Conditional large and moderate deviations for sums of discrete random variables. Combinatoric applications

International audienceWe prove large and moderate deviation principles for the distribution of an empirical mean conditioned by the value of the sum of discrete i.i.d. random variables. Some applications for combinatoric problems are discussed

Sensitivity indices for multivariate outputs

International audienceWe define and study a generalization of Sobol sensitivity indices for the case of a vector output.Nous définissons et étudions une généralisation des indices de Sobol pour des sorties vectorielles

Sensitivity analysis for multidimensional and functional outputs

International audienceLet $X:=(X_1, \ldots, X_p)$ be random objects (the inputs), defined on some probability space $(\Omega,{\mathcal{F}}, \mathbb P)$ and valued in some measurable space $E=E_1\times\ldots \times E_p$. Further, let $Y:=Y = f(X_1, \ldots, X_p)$ be the output. Here, $f$ is a measurable function from $E$ to some Hilbert space $\mathbb{H}$ ($\mathbb{H}$ could be either of finite or infinite dimension). In this work, we give a natural generalization of the Sobol indices (that are classically defined when $Y\in\R$ ), when the output belongs to $\mathbb{H}$. These indices have very nice properties. First, they are invariant. under isometry and scaling. Further they can be, as in dimension $1$, easily estimated by using the so-called Pick and Freeze method. We investigate the asymptotic behaviour of such estimation scheme

New estimation of Sobol' indices using kernels

In this work, we develop an approach mentioned by da Veiga and Gamboa in 2013. It consists in extending the very interestingpoint of view introduced in \cite{gine2008simple} to estimate general nonlinear integral functionals of a density on the real line, by using empirically a kernel estimator erasing the diagonal terms. Relaxing the positiveness assumption on the kernel and choosing a kernel of order large enough, we are able to prove a central limit theorem for estimating Sobol' indices of any order (the bias is killed thanks to this signed kernel)

Statistical inference for Sobol pick freeze Monte Carlo method

International audienceMany mathematical models involve input parameters, which are not precisely known. Global sensitivity analysis aims to identify the parameters whose uncertainty has the largest impact on the variability of a quantity of interest (output of the model). One of the statistical tools used to quantify the influence of each input variable on the output is the Sobol sensitivity index. We consider the statistical estimation of this index from a finite sample of model outputs. We study asymptotic and non-asymptotic properties of two estimators of Sobol indices. These properties are applied to significance tests and estimation by confidence intervals

Understanding brain dysfunction in sepsis

Sepsis often is characterized by an acute brain dysfunction, which is associated with increased morbidity and mortality. Its pathophysiology is highly complex, resulting from both inflammatory and noninflammatory processes, which may induce significant alterations in vulnerable areas of the brain. Important mechanisms include excessive microglial activation, impaired cerebral perfusion, blood–brain-barrier dysfunction, and altered neurotransmission. Systemic insults, such as prolonged inflammation, severe hypoxemia, and persistent hyperglycemia also may contribute to aggravate sepsis-induced brain dysfunction or injury. The diagnosis of brain dysfunction in sepsis relies essentially on neurological examination and neurological tests, such as EEG and neuroimaging. A brain MRI should be considered in case of persistent brain dysfunction after control of sepsis and exclusion of major confounding factors. Recent MRI studies suggest that septic shock can be associated with acute cerebrovascular lesions and white matter abnormalities. Currently, the management of brain dysfunction mainly consists of control of sepsis and prevention of all aggravating factors, including metabolic disturbances, drug overdoses, anticholinergic medications, withdrawal syndromes, and Wernicke’s encephalopathy. Modulation of microglial activation, prevention of blood–brain-barrier alterations, and use of antioxidants represent relevant therapeutic targets that may impact significantly on neurologic outcomes. In the future, investigations in patients with sepsis should be undertaken to reduce the duration of brain dysfunction and to study the impact of this reduction on important health outcomes, including functional and cognitive status in survivors

Gauge fields for ultracold atoms in optical superlattices

We present a scheme that produces a strong U(1)-like gauge field on cold atoms confined in a two-dimensional square optical lattice. Our proposal relies on two essential features, a long-lived metastable excited state that exists for alkaline-earth or Ytterbium atoms, and an optical superlattice. As in the proposal by Jaksch and Zoller [New Journal of Physics 5, 56 (2003)], laser-assisted tunneling between adjacent sites creates an effective magnetic field. In the tight-binding approximation, the atomic motion is described by the Harper Hamiltonian, with a flux across each lattice plaquette that can realistically take any value between 0 and $\pi$. We show how to take advantage of the superlattice to ensure that each plaquette acquires the same phase, thus simulating a uniform magnetic field. We discuss the observable consequences of the artificial gauge field on non-interacting bosonic and fermionic gases. We also outline how the scheme can be generalized to non-Abelian gauge fields

Structure of a single-chain Fv bound to the 17 N-terminal residues of huntingtin provides insights into pathogenic amyloid formation and suppression.

Huntington's disease is triggered by misfolding of fragments of mutant forms of the huntingtin protein (mHTT) with aberrant polyglutamine expansions. The C4 single-chain Fv antibody (scFv) binds to the first 17 residues of huntingtin [HTT(1-17)] and generates substantial protection against multiple phenotypic pathologies in situ and in vivo. We show in this paper that C4 scFv inhibits amyloid formation by exon1 fragments of huntingtin in vitro and elucidate the structural basis for this inhibition and protection by determining the crystal structure of the complex of C4 scFv and HTT(1-17). The peptide binds with residues 3-11 forming an amphipathic helix that makes contact with the antibody fragment in such a way that the hydrophobic face of this helix is shielded from the solvent. Residues 12-17 of the peptide are in an extended conformation and interact with the same region of another C4 scFv:HTT(1-17) complex in the asymmetric unit, resulting in a β-sheet interface within a dimeric C4 scFv:HTT(1-17) complex. The nature of this scFv-peptide complex was further explored in solution by high-resolution NMR and physicochemical analysis of species in solution. The results provide insights into the manner in which C4 scFv inhibits the aggregation of HTT, and hence into its therapeutic potential, and suggests a structural basis for the initial interactions that underlie the formation of disease-associated amyloid fibrils by HTT.E.D.G. and C.M.D. are grateful for support by the Medical Research Council (G1002272). We also thank the Hereditary Disease Foundation (A.M.). D.Y.C. is supported by the Crystallographic X-ray Facility at the Department of Biochemistry, University of Cambridge. We would like to acknowledge Dr. Katherine Stott at the Biophysics Facility at the Department of Biochemistry, University of Cambridge, for her help with the ultracentrifugation experiments and Prof. Weiss and Dr. Desplancq at the Ecole Supérieure de Biotechnologie de Strasbourg for the kind gift of the gankyrin-specific scFv, scFvR19 as a control for our in vitro aggregation experiments.This is the final published version. It first appeared at http://www.sciencedirect.com/science/article/pii/S002228361500217X#