Generation of tooth profile for roots rotor based on virtual linkage associated with Assur group

This article, for the first time, presents the generation of Roots rotor tooth profiles based on an Assur-group-associated virtual linkage method. Taking the original Roots rotor as an example, structure and geometry of the Roots rotor are introduced, and based on the principle of inversion, an equivalent virtual linkage is identified for generating dedendum tooth profile of the rotor. Using linkage decomposition associated with elemental Assur groups, algorithm for computing the tooth curve is constructed leading to the explicit expression of rotor profile and the corresponding numerical simulation, verifying the validity of the proposed approach. For demonstration purpose, the virtual linkage method is then extended to the generation of tooth profiles for the variants of Roots rotors with arc-cycloidal curves and arc-involute curves. Integrated with computer-aided design, computer-aided engineering and computer-aided manufacturing software platforms, as well as the three-dimensional printing technology, this article provides an efficient and intuitive approach for Roots rotor system design, analysis and development

Looking backward: From Euler to Riemann

We survey the main ideas in the early history of the subjects on which Riemann worked and that led to some of his most important discoveries. The subjects discussed include the theory of functions of a complex variable, elliptic and Abelian integrals, the hypergeometric series, the zeta function, topology, differential geometry, integration, and the notion of space. We shall see that among Riemann's predecessors in all these fields, one name occupies a prominent place, this is Leonhard Euler. The final version of this paper will appear in the book \emph{From Riemann to differential geometry and relativity} (L. Ji, A. Papadopoulos and S. Yamada, ed.) Berlin: Springer, 2017

Pb(II) Induces Scramblase Activation and Ceramide-Domain Generation in Red Blood Cells

The mechanisms of Pb(II) toxicity have been studied in human red blood cells using confocal microscopy, immunolabeling, fluorescence-activated cell sorting and atomic force microscopy. The process follows a sequence of events, starting with calcium entry, followed by potassium release, morphological change, generation of ceramide, lipid flip-flop and finally cell lysis. Clotrimazole blocks potassium channels and the whole process is inhibited. Immunolabeling reveals the generation of ceramide-enriched domains linked to a cell morphological change, while the use of a neutral sphingomyelinase inhibitor greatly delays the process after the morphological change, and lipid flip-flop is significantly reduced. These facts point to three major checkpoints in the process: first the upstream exchange of calcium and potassium, then ceramide domain formation, and finally the downstream scramblase activation necessary for cell lysis. In addition, partial non-cytotoxic cholesterol depletion of red blood cells accelerates the process as the morphological change occurs faster. Cholesterol could have a role in modulating the properties of the ceramide-enriched domains. This work is relevant in the context of cell death, heavy metal toxicity and sphingolipid signaling.AGA was a predoctoral student supported by the Basque Government and later by the University of the Basque Country (UPV/EHU). This work was also supported in part by grants from the Spanish Government (FEDER/MINECO BFU 2015-66306-P to F.M.G. and A.A.) and the Basque Government (IT849-13 to F.M.G. and IT838-13 to A.A.), and by the Swiss National Science Foundation

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)

Molecular mechanisms of cell death: recommendations of the Nomenclature Committee on Cell Death 2018.

Over the past decade, the Nomenclature Committee on Cell Death (NCCD) has formulated guidelines for the definition and interpretation of cell death from morphological, biochemical, and functional perspectives. Since the field continues to expand and novel mechanisms that orchestrate multiple cell death pathways are unveiled, we propose an updated classification of cell death subroutines focusing on mechanistic and essential (as opposed to correlative and dispensable) aspects of the process. As we provide molecularly oriented definitions of terms including intrinsic apoptosis, extrinsic apoptosis, mitochondrial permeability transition (MPT)-driven necrosis, necroptosis, ferroptosis, pyroptosis, parthanatos, entotic cell death, NETotic cell death, lysosome-dependent cell death, autophagy-dependent cell death, immunogenic cell death, cellular senescence, and mitotic catastrophe, we discuss the utility of neologisms that refer to highly specialized instances of these processes. The mission of the NCCD is to provide a widely accepted nomenclature on cell death in support of the continued development of the field

Consensus statement on abusive head trauma in infants and young children

Abusive head trauma (AHT) is the leading cause of fatal head injuries in children younger than 2 years. A multidisciplinary team bases this diagnosis on history, physical examination, imaging and laboratory findings. Because the etiology of the injury is multifactorial (shaking, shaking and impact, impact, etc.) the current best and inclusive term is AHT. There is no controversy concerning the medical validity of the existence of AHT, with multiple components including subdural hematoma, intracranial and spinal changes, complex retinal hemorrhages, and rib and other fractures that are inconsistent with the provided mechanism of trauma. The workup must exclude medical diseases that can mimic AHT. However, the courtroom has become a forum for speculative theories that cannot be reconciled with generally accepted medical literature. There is no reliable medical evidence that the following processes are causative in the constellation of injuries of AHT: cerebral sinovenous thrombosis, hypoxic-ischemic injury, lumbar puncture or dysphagic choking/vomiting. There is no substantiation, at a time remote from birth, that an asymptomatic birth-related subdural hemorrhage can result in rebleeding and sudden collapse. Further, a diagnosis of AHT is a medical conclusion, not a legal determination of the intent of the perpetrator or a diagnosis of murder. We hope that this consensus document reduces confusion by recommending to judges and jurors the tools necessary to distinguish genuine evidence-based opinions of the relevant medical community from legal arguments or etiological speculations that are unwarranted by the clinical findings, medical evidence and evidence-based literature