Hydrodynamic Limit for an Hamiltonian System with Boundary Conditions and Conservative Noise

We study the hyperbolic scaling limit for a chain of N coupled anharmonic oscillators. The chain is attached to a point on the left and there is a force (tension) $\tau$ acting on the right. In order to provide good ergodic properties to the system, we perturb the Hamiltonian dynamics with random local exchanges of velocities between the particles, so that momentum and energy are locally conserved. We prove that in the macroscopic limit the distributions of the elongation, momentum and energy, converge to the solution of the Euler system of equations, in the smooth regime.Comment: New deeply revised version. 1 figure adde

The Ground State Energy of Dilute Bose Gas in Potentials with Positive Scattering Length

The leading term of the ground state energy/particle of a dilute gas of bosons with mass $m$ in the thermodynamic limit is $2\pi \hbar^2 a \rho/m$ when the density of the gas is $\rho$, the interaction potential is non-negative and the scattering length $a$ is positive. In this paper, we generalize the upper bound part of this result to any interaction potential with positive scattering length, i.e, $a>0$ and the lower bound part to some interaction potentials with shallow and/or narrow negative parts.Comment: Latex 28 page

Hydrodynamic limit for the velocity flip model

We study the diffusive scaling limit for a chain of $N$ coupled oscillators. In order to provide the system with good ergodic properties, we perturb the Hamiltonian dynamics with random flips of velocities, so that the energy is locally conserved. We derive the hydrodynamic equations by estimating the relative entropy with respect to the local equilibrium state modified by a correction term

Superdiffusion of energy in Hamiltonian systems perturbed by a conservative noise

We review some recent results on the anomalous diffusion of energy in systems of 1D coupled oscillators and we revisit the role of momentum conservation.Comment: Proceedings of the conference PSPDE 2012 https://sites.google.com/site/meetingpspde

Bosonization, vicinal surfaces, and hydrodynamic fluctuation theory

Through a Euclidean path integral we establish that the density fluctuations of a Fermi fluid in one dimension are related to vicinal surfaces and to the stochastic dynamics of particles interacting through long range forces with inverse distance decay. In the surface picture one easily obtains the Haldane relation and identifies the scaling exponents governing the low energy, Luttinger liquid behavior. For the stochastic particle model we develop a hydrodynamic fluctuation theory, through which in some cases the large distance Gaussian fluctuations are proved nonperturbatively

Free Energies of Dilute Bose gases: upper bound

We derive a upper bound on the free energy of a Bose gas system at density $\rho$ and temperature $T$. In combination with the lower bound derived previously by Seiringer \cite{RS1}, our result proves that in the low density limit, i.e., when $a^3\rho\ll 1$, where $a$ denotes the scattering length of the pair-interaction potential, the leading term of $\Delta f$ the free energy difference per volume between interacting and ideal Bose gases is equal to 4\pi a (2\rho^2-[\rho-\rhoc]^2_+). Here, \rhoc(T) denotes the critical density for Bose-Einstein condensation (for the ideal gas), and $[\cdot ]_+$ $=$ $\max\{\cdot, 0\}$ denotes the positive part.Comment: 56 pages, no figure

Association of inflammatory biomarkers with clinical outcomes in nivolumab-treated patients with advanced hepatocellular carcinoma

Background & Aims: Nivolumab, a programmed death (PD)-1 (PD-1) inhibitor, led to durable responses, manageable safety, and increased survival in patients with advanced hepatocellular carcinoma (HCC). In our retrospective analysis, we studied the immunobiology and potential associations between biomarkers and outcomes with nivolumab in HCC. Methods: Fresh and archival tumour samples from dose-escalation and dose-expansion phases of the CheckMate 040 trial were analysed by immunohistochemistry and RNA sequencing to assess several inflammatory gene expression signatures, including CD274 (PD-ligand 1 [PD-L1]), CD8A, LAG3, and STAT1. Biomarkers were assessed for association with clinical outcomes (best overall response by blinded independent central review per RECIST v1.1 and overall survival [OS]). Results: Complete or partial tumour responses were observed in PD-L1-positive and PD-L1-negative patients treated with nivolumab monotherapy. Median OS was 28.1 (95% CI 18.2-n.a.) vs. 16.6 months (95% CI 14.2-20.2) for patients with tumour PD-L1 >= 1% vs. <1% (p = 0.03). Increased CD3 and CD8 showed a non-significant trend towards improved OS (both p = 0.08), and macrophage markers were not associated with OS. Tumour PD-1 and PD-L1 expression were associated with improved OS (p = 0.05 and p = 0.03, respectively). An inflammatory gene signature consisting of 4 genes was associated with improved objective response rate (p = 0.05) and OS (p = 0.01). Conclusions: PD-1 and PD-L1 expression, biomarkers of inflammation, and inflammatory gene signatures trended with improved survival and response. While further confirmation within a larger phase III trial is needed to evaluate predictive value of these biomarkers, these exploratory analyses suggest that anti-tumour immune response may play a role in the treatment benefit of nivolumab in HCC. Lay summary: Certain tests may be used to provide a picture of how a tumour is escaping the immune system, allowing it to continue to grow and create more tumours. Therapies such as nivolumab are designed to help the immune system fight the tumour. These tests may be used to determine how effective such therapies will be in the treatment of advanced liver cancer. (C) 2020 European Association for the Study of the Liver. Published by Elsevier B.V