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Mathematisches Denken
No full textZahlreich sind die Vorgehensweisen zur Charakterisierung Mathematischen Denkens, Modelle, die durch zahlreiche Determinanten bestimmt sind. Das erste Kapitel widmet sich diesen Modellen.
Im zweiten Kapitel werden die einzelnen als Kategorien klassifizierten Determinanten Mathematischen Denkens diskutiert:
2.1 Kategorie Basic Ideas, Big Ideas, Fundamentale Ideen
2.2 Kategorie Grundvorstellungen
2.3 Kategorie Muster und Struktur
2.4 Kategorie Veranschaulichung
Im dritten Kapitel werden die spezifischen Formen Mathematischen Denkens in den Teildisziplinen diskutiert.
Das vierte Kapitel gilt dem Gedächtnis als Ort der Konstruktion bzw. Rekonstruktion von Wissen.
Mathematisches Denken bildet sich letztendlich in unterschiedlichen Persönlichkeitsmerkmalen ab. Wir differenzieren in …
• Kognitionspsychologische Merkmale wie INTELLIGENZ, KREATIVITÄT & UMGANG MIT MATHEMATIK,
• in ein Selbstbezogenes Merkmal wie das SELBSTKONZEPT,
• Handlungsbezogene Merkmale wie PERSISTENZ & INTERESSE
Origin of 182W Anomalies in Ocean Island Basalts
No full textOcean island basalts (OIB) show variable 182W deficits that have been attributed to either early differentiation of the mantle or core-mantle interaction. However, 182W variations may also reflect nucleosynthetic isotope heterogeneity inherited from Earth's building material, which would be evident from correlated 182W and 183W anomalies. Some datasets for OIB indeed show hints for such correlated variations, meaning that a nucleosynthetic origin of W isotope anomalies in OIB cannot be excluded. We report high-precision W isotope data for OIB from Samoa and Hawaii, which confirm previously reported 182W deficits for these samples, but also demonstrate that none of these samples have resolvable 183W anomalies. These data therefore rule out a nucleosynthetic origin of the 182W deficits in OIB, which most likely reflect the entrainment of either core material or an overabundance of late-accreted materials within OIB mantle sources. If these processes occurred over Earth's history, they may have also been responsible for shifting the 182W composition of the bulk mantle to its modern-day value. We also report Mo isotope data for some Hawaiian OIB, which reveal no resolved nucleosynthetic Mo isotopic anomalies. This is consistent with inheritance of 182W deficits in OIB from the addition of either core or late-accreted material, but only if these materials have a non-carbonaceous (NC) meteorite-like heritage. As such, these data rule out significant contributions of carbonaceous chondrite (CC)-like materials to either Earth's core or late accretion
Photoproducts of Porphyrins with a Focus on Protoporphyrin IX
No full textPorphyrins play important roles in biological systems including oxygen transport and catalysis. Due to their tetrapyrrole core structure, they exhibit exceptional photophysical and electrochemical properties and find many applications in both technical and life science fields, including photodynamic therapy and neurosurgery. The irradiation of porphyrins may cause modifications to their molecular structure or their degradation. Such photobleaching processes potentially affect the success and sensitivity of photosensitizer applications. While there have been many studies using fluorescence spectroscopy to
investigate this phenomenon, reports about analytically validated structures of photoproducts are scarce. It is, however, necessary to know the individual contributions of different molecules to the fluorescence signal in order to evaluate it correctly. This review provides a summary of the current state of knowledge in this respect, discussing especially the validated hydroxyaldehyde and formyl photo-oxidation products of protoporphyrin IX
Predicting Locomotion Intention using Eye Movements and EEG with LSTM and Transformers
No full textDie Vorhersage zukünftiger Bewegungsabläufe auf der Grundlage intrinsischer Daten dient vielen Zwecken, z. B. der Optimierung der Nutzung des physischen Raums in Virtual-Reality-Umgebungen und der Verbesserung der Steuerung elektronischer Hilfsmittel für Patienten mit motorischen Beeinträchtigungen. Die Vorhersage menschlicher Fortbewegungsabsichten erweist sich jedoch aufgrund der hochkomplexen und nichtlinearen Wechselwirkungen zwischen den relevanten Parametern als schwierig. Tiefe neuronale Netze bieten einen erheblichen Vorteil gegenüber herkömmlichen Ansätzen, um diese Herausforderung zu bewältigen. Wir behandeln diese Aufgabe als ein Problem der Zeitreihenvorhersage und vergleichen LSTM-Netzwerke mit Transformatormodellen. Ein besonderer Aspekt unserer Arbeit ist die Betonung der Augenbewegungen als zentrales Merkmal, was zu den neuartigen