The Saito-Kurokawa lifting and Darmon points

Let E_{/_\Q} be an elliptic curve of conductor $Np$ with $p\nmid N$ and let $f$ be its associated newform of weight 2. Denote by $f_\infty$ the $p$-adic Hida family passing though $f$, and by $F_\infty$ its $\Lambda$-adic Saito-Kurokawa lift. The $p$-adic family $F_\infty$ of Siegel modular forms admits a formal Fourier expansion, from which we can define a family of normalized Fourier coefficients $\{\widetilde A_T(k)\}_T$ indexed by positive definite symmetric half-integral matrices $T$ of size $2\times 2$. We relate explicitly certain global points on $E$ (coming from the theory of Stark-Heegner points) with the values of these Fourier coefficients and of their $p$-adic derivatives, evaluated at weight $k=2$.Comment: 14 pages. Title change

Intravascular lymphoma presenting as a specific pulmonary embolism and acute respiratory failure: a case report

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Acute kidney injury in the critically ill: an updated review on pathophysiology and management.

Acute kidney injury (AKI) is now recognized as a heterogeneous syndrome that not only affects acute morbidity and mortality, but also a patient's long-term prognosis. In this narrative review, an update on various aspects of AKI in critically ill patients will be provided. Focus will be on prediction and early detection of AKI (e.g., the role of biomarkers to identify high-risk patients and the use of machine learning to predict AKI), aspects of pathophysiology and progress in the recognition of different phenotypes of AKI, as well as an update on nephrotoxicity and organ cross-talk. In addition, prevention of AKI (focusing on fluid management, kidney perfusion pressure, and the choice of vasopressor) and supportive treatment of AKI is discussed. Finally, post-AKI risk of long-term sequelae including incident or progression of chronic kidney disease, cardiovascular events and mortality, will be addressed

Galois Theory, discriminants and torsion subgroups of elliptic curves

We find a tight relationship between the torsion subgroup and the image of the mod 2 Galois representation associated to an elliptic curve defined over the rationals. This is shown using some characterizations for the squareness of the discriminant of the elliptic curve.Comment: New version, some typos fixed and the proof of the lemma in the Appendix has been expande

Renal recovery after acute kidney injury

Acute kidney injury (AKI) is a frequent complication of critical illness and carries a significant risk of short-and long-term mortality, chronic kidney disease (CKD) and cardiovascular events. The degree of renal recovery from AKI may substantially affect these long-term endpoints. Therefore maximising recovery of renal function should be the goal of any AKI prevention and treatment strategy. Defining renal recovery is far from straightforward due in part to the limitations of the tests available to assess renal function. Here, we discuss common pitfalls in the evaluation of renal recovery and provide suggestions for improved assessment in the future. We review the epidemiology of renal recovery and of the association between AKI and the development of CKD. Finally, we stress the importance of post-discharge follow-up of AKI patients and make suggestions for its incorporation into clinical practice. Summary key points are that risk factors for non-recovery of AKI are age, CKD, comorbidity, higher severity of AKI and acute disease scores. Second, AKI and CKD are mutually related and seem to have a common denominator. Third, despite its limitations full recovery of AKI may best be defined as the absence of AKI criteria, and partial recovery as a fall in AKI stage. Fourth, after an episode of AKI, serial follow-up measurements of serum creatinine and proteinuria are warranted to diagnose renal impairment and prevent further progression. Measures to promote recovery are similar to those preventing renal harm. Specific interventions promoting repair are still experimental.Peer reviewe

Theatrical dialogue in teaching the classics

This article addresses some fundamental affinities between theatre and teaching and is based on emerging work in a long-term experiment which we began in the conference ‘Weber/Simmel Antagonisms: Staged Dialogues’, held at the University of Edinburgh on December 2015. Aimed at exploring the possibilities of the theatrical and dialogical forms for teaching the classics of social and cultural theory, it is a risky experiment whose initial results are presented in this special issue. In order to introduce the dialogues and situate them in the context of the broader project, the article does three things: first, it expounds the process of subjectivation at work in both theatre and teaching and explores some of the modalities of the subjective shift sought for in spectators and students. Second, it explains the specificity of this experiment by contrasting it with other uses of theatrical dialogue in teaching. Finally, before briefly introducing each of the dialogues, the article clarifies the fundamental difference between the dialogical form and debate, as radically separating them is at the heart of any experiment in subjectivation, away from the stirring of opinions

On px2+q2n=yppx^2 + q^{2n}= y^p and related Diophantine equations

The title equation, where $p>3$ is a prime number $\not\equiv 7 \pmod 8$, $q$ is an odd prime number and $x,y,n$ are positive integers with $x,y$ relatively prime, is studied. When $p\equiv 3\pmod 8$, we prove (Theorem 2.3) that there are no solutions. For $p\not\equiv 3\pmod 8$ the treatment of the equation turns out to be a difficult task. We focus our attention to $p=5$, by reason of an article by F. Abu Muriefah, published in this journal, vol. 128 (2008), 1670-1675. Our main result concerning this special equation is Theorem 1.1, whose proof is based on results around the Diophantine equation $5x^2-4=y^n$ (integer solutions), interesting in themselves, which are exposed in Sections 3 and 4. These last results are obtained by using tools such as Linear Forms in Two Logarithms and Hypergeometric Series.Comment: 23 pages, second version with minor revision

A novel class of heat and secretion stress-responsive genes is controlled by the autoregulated CssRS two-component system of Bacillus subtilis

Bacteria need dedicated systems that allow appropriate adaptation to the perpetual changes in their environments. In Bacillus subtilis, two HtrA-like proteases, HtrA and HtrB, play critical roles in the cellular response to secretion and heat stresses. Transcription of these genes is induced by the high-level production of a secreted protein or by a temperature upshift. The CssR-CssS two-component regulatory system plays an essential role in this transcriptional activation. Transcription of the cssRS operon is autoregulated and can be induced by secretion stress, by the absence of either HtrA or HtrB, and by heat stress in a HtrA null mutant strain. Two start sites are used for cssRS transcription, only one of which is responsive to heat and secretion stress. The divergently transcribed htrB and cssRS genes share a regulatory region through which their secretion and heat stress-induced expression is linked. This study shows that CssRS-regulated genes represent a novel class of heat-inducible genes, which is referred to as class V and currently includes two genes: htrA and htrB

Expert statement for the management of hypovolemia in sepsis

Hypovolemia is frequent in patients with sepsis and may contribute to worse outcome. The management of these patients is impeded by the low quality of the evidence for many of the specific components of the care. In this paper, we discuss recent advances and controversies in this field and give expert statements for the management of hypovolemia in patients with sepsis including triggers and targets for fluid therapy and volumes and types of fluid to be given. Finally, we point to unanswered questions and suggest a roadmap for future research.Peer reviewe