Difference schemes with point symmetries and their numerical tests

Symmetry preserving difference schemes approximating second and third order ordinary differential equations are presented. They have the same three or four-dimensional symmetry groups as the original differential equations. The new difference schemes are tested as numerical methods. The obtained numerical solutions are shown to be much more accurate than those obtained by standard methods without an increase in cost. For an example involving a solution with a singularity in the integration region the symmetry preserving scheme, contrary to standard ones, provides solutions valid beyond the singular point.Comment: 26 pages 7 figure

Symmetry preserving discretization of SL(2,R) invariant equations

Nonlinear ODEs invariant under the group SL(2,R) are solved numerically. We show that solution methods incorporating the Lie point symmetries provide better results than standard methods.Comment: 12 pages, 3 figures, submitted to Journal of Nonlinear Mathematical Physic

Multiscale expansions of difference equations in the small lattice spacing regime, and a vicinity and integrability test. I

We propose an algorithmic procedure i) to study the ``distance'' between an integrable PDE and any discretization of it, in the small lattice spacing epsilon regime, and, at the same time, ii) to test the (asymptotic) integrability properties of such discretization. This method should provide, in particular, useful and concrete informations on how good is any numerical scheme used to integrate a given integrable PDE. The procedure, illustrated on a fairly general 10-parameter family of discretizations of the nonlinear Schroedinger equation, consists of the following three steps: i) the construction of the continuous multiscale expansion of a generic solution of the discrete system at all orders in epsilon, following the Degasperis - Manakov - Santini procedure; ii) the application, to such expansion, of the Degasperis - Procesi (DP) integrability test, to test the asymptotic integrability properties of the discrete system and its ``distance'' from its continuous limit; iii) the use of the main output of the DP test to construct infinitely many approximate symmetries and constants of motion of the discrete system, through novel and simple formulas.Comment: 34 pages, no figur

Lysozyme transgenic goats’ milk positively impacts intestinal cytokine expression and morphology

In addition to its well-recognized antimicrobial properties, lysozyme can also modulate the inflammatory response. This ability may be particularly important in the gastrointestinal tract where inappropriate inflammatory reactions can damage the intestinal epithelium, leading to significant health problems. The consumption of milk from transgenic goats producing human lysozyme (hLZ) in their milk therefore has the potential to positively impact intestinal health. In order to investigate the effect of hLZ-containing milk on the inflammatory response, young pigs were fed pasteurized milk from hLZ or non-transgenic control goats and quantitative real-time PCR was performed to assess local expression of TNF-α, IL-8, and TGF-β1 in the small intestine. Histological changes were also investigated, specifically looking at villi width, length, crypt depth, and lamina propria thickness along with cell counts for intraepithelial lymphocytes and goblet cells. Significantly higher expression of anti-inflammatory cytokine TGF-β1 was seen in the ileum of pigs fed pasteurized milk containing hLZ (P = 0.0478), along with an increase in intraepithelial lymphocytes (P = 0.0255), and decrease in lamina propria thickness in the duodenum (P = 0.0001). Based on these results we conclude that consuming pasteurized milk containing hLZ does not induce an inflammatory response and improves the health of the small intestine in pigs

Toward transient finite element simulation of thermal deformation of machine tools in real-time

Finite element models without simplifying assumptions can accurately describe the spatial and temporal distribution of heat in machine tools as well as the resulting deformation. In principle, this allows to correct for displacements of the Tool Centre Point and enables high precision manufacturing. However, the computational cost of FE models and restriction to generic algorithms in commercial tools like ANSYS prevents their operational use since simulations have to run faster than real-time. For the case where heat diffusion is slow compared to machine movement, we introduce a tailored implicit–explicit multi-rate time stepping method of higher order based on spectral deferred corrections. Using the open-source FEM library DUNE, we show that fully coupled simulations of the temperature field are possible in real-time for a machine consisting of a stock sliding up and down on rails attached to a stand

The Role of Intestinal Microbiota in the Development and Severity of Chemotherapy-Induced Mucositis

Mucositis, also referred to as mucosal barrier injury, is one of the most debilitating side effects of radiotherapy and chemotherapy treatment. Clinically, mucositis is associated with pain, bacteremia, and malnutrition. Furthermore, mucositis is a frequent reason to postpone chemotherapy treatment, ultimately leading towards a higher mortality in cancer patients. According to the model introduced by Sonis, both inflammation and apoptosis of the mucosal barrier result in its discontinuity, thereby promoting bacterial translocation. According to this five-phase model, the intestinal microbiota plays no role in the pathophysiology of mucositis. However, research has implicated a prominent role for the commensal intestinal microbiota in the development of several inflammatory diseases like inflammatory bowel disease, pouchitis, and radiotherapy-induced diarrhea. Furthermore, chemotherapeutics have a detrimental effect on the intestinal microbial composition (strongly decreasing the numbers of anaerobic bacteria), coinciding in time with the development of chemotherapy-induced mucositis. We hypothesize that the commensal intestinal microbiota might play a pivotal role in chemotherapy-induced mucositis. In this review, we propose and discuss five pathways in the development of mucositis that are potentially influenced by the commensal intestinal microbiota: 1) the inflammatory process and oxidative stress, 2) intestinal permeability, 3) the composition of the mucus layer, 4) the resistance to harmful stimuli and epithelial repair mechanisms, and 5) the activation and release of immune effector molecules. Via these pathways, the commensal intestinal microbiota might influence all phases in the Sonis model of the pathogenesis of mucositis. Further research is needed to show the clinical relevance of restoring dysbiosis, thereby possibly decreasing the degree of intestinal mucositis