Straight Line Orbits in Hamiltonian Flows

We investigate periodic straight-line orbits (SLO) in Hamiltonian force fields using both direct and inverse methods. A general theorem is proven for natural Hamiltonians quadratic in the momenta in arbitrary dimension and specialized to two and three dimension. Next we specialize to homogeneous potentials and their superpositions, including the familiar H\'enon-Heiles problem. It is shown that SLO's can exist for arbitrary finite superpositions of $N$-forms. The results are applied to a family of generalized H\'enon-Heiles potentials having discrete rotational symmetry. SLO's are also found for superpositions of these potentials.Comment: laTeX with 6 figure

Reconstructing initial data using observers: error analysis of the semi-discrete and fully discrete approximations

A new iterative algorithm for solving initial data inverse problems from partial observations has been recently proposed in Ramdani et al. (Automatica 46(10), 1616-1625, 2010 ). Based on the concept of observers (also called Luenberger observers), this algorithm covers a large class of abstract evolution PDE's. In this paper, we are concerned with the convergence analysis of this algorithm. More precisely, we provide a complete numerical analysis for semi-discrete (in space) and fully discrete approximations derived using finite elements in space and an implicit Euler method in time. The analysis is carried out for abstract Schrödinger and wave conservative systems with bounded observation (locally distributed)

Weakly Consistent Regularisation Methods for Ill-Posed Problems

This Chapter takes its origin in the lecture notes for a 9 h course at the Institut Henri Poincaré in September 2016. The course was divided in three parts. In the first part, which is not included herein, the aim was to first recall some basic aspects of stabilised finite element methods for convection-diffusion problems. We focus entirely on the second and third parts which were dedicated to ill-posed problems and their approximation using stabilised finite element methods. First we introduce the concept of conditional stability. Then we consider the elliptic Cauchy-problem and a data assimilation problem in a unified setting and show how stabilised finite element methods may be used to derive error estimates that are consistent with the stability properties of the problem and the approximation properties of the finite element space. Finally, we extend the result to a data assimilation problem subject to the heat equation

Homeomorphic Embedding for Online Termination of Symbolic Methods

Well-quasi orders in general, and homeomorphic embedding in particular, have gained popularity to ensure the termination of techniques for program analysis, specialisation, transformation, and verification. In this paper we survey and discuss this use of homeomorphic embedding and clarify the advantages of such an approach over one using well-founded orders. We also discuss various extensions of the homeomorphic embedding relation. We conclude with a study of homeomorphic embedding in the context of metaprogramming, presenting some new (positive and negative) results and open problems

The human OPA1delTTAG mutation induces premature age-related systemic neurodegeneration in mouse

Dominant optic atrophy is a rare inherited optic nerve degeneration caused by mutations in the mitochondrial fusion gene OPA1. Recently, the clinical spectrum of dominant optic atrophy has been extended to frequent syndromic forms, exhibiting various degrees of neurological and muscle impairments frequently found in mitochondrial diseases. Although characterized by a specific loss of retinal ganglion cells, the pathophysiology of dominant optic atrophy is still poorly understood. We generated an Opa1 mouse model carrying the recurrent Opa1(delTTAG) mutation, which is found in 30% of all patients with dominant optic atrophy. We show that this mouse displays a multi-systemic poly-degenerative phenotype, with a presentation associating signs of visual failure, deafness, encephalomyopathy, peripheral neuropathy, ataxia and cardiomyopathy. Moreover, we found premature age-related axonal and myelin degenerations, increased autophagy and mitophagy and mitochondrial supercomplex instability preceding degeneration and cell death. Thus, these results support the concept that Opa1 protects against neuronal degeneration and opens new perspectives for the exploration and the treatment of mitochondrial diseases

Human Inborn Errors of Immunity : 2022 Update on the Classification from the International Union of Immunological Societies Expert Committee

We report the updated classification of inborn errors of immunity, compiled by the International Union of Immunological Societies Expert Committee. This report documents the key clinical and laboratory features of 55 novel monogenic gene defects, and 1 phenocopy due to autoantibodies, that have either been discovered since the previous update (published January 2020) or were characterized earlier but have since been confirmed or expanded in subsequent studies. While variants in additional genes associated with immune diseases have been reported in the literature, this update includes only those that the committee assessed that reached the necessary threshold to represent novel inborn errors of immunity. There are now a total of 485 inborn errors of immunity. These advances in discovering the genetic causes of human immune diseases continue to significantly further our understanding of molecular, cellular, and immunological mechanisms of disease pathogenesis, thereby simultaneously enhancing immunological knowledge and improving patient diagnosis and management. This report is designed to serve as a resource for immunologists and geneticists pursuing the molecular diagnosis of individuals with heritable immunological disorders and for the scientific dissection of cellular and molecular mechanisms underlying monogenic and related human immune diseases.Peer reviewe

The Ever-Increasing Array of Novel Inborn Errors of Immunity : an Interim Update by the IUIS Committee

The most recent updated classification of inborn errors of immunity/primary immunodeficiencies, compiled by the International Union of Immunological Societies Expert Committee, was published in January 2020. Within days of completing this report, it was already out of date, evidenced by the frequent publication of genetic variants proposed to cause novel inborn errors of immunity. As the next formal report from the IUIS Expert Committee will not be published until 2022, we felt it important to provide the community with a brief update of recent contributions to the field of inborn errors of immunity. Herein, we highlight studies that have identified 26 additional monogenic gene defects that reach the threshold to represent novel causes of immune defects.Peer reviewe

Genome-wide association and HLA fine-mapping studies identify risk loci and genetic pathways underlying allergic rhinitis

Allergic rhinitis is the most common clinical presentation of allergy, affecting 400 million people worldwide, with increasing incidence in westernized countries1,2. To elucidate the genetic architecture and understand the underlying disease mechanisms, we carried out a meta-analysis of allergic rhinitis in 59,762 cases and 152,358 controls of European ancestry and identified a total of 41 risk loci for allergic rhinitis, including 20 loci not previously associated with allergic rhinitis, which were confirmed in a replication phase of 60,720 cases and 618,527 controls. Functional annotation implicated genes involved in various immune pathways, and fine mapping of the HLA region suggested amino acid variants important for antigen binding. We further performed genome-wide association study (GWAS) analyses of allergic sensitization against inhalant allergens and nonallergic rhinitis, which suggested shared genetic mechanisms across rhinitis-related traits. Future studies of the identified loci and genes might identify novel targets for treatment and prevention of allergic rhinitis