A Singular Perturbation Analysis for \\Unstable Systems with Convective Nonlinearity

We use a singular perturbation method to study the interface dynamics of a non-conserved order parameter (NCOP) system, of the reaction-diffusion type, for the case where an external bias field or convection is present. We find that this method, developed by Kawasaki, Yalabik and Gunton for the time-dependant Ginzburg-Landau equation and used successfully on other NCOP systems, breaks down for our system when the strength of bias/convection gets large enough.Comment: 5 pages, PostScript forma

Critical points of Wang-Yau quasi-local energy

In this paper, we prove the following theorem regarding the Wang-Yau quasi-local energy of a spacelike two-surface in a spacetime: Let $\Sigma$ be a boundary component of some compact, time-symmetric, spacelike hypersurface $\Omega$ in a time-oriented spacetime $N$ satisfying the dominant energy condition. Suppose the induced metric on $\Sigma$ has positive Gaussian curvature and all boundary components of $\Omega$ have positive mean curvature. Suppose $H \le H_0$ where $H$ is the mean curvature of $\Sigma$ in $\Omega$ and $H_0$ is the mean curvature of $\Sigma$ when isometrically embedded in $R^3$. If $\Omega$ is not isometric to a domain in $R^3$, then 1. the Brown-York mass of $\Sigma$ in $\Omega$ is a strict local minimum of the Wang-Yau quasi-local energy of $\Sigma$, 2. on a small perturbation $\tilde{\Sigma}$ of $\Sigma$ in $N$, there exists a critical point of the Wang-Yau quasi-local energy of $\tilde{\Sigma}$.Comment: substantially revised, main theorem replaced, Section 3 adde

An investigation of the clinical impact and therapeutic relevance of a DNA damage immune response (DDIR) signature in patients with advanced gastroesophageal adenocarcinoma

Background: An improved understanding of which gastroesophageal adenocarcinoma (GOA) patients respond to both chemotherapy and immune checkpoint inhibitors (ICI) is needed. We investigated the predictive role and underlying biology of a 44-gene DNA damage immune response (DDIR) signature in patients with advanced GOA. Materials and methods: Transcriptional profiling was carried out on pretreatment tissue from 252 GOA patients treated with platinum-based chemotherapy (three dose levels) within the randomized phase III GO2 trial. Cross-validation was carried out in two independent GOA cohorts with transcriptional profiling, immune cell immunohistochemistry and epidermal growth factor receptor (EGFR) fluorescent in situ hybridization (FISH) (n = 430). Results: In the GO2 trial, DDIR-positive tumours had a greater radiological response (51.7% versus 28.5%, P = 0.022) and improved overall survival in a dose-dependent manner (P = 0.028). DDIR positivity was associated with a pretreatment inflamed tumour microenvironment (TME) and increased expression of biomarkers associated with ICI response such as CD274 (programmed death-ligand 1, PD-L1) and a microsatellite instability RNA signature. Consensus pathway analysis identified EGFR as a potential key determinant of the DDIR signature. EGFR amplification was associated with DDIR negativity and an immune cold TME. Conclusions: Our results indicate the importance of the GOA TME in chemotherapy response, its relationship to DNA damage repair and EGFR as a targetable driver of an immune cold TME. Chemotherapy-sensitive inflamed GOAs could benefit from ICI delivered in combination with standard chemotherapy. Combining EGFR inhibitors and ICIs warrants further investigation in patients with EGFR-amplified tumours

An investigation of the clinical impact and therapeutic relevance of a DNA damage immune response (DDIR) signature in patients with advanced gastroesophageal adenocarcinoma

BackgroundAn improved understanding of which gastroesophageal adenocarcinoma (GOA) patients respond to both chemotherapy and immune checkpoint inhibitors (ICI) is needed. We investigated the predictive role and underlying biology of a 44-gene DNA damage immune response (DDIR) signature in patients with advanced GOA.Materials and methodsTranscriptional profiling was carried out on pretreatment tissue from 252 GOA patients treated with platinum-based chemotherapy (three dose levels) within the randomized phase III GO2 trial. Cross-validation was carried out in two independent GOA cohorts with transcriptional profiling, immune cell immunohistochemistry and epidermal growth factor receptor (EGFR) fluorescent in situ hybridization (FISH) (n = 430).ResultsIn the GO2 trial, DDIR-positive tumours had a greater radiological response (51.7% versus 28.5%, P = 0.022) and improved overall survival in a dose-dependent manner (P = 0.028). DDIR positivity was associated with a pretreatment inflamed tumour microenvironment (TME) and increased expression of biomarkers associated with ICI response such as CD274 (programmed death-ligand 1, PD-L1) and a microsatellite instability RNA signature. Consensus pathway analysis identified EGFR as a potential key determinant of the DDIR signature. EGFR amplification was associated with DDIR negativity and an immune cold TME.ConclusionsOur results indicate the importance of the GOA TME in chemotherapy response, its relationship to DNA damage repair and EGFR as a targetable driver of an immune cold TME. Chemotherapy-sensitive inflamed GOAs could benefit from ICI delivered in combination with standard chemotherapy. Combining EGFR inhibitors and ICIs warrants further investigation in patients with EGFR-amplified tumours

Spatially heterogeneous ages in glassy dynamics

We construct a framework for the study of fluctuations in the nonequilibrium relaxation of glassy systems with and without quenched disorder. We study two types of two-time local correlators with the aim of characterizing the heterogeneous evolution: in one case we average the local correlators over histories of the thermal noise, in the other case we simply coarse-grain the local correlators. We explain why the former describe the fingerprint of quenched disorder when it exists, while the latter are linked to noise-induced mesoscopic fluctuations. We predict constraints on the pdfs of the fluctuations of the coarse-grained quantities. We show that locally defined correlations and responses are connected by a generalized local out-of-equilibrium fluctuation-dissipation relation. We argue that large-size heterogeneities in the age of the system survive in the long-time limit. The invariance of the theory under reparametrizations of time underlies these results. We relate the pdfs of local coarse-grained quantities and the theory of dynamic random manifolds. We define a two-time dependent correlation length from the spatial decay of the fluctuations in the two-time local functions. We present numerical tests performed on disordered spin models in finite and infinite dimensions. Finally, we explain how these ideas can be applied to the analysis of the dynamics of other glassy systems that can be either spin models without disorder or atomic and molecular glassy systems.Comment: 47 pages, 60 Fig