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

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

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

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

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

Pull out all the stops : textual analysis via punctuation sequences

Whether enjoying the lucid prose of a favourite author or slogging through some other writer’s cumbersome, heavy-set prattle (full of parentheses, em dashes, compound adjectives, and Oxford commas), readers will notice stylistic signatures not only in word choice and grammar but also in punctuation itself. Indeed, visual sequences of punctuation from different authors produce marvellously different (and visually striking) sequences. Punctuation is a largely overlooked stylistic feature in stylometry, the quantitative analysis of written text. In this paper, we examine punctuation sequences in a corpus of literary documents and ask the following questions: Are the properties of such sequences a distinctive feature of different authors? Is it possible to distinguish literary genres based on their punctuation sequences? Do the punctuation styles of authors evolve over time? Are we on to something interesting in trying to do stylometry without words, or are we full of sound and fury (signifying nothing)