Boundary fluxes for non-local diffusion

We study a nonlocal diffusion operator in a bounded smooth domain prescribing the flux through the boundary. This problem may be seen as a generalization of the usual Neumann problem for the heat equation. First, we prove existence, uniqueness and a comparison principle. Next, we study the behavior of solutions for some prescribed boundary data including blowing up ones. Finally, we look at a nonlinear flux boundary condition

A nonlocal inhomogeneous dispersal process

AbstractThis article in devoted to the study of the nonlocal dispersal equationut(x,t)=∫RJ(x−yg(y))u(y,t)g(y)dy−u(x,t)in R×[0,∞), and its stationary counterpart. We prove global existence for the initial value problem, and under suitable hypothesis on g and J, we prove that positive bounded stationary solutions exist. We also analyze the asymptotic behavior of the finite mass solutions as t→∞, showing that they converge locally to zero

2-Vector Spaces and Groupoids

This paper describes a relationship between essentially finite groupoids and 2-vector spaces. In particular, we show to construct 2-vector spaces of Vect-valued presheaves on such groupoids. We define 2-linear maps corresponding to functors between groupoids in both a covariant and contravariant way, which are ambidextrous adjoints. This is used to construct a representation--a weak functor--from Span(Gpd) (the bicategory of groupoids and spans of groupoids) into 2Vect. In this paper we prove this and give the construction in detail.Comment: 44 pages, 5 figures - v2 adds new theorem, significant changes to proofs, new sectio

The differential influences of human-induced disturbances on tree regeneration community: a landscape approach

Understanding the processes shaping biological communities under interacting disturbances is\ud a core challenge in ecology. Although the impacts of human-induced disturbances on forest ecosystems have\ud been extensively studied, less attention has been paid to understanding how tree regeneration at the\ud community level responds to such disturbances. Moreover, these previous studies have not considered how\ud these effects change according to major social and environmental factors that can influence forest use at a\ud landscape scale. In this study, we investigate the effects of cattle grazing and selective logging on the\ud composition of tree regeneration communities in relation to forest successional stage and land tenure regime\ud in Chilean temperate forests, a global biodiversity hotspot. We recorded seedlings, saplings and basal area of\ud stumps of tree species (as a surrogate for selective logging), and number of cattle dung pats (as a surrogate\ud for cattle pressure) in 129 25 3 20 m plots in small (,200 ha) and large properties in different successional\ud stages (old-growth, intermediate, secondary forests). The regeneration of the ten more abundant species as\ud predicted by human disturbance, land tenure, forest successional stage, and number of parent trees was\ud modelled using generalised linear models. Predictions for each individual model were made under different\ud scenarios of human disturbance. The predicted regeneration results were assembled and subjected to\ud ordination analyses and permutation multivariate analyses of variance to determine differences in\ud regeneration composition under each scenario. In most cases, best-fit models contained at least one of the\ud explanatory variables accounting for human disturbance. The effects of selective logging on tree regeneration\ud varied depending on land tenure regime, but cattle grazing always exhibited a negative effect. Our results\ud revealed that cattle have a more negative effect on forest regeneration than selective logging, especially in\ud old-growth forests and small properties. Our analytical approach contributes to the understanding of the\ud differential influence of human-induced disturbances on the tree regeneration community at a landscape\ud scale. It can inform conservation policies and actions, which should focus on addressing themain disturbance\ud factors and on developing strategies to conserve the most sensitive species to such disturbances.C. Zamorano-Elgueta was supported by a CON-\ud ICYT pre-doctoral fellowship (Government of Chile),\ud the European Comission (Project contract DCI-ENV/\ud 2010/222-412), the Chilean NGO Forest Engineers for\ud Native Forest (Forestales por el Bosque Nativo, www.\ud bosquenativo.cl) and project REMEDINAL-2 (Comu-\ud nidad de Madrid, S2009/AMB-1783). L. Cayuela was\ud supported by project REMEDINAL-2. This work is\ud part of the objectives of projects CGL2010-18312\ud (CICYT, Ministerio de Economı́a y Competividad de\ud Espana). The authors acknowledge the valuable\ud support of Vero ́nica Pı́riz, Cony Becerra, Rodrigo\ud Gangas, Oscar Concha, Eduardo Neira and staff from\ud the Valdivian Coastal Reserve, as well as the National\ud Forest Service of Chile (Corporación Nacional Forestal

Endothelial Plasmalemma Vesicle-Associated Protein Regulates the Homeostasis of Splenic Immature B Cells and B-1 B Cells.

