Informatik und Mathematik
Refine
Document Type
- Article (16)
Language
- English (16)
Has Fulltext
- yes (16)
Is part of the Bibliography
- no (16)
Keywords
Institute
- Informatik (7)
- Informatik und Mathematik (5)
- Mathematik (4)
- Gesellschaftswissenschaften (1)
- Medizin (1)
Cone photoreceptor cells are wavelength-sensitive neurons in the retinas of vertebrate eyes and are responsible for color vision. The spatial distribution of these nerve cells is commonly referred to as the cone photoreceptor mosaic. By applying the principle of maximum entropy, we demonstrate the universality of retinal cone mosaics in vertebrate eyes by examining various species, namely, rodent, dog, monkey, human, fish, and bird. We introduce a parameter called retinal temperature, which is conserved across the retinas of vertebrates. The virial equation of state for two-dimensional cellular networks, known as Lemaître’s law, is also obtained as a special case of our formalism. We investigate the behavior of several artificially generated networks and the natural one of the retina concerning this universal, topological law.
Graph4Med: a web application and a graph database for visualizing and analyzing medical databases
(2022)
Background: Medical databases normally contain large amounts of data in a variety of forms. Although they grant significant insights into diagnosis and treatment, implementing data exploration into current medical databases is challenging since these are often based on a relational schema and cannot be used to easily extract information for cohort analysis and visualization. As a consequence, valuable information regarding cohort distribution or patient similarity may be missed. With the rapid advancement of biomedical technologies, new forms of data from methods such as Next Generation Sequencing (NGS) or chromosome microarray (array CGH) are constantly being generated; hence it can be expected that the amount and complexity of medical data will rise and bring relational database systems to a limit.
Description: We present Graph4Med, a web application that relies on a graph database obtained by transforming a relational database. Graph4Med provides a straightforward visualization and analysis of a selected patient cohort. Our use case is a database of pediatric Acute Lymphoblastic Leukemia (ALL). Along routine patients’ health records it also contains results of latest technologies such as NGS data. We developed a suitable graph data schema to convert the relational data into a graph data structure and store it in Neo4j. We used NeoDash to build a dashboard for querying and displaying patients’ cohort analysis. This way our tool (1) quickly displays the overview of patients’ cohort information such as distributions of gender, age, mutations (fusions), diagnosis; (2) provides mutation (fusion) based similarity search and display in a maneuverable graph; (3) generates an interactive graph of any selected patient and facilitates the identification of interesting patterns among patients.
Conclusion: We demonstrate the feasibility and advantages of a graph database for storing and querying medical databases. Our dashboard allows a fast and interactive analysis and visualization of complex medical data. It is especially useful for patients similarity search based on mutations (fusions), of which vast amounts of data have been generated by NGS in recent years. It can discover relationships and patterns in patients cohorts that are normally hard to grasp. Expanding Graph4Med to more medical databases will bring novel insights into diagnostic and research.
Geometry is part of the core of mathematics. It has been relevant ever since people have interacted with nature and its phenomena. Geometry’s relevance to the teaching and learning of mathematics can be emphasized, too. Nevertheless, a current potential shift in the topics of mathematics education to the detriment of geometry might be emerging. That is, other topics related to mathematics are seeming to grow in importance in comparison to geometry. Despite this, or perhaps because of it, geometry is an important component of current research in mathematics education. In the literature review, we elaborate relevant foci on the basis of current conference proceedings. By means of about 50 journal articles, five main topics are elaborated in more detail: geometric thinking and practices, geometric contents and topics, teacher education in geometry, argumentation and proof in geometry, as well as the use of digital tools for the teaching and learning of geometry. Conclusions and limitations for current and future research on geometry are formulated at the end of the article. In particular, the transfer to the practices of geometric teaching is explored on the basis of the elaborated research findings in order to combine both aspects of the teaching and learning of geometry.
We show that the non-Archimedean skeleton of the d-th symmetric power of a smooth projective algebraic curve X is naturally isomorphic to the d-th symmetric power of the tropical curve that arises as the non-Archimedean skeleton of X. The retraction to the skeleton is precisely the specialization map for divisors. Moreover, we show that the process of tropicalization naturally commutes with the diagonal morphisms and the Abel-Jacobi map and we exhibit a faithful tropicalization for symmetric powers of curves. Finally, we prove a version of the Bieri-Groves Theorem that allows us, under certain tropical genericity assumptions, to deduce a new tropical Riemann-Roch-Theorem for the tropicalization of linear systems.
Abstract: The human visual cortex enables visual perception through a cascade of hierarchical computations in cortical regions with distinct functionalities. Here, we introduce an AI-driven approach to discover the functional mapping of the visual cortex. We related human brain responses to scene images measured with functional MRI (fMRI) systematically to a diverse set of deep neural networks (DNNs) optimized to perform different scene perception tasks. We found a structured mapping between DNN tasks and brain regions along the ventral and dorsal visual streams. Low-level visual tasks mapped onto early brain regions, 3-dimensional scene perception tasks mapped onto the dorsal stream, and semantic tasks mapped onto the ventral stream. This mapping was of high fidelity, with more than 60% of the explainable variance in nine key regions being explained. Together, our results provide a novel functional mapping of the human visual cortex and demonstrate the power of the computational approach.
Author Summary: Human visual perception is a complex cognitive feat known to be mediated by distinct cortical regions of the brain. However, the exact function of these regions remains unknown, and thus it remains unclear how those regions together orchestrate visual perception. Here, we apply an AI-driven brain mapping approach to reveal visual brain function. This approach integrates multiple artificial deep neural networks trained on a diverse set of functions with functional recordings of the whole human brain. Our results reveal a systematic tiling of visual cortex by mapping regions to particular functions of the deep networks. Together this constitutes a comprehensive account of the functions of the distinct cortical regions of the brain that mediate human visual perception.
In 2020, Germany and Spain experienced lockdowns of their school systems. This resulted in a new challenge for learners and teachers: lessons moved from the classroom to the children’s homes. Therefore, teachers had to set rules, implement procedures and make didactical–methodical decisions regarding how to handle this new situation. In this paper, we focus on the roles of mathematics teachers in Germany and Spain. The article first describes how mathematics lessons were conducted using distance learning. Second, problems encountered throughout this process were examined. Third, teachers drew conclusions from their mathematics teaching experiences during distance learning. To address these research interests, a questionnaire was answered by N = 248 teachers (N1 = 171 German teachers; N2 = 77 Spanish teachers). Resulting from a mixed methods approach, differences between the countries can be observed, e.g., German teachers conducted more lessons asynchronously. In contrast, Spanish teachers used synchronous teaching more frequently, but still regard the lack of personal contact as a main challenge. Finally, for both countries, the digitization of mathematics lessons seems to have been normalized by the pandemic.
Co-design of a trustworthy AI system in healthcare: deep learning based skin lesion classifier
(2021)
This paper documents how an ethically aligned co-design methodology ensures trustworthiness in the early design phase of an artificial intelligence (AI) system component for healthcare. The system explains decisions made by deep learning networks analyzing images of skin lesions. The co-design of trustworthy AI developed here used a holistic approach rather than a static ethical checklist and required a multidisciplinary team of experts working with the AI designers and their managers. Ethical, legal, and technical issues potentially arising from the future use of the AI system were investigated. This paper is a first report on co-designing in the early design phase. Our results can also serve as guidance for other early-phase AI-similar tool developments.
The ongoing digitalization of educational resources and the use of the internet lead to a steady increase of potentially available learning media. However, many of the media which are used for educational purposes have not been designed specifically for teaching and learning. Usually, linguistic criteria of readability and comprehensibility as well as content-related criteria are used independently to assess and compare the quality of educational media. This also holds true for educational media used in economics. This article aims to improve the analysis of textual learning media used in economic education by drawing on threshold concepts. Threshold concepts are key terms in knowledge acquisition within a domain. From a linguistic perspective, however, threshold concepts are instances of specialized vocabularies, exhibiting particular linguistic features. In three kinds of (German) resources, namely in textbooks, in newspapers, and on Wikipedia, we investigate the distributive profiles of 63 threshold concepts identified in economics education (which have been collected from threshold concept research). We looked at the threshold concepts' frequency distribution, their compound distribution, and their network structure within the three kinds of resources. The two main findings of our analysis show that firstly, the three kinds of resources can indeed be distinguished in terms of their threshold concepts' profiles. Secondly, Wikipedia definitely shows stronger associative connections between economic threshold concepts than the other sources. We discuss the findings in relation to adequate media use for teaching and learning—not only in economic education.
Generic tasks for algorithms
(2020)
Due to its links to computer science (CS), teaching computational thinking (CT) often involves the handling of algorithms in activities, such as their implementation or analysis. Although there already exists a wide variety of different tasks for various learning environments in the area of computer science, there is less material available for CT. In this article, we propose so-called Generic Tasks for algorithms inspired by common programming tasks from CS education. Generic Tasks can be seen as a family of tasks with a common underlying structure, format, and aim, and can serve as best-practice examples. They thus bring many advantages, such as facilitating the process of creating new content and supporting asynchronous teaching formats. The Generic Tasks that we propose were evaluated by 14 experts in the field of Science, Technology, Engineering, and Mathematics (STEM) education. Apart from a general estimation in regard to the meaningfulness of the proposed tasks, the experts also rated which and how strongly six core CT skills are addressed by the tasks. We conclude that, even though the experts consider the tasks to be meaningful, not all CT-related skills can be specifically addressed. It is thus important to define additional tasks for CT that are detached from algorithms and programming.
Density visualization pipeline: a tool for cellular and network density visualization and analysis
(2020)
Neuron classification is an important component in analyzing network structure and quantifying the effect of neuron topology on signal processing. Current quantification and classification approaches rely on morphology projection onto lower-dimensional spaces. In this paper a 3D visualization and quantification tool is presented. The Density Visualization Pipeline (DVP) computes, visualizes and quantifies the density distribution, i.e., the “mass” of interneurons. We use the DVP to characterize and classify a set of GABAergic interneurons. Classification of GABAergic interneurons is of crucial importance to understand on the one hand their various functions and on the other hand their ubiquitous appearance in the neocortex. 3D density map visualization and projection to the one-dimensional x, y, z subspaces show a clear distinction between the studied cells, based on these metrics. The DVP can be coupled to computational studies of the behavior of neurons and networks, in which network topology information is derived from DVP information. The DVP reads common neuromorphological file formats, e.g., Neurolucida XML files, NeuroMorpho.org SWC files and plain ASCII files. Full 3D visualization and projections of the density to 1D and 2D manifolds are supported by the DVP. All routines are embedded within the visual programming IDE VRL-Studio for Java which allows the definition and rapid modification of analysis workflows.