Vorhersagefähigkeiten beiträgt. Neben den Blickdaten evaluieren wir die Hinzunahme von EEG als Datenquelle für diese Vorhersageaufgabe, die in Gehirn-Computer-Schnittstellen verwendet werden soll. Um dies zu erreichen, haben wir zwei Experimente zur Datenerfassung in benutzerdefinierten virtuellen Umgebungen durchgeführt, die verschiedene Aufgaben mit Joystick-Steuerung beinhalten. Wir stellen diese neuen Datensätze in Verbindung mit dieser Arbeit vor. Die Ergebnisse zeigen, dass Blickdaten ein wertvolles Werkzeug für die Vorhersage der Fortbewegung in verschiedenen Kontexten sind, selbst wenn es keine starke und direkte Verbindung zwischen Blick und zukünftigen Wegpunkten gibt. Transformer-Modelle konnten eine bessere Leistung erzielen als LSTM-Netzwerke, und wir kommen zu dem Schluss, dass für eine erfolgreiche Vorhersage in verschiedenen Situationen Datensätze erforderlich sind, die ein breites Spektrum von Bewegungsszenarien enthalten.Predicting future locomotion based on intrinsic data serves many purposes, including optimizing the utilization of physical space in virtual reality environments and enhancing the control of electronic aids for patients with motor impairments. However, predicting human locomotion intentions proves challenging due to the inherent difficulty arising from the highly complex and nonlinear interactions among the relevant parameters. Deep neural networks offer a significant advantage over conventional approaches in addressing this challenge. We treat this task as a time series prediction problem and compare LSTM networks to transformer models. A distinctive aspect of our work is our approach’s emphasis on eye movements as a central feature, contributing to its novel predictive capabilities. Besides gaze data, we evaluate the addition of EEG as a data source for this prediction task to be used in brain-computer interfaces. To achieve this, we conducted two data collection experiments in custom virtual environments that feature different tasks utilizing joystick control. We present these novel datasets in conjunction with this work. The results demonstrate that gaze data proves to be a valuable tool for locomotion prediction in different contexts, even when there is not a strong and direct connection between gaze and future waypoints. Transformer models were able to achieve better performance than LSTM networks, and we conclude that successful prediction across diverse situations requires datasets containing a wide range of movement scenarios
Prospect-Theorie und psychologische Faktoren im Fußball:Auswirkungen des Video-Assistenten-Schiedsrichters auf Elfmeter-Erfolgsquoten in der deutschen Bundesliga
No full textThe increasing integration of technological aids, such as the video assistant referee (VAR), is fundamentally transforming decision-making processes in professional football, especially influencing critical match moments. Penalty kicks, characterised by technical simplicity but intense psychological pressure, may be particularly affected by delays caused by VAR reviews. An analysis of 737 penalty kicks in the German Bundesliga and second Bundesliga (2019-2023) reveals that penalties confirmed following VAR interventions show significantly lower conversion rates. This impact is especially pronounced during the early stages of matches, suggesting prolonged delays disrupt players’ established pre-performance routines and heighten psychological stress, which aligns with prospect theory’s insights on decision-making under uncertainty. Thus, these insights emphasise how technological innovations enhance officiating accuracy and introduce new psychological demands on athletes at the same time.Der Einsatz technischer Hilfsmittel, wie des Videoschiedsrichters (VAR), verändert zunehmend die Entscheidungsprozesse im Profifußball und beeinflusst damit auch die Dynamik entscheidender Spielsituationen. Insbesondere beim Elfmeterschießen, einer scheinbar einfachen technischen Aktion mit erheblicher psychologischer Komplexität, können Verzögerungen durch VAR-Überprüfungen erhebliche Auswirkungen auf die Leistung der Spieler haben. Eine Untersuchung von 737 Elfmetern in der 1. und 2. Bundesliga (2019-2023) zeigt, dass besonders Elfmeter, die nach einer VAR-Überprüfung bestätigt werden, eine niedrigere Erfolgsquote aufweisen. Dieser Effekt tritt insbesondere in frühen Spielphasen auf, wo lange Wartezeiten möglicherweise die Routinen der Spieler stören und zusätzlichen psychologischen Druck erzeugen, was mit den Erkenntnissen der Prospect-Theorie zur Entscheidungsfindung unter Unsicherheit übereinstimmt. Die Untersuchung liefert wertvolle Erkenntnisse darüber, wie technologische Veränderungen Schiedsrichterentscheidungen verbessern und zugleich neue psychologische Herausforderungen für Sportler schaffen
