The Groebner basis of the ideal of vanishing polynomials

We construct an explicit minimal strong Groebner basis of the ideal of vanishing polynomials in the polynomial ring over Z/m for m>=2. The proof is done in a purely combinatorial way. It is a remarkable fact that the constructed Groebner basis is independent of the monomial order and that the set of leading terms of the constructed Groebner basis is unique, up to multiplication by units. We also present a fast algorithm to compute reduced normal forms, and furthermore, we give a recursive algorithm for building a Groebner basis in Z/m[x_1,x_2,...,x_n] along the prime factorization of m. The obtained results are not only of mathematical interest but have immediate applications in formal verification of data paths for microelectronic systems-on-chip.Comment: 15 pages, 1 table, 2 algorithms (corrected version with new Prop. 3.8 and proof); Journal of Symbolic Computation 46 (2011

Haemorrhagic ulcerative duodenitis in a patient with COVID-19 infection: clinical improvement following treatment with budesonide

We present a case of a male patient in his mid-30s with COVID-19-induced lung failure requiring extracorporeal membrane oxygenation, who needed an emergency oesophagogastroduodenoscopy due to major upper gastrointestinal bleeding. Endoscopy exposed severe ulcerative duodenitis with diffuse mucosal bleeding. While CT angiography did not show any signs of ischaemia, histopathology revealed duodenitis with substantial inflammatory cell infiltrates consisting of neutrophils and CD3(+) T lymphocytes with equal CD4(+)/CD8(+) distribution. Since the composition of cell infiltrates coincides with changes in inflammatory patterns of the respiratory mucosa from patients with COVID-19 and in COVID-19-associated enterocolitis, and systemic dexamethasone treatment became standard of care in ventilated intensive care unit patients with COVID-19 infection, we initiated an individualised therapeutic attempt to treat the duodenitis with topical enteral budesonide. Follow-up oesophagogastroduodenoscopies within 4 weeks of enteral budesonide administration revealed a full clinical and histological healing of the duodenal mucosa with marked reduction of neutrophilic and lymphocytic infiltrates. To our knowledge, the current report is the first description of enteral budesonide treatment of duodenitis in a patient with COVID-19 infection and warrants further investigation, whether budesonide might constitute a novel therapeutic strategy for the management of COVID-19-related intestinal mucosal damage

Normalization of Rings

We present a new algorithm to compute the integral closure of a reduced Noetherian ring in its total ring of fractions. A modification, applicable in positive characteristic, where actually all computations are over the original ring, is also described. The new algorithm of this paper has been implemented in Singular, for localizations of affine rings with respect to arbitrary monomial orderings. Benchmark tests show that it is in general much faster than any other implementation of normalization algorithms known to us.Comment: Final version, to be published in JSC 201

Evaluation in der Radikalisierungsprävention: Ansätze und Kontroversen

Dieser Report nimmt das ge­steig­erte öffent­liche In­te­resse an ver­schie­denen Maß­nahmen und An­sätzen der Ra­di­ka­li­sierungs­prä­ven­tion zum Aus­gangs­punkt einer Dis­kus­sion über Eva­lua­tion. Eva­lua­tionen helfen zu ver­stehen, wie die Prä­ven­tion von Ra­di­kali­sierung und Ex­tre­mis­mus im ge­sell­schaft­lichen Kon­text wirkt. Sie können damit we­sent­liche An­halts­punkte für die häufig ar­ti­ku­lierte Frage nach den sicht­baren Er­folgen von Prä­ven­tion liefern. Gleich­zei­tig exis­tieren in der De­batte um die so­ge­nannte "evidenz­basierte" Prä­ven­tion teil­weise über­zo­gene Er­war­tungen hin­sicht­lich der Leistungs­fähig­keit und Durch­führ­bar­keit von Wir­kungs­eva­lua­tionen. Das be­rechtigte In­teresse an be­last­baren Wirk­sam­keits­nach­weisen stößt bei der Pla­nung und Um­setz­ung von Eva­lu­ations­stu­dien im Bereich der De­ra­di­ka­li­sierung, Dis­tan­zierung und Prä­ven­tion von Ra­di­ka­li­sierung auf be­trächt­liche Heraus­for­der­ungen. Dieser Report geht auf einige dieser Schwierig­keiten ein und zeigt bei­spiel­haft ver­schiedene An­sätze dafür, wie sich Eva­lu­ationen im Rahmen re­a­lis­tischer Mö­glich­keiten um­setzen lassen. Die Idee einer "evidenz­ba­sierten" Prä­ven­tion kann nur dann funk­tionieren, wenn der Eva­lua­tions­for­schung die Eigen­heiten, Wider­sprüche und Kon­tro­versen in Wissen­schaft und Praxis be­wusst sind und sie diese kritisch re­flek­tiert

