Institutes
Refine
Document Type
- Article (54) (remove)
Language
- English (54)
Has Fulltext
- yes (54)
Is part of the Bibliography
- no (54)
Keywords
- mathematics education (3)
- Artificial intelligence (2)
- Experimental nuclear physics (2)
- Experimental particle physics (2)
- Machine learning (2)
- Positive polynomials (2)
- Sums of arithmetic-geometric exponentials (2)
- 11N45 (1)
- 14N10 (secondary) (1)
- 2-SAT (1)
- 30F30 (1)
- 32G15 (primary) (1)
- Algebraic Hodge polynomial (1)
- Anemia management (1)
- Annotation (1)
- Arithmetic-geometric exponentials (1)
- Augmented reality (1)
- BIOfid (1)
- Belief Propagation (1)
- Biodiversity (1)
- Biological sciences (1)
- Blood loss calculator (1)
- Blood loss formula (1)
- Blood management (1)
- Boundary elements (1)
- COGNIMUSE (1)
- COVID-19 pandemic (1)
- Calderón operator (1)
- Changes in labor markets (1)
- Convexity (1)
- Convolution quadrature (1)
- Curvature measure (1)
- Cycle class (1)
- Diagnostic markers (1)
- Distributional super-solution (1)
- Dual cone (1)
- Exponential sums (1)
- Finite elements (1)
- Finitely many measurements (1)
- Fractional Laplacian (1)
- Functional magnetic resonance imaging (1)
- Future of work (1)
- GABAergic (1)
- Gale-dual pairs (1)
- Hadron-hadron interactions (1)
- Hardy’s inequality (1)
- Higher education (1)
- Hodge conjecture (1)
- Hopf boundary lemma (1)
- Human factors (1)
- Human-enhancing technologies (1)
- Immunology (1)
- Individual differences (1)
- Intelligence augmentation (1)
- Inter-annotator agreement (1)
- Inverse Problem (1)
- K–12 (1)
- Lattice path matroids (1)
- Leapfrog (1)
- Learning analytics (1)
- Limit mixed Hodge structures (1)
- Linear regression analysis (1)
- Lipschitz–Killing measures (1)
- Loewner order (1)
- Log convex sets (1)
- MathCityMap (1)
- Mathematical biosciences (1)
- MediaEval 2016 (1)
- Moduli space of semi-stable sheaves (1)
- Mollifier decorrelation (1)
- Mollifier multiscale reconstruction and decomposition (1)
- Monotonicity (1)
- Multiparametric MRI (1)
- Multiplicative convexity (1)
- Named entity recognition (1)
- Neural networks (1)
- Neuroscience (1)
- Nodal curves (1)
- Non-negativity certificate (1)
- Nonlinear Schrödinger equation (1)
- Nonlocal Neumann conditions (1)
- Nonlocal normal derivative (1)
- Nonlocal operators (1)
- OpenStreetMap quality evaluation (1)
- Orbital stability (1)
- Perfect graphs (1)
- Permutation (1)
- Pointwise super-solution (1)
- Polyhedron (1)
- Positive function (1)
- Positive signomials (1)
- Potential methods in exploration (1)
- Preclinical research (1)
- Predictive markers (1)
- Prognostic markers (1)
- Prostate cancer (1)
- Pseudo-Riemannian manifolds (1)
- Radiomics (1)
- Reflexive polytopes (1)
- Regional Laplacian (1)
- Regional fractional Laplacian (1)
- Relativistic heavy-ion collisions (1)
- STEM education (1)
- Second-order cone (1)
- Semantic portal (1)
- Semantics (1)
- Sensory perception (1)
- Sign-changing solutions (1)
- Signed Birkhoff polytopes (1)
- Simplicial complexes (1)
- Specialized information service (1)
- Standard monomials (1)
- Standing waves (1)
- Student expectations (1)
- Sublinear circuit (1)
- Sums of non-negative circuit polynomials (1)
- Sums of nonnegative circuit polynomials (SONC) (1)
- Surgical blood loss (1)
- Symmetries (1)
- Taxon (1)
- Thermoelastic wave equation (1)
- Translational research (1)
- Transparent boundary conditions (1)
- Unconditional polytopes (1)
- Unimodular triangulations (1)
- Valuation (1)
- Virtual reality (1)
- Vision (1)
- Visual cortex (1)
- Wavelet decomposition (1)
- Weak super-solution (1)
- Weyl principle (1)
- affective computing (1)
- algebraic thinking (1)
- algorithms (1)
- autoregressive GANs (1)
- barrel cortex (1)
- chatbots (1)
- co-located collaboration analytics (1)
- collaboration (1)
- collaboration analytics (1)
- computational thinking (1)
- computer vision (1)
- density maps (1)
- density visualization (1)
- digital distractions (1)
- digital learning (1)
- digitization (1)
- disaster risk management (1)
- distance learning (1)
- domains (1)
- education (1)
- educational technology (1)
- emotion generation (1)
- emotion prediction (1)
- equity and access to technology (1)
- field mapping (1)
- field papers (1)
- flood risk perception (1)
- flooding (1)
- generic tasks (1)
- group speech analytics (1)
- inquiry-based education (1)
- interactive data analysis (1)
- literature review (1)
- math trails (1)
- media multitasking (1)
- multimodal fusion (1)
- multimodal learning analytics (1)
- neural networks (1)
- neuronal morphology (1)
- outdoor activities (1)
- outdoors (1)
- pedagogical roles (1)
- point inversion (1)
- positivity preserving property (1)
- problem solving (1)
- real world problems ; (1)
- satisfiability problem (1)
- self-attention (1)
- self-control (1)
- self-regulation (1)
- synaptogenesis (1)
- synchronous teaching (1)
- task design (1)
- teaching with technology (1)
- technology-enhanced learning (1)
- torsion function (1)
- video prediction (1)
- visual programming (1)
- 𝒮-cone (1)
Institute
We show explicit formulas for the evaluation of (possibly higher-order) fractional Laplacians (-△)ˢ of some functions supported on ellipsoids. In particular, we derive the explicit expression of the torsion function and give examples of s-harmonic functions. As an application, we infer that the weak maximum principle fails in eccentric ellipsoids for s ∈ (1; √3 + 3/2) in any dimension n ≥ 2. We build a counterexample in terms of the torsion function times a polynomial of degree 2. Using point inversion transformations, it follows that a variety of bounded and unbounded domains do not satisfy positivity preserving properties either and we give some examples.
