the formulation in terms of concentration and flux leads to a short and simple proof of the Γ-convergence; the price to pay is a more involved compactness proof. Finally, the method of proof deals with approximate solutions, for which the functional is not zero but small, without any changes.