Functional Expansions

Path dependence is omnipresent in social science, engineering, and finance. It reflects the influence of the past on the future, often expressed through functionals. However, non-Markovian problems are often infinite-dimensional, thus challenging from a conceptual and computational perspective. In this work, we shed light on expansions of functionals. First, we treat static expansions made around paths of fixed length and propose a generalization of the Wiener series$-$the intrinsic value expansion (IVE). In the dynamic case, we revisit the functional Taylor expansion (FTE). The latter connects the functional It\^o calculus with the signature to quantify the effect in a functional when a "perturbation" path is concatenated with the source path. In particular, the FTE elegantly separates the functional from future trajectories. The notions of real analyticity and radius of convergence are also extended to the path space. We discuss other dynamic expansions arising from Hilbert projections and the Wiener chaos, and finally show financial applications of the FTE to the pricing and hedging of exotic contingent claims.Comment: 39 pages, 7 figure

Host hindrance to HIV-1 replication in monocytes and macrophages

Monocytes and macrophages are targets of HIV-1 infection and play critical roles in multiple aspects of viral pathogenesis. HIV-1 can replicate in blood monocytes, although only a minor proportion of circulating monocytes harbor viral DNA. Resident macrophages in tissues can be infected and function as viral reservoirs. However, their susceptibility to infection, and their capacity to actively replicate the virus, varies greatly depending on the tissue localization and cytokine environment. The susceptibility of monocytes to HIV-1 infection in vitro depends on their differentiation status. Monocytes are refractory to infection and become permissive upon differentiation into macrophages. In addition, the capacity of monocyte-derived macrophages to sustain viral replication varies between individuals. Host determinants regulate HIV-1 replication in monocytes and macrophages, limiting several steps of the viral life-cycle, from viral entry to virus release. Some host factors responsible for HIV-1 restriction are shared with T lymphocytes, but several anti-viral mechanisms are specific to either monocytes or macrophages. Whilst a number of these mechanisms have been identified in monocytes or in monocyte-derived macrophages in vitro, some of them have also been implicated in the regulation of HIV-1 infection in vivo, in particular in the brain and the lung where macrophages are the main cell type infected by HIV-1. This review focuses on cellular factors that have been reported to interfere with HIV-1 infection in monocytes and macrophages, and examines the evidences supporting their role in vivo, highlighting unique aspects of HIV-1 restriction in these two cell types

Stopping Times of Boundaries: Relaxation and Continuity

We study boundaries and their hitting times in the context of optimal stopping and Bermudan-style options. We prove the continuity of the map linking the boundary to the value of its associated stopping policy. While the supremum norm is used to compare continuous boundaries, a weaker topology induced by the so-called relaxed $L^{\infty}$ distance is used in the semicontinuous case. Relaxed stopping rules and their properties are also discussed. Incidentally, we provide a convergence analysis for neural stopping boundaries [Reppen, Soner, and Tissot-Daguette, Neural Optimal Stopping Boundary, 2022] entailing the universal approximation capability of neural networks and the notion of inf/sup convolution.Comment: 22 pages, 4 figure

Incidence des infections nosocomiales à l'Hôpital gériatrique Pierre Garraud au cours du premier semestre 2004 (révision de 347 dossiers)

LYON1-BU Santé (693882101) / SudocPARIS-BIUM (751062103) / SudocSudocFranceF

External validation of a D-dimer age-adjusted cut-off for the exclusion of pulmonary embolism.

International audienc

Value of spontaneous hyperdensity of cerebral venous thrombosis on helical CT

International audienceBACKGROUND: Excluding a cerebral venous thrombosis (CVT) through imaging is a frequent request in the emergency setting. This assessment often starts by an unenhanced brain computed tomography (CT). PURPOSE: Re-evaluate the value of spontaneous hyperdensity of CVT on helical unenhanced brain CT. METHODS: Multicentric retrospective study on CVT probability based on visual assessment of spontaneous hyperdensity of cerebral venous system, performed by four blinded radiologists, individually then collectively, on a population including 14 helical unenhanced brain CTs with CVT and 102 unenhanced brain CTs without CVT (all confirmed by CT or magnetic resonance [MR] venography). Exclusion criteria: no DICOM image, symptoms >15 days, CVT indirect signs on unenhanced CT. A fifth radiologist set 768 regions of interest to measure and to compare the density within the normal venous sinuses and the CVTs. RESULTS: After consensus reading, sensitivity of this sign for CVT diagnosis was 100%, specificity 95.1%, and negative predictive value (NPV) 100%, with high individual NPV (99-100%). Area under the receiver-operating characteristic curve was 0.992 after consensus (0.976-0.986 individually). The spontaneous density was significantly different (P 70 HU reported only within the CVTs, except for the horizontal part of the superior sagittal sinus (hSSS). CONCLUSION: The dense triangle sign on helical unenhanced brain CT has an excellent NPV to exclude a sinus thrombosis during the first 2 weeks. However, we believe that visual assessment of spontaneous hyperdensity is not sufficient for the diagnosis of CVT, with possible false-positive of the hSSS on unenhanced CT