Ultraviolet Renormalization of the Nelson Hamiltonian through Functional Integration

Starting from the N-particle Nelson Hamiltonian defined by imposing an ultraviolet cutoff, we perform ultraviolet renormalization by showing that in the zero cutoff limit a self-adjoint operator exists after a logarithmically divergent term is subtracted from the original Hamiltonian. We obtain this term as the diagonal part of a pair interaction appearing in the density of a Gibbs measure derived from the Feynman-Kac representation of the Hamiltonian. Also, we show existence of a weak coupling limit of the renormalized Hamiltonian and derive an effective Yukawa interaction potential between the particles.Comment: 28 pages, revision of section 2 and typos correcte

Flows driven by Banach space-valued rough paths

We show in this note how the machinery of C^1-approximate flows devised in the work "Flows driven by rough paths", and applied there to reprove and extend most of the results on Banach space-valued rough differential equations driven by a finite dimensional rough path, can be used to deal with rough differential equations driven by an infinite dimensional Banach space-valued weak geometric Holder p-rough paths, for any p>2, giving back Lyons' theory in its full force in a simple way.Comment: 8 page

Quenched central limit theorem for the stochastic heat equation in weak disorder

We continue with the study of the mollified stochastic heat equation in $d\geq 3$ given by $d u_{\epsilon,t}=\frac 12\Delta u_{\epsilon,t}+ \beta \epsilon^{(d-2)/2} \,u_{\epsilon,t} \,d B_{\epsilon,t}$ with spatially smoothened cylindrical Wiener process $B$, whose (renormalized) Feynman-Kac solution describes the partition function of the continuous directed polymer. In an earlier work (\cite{MSZ16}), a phase transition was obtained, depending on the value of $\beta>0$ in the limiting object of the smoothened solution $u_\epsilon$ as the smoothing parameter $\epsilon\to 0$ This partition function naturally defines a quenched polymer path measure and we prove that as long as $\beta>0$ stays small enough while $u_\epsilon$ converges to a strictly positive non-degenerate random variable, the distribution of the diffusively rescaled Brownian path converges under the aforementioned polymer path measure to standard Gaussian distribution.Comment: Minor revisio

NMR interaction studies of Neu5Ac-α-(2,6)-Gal-β-(1-4)-GlcNAc with influenza-virus hemagglutinin expressed in transfected human cells

The emergence of escape-mutants of influenza hemagglutinin (HA) following vaccination compels the yearly re-formulation of flu vaccines. Since binding the sialic acid receptor remains in all cases essential for infection, small-molecule inhibitors of HA binding to sialic acid could be interesting therapeutic complements or alternatives to immuno-prophylaxis in the control of flu epidemics. In this work, we made use of NMR spectroscopy to study the interaction between a derivative of sialic acid (the Neu5Ac-\u3b1-(2,6)-Gal-\u3b2-(1-4)-GlcNAc trisaccharide) and HAs (H1 and H5) from human and avian strains of influenza virus, directly expressed on the surface of stable transfected 293 T human cells. The HAs were shown to retain their native trimeric conformation and binding properties. Exploiting the magnetization transfer between the proteins and the ligand, we obtained evidence of the binding event and mapped the (non-identical) sugar epitopes recognized by the two HA species. The rapid and reliable method for screening sialic acid-related HA ligands we have developed could yield useful information for an efficient drug design

Malliavin calculus for fractional heat equation

In this article, we give some existence and smoothness results for the law of the solution to a stochastic heat equation driven by a finite dimensional fractional Brownian motion with Hurst parameter $H>1/2$. Our results rely on recent tools of Young integration for convolutional integrals combined with stochastic analysis methods for the study of laws of random variables defined on a Wiener space.Comment: Dedicated to David Nualart on occasion of his 60th birthda

On small time asymptotics for rough differential equations driven by fractional Brownian motions

We survey existing results concerning the study in small times of the density of the solution of a rough differential equation driven by fractional Brownian motions. We also slightly improve existing results and discuss some possible applications to mathematical finance.Comment: This is a survey paper, submitted to proceedings in the memory of Peter Laurenc

Long-Term Safety of Anti-TNF Adalimumab in HBc Antibody-Positive Psoriatic Arthritis Patients: A Retrospective Case Series of 8 Patients

Immunosuppressive drugs commonly used in the treatment of psoriatic arthritis make patients more susceptible to viral, bacterial, and fungal infections because of their mechanism of action. They not only increase the risk of new infections but also act altering the natural course of preexisting infections. While numerous data regarding the reactivation of tuberculosis infection are available in the literature, poor information about the risk of reactivation or exacerbation of hepatitis viruses B and C infections during treatment with biologics has been reported. Furthermore, reported series with biological therapy included short periods of followup, and therefore, they are not adequate to verify the risk of reactivation in the long-term treatment. Our study evaluated patients with a history of hepatitis B and psoriatic arthritis treated with adalimumab and monitored up to six years. During the observation period, treatment was effective and well tolerated in all patients, and liver function tests and viral load levels remained unchanged