Rearranged Stochastic Heat Equation

The purpose of this work is to provide an explicit construction of a strong Feller semigroup on the space of probability measures over the real line that additionally maps bounded measurable functions into Lipschitz continuous functions, with a Lipschitz constant that blows up in an integrable manner in small time. Our construction relies on a rearranged version of the stochastic heat equation on the circle driven by a coloured noise. Formally, this stochastic equation writes as a reflected equation in infinite dimension, a topic that is known to be challenging. Under the action of the rearrangement, the solution is forced to live in a space of quantile functions that is isometric to the space of probability measures on the real line. We prove the equation to be solvable by means of an Euler scheme in which we alternate flat dynamics in the space of random variables on the circle with a rearrangement operation that projects back the random variables onto the subset of quantile functions. A first challenge is to prove that this scheme is tight. A second one is to provide a consistent theory for the limiting reflected equation and in particular to interpret in a relevant manner the reflection term. The last step in our work is to establish the aforementioned Lipschitz property of the semigroup by adapting earlier ideas from the Bismut-Elworthy-Li formula in stochastic analysis

EczemaPred: a computational framework for personalised prediction of eczema severity dynamics

Background: Atopic dermatitis (AD) is a chronic inflammatory skin disease leading to substantial quality of life impairment with heterogeneous treatment responses. People with AD would benefit from personalised treatment strategies, whose design requires predicting how AD severity evolves for each individual. Objective: This study aims to develop a computational framework for personalised prediction of AD severity dynamics. Methods: We introduced EczemaPred, a computational framework to predict patient-dependent dynamic evolution of AD severity using Bayesian state-space models that describe latent dynamics of AD severity items and how they are measured. We used EczemaPred to predict the dynamic evolution of validated patient-oriented scoring atopic dermatitis (PO-SCORAD) by combining predictions from the models for the nine severity items of PO-SCORAD (six intensity signs, extent of eczema, and two subjective symptoms). We validated this approach using longitudinal data from two independent studies: a published clinical study in which PO-SCORAD was measured twice weekly for 347 AD patients over 17 weeks, and another one in which PO-SCORAD was recorded daily by 16 AD patients for 12 weeks. Results: EczemaPred achieved good performance for personalised predictions of PO-SCORAD and its severity items daily to weekly. EczemaPred outperformed standard time-series forecasting models such as a mixed effect autoregressive model. The uncertainty in predicting PO-SCORAD was mainly attributed to that in predicting intensity signs (75% of the overall uncertainty). Conclusions: EczemaPred serves as a computational framework to make a personalised prediction of AD severity dynamics relevant to clinical practice. EczemaPred is available as an R package

Structural Basis for Potentiation by Alcohols and Anaesthetics in a Ligand-gated Ion Channel

Ethanol alters nerve signalling by interacting with proteins in the central nervous system, particularly pentameric ligand-gated ion channels. A recent series of mutagenesis experiments on Gloeobacter violaceus ligand-gated ion channel, a prokaryotic member of this family, identified a single-site variant that is potentiated by pharmacologically relevant concentrations of ethanol. Here we determine crystal structures of the ethanol-sensitized variant in the absence and presence of ethanol and related modulators, which bind in a transmembrane cavity between channel subunits and may stabilize the open form of the channel. Structural and mutagenesis studies defined overlapping mechanisms of potentiation by alcohols and anaesthetics via the inter-subunit cavity. Furthermore, homology modelling show this cavity to be conserved in human ethanol-sensitive glycine and GABA(A) receptors, and to involve residues previously shown to influence alcohol and anaesthetic action on these proteins. These results suggest a common structural basis for ethanol potentiation of an important class of targets for neurological actions of ethanol

Large Deviations Analysis for Distributed Algorithms in an Ergodic Markovian Environment

We provide a large deviations analysis of deadlock phenomena occurring in distributed systems sharing common resources. In our model transition probabilities of resource allocation and deallocation are time and space dependent. The process is driven by an ergodic Markov chain and is reflected on the boundary of the d-dimensional cube. In the large resource limit, we prove Freidlin-Wentzell estimates, we study the asymptotic of the deadlock time and we show that the quasi-potential is a viscosity solution of a Hamilton-Jacobi equation with a Neumann boundary condition. We give a complete analysis of the colliding 2-stacks problem and show an example where the system has a stable attractor which is a limit cycle