Plasmalemma vesicle associated protein (Plvap) is an endothelial protein with roles in endothelial diaphragm formation and maintenance of basal vascular permeability. At the same time Plvap has roles in immunity by facilitating leukocyte diapedesis at inflammatory sites and controlling peripheral lymph node morphogenesis and the entry of soluble antigens into lymph node conduits. Based on its postulated role in diapedesis, we have investigated the role of Plvap in hematopoiesis and show that deletion of Plvap results in a dramatic decrease of IgM(+)IgD(lo) B cells in both the spleen and peritoneal cavity. Tissue specific deletion of Plvap demonstrates that the defect is B cell extrinsic, as B cell and pan hematopoietic Plvap deletion has no effect on IgM(+)IgD(lo) B cell numbers. Endothelial specific deletion of Plvap in the embryo or at adult stage recapitulates the full Plvap knockout phenotype whereas endothelial specific reconstitution of Plvap under the Chd5 promoter rescues the IgM(+)IgD(lo) B cell phenotype. Taken together, these results show that Plvap expression in endothelial cells is important in the maintenance of IgM(+) B cells in the spleen and peritoneal cavity

Diversity of gut microflora is required for the generation of B cell with regulatory properties in a skin graft model

B cells have been reported to promote graft rejection through alloantibody production. However, there is growing evidence that B cells can contribute to the maintenance of tolerance. Here, we used a mouse model of MHC-class I mismatched skin transplantation to investigate the contribution of B cells to graft survival. We demonstrate that adoptive transfer of B cells prolongs skin graft survival but only when the B cells were isolated from mice housed in low sterility "conventional" (CV) facilities and not from mice housed in pathogen free facilities (SPF). However, prolongation of skin graft survival was lost when B cells were isolated from IL-10 deficient mice housed in CV facilities. The suppressive function of B cells isolated from mice housed in CV facilities correlated with an anti-inflammatory environment and with the presence of a different gut microflora compared to mice maintained in SPF facilities. Treatment of mice in the CV facility with antibiotics abrogated the regulatory capacity of B cells. Finally, we identified transitional B cells isolated from CV facilities as possessing the regulatory function. These findings demonstrate that B cells, and in particular transitional B cells, can promote prolongation of graft survival, a function dependent on licensing by gut microflora

AQFT from n-functorial QFT

There are essentially two different approaches to the axiomatization of quantum field theory (QFT): algebraic QFT, going back to Haag and Kastler, and functorial QFT, going back to Atiyah and Segal. More recently, based on ideas by Baez and Dolan, the latter is being refined to "extended" functorial QFT by Freed, Hopkins, Lurie and others. The first approach uses local nets of operator algebras which assign to each patch an algebra "of observables", the latter uses n-functors which assign to each patch a "propagator of states". In this note we present an observation about how these two axiom systems are naturally related: we demonstrate under mild assumptions that every 2-dimensional extended Minkowskian QFT 2-functor ("parallel surface transport") naturally yields a local net. This is obtained by postcomposing the propagation 2-functor with an operation that mimics the passage from the Schroedinger picture to the Heisenberg picture in quantum mechanics. The argument has a straightforward generalization to general pseudo-Riemannian structure and higher dimensions.Comment: 39 pages; further examples added: Hopf spin chains and asymptotic inclusion of subfactors; references adde

Comprehensive Cell Surface Antigen Analysis Identifies Transferrin Receptor Protein-1 (CD71) as a Negative Selection Marker for Human Neuronal Cells.

Cell state-, developmental stage-, and lineage-specific combinatorial expression of cluster of differentiation (CD) molecules enables the identification of cellular subsets via multicolor flow cytometry. We describe an exhaustive characterization of neural cell types by surface antigens, exploiting human pluripotent stem cell-derived neural cell systems. Using multiwell screening approaches followed by detailed validation of expression patterns and dynamics, we exemplify a strategy for resolving cellular heterogeneity in stem cell paradigms. In addition to providing a catalog of surface antigens expressed in the neural lineage, we identified the transferrin receptor-1 (CD71) to be differentially expressed in neural stem cells and differentiated neurons. In this context, we describe a role for N-Myc proto-oncogene (MYCN) in maintaining CD71 expression in proliferating neural cells. We report that in vitro human stem cell-derived neurons lack CD71 surface expression and that the observed differential expression can be used to identify and enrich CD71- neuronal derivatives from heterogeneous cultures. Stem Cells 2019;37:1293-1306