Error estimates of residual minimization using neural networks for linear PDEs

We propose an abstract framework for analyzing the convergence of least-squares methods based on residual minimization when feasible solutions are neural networks. With the norm relations and compactness arguments, we derive error estimates for both continuous and discrete formulations of residual minimization in strong and weak forms. The formulations cover recently developed physics-informed neural networks based on strong and variational formulations

Deep Neural Networks - A Brief History

Introduction to deep neural networks and their history.Comment: 14 pages, 14 figure

Colour preferences for traditional Korean colours

Colour perception and preference have often been considered to be culturally linked. In this study, samples of young Korean and UK consumers have been tested to examine their colour preferences and also what they considered to be successful fashion colours. The traditional Korean colours (in various degrees of saturation) have been used for the test and, in the case of the Korean participants, they were also asked which colours they considered to the more traditional. Though there were some differences between the young Korean and young UK participants, the degree of similarly in choice and preference was quite marked. It is suggested that this may be due to exposure to global media and internet products in the modern environment. Also it was found that the reliability of both test groups was high

Drawing Trees with Perfect Angular Resolution and Polynomial Area

We study methods for drawing trees with perfect angular resolution, i.e., with angles at each node v equal to 2{\pi}/d(v). We show: 1. Any unordered tree has a crossing-free straight-line drawing with perfect angular resolution and polynomial area. 2. There are ordered trees that require exponential area for any crossing-free straight-line drawing having perfect angular resolution. 3. Any ordered tree has a crossing-free Lombardi-style drawing (where each edge is represented by a circular arc) with perfect angular resolution and polynomial area. Thus, our results explore what is achievable with straight-line drawings and what more is achievable with Lombardi-style drawings, with respect to drawings of trees with perfect angular resolution.Comment: