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- ItemDFG Final Report for Automatic Fact Checking for Biomedical Information in Social Media and Scientific Literature (FIBISS), project number 667374(Hannover : Technische Informationsbibliothek, 2025-04-10) Klinger, Roman; Wührl, AmelieResearch into methods for the automatic verification of facts, i.e., computational models that can distinguish correct information from misinformation or disinformation, is largely focused on the news domain and on the analysis of posts in social media. Among other things, texts are checked for their truthfulness. This can be done by analyzing linguistic features that suggest an intention to deceive or by comparing them with other sources that make comparable statements in terms of content. Most studies focus on politically relevant areas. The biomedical domain is also an area of particular social relevance. In social media, various actors and medical laypersons share reports on treatment methods, successes and failures, such as the (disproven) method of treating viral infections with deworming agents or disinfectants. There are also reports on (disproven) links between treatments and adverse effects, such as the causation of autism by vaccination. However, the biomedical domain, unlike other areas relevant for automated fact checking, benefits from a large resource of reliable scientific articles. The aim of the FIBISS project was therefore to develop and evaluate methods that can extract biomedical claims in social media and compare them with reliable sources. One challenge here is that social media does not typically use technical language, so different vocabularies have to be combined. The approach in FIBISS was therefore to develop generalizing information extraction methods. In the course of the project, large language models also became prominent as a further methodological approach. The project was therefore adapted to optimize general representations of claims in such a way that they are suitable for comparison using automatic fact-checking procedures. As a result, we contribute text corpora that are used to develop and evaluate automated biomedical fact-checking systems. We propose methods that automatically reformulate claims so that they are suitable to be automatically verified. Furthermore, we present approaches that can automatically assess the credibility of claims, even independently of existing evidence.
- ItemFinal Report of the DFG Project "Drawing Graphs: Geometric Aspects Beyond Planarity" (project number 654838)(Hannover : Technische Informationsbibliothek, 2025-04) Wolff, AlexanderThe aim of our project was to get a better understanding of the mathematical structures that correspond to the different ways of measuring the visual complexity of a drawing of a graph. Examples for such measures are the local crossing number, that is, the maximum number of crossings per edge, the slope number, that is, the number of different slopes in a crossing-free straight-line drawing, the segment number or the line cover number, that is, the number of straight-line segments or straight lines needed to cover a crossing-free straight-line drawing. For a graph, the measures are defined as the minimum over all drawings (of the corresponding type). The center of our studies became the measure segment number, which is known to be NP-hard to compute. In particular, we showed that there is a parameterized algorithm for computing the segment number of a given graph with respect to the several parameters; the natural parameter, the line cover number, and the vertex cover number. The latter proof was the technically most challenging. In a different work, we showed that it is ETR-complete to compute the segment number of a given graph, that is, the segment number of a graph can be expressed in terms of the existential theory of the reals, but its computation is at least as hard as every problem in the complexity class ETR. Moreover, we extended a result concerning the segment number of triconnected cu- bic planar graphs by showing that the segment number of every triconnected 4-regular planar graph with n vertices is at most n + 3, which is tight up to the additive constant. We have proved the first linear universal lower bounds for the segment number of out- erpaths, maximal outerplanar graphs, 2-trees, and planar 3-trees. This shows that the existing algorithms for these graph classes are in fact constant-factor approximation algorithms. For maximal outerpaths, our universal lower bound is best possible.
- ItemMultiscale phenomena: Green's functions, the Dirichlet-to-Neumann formulation, subgrid scale models, bubbles and the origins of stabilized methods(Amsterdam [u.a.] : Elsevier Science, 1995) Hughes, Thomas J. R.An approach is developed for deriving variational methods capable of representing multiscale phenomena. The ideas are first illustrated on the exterior problem for the Helmholtz equation. This leads to the well-known Dirichlet-to-Neumann formulation. Next, a class of subgrid scale models is developed and the relationships to 'bubble function' methods and stabilized methods are established. It is shown that both the latter methods are approximate subgrid scale models. The identification for stabilized methods leads to an analytical formula for τ, the 'intrinsic time scale', whose origins have been a mystery heretofore. © 1995.
- ItemImplementation of an adaptive BDF2 formula and comparison with the MATLAB Ode15s(Amsterdam [u.a.] : Elsevier, 2014) Celaya, E. Alberdi; Aguirrezabala, J. J. Anza; Chatzipantelidis, P.After applying the Finite Element Method (FEM) to the diffusion-type and wave-type Partial Differential Equations (PDEs), a first order and a second order Ordinary Differential Equation (ODE) systems are obtained respectively. These ODE systems usually present high stiffness, so numerical methods with good stability properties are required in their resolution. MATLAB offers a set of open source adaptive step functions for solving ODEs. One of these functions is the ode15s recommended to solve stiff problems and which is based on the Backward Differentiation Formulae (BDF). We describe the error estimation and the step size control implemented in this function. The ode15s is a variable order algorithm, and even though it has an adaptive step size implementation, the advancing formula and the local error estimation that uses correspond to the constant step size formula. We have focused on the second order accurate and unconditionally stable BDF (BDF2) and we have implemented a real adaptive step size BDF2 algorithm using the same strategy as the BDF2 implemented in the ode15s, resulting the new algorithm more efficient than the one implemented in MATLAB. © The Authors. Published by Elsevier B.V.
- ItemThe finite volume-complete flux scheme for advection-diffusion-reaction equations(New York, NY [u.a.] : Springer Science + Business Media B.V., 2010) ten Thije Boonkkamp, J. H. M.; Anthonissen, M. J. H.We present a new finite volume scheme for the advection-diffusion-reaction equation. The scheme is second order accurate in the grid size, both for dominant diffusion and dominant advection, and has only a three-point coupling in each spatial direction. Our scheme is based on a new integral representation for the flux of the one-dimensional advection-diffusion-reaction equation, which is derived from the solution of a local boundary value problem for the entire equation, including the source term. The flux therefore consists of two parts, corresponding to the homogeneous and particular solution of the boundary value problem. Applying suitable quadrature rules to the integral representation gives the complete flux scheme. Extensions of the complete flux scheme to two-dimensional and time-dependent problems are derived, containing the cross flux term or the time derivative in the inhomogeneous flux, respectively. The resulting finite volume-complete flux scheme is validated for several test problems. © 2010 The Author(s).