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    Heimvorteil und Schiedsrichterbias im europäischen Fußball:Die Rolle der Nachspielzeit

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    Football referees possess substantial discretion in allocating stoppage time, a decision that is comparatively opaque yet potentially consequential for match outcomes. This paper examines whether stoppage time allocation contributes to home advantage in contemporary European professional football. Using a dataset of 18,085 matches across the 2014/15–2023/24 seasons, we analyse first- and second-half stoppage time separately. Our results indicate that first-half stoppage time is largely explained by interruptions and shows no systematic dependence on match context. In contrast, second-half stoppage time is strongly context-dependent: close matches receive more stoppage time on average, no matter whether the home team is leading or trailing.Schiedsrichter haben bei der Festlegung der Nachspielzeit einen großen Ermessensspielraum, wobei ihre Entscheidung vergleichsweise intransparent ist, aber den Spielausgang maßgeblich beeinflussen kann. Diese Studie untersucht, ob die Vergabe von Nachspielzeit im heutigen europäischen Profifußball zum Heimvorteil beiträgt. Auf Basis eines Datensatzes mit 18.085 Partien aus den Saisons 2014/15 bis 2023/24 wird die Nachspielzeit getrennt nach erster und zweiter Halbzeit analysiert. Die Ergebnisse zeigen, dass die Nachspielzeit in der ersten Halbzeit überwiegend durch Unterbrechungen erklärt wird und nicht systematisch vom Spielkontext abhängt. In der zweiten Halbzeit ist die Nachspielzeit dagegen kontextabhängig: Enge Spiele erhalten im Durchschnitt mehr Nachspielzeit, wenn eines der beiden Teams zurückliegt

    The war in Ukraine and the independence of Taiwan:Humanitarian implications of ending the war in Ukraine and maintaining peace in Taiwan

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    Russian invasion of Ukraine in February of 2022 was the most significant military event in Europe following WW2. It took the lives of tens of thousands of civilians and negatively impacted the economies of European countries. Russia will stay adamant for its geopolitical objectives in Ukraine and unless western democracies don’t take a serious standpoint, Russian success will have major geopolitical consequences globally. One of these major geopolitical consequences will be the change of the status quo in the relations between China and Taiwan. China as a reemergent global power seeks to restore its influence in southeast Asia and subsuming Taiwan is a major step for this ambition. Russia´s victory in Ukraine will boost Chinese confidence for its geopolitical aims which will disrupt the balance in the current international order based on the Westphalian system. The purpose of this article is to analyze the current Russo-Ukrainian conflict, China-Taiwan relationship, hypothetical invasion of Taiwan by China, and suggest a framework for the peaceful resolution of the Russo-Ukrainian conflict and prevention of the escalation of the crisis in southeast Asia

    Leistung, Identifikation oder die Unsicherheit über den Spielausgang – was zählt wirklich?:Relevante Einflussfaktoren auf die Zuschauerzahlen in der Basketball-Bundesliga

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    Medien sowie Vertreter des Deutschen Basketball-Bundes kritisieren immer wieder die gerin-gen Einsatzzeiten deutscher Spieler in der Basketball-Bundesliga und die daraus resultieren-den mangelnden Identifikationsmöglichkeiten der Zuschauer mit den Spielern. Der Artikel analysiert daher mögliche Einflussfaktoren auf die Zuschauerzahlen in der Basketball-Bundesliga mit speziellem Fokus auf die Auswirkungen des Einsatzes deutscher Spieler. Es zeigt sich nicht nur, dass die Leistung der Mannschaften sowie die Unsicherheit über den Spielausgang einen wesentlich größeren Einfluss auf die Zuschauerzahlen haben als Einsatz-zeiten oder Anzahl deutscher Spieler, sondern die Ergebnisse deuten sogar auf zum Teil nega-tive Effekte des Einsatzes dieser Spieler auf die Zuschauerzahlen hin.Media as well as representatives of the German Basketball Federation time and again criticise short playing times for German players in the German Basketball League and hence the re-sulting lack of possibilities for fans and spectators to identify with their players. This paper therefore analyses possible factors of influence on attendance with a special focus on the in-fluence of playing times for German players. The results not only show that performance of the teams as well as outcome uncertainty has a considerably higher effect on audience figures as playing times or number of German players. They also point to the fact that there are partly negative effects of playing time as well as number of German players on audience figures

    An integrated precision medicine approach in major depressive disorder: a study protocol to create a new algorithm for the prediction of treatment response