Stimulus awareness is associated with secondary somatosensory cortex activation in an inattentional numbness paradigm
No full textWhile inattentional blindness and deafness studies have revealed neural correlates of consciousness (NCC) without the confound of task relevance in the visual and auditory modality, comparable studies for the somatosensory modality are lacking. Here, we investigated NCC using functional magnetic resonance imaging (fMRI) in an inattentional numbness paradigm. Participants (N = 44) received weak electrical stimulation on the left hand while solving a demanding visual task. Half of the participants were informed that task-irrelevant weak tactile stimuli above the detection threshold would be applied during the experiment, while the other half expected stimuli below the detection threshold. Unexpected awareness assessments after the experiment revealed that altogether 10 participants did not consciously perceive the somatosensory stimuli during the visual task. Awareness was not significantly modulated by prior information. The fMRI data show that awareness of stimuli led to increased activation in the contralateral secondary somatosensory cortex. We found no significant effects of stimulus awareness in the primary somatosensory cortex or frontoparietal areas. Thus, our results support the hypothesis that somatosensory stimulus awareness is mainly based on activation in higher areas of the somatosensory cortex and does not require strong activation in extended anterior or posterior networks, which is usually seen when perceived stimuli are task-relevant
The Long-Lasting Exhumation History of the Ötztal-Stubai Complex (Eastern European Alps): New Constraints from Zircon (U–Th)/He Age-Elevation Profiles and Thermokinematic Modeling
No full textThe Eastern European Alps formed during two orogenic cycles, which took place in the Cretaceous and Cenozoic, respectively. In the Ötztal-Stubai Complex—a thrust sheet of Variscan basement and Permo-Mesozoic cover rocks—the record of the first (Eoalpine) orogeny is well preserved because during the second (Alpine) orogeny, the complex remained largely undeformed. Here, new zircon (U–Th)/He (ZHe) ages are presented, and thermokinematic modeling is applied to decipher the cooling and exhumation histories of the central part of the Ötztal-Stubai Complex since the Late Cretaceous. The ZHe ages from two elevation profiles increase over a vertical distance of 1500 m from 56 ± 3 to 69 ± 3 Ma (Stubaital) and from 50 ± 2 to 71 ± 4 Ma (Kaunertal), respectively. These ZHe ages and a few published zircon and apatite fission track ages were used for inverse thermokinematic modeling. The modeling results show that the age data are well reproduced with a three-phase exhumation history. The first phase with relatively fast exhumation (~250 m/Myr) during the Late Cretaceous ended at ~70 Ma and is interpreted to reflect the erosion of the Eoalpine mountain belt. As Late Cretaceous normal faults occur at the margins of the Ötztal-Stubai Complex, normal faulting may have also contributed to the exhumation of the study area. Subsequently, a long period with slow exhumation (<10 m/Myr) prevailed until ~16 Ma. This long-lasting phase of slow exhumation suggests a rather low topography with little relief in the Ötztal-Stubai Complex until the mid-Miocene, even though the Alpine orogeny had already begun in the Eocene with the subduction of the European continental margin. Accelerated exhumation since the mid-Miocene (~230 m/Myr) is interpreted to reflect the erosion of the mountain belt due to the development of high topography in front of the Adriatic indenter and repeated glaciations during the Quaternary
Untersuchung von Dynamiken und Transportprozessen in hybriden Elektrolyten und heterogenen Katalysatoren
No full textDer Fokus dieser Arbeit lag auf der Untersuchung hybrider Batterieelektrolyte auf Basis ionischer Flüssigkeiten (IL). Dabei wurde der Einfluss der Koordinationsumgebung auf die Dynamik und den Transport der Lithium-Ionen analysiert. Der Einschluss eines IL-Elektrolyten in den Poren von ZIF-8 führte zu einer deutlich schnelleren lokalen Li-Dynamik als im Bulk-Elektrolyten. Ein verbesserter Li-Transport im Hybridelektrolyten konnte hierbei mit vorteilhaften IL-Kationen-Porenwandwechselwirkungen in Verbindung gebracht werden. In einem ternären PEO-basierten Polymerelektrolyten wurde ein korrelierter Transport von Polymer und Li festgestellt, der vermutlich auf den Volumenerhaltungseffekt zurückzuführen ist. Zudem wurde ein neuartiges Poly(vinylimidazol)-basiertes Ionengel hergestellt. Aufgrund starker Li-Polymer-Wechselwirkungen kam es hier nicht nur zu einer Quervernetzung der Polymerketten durch Li, sondern auch zu höheren Leitfähigkeiten als im reinen IL-Elektrolyten. Das letzte Kapitel befasste sich mit Transportprozessen in heterogenen Katalysatoren. Hier konnte gezeigt werden, dass Porenwandwechselwirkungen in kleinen Poren zu Transportlimitierungen führen können