Causes of death and comorbidities in hospitalized patients with COVID-19

Infection by the new corona virus strain SARS-CoV-2 and its related syndrome COVID-19 has been associated with more than two million deaths worldwide. Patients of higher age and with preexisting chronic health conditions are at an increased risk of fatal disease outcome. However, detailed information on causes of death and the contribution of pre-existing health conditions to death yet is missing, which can be reliably established by autopsy only. We performed full body autopsies on 26 patients that had died after SARS-CoV-2 infection and COVID-19 at the Charite University Hospital Berlin, Germany, or at associated teaching hospitals. We systematically evaluated causes of death and pre-existing health conditions. Additionally, clinical records and death certificates were evaluated. We report findings on causes of death and comorbidities of 26 decedents that had clinically presented with severe COVID-19. We found that septic shock and multi organ failure was the most common immediate cause of death, often due to suppurative pulmonary infection. Respiratory failure due to diffuse alveolar damage presented as immediate cause of death in fewer cases. Several comorbidities, such as hypertension, ischemic heart disease, and obesity were present in the vast majority of patients. Our findings reveal that causes of death were directly related to COVID-19 in the majority of decedents, while they appear not to be an immediate result of preexisting health conditions and comorbidities. We therefore suggest that the majority of patients had died of COVID-19 with only contributory implications of preexisting health conditions to the mechanism of death

On the Geometry of Super Yang-Mills Theories: Phases and Irreducible Polynomials

We study the algebraic and geometric structures that underly the space of vacua of N=1 super Yang-Mills theories at the non-perturbative level. Chiral operators are shown to satisfy polynomial equations over appropriate rings, and the phase structure of the theory can be elegantly described by the factorization of these polynomials into irreducible pieces. In particular, this idea yields a powerful method to analyse the possible smooth interpolations between different classical limits in the gauge theory. As an application in U(Nc) theories, we provide a simple and completely general proof of the fact that confining and Higgs vacua are in the same phase when fundamental flavors are present, by finding an irreducible polynomial equation satisfied by the glueball operator. We also derive the full phase diagram for the theory with one adjoint when Nc is less than or equal to 7 using computational algebraic geometry programs.Comment: 87 pages; v2: typos and eq. (4.44) correcte

„Vom rechten Rand wieder eher ein stückweit in die Mitte" – Ausstiegs- und Distanzierungsarbeit als institutionelle De- und Resozialisierungsinstanz?

Im Beitrag werden Hinwendungen zum Rechtsextremismus aus theoretischer Perspektive als Prozesse (politischer) Sozialisation begriffen, in denen junge Menschen – entgegen den Erwartungen demokratischer Gesellschaften – extremistische Weltsichten und Zugehörigkeiten entwickeln und konsolidieren. Ausgehend von der Überlegung, dass eine Sozialisation in den Rechtsextremismus grundsätzlich ein offener und damit auch umkehrbarer Prozess ist, wird die Abkehr vom Rechtsextremismus ebenfalls als sozialisatorischer Prozess begriffen. Wir adaptieren die Konzepte der Desozialisierung und Resozialisierung, um die Vorgehensweisen und Zielsetzungen von professionellen Angeboten der Ausstiegs- und Distanzierungsarbeit zu systematisieren. Auf Basis zweier empirisch-qualitativer Studien zu Praxiserfahrungen von Angeboten der Ausstiegs- und Distanzierungsarbeit zeichnen wir nach, wie Prozesse der Desozialisierung und Resozialisierung auf zentralen Zielebenen der Arbeit angestoßen werden und ineinandergreifen sollen. Betrachtet wird dabei auch, welche Zielvorstellungen in der Arbeit mit den Adressat:innen existieren und den normativen Korridor des Erwünschten darstellen