Probabilistic analysis of the upwind scheme for transport

We provide a probabilistic analysis of the upwind scheme for multi-dimensional transport equations. We associate a Markov chain with the numerical scheme and then obtain a backward representation formula of Kolmogorov type for the numerical solution. We then understand that the error induced by the scheme is governed by the fluctuations of the Markov chain around the characteristics of the flow. We show, in various situations, that the fluctuations are of diffusive type. As a by-product, we prove that the scheme is of order 1/2 for an initial datum in BV and of order 1/2-a, for all a>0, for a Lipschitz continuous initial datum. Our analysis provides a new interpretation of the numerical diffusion phenomenon

Targeting intratumoral B cells with rituximab in addition to CHOP in angioimmunoblastic T-cell lymphoma. A clinicobiological study of the GELA.

Background In angioimmunoblastic T-cell lymphoma, symptoms linked to B-lymphocyte activation are common, and variable numbers of CD20(+) large B-blasts, often infected by Epstein-Barr virus, are found in tumor tissues. We postulated that the disruption of putative B-T interactions and/or depletion of the Epstein-Barr virus reservoir by an anti-CD20 monoclonal antibody (rituximab) could improve the clinical outcome produced by conventional chemotherapy. DESIGN AND METHODS: Twenty-five newly diagnosed patients were treated, in a phase II study, with eight cycles of rituximab + chemotherapy (R-CHOP21). Tumor infiltration, B-blasts and Epstein-Barr virus status in tumor tissue and peripheral blood were fully characterized at diagnosis and were correlated with clinical outcome. RESULTS: A complete response rate of 44% (95% CI, 24% to 65%) was observed. With a median follow-up of 24 months, the 2-year progression-free survival rate was 42% (95% CI, 22% to 61%) and overall survival rate was 62% (95% CI, 40% to 78%). The presence of Epstein-Barr virus DNA in peripheral blood mononuclear cells (14/21 patients) correlated with Epstein-Barr virus score in lymph nodes (P<0.004) and the detection of circulating tumor cells (P=0.0019). Despite peripheral Epstein-Barr virus clearance after treatment, the viral load at diagnosis (>100 copy/μg DNA) was associated with shorter progression-free survival (P=0.06). Conclusions We report here the results of the first clinical trial targeting both the neoplastic T cells and the microenvironment-associated CD20(+) B lymphocytes in angioimmunoblastic T-cell lymphoma, showing no clear benefit of adding rituximab to conventional chemotherapy. A strong relationship, not previously described, between circulating Epstein-Barr virus and circulating tumor cells is highlighted

Verticalization of bacterial biofilms

Biofilms are communities of bacteria adhered to surfaces. Recently, biofilms of rod-shaped bacteria were observed at single-cell resolution and shown to develop from a disordered, two-dimensional layer of founder cells into a three-dimensional structure with a vertically-aligned core. Here, we elucidate the physical mechanism underpinning this transition using a combination of agent-based and continuum modeling. We find that verticalization proceeds through a series of localized mechanical instabilities on the cellular scale. For short cells, these instabilities are primarily triggered by cell division, whereas long cells are more likely to be peeled off the surface by nearby vertical cells, creating an "inverse domino effect". The interplay between cell growth and cell verticalization gives rise to an exotic mechanical state in which the effective surface pressure becomes constant throughout the growing core of the biofilm surface layer. This dynamical isobaricity determines the expansion speed of a biofilm cluster and thereby governs how cells access the third dimension. In particular, theory predicts that a longer average cell length yields more rapidly expanding, flatter biofilms. We experimentally show that such changes in biofilm development occur by exploiting chemicals that modulate cell length.Comment: Main text 10 pages, 4 figures; Supplementary Information 35 pages, 15 figure

RNA fusions involving CD28 are rare in peripheral T-cell lymphomas and concentrate mainly in those derived from follicular helper T cells.

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