Fuchsian convex bodies: basics of Brunn--Minkowski theory

The hyperbolic space \H^d can be defined as a pseudo-sphere in the $(d+1)$ Minkowski space-time. In this paper, a Fuchsian group $\Gamma$ is a group of linear isometries of the Minkowski space such that \H^d/\Gamma is a compact manifold. We introduce Fuchsian convex bodies, which are closed convex sets in Minkowski space, globally invariant for the action of a Fuchsian group. A volume can be associated to each Fuchsian convex body, and, if the group is fixed, Minkowski addition behaves well. Then Fuchsian convex bodies can be studied in the same manner as convex bodies of Euclidean space in the classical Brunn--Minkowski theory. For example, support functions can be defined, as functions on a compact hyperbolic manifold instead of the sphere. The main result is the convexity of the associated volume (it is log concave in the classical setting). This implies analogs of Alexandrov--Fenchel and Brunn--Minkowski inequalities. Here the inequalities are reversed

Shapes of polyhedra, mixed volumes and hyperbolic geometry

We generalize to higher dimensions the Bavard–Ghys construction of the hyperbolic metric on the space of polygons with fixed directions of edges. The space of convex d -dimensional polyhedra with fixed directions of facet normals has a decomposition into type cones that correspond to different combinatorial types of polyhedra. This decomposition is a subfan of the secondary fan of a vector configuration and can be analyzed with the help of Gale diagrams. We construct a family of quadratic forms on each of the type cones using the theory of mixed volumes. The Alexandrov–Fenchel inequalities ensure that these forms have exactly one positive eigenvalue. This introduces a piecewise hyperbolic structure on the space of similarity classes of polyhedra with fixed directions of facet normals. We show that some of the dihedral angles on the boundary of the resulting cone-manifold are equal to π/2

Major combined electrolyte deficiency during therapy with low-dose Cisplatin, 5-Fluorouracil and Interferon alpha: report on several cases and review of the literature [ISRCTN62866759]

BACKGROUND: Low-dose Cisplatin and Interferon alpha treatment of solid tumors rarely has been associated with severe hypocalcaemia. To the authors knowledge the phenomenon has not been reported previously in patients with pancreatic carcinoma. CASE PRESENTATION: A patient with resected adenocarcinoma of the pancreas was treated with adjuvant radio-chemo-immunotherapy using a combination of low-dose Cisplatin, 5-Fluorouracil and Interferon alpha together with external beam radiation. Severe hypocalcaemia without signs of acute renal failure or electrolyte disturbance occurred within 2 days at the 4th week of treatment and required intensive care treatment. CONCLUSION: Combination of biological and cytotoxic therapies may increase the incidence of severe hypocalcaemia in pancreatic cancer. Oncologists should remain attentive of this problem as more highly active regimes become available

A glimpse into Thurston's work

We present an overview of some significant results of Thurston and their impact on mathematics. The final version of this paper will appear as Chapter 1 of the book "In the tradition of Thurston: Geometry and topology", edited by K. Ohshika and A. Papadopoulos (Springer, 2020)

Criticality safety control at CEA Paris-Saclay Abstract

International audienceThe CEA's organization regarding criticality-safety is the same for each of its nuclear center. First, one or more qualified criticality engineer (QCE) is located directly on nuclear installations containing fissile material. The QCE manages criticality safety in the installations. He develops criticality safety analyses for the installations and participates in the implementation of the resulting rules. Second, a center's criticality engineer (CCE) is in charge of the verification for every modification in each nuclear facilities. He is also in charge to support qualified criticality engineer, and capitalise the knowledge of all the installations. Third, a Criticality Specialist (CS) controls the good functioning of the criticality organization in the center. Furthermore, a criticality safety experts group could assist every criticality engineer of each center's organisation for the criticality calculations and analysis. This paper details the role of the Criticality Specialist, which is to define an independent opinion on nuclear facilities modifications that could affect the criticality analysis. Its role is also to be an interface between CEA and the French nuclear safety authority for criticality risks in the center. Its action is thus to ensure the quality and consistency of the files sent to the authorities, but without participating in the technical solutions choices. Then, this paper presents an example of a control carried out on one of the nuclear facilities in Paris-Saclay center. This control is about an implementation of a future operation that may present a criticality risk. The criticality specialist did several further requirements for this operation. In the end, this paper presents how this second line control has been taken into account by the nuclear installation. Finally, this paper establishes a feedback on the positioning of the criticality specialist regarding the controls performed on nuclear facilities

Pharmacokinetics of meropenem (ICI 194,660) and its metabolite (ICI 213,689) in healthy subjects and in patients with renal impairment.

The pharmacokinetics of meropenem (ICI 194,660) and its open-ring metabolite (ICI 213,689) were studied in 6 healthy volunteers and 16 patients with moderate to severe renal impairment after a single intravenous dose of 500 mg given as a 30-min infusion. Concentrations of unchanged meropenem in plasma and urine were measured by both microbiological and high-pressure liquid chromatographic (HPLC) assays. A good correlation was found between the two techniques. Pharmacokinetic parameters of unchanged meropenem were determined by using the HPLC data. The terminal half-life of unchanged meropenem increased in relation to the degree of renal impairment, being 1.2 h in subjects with normal renal function and 10 h in patients with end-stage renal failure. Total body clearance and renal clearance of unchanged meropenem are linearly related to creatinine clearance. The concentrations of the metabolite in plasma, which are very low in healthy subjects, significantly increased in uremic patients. The apparent half-life of ICI 213,689 increased in uremic patients and was about 35 h in patients with severe renal insufficiency. Meropenem and its metabolite are effectively removed by hemodialysis. The dialysis clearance of the unchanged drug was 81 +/- 22 ml/min. Dosage adjustments of meropenem will be necessary in patients with severe renal impairment

Gentamicin-induced Nephrotoxicity - a Cell Biology Approach

Gentamicin is an antibiotic that exhibits a broad spectrum of activity and is particularly valuable in severe sepsis. Its use is, however, restricted because of the development of ototoxicity and nephrotoxicity (for the latter, see review in Ref. 1). At physiologic pH, the drug is highly charged and water soluble, and therefore it is practically unable to diffuse through biologic membranes.Nephrotoxicity has been related to a selective accumulation of gentamicin in the renal cortex [2, 3]. Morphologic lesions of proximal tubules have been documented in optic microscopy [4–6]. At the ultra-structural level, the earliest lesions observed concern the lysosomes, which show an accumulation of myeloid bodies [7–9].The mechanism of the gentamicin toxicity is, however, unknown. In this paper, we present studies on the localization of the drug at the cellular and subcellular levels, and on the enzymatic alterations that develop during gentamicin treatment