On the regularity of stochastic currents, fractional Brownian motion and applications to a turbulence model

38 pagesInternational audienceWe study the pathwise regularity of the map $$\varphi \mapsto I(\varphi) = \int_0^T \langle \varphi(X_t), dX_t \rangle$$ where $\varphi$ is a vector function on $\R^d$ belonging to some Banach space $V$, $X$ is a stochastic process and the integral is some version of a stochastic integral defined via regularization. A \emph{stochastic current} is a continuous version of this map, seen as a random element of the topological dual of $V$. We give sufficient conditions for the current to live in some Sobolev space of distributions and we provide elements to conjecture that those are also necessary. Next we verify the sufficient conditions when the process $X$ is a $d$-dimensional fractional Brownian motion (fBm); we identify regularity in Sobolev spaces for fBm with Hurst index $H \in (1/4,1)$. Next we provide some results about general Sobolev regularity of Brownian currents. Finally we discuss applications to a model of random vortex filaments in turbulent fluids

A singular integration by parts formula for the exponential Euclidean QFT on the plane

We give a novel characterization of the Euclidean quantum field theory with exponential interaction $\nu$ on $\mathbb{R}^2$ through a renormalized integration by parts (IbP) formula, or otherwise said via an Euclidean Dyson-Schwinger equation for expected values of observables. In order to obtain the well-posedness of the singular IbP problem, we import some ideas used to analyse singular SPDEs and we require the measure to "look like" the Gaussian free field (GFF) in the sense that a suitable Wasserstein distance from the GFF is finite. This guarantees the existence of a nice coupling with the GFF which allows to control the renormalized IbP formula.Comment: 78 page

Chim3 confers survival advantage to CD4+ T cells upon HIV-1 infection by preventing HIV-1 DNA integration and HIV-1–induced G2 cell-cycle delay

AbstractThe long-term expression and the ability of a therapeutic gene to confer survival advantage to transduced cells are mandatory requirements for successful anti-HIV gene therapy. In this context, we developed lentiviral vectors (LVs) expressing the F12–viral infectivity factor (Vif) derivative Chim3. We recently showed that Chim3 inhibits HIV-1 replication in primary cells by both blocking the accumulation of retrotranscripts, independently of either human APOBEC3G (hA3G) or Vif, and by preserving the antiviral function of hA3G. These results were predictive of long-lasting survival of Chim3+ cells after HIV-1 infection. Furthermore, Vif, like Vpr, deregulates cell-cycle progression by inducing a delay in G2 phase. Thus, the aim of this study was to investigate the role of Chim3 on both cell survival and cell-cycle regulation after HIV-1 infection. Here, we provide evidence that infected Chim3+ T cells prevail over either mock- or empty-LV engineered cells, show reduced G2 accumulation, and, as a consequence, ultimately extend their lifespan. Based on these findings, Chim3 rightly belongs to the most efficacious class of antiviral genes. In conclusion, Chim3 usage in anti-HIV gene therapy based on hematopoietic stem cell (HSC) modification has to be considered as a promising therapeutic intervention to eventually cope with HIV-1 infection

A numerical approach to copolymers at selective interfaces

We consider a model of a random copolymer at a selective interface which undergoes a localization/delocalization transition. In spite of the several rigorous results available for this model, the theoretical characterization of the phase transition has remained elusive and there is still no agreement about several important issues, for example the behavior of the polymer near the phase transition line. From a rigorous viewpoint non coinciding upper and lower bounds on the critical line are known. In this paper we combine numerical computations with rigorous arguments to get to a better understanding of the phase diagram. Our main results include: - Various numerical observations that suggest that the critical line lies strictly in between the two bounds. - A rigorous statistical test based on concentration inequalities and super-additivity, for determining whether a given point of the phase diagram is in the localized phase. This is applied in particular to show that, with a very low level of error, the lower bound does not coincide with the critical line. - An analysis of the precise asymptotic behavior of the partition function in the delocalized phase, with particular attention to the effect of rare atypical stretches in the disorder sequence and on whether or not in the delocalized regime the polymer path has a Brownian scaling. - A new proof of the lower bound on the critical line. This proof relies on a characterization of the localized regime which is more appealing for interpreting the numerical data.Comment: accepted for publication on J. Stat. Phy