Blood group O attributes to prolonged progression-free survival, overall survival, and 5-year survival in isocitrate dehydrogenase-wildtype glioblastoma patients with MGMT promoter methylation
No full textBackground. Glioblastoma (GBM) remains incurable despite multimodal therapeutic approaches. Here, we assessed the relevance of ABO blood groups for progression-free survival (PFS), overall survival (OS), and long-term survival in a large cohort of isocitrate dehydrogenase (IDH)-wildtype (wt) GBM patients. Methods. Consecutive GBM patients (2009-2020) at a large tertiary brain tumor center were included, and clinical data were retrospectively abstracted. We dichotomized patients into those with blood group O and those with a Non-O blood group. Patient, tumor, and treatment characteristics were compared between these groups. Association with outcomes was assessed in univariable and multivariable settings via log-rank tests and Cox proportional hazards regressions, respectively.
Results. Five hundred fifty-four GBM IDH-wt had available ABO information. There were no substantial differences in patient, tumor, or treatment characteristics between group O and group Non-O. In contrast, blood group O patients showed increased PFS, OS, and 5-year survivals in both univariable and multivariable analyses. Differences were strongly pronounced in patients with MGMT promoter methylated tumors receiving standardized radiochemotherapy (OS blood group O 24.6 months [95%CI 17.8-31.4] vs Non-O 17.7 months [14.1-21.3], P = .015 log-rank analysis, hazard ratio 0.70 [95%CI 0.53-0.94]), but not apparent in MGMT promoter unmethylated tumors and in patients without (standardized) adjuvant therapy. Conclusion. Blood group O status in conjunction with MGMT promoter methylation (including weak methylation) is an independent favorable prognostic marker in GBM IDH-wt patients receiving standardized radiochemotherapy. This finding is unprecedented, suggesting a linkage between the downregulation of a DNA repair protein and the absence of a functional blood cell surface glycosyltransferase
Context matters: athletes' perception of dopers' values, actions and vulnerabilities
No full textBackground: Although athletes seem to hold uniform views towards non-dopers, their perception of dopers is more nuanced, reflecting positive and negative attributes. Research also indicates that rarely a single factor can explain doping, but a host of reasons that intertwine. A holistic understanding of how values play a role in decisions in anti-doping and the elements that influence athletes’ doping vulnerability is timely and warranted. Methods: We recruited elite athletes from 13 countries representing 27 sports at a national or international level (N = 60) to participate as part of a larger research project. Data were collected via focus group interviews focusing on values, value priorities and perceptions about the role of values in doping as a phenomenon and in dopers' actions. Data were analysed using iterative thematic analysis. Results: Three themes were identified: (1) athletes' personal stance on doping, (2) dopers in the eyes of the anti-doping-compliant athletes, and (3) doping vulnerability is a balance. Athletes in this study strongly opposed doping but showed empathy and understanding toward athletes who doped under certain circumstances. Furthermore, athletes believed that "clean" and "doping" athletes are not always distinguished by the values they hold, leading to the realisation that all athletes can be vulnerable to doping at some point. This vulnerability is a balance between risks and protective factors in a complex interaction between environmental, personal, and situational influences. Each element (e.g., values, environment) can be a motivator or a barrier. Consequently, doping vulnerability is highly idiosyncratic and dynamic. Conclusion: If doping is not due to a lack of moral values but the consequences of combined risk factors that override the guiding function of values, then doping can happen to anyone, "good" athletes included. Developers and facilitators of anti-doping education programmes are advised to embrace this important aspect. The results also contribute to developing the doping vulnerability concept as a balance between risks and protective factors and draw attention to the clean athlete vulnerability, which is rooted in the combination of strategic performance enhancement via non-prohibited means, their exposure to anti-doping requirements and the constant high level of suspicion that surrounds them