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    Major depressive disorder (MDD) is the most common psychiatric disease worldwide with a huge socio-economic impact. Pharmacotherapy represents the most common option among the first-line treatment choice; however, only about one third of patients respond to the first trial and about 30% are classified as treatment-resistant depression (TRD). TRD is associated with specific clinical features and genetic/gene expression signatures. To date, single sets of markers have shown limited power in response prediction. Here we describe the methodology of the PROMPT project that aims at the development of a precision medicine algorithm that would help early detection of non-responder patients, who might be more prone to later develop TRD. To address this, the project will be organized in 2 phases. Phase 1 will involve 300 patients with MDD already recruited, comprising 150 TRD and 150 responders, considered as extremes phenotypes of response. A deep clinical stratification will be performed for all patients; moreover, a genomic, transcriptomic and miRNomic profiling will be conducted. The data generated will be exploited to develop an innovative algorithm integrating clinical, omics and sex-related data, in order to predict treatment response and TRD development. In phase 2, a new naturalistic cohort of 300 MDD patients will be recruited to assess, under real-world conditions, the capability of the algorithm to correctly predict the treatment outcomes. Moreover, in this phase we will investigate shared decision making (SDM) in the context of pharmacogenetic testing and evaluate various needs and perspectives of different stakeholders toward the use of predictive tools for MDD treatment to foster active participation and patients’ empowerment. This project represents a proof-of-concept study. The obtained results will provide information about the feasibility and usefulness of the proposed approach, with the perspective of designing future clinical trials in which algorithms could be tested as a predictive tool to drive decision making by clinicians, enabling a better prevention and management of MDD resistance

    Bounded functions on the character variety:With an appendix by Dragos, Cris, an and Jingjie Yang

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    This paper is motivated by an open question in p-adic Fourier theory, that seems to be more difficult than it appears at first glance. Let L be a finite extension of Qp with ring of integers oL and let Cp denote the completion of an algebraic closure of Qp. In their work on p-adic Fourier theory, Schneider and Teitelbaum defined and studied the character variety X. This character variety is a rigid analytic curve over L that parameterizes the set of locally L-analytic characters λ : (oL,+) → (C×p ,×). One of the main results of Schneider and Teitelbaum is that, over Cp, the curve X becomes isomorphic to the open unit disk. Let ΛL(X) denote the ring of bounded-by-one functions on X. If μ ∈ oLJoLK is a measure on oL, then λ 7→ μ(λ) gives rise to an element of ΛL(X). The resulting map oL[oL] → ΛL(X) is injective. The question is: do we have ΛL(X) = oL[oL]? In this paper, we prove various results that were obtained while studying this question. In particular, we give several criteria for a positive answer to the above question. We also recall and prove the "Katz isomorphism" that describes the dual of a certain space of continuous functions on oL. An important part of our paper is devoted to providing a proof of this theorem which was stated in 1977 by Katz. We then show how it applies to the question. Besides p-adic Fourier theory, the above question is related to the theory of formal groups, the theory of integer-valued polynomials on oL, p-adic Hodge theory, and Iwasawa theory

    C*-algebra extensions associated to continued fraction expansions of rational numbers

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    COL6A1 als prognostischer Faktor bei der Akuten Myeloischen Leukämie

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    Trotz intensiver zytostatischer Therapie hat die Akute Myeloische Leukämie (AML) eine schlechte Prognose. Im Rahmen subtypenspezifischer Therapieansätze werden aktuell vor allem Oberflächenproteine als Targets adressiert. Jedoch ist auch das Mikroumfeld von der Erkrankung betroffen, zum Beispiel ist Kollagen Typ VI im leukämischen Knochenmark hochreguliert. In anderen Krebsentitäten konnte bereits ein Einfluss auf die Prognose und Chemoresistenz durch direkte oder indirekte Interaktionen mit der Krebszelle belegt werden. In dieser Arbeit konnte bestätigt werden, dass eine erhöhte Expression von Kollagen Typ VI im Knochenmark von AML-Erkrankten mit einem schlechteren Gesamtüberleben, ereignisfreien Überleben und einer höheren Rezidivrate nach Erreichen einer CR assoziiert ist. Somit kann Kollagen Typ VI als prognostischer Faktor dienen. Durch die vorhandene Blutstromexposition und Hochregulierung wäre aber auch ein Therapieansatz mit Kollagen Typ VI selbst als mögliches Target möglich

    Generation of a whole-brain hemodynamic response function and sex-specific differences in cerebral processing of mechano-sensation in mice detected by BOLD fMRI

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    BOLD fMRI has become a prevalent method to study cerebral sensory processing in rodent disease models, including pain and mechanical hypersensitivity. fMRI data analysis is frequently combined with a general-linear-model (GLM) -based analysis, which uses the convolution of a hemodynamic response function (HRF) with the stimulus paradigm. However, several studies indicated that the HRF differs across species, sexes, brain structures, and experimental factors, including stimulation modalities or anesthesia, and hence might strongly affect the outcome of BOLD analyzes. While considerable work has been done in humans and rats to understand the HRF, much less is known in mice. As a prerequisite to investigate mechano-sensory processing and BOLD fMRI data in male and female mice, we (1) designed a rotating stimulator that allows application of two different mechanical modalities, including innocuous von Frey and noxious pinprick stimuli and (2) determined and statistically compared HRFs across 30 brain structures and experimental conditions, including sex and, stimulus modalities. We found that mechanical stimulation lead to brain-wide BOLD signal changes thereby allowing extraction of HRFs from multiple brain structures. However, we did not find differences in HRFs across all brain structures and experimental conditions. Hence, we computed a whole-brain mouse HRF, which is based on 88 functional scans from 30 mice. A comparison of this mouse-specific HRF with our previously reported rat-derived HRF showed significantly slower kinetics in mice. Finally, we detected pronounced differences in cerebral BOLD activation between male and female mice with mechanical stimulation, thereby exposing divergent processing of noxious and innocuous stimuli in both sexes

    Higher spin representations of maximal compact subalgebras of simply laced Kac–Moody algebras

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    Given the maximal compact subalgebra k(A) of a split-real Kac–Moody algebra g(A) of type A, we study certain finite-dimensional representations of k(A) that do not lift to the maximal compact subgroup K(A) of the minimal Kac–Moody group G(A) associated to g(A) but only to its spin cover Spin(A) described in [11]. Currently, four elementary of these so-called spin representations are known. We study their (ir)reducibility, semisimplicity, and lift to the group level. The interaction of these representations with the spin-extended Weyl group is used to derive a partial parametrization result of the representation matrices by the real roots of g(A)

    Heimvorteil in verschiedenen deutschen Fußballligen

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    This study investigates the presence and variation of home bias across different hierarchical levels in German men’s football. Based on an extensive dataset comprising 357,530 matches from the 2023/2024 season—collected via a Python script—the analysis includes match outcomes, attendance figures, club locations, and prior season standings across 165 divisions in 28 football associations. These leagues span 13 hierarchical levels, from professional to amateur football. The results show that home bias is significantly more pronounced in lower divisions. This effect manifests itself through a higher frequency of home wins, fewer draws, and greater sensitivity to travel distance in amateur divisions. In contrast, more professional leagues may benefit from standardised conditions, which mitigate home bias. Overall, the findings highlight the strong influence of professionalisation on competitive balance. The study contributes to a deeper understanding of how contextual factors shape match outcomes and demonstrates the need for differentiated analysis across league levels when examining behavioural biases in sports.Diese Studie untersucht das Vorhandensein und die Unterschiede des Heimvorteils auf verschiedenen Spielklassenebenen im deutschen Herrenfußball. Grundlage ist ein umfassender Datensatz mit 357.530 Begegnungen aus der Spielzeit 2023/2024, der mittels eines Python-Skripts zusammengestellt wurde. Die Analyse berücksichtigt Spielausgänge, Zuschauerzahlen, Vereinsstandorte und Tabellenplatzierungen der Vorsaison aus 165 Spielklassen in 28 Landesverbänden. Diese Ligen verteilen sich auf 13 Spielklassenebenen vom Profi- bis zum Amateurbereich. Die Ergebnisse belegen, dass der Heimvorteil in unteren Spielklassen deutlich stärker ausgeprägt ist. Dies zeigt sich durch eine höhere Quote an Heimsiegen, weniger Remis und eine stärkere Abhängigkeit von Anfahrtswegen in Amateurligen. Stärker professionalisierte Ligen dagegen profitieren vermutlich von einheitlicheren Rahmenbedingungen, die den Heimvorteil abschwächen. Insgesamt unterstreichen die Erkenntnisse den erheblichen Einfluss der Professionalisierung auf die Ausgeglichenheit des Wettbewerbs. Die Untersuchung trägt zu einem besseren Verständnis bei, wie Rahmenbedingungen die Spielergebnisse beeinflussen, und verdeutlicht die Notwendigkeit einer differenzierten Betrachtung über verschiedene Spielklassen hinweg bei der Analyse von Verhaltensmustern im Sport

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