A structure theorem for elliptic and parabolic operators with applications to homogenization of operators of Kolmogorov type

We consider the operators $$\nabla_X\cdot(A(X)\nabla_X),\ \nabla_X\cdot(A(X)\nabla_X)-\partial_t,\ \nabla_X\cdot(A(X)\nabla_X)+X\cdot\nabla_Y-\partial_t,$$ where $X\in \Omega$, $(X,t)\in \Omega\times \mathbb R$ and $(X,Y,t)\in \Omega\times \mathbb R^m\times \mathbb R$, respectively, and where $\Omega\subset\mathbb R^m$ is a (unbounded) Lipschitz domain with defining function $\psi:\mathbb R^{m-1}\to\mathbb R$ being Lipschitz with constant bounded by $M$. Assume that the elliptic measure associated to the first of these operators is mutually absolutely continuous with respect to the surface measure $\mathrm{d} \sigma(X)$, and that the corresponding Radon-Nikodym derivative or Poisson kernel satisfies a scale invariant reverse H\"older inequality in $L^p$, for some fixed $p$, $1<p<\infty$, with constants depending only on the constants of $A$, $m$ and the Lipschitz constant of $\psi$, $M$. Under this assumption we prove that then the same conclusions are also true for the parabolic measures associated to the second and third operator with $\mathrm{d} \sigma(X)$ replaced by the surface measures $\mathrm{d} \sigma(X)\mathrm{d} t$ and $\mathrm{d} \sigma(X)\mathrm{d} Y\mathrm{d} t$, respectively. This structural theorem allows us to reprove several results previously established in the literature as well as to deduce new results in, for example, the context of homogenization for operators of Kolmogorov type. Our proof of the structural theorem is based on recent results established by the authors concerning boundary Harnack inequalities for operators of Kolmogorov type in divergence form with bounded, measurable and uniformly elliptic coefficients

Spatiotemporal Modeling of Swedish Scots Pine Stands

The growth-interaction (GI) process is used for the spatiotemporal modeling of measurements of locations and radii at breast height made at three different time points of the individual trees in 10 Scots pine (Pinus sylvestris) plots from the Swedish National Forest Inventory. The GI process places trees at random locations in the study region and assigns sizes to the trees, which interact and grow with time. It has been used to model plots in previous studies and to improve the fit we suggest some modifications: a different location assignment strategy and a different open-growth (growth under negligible competition) function. We believe that the calibration data contain trees that are too small to reflect the open growth properly, which primarily affects the carrying capacity parameter. To better represent the open growth of Scots pines, we evaluate the open growth from a separate set of data (size and age measurements of older and larger single Scots pines). A linear relationship is found between the plot's estimated site indices and the sizes, and this is exploited in the estimation of the carrying capacity. We finally estimate the remaining GI process parameters and test the goodness of fit on simulated predictions from the fitted model

Secretory leukocyte protease inhibitor in punch biopsies from human colonic mucosa.

Secretory leukocyte protease inhibitor (SLPI) is a well-known protease inhibitor. Its function is thought to be protease/protease-inhibitor balance. Free proteolytic activity, mainly pancreatic elastase, anionic trypsin and granulocytic elastase, has been demonstrated in faecal extracts from patients with ulcerative colitis. We wanted to verify that SLPI is actually secreted from normal human colonic mucosa. Also, we wanted to ascertain whether studies of SLPI secretion based on punch biopsies were dependent on biopsy area or on biopsy circumference. Normal colonic mucosa was sampled during surgery for colonic cancer. A total of 36 samples from four patients were used. Mucosa preparation was carried out using a punch biopsy technique, and samples of 3, 4 and 6 mm diameter were used. All media contained SLPI at varying concentrations. When expressed in terms of the sample area, the secretion per millimetre-squared seemed to decrease with increasing area. When calculated as secretion per circumference, secretion seemed to be constant. In conclusion, SLPI was secreted from normal human colonic mucosa. The SLPI secretion seemed dependent on the circumference of the biopsy rather than on the area of the biopsy

The presence of elafin, SLPI, IL1-RA and STNFalpha RI in head and neck squamous cell carcinomas and their relation to the degree of tumour differentiation.

Biopsy samples of head and neck carcinomas were investigated with regard to elafin, secretory leukocyte protease inhibitor (SLPI), interleukin 1-receptor antagonist [(IL)1-RA] and soluble tumour necrosis factor alpha receptor antagonist (STNFalpha RI). SLPI and elafin are serine protease inhibitors produced in the serous cells of the upper respiratory airways and in the keratinocytes, respectively. We have now found the presence of elafin and SLPI in squamous cell carcinomas of the upper respiratory tract (tonsillar, hypopharyngeal, tongue, mouth floor, gingival and laryngeal cancer). Significantly higher amounts of SLPI and elafin are present in well-differentiated and moderately differentiated tumours than in poorly differentiated tumours (p < 0.0001 and p < 0.0015). Tumour necrosis factor-alpha and IL-1beta have been shown to stimulate the production of SLPI and elafin. Since these cytokines can both be difficult to detect, we chose to study their inhibitors, STNFalpha RI and IL1-RA, instead. IL1-RA was expressed in highly differentiated tumours as well as in poorly differentiated ones. No significant difference was seen between the groups. STNFalpha RI was only found in very small amounts, sparsely distributed in the tumours, and was not related to the degree of differentiation

Diet, microbiota, and the mucus layer: The guardians of our health

The intestinal tract is an ecosystem in which the resident microbiota lives in symbiosis with its host. This symbiotic relationship is key to maintaining overall health, with dietary habits of the host representing one of the main external factors shaping the microbiome-host relationship. Diets high in fiber and low in fat and sugars, as opposed to Western and high-fat diets, have been shown to have a beneficial effect on intestinal health by promoting the growth of beneficial bacteria, improve mucus barrier function and immune tolerance, while inhibiting pro-inflammatory responses and their downstream effects. On the contrary, diets low in fiber and high in fat and sugars have been associated with alterations in microbiota composition/functionality and the subsequent development of chronic diseases such as food allergies, inflammatory bowel disease, and metabolic disease. In this review, we provided an updated overview of the current understanding of the connection between diet, microbiota, and health, with a special focus on the role of Western and high-fat diets in shaping intestinal homeostasis by modulating the gut microbiota

Estimating Forest Age and Site Productivity using Time Series of 3D Remote Sensing Data

ABSTRACT Three-dimensional (3D) data about forest captured by airborne laser scanning (ALS) have revolutionized forest management planning. Accurate, updated large-scale maps of forest variables produced with low costs today support greatly improved decisions about silvicultural treatments compared to the past practice based on field surveyed data only. These maps usually lack important information about forest age and site productivity, as this cannot be accurately assessed from the available ALS data. In Sweden, ALS has recently been performed nation-wide, except the mountainous area, to produce a new and accurate digital terrain model (DTM). This DTM enables extremely costefficient extraction of 3D data about the forest from other sources than ALS, such as automatic stereo-matching of aerial images as well as from single-pass spaceborne interferometric synthetic aperture radar (InSAR). In contrast to ALS, these data sources can provide low-cost time-series of 3D data. Aerial images of Sweden are often available in archives back to approximately 1960, and the TanDEM-X SAR system has the potential to provide new data every second week over large areas. These data have a potentially high value for forest management planning, since they may provide missing and highly important information -forest site productivity, Site Index (SI) and forest age. This pilot study explores a least-squares minimization approach to estimate forest age and SI from time series of 3D data produced by 1) image matching of DMC aerial images, and 2) TanDEM-X SAR data