A convex body is unconditional if it is symmetric with respect to reflections in all coordinate hyperplanes. We investigate unconditional lattice polytopes with respect to geometric, combinatorial, and algebraic properties. In particular, we characterize unconditional reflexive polytopes in terms of perfect graphs. As a prime example, we study the signed Birkhoff polytope. Moreover, we derive constructions for Gale-dual pairs of polytopes and we explicitly describe Gröbner bases for unconditional reflexive polytopes coming from partially ordered sets.
Adaptive, synchronous, and mobile online education: developing the ASYMPTOTE learning environment
(2022)
The COVID-19-induced distance education was perceived as highly challenging by teachers and students. A cross-national comparison of five European countries identified several challenges occurred during the distance learning period. On this basis, the article aims to develop a theoretical framework and design requirements for distance and online learning tools. As one example for online learning in mathematics education, the ASYMPTOTE system is introduced. It will be freely available by May 2022. ASYMPTOTE is aimed at the adaptive and synchronous delivery of online education by taking a mobile learning approach. Its core is the so-called digital classroom, which not only allows students to interact with each other or with the teacher but also enables teachers to monitor their students’ work progress in real time. With respect to the theoretical framework, this article analyses to what extent the ASYMPTOTE system meets the requirements of online learning. Overall, the digital classroom can be seen as a promising tool for teachers to carry out appropriate formative assessment and—partly—to maintain personal and content-related interaction at a distance. Moreover, we highlight the availability of this tool. Due to its mobile learning approach, almost all students will be able to participate in lessons conducted with ASYMPTOTE.
FEM–BEM coupling for the thermoelastic wave equation with transparent boundary conditions in 3D
(2022)
We consider the thermoelastic wave equation in three dimensions with transparent boundary conditions on a bounded, not necessarily convex domain. In order to solve this problem numerically, we introduce a coupling of the thermoelastic wave equation in the interior domain with time-dependent boundary integral equations. Here, we want to highlight that this type of problem differs from other wave-type problems that dealt with FEM–BEM coupling so far, e.g., the acoustic as well as the elastic wave equation, since our problem consists of coupled partial differential equations involving a vector-valued displacement field and a scalar-valued temperature field. This constitutes a nontrivial challenge which is solved in this paper. Our main focus is on a coercivity property of a Calderón operator for the thermoelastic wave equation in the Laplace domain, which is valid for all complex frequencies in a half-plane. Combining Laplace transform and energy techniques, this coercivity in the frequency domain is used to prove the stability of a fully discrete numerical method in the time domain. The considered numerical method couples finite elements and the leapfrog time-stepping in the interior with boundary elements and convolution quadrature on the boundary. Finally, we present error estimates for the semi- and full discretization.
The development of epilepsy (epileptogenesis) involves a complex interplay of neuronal and immune processes. Here, we present a first-of-its-kind mathematical model to better understand the relationships among these processes. Our model describes the interaction between neuroinflammation, blood-brain barrier disruption, neuronal loss, circuit remodeling, and seizures. Formulated as a system of nonlinear differential equations, the model reproduces the available data from three animal models. The model successfully describes characteristic features of epileptogenesis such as its paradoxically long timescales (up to decades) despite short and transient injuries or the existence of qualitatively different outcomes for varying injury intensity. In line with the concept of degeneracy, our simulations reveal multiple routes toward epilepsy with neuronal loss as a sufficient but non-necessary component. Finally, we show that our model allows for in silico predictions of therapeutic strategies, revealing injury-specific therapeutic targets and optimal time windows for intervention.
AttendAffectNet-emotion prediction of movie viewers using multimodal fusion with self-attention
(2021)
In this paper, we tackle the problem of predicting the affective responses of movie viewers, based on the content of the movies. Current studies on this topic focus on video representation learning and fusion techniques to combine the extracted features for predicting affect. Yet, these typically, while ignoring the correlation between multiple modality inputs, ignore the correlation between temporal inputs (i.e., sequential features). To explore these correlations, a neural network architecture—namely AttendAffectNet (AAN)—uses the self-attention mechanism for predicting the emotions of movie viewers from different input modalities. Particularly, visual, audio, and text features are considered for predicting emotions (and expressed in terms of valence and arousal). We analyze three variants of our proposed AAN: Feature AAN, Temporal AAN, and Mixed AAN. The Feature AAN applies the self-attention mechanism in an innovative way on the features extracted from the different modalities (including video, audio, and movie subtitles) of a whole movie to, thereby, capture the relationships between them. The Temporal AAN takes the time domain of the movies and the sequential dependency of affective responses into account. In the Temporal AAN, self-attention is applied on the concatenated (multimodal) feature vectors representing different subsequent movie segments. In the Mixed AAN, we combine the strong points of the Feature AAN and the Temporal AAN, by applying self-attention first on vectors of features obtained from different modalities in each movie segment and then on the feature representations of all subsequent (temporal) movie segments. We extensively trained and validated our proposed AAN on both the MediaEval 2016 dataset for the Emotional Impact of Movies Task and the extended COGNIMUSE dataset. Our experiments demonstrate that audio features play a more influential role than those extracted from video and movie subtitles when predicting the emotions of movie viewers on these datasets. The models that use all visual, audio, and text features simultaneously as their inputs performed better than those using features extracted from each modality separately. In addition, the Feature AAN outperformed other AAN variants on the above-mentioned datasets, highlighting the importance of taking different features as context to one another when fusing them. The Feature AAN also performed better than the baseline models when predicting the valence dimension.
Linking mathematics with reality is not new. It is also not new to use outdoor activities to learn mathematics. It seems to be new, to combine such mathematical outdoor activities with mobile technology, like the geocache community which makes use of GPS technology to guide their members to special places and points of interest. The use of mobile technologies to learn at any time and any location is known as “mobile learning”. This type of learning can be seen as an extension of eLearning. Considering the definition of O’Malley one notices that this definition does not exactly match with the idea of the MathCityMap-Project (MCM), because the learning environment in the MCM-Project is predetermined. Combined with the math trail method the project enables mobile learning within math trails with latest technology.In the MCM-Project students experience mathematics at real places and within real situations in out-of-school activities,with help of GPS-enabled smartphones and special math problems. In contrast to the paper versions of math trails we are able to give direct feedback on the solutions by using “mobile devices” such as smartphones or tablets. If the user has difficulties in solving the modeling task, stepped hints can be provided. The teacher is able to use the MCM-Portal to upload tasks developed by himself or by his students and he is also able to build a personal math trail for his students.
The present paper is concerned with the half-space Dirichlet problem [...] where ℝ𝑁+:={𝑥∈ℝ𝑁:𝑥𝑁>0} for some 𝑁≥1 and 𝑝>1, 𝑐>0 are constants. We analyse the existence, non-existence and multiplicity of bounded positive solutions to (𝑃𝑐). We prove that the existence and multiplicity of bounded positive solutions to (𝑃𝑐) depend in a striking way on the value of 𝑐>0 and also on the dimension N. We find an explicit number 𝑐𝑝∈(1,𝑒√), depending only on p, which determines the threshold between existence and non-existence. In particular, in dimensions 𝑁≥2, we prove that, for 0<𝑐<𝑐𝑝, problem (𝑃𝑐) admits infinitely many bounded positive solutions, whereas, for 𝑐>𝑐𝑝, there are no bounded positive solutions to (𝑃𝑐).
Nowadays, digitalization has an immense impact on the landscape of jobs. This technological revolution creates new industries and professions, promises greater efficiency and improves the quality of working life. However, emerging technologies such as robotics and artificial intelligence (AI) are reducing human intervention, thus advancing automation and eliminating thousands of jobs and whole occupational images. To prepare employees for the changing demands of work, adequate and timely training of the workforce and real-time support of workers in new positions is necessary. Therefore, it is investigated whether user-oriented technologies, such as augmented reality (AR) and virtual reality (VR) can be applied “on-the-job” for such training and support—also known as intelligence augmentation (IA). To address this problem, this work synthesizes results of a systematic literature review as well as a practically oriented search on augmented reality and virtual reality use cases within the IA context. A total of 150 papers and use cases are analyzed to identify suitable areas of application in which it is possible to enhance employees' capabilities. The results of both, theoretical and practical work, show that VR is primarily used to train employees without prior knowledge, whereas AR is used to expand the scope of competence of individuals in their field of expertise while on the job. Based on these results, a framework is derived which provides practitioners with guidelines as to how AR or VR can support workers at their job so that they can keep up with anticipated skill demands. Furthermore, it shows for which application areas AR or VR can provide workers with sufficient training to learn new job tasks. By that, this research provides practical recommendations in order to accompany the imminent distortions caused by AI and similar technologies and to alleviate associated negative effects on the German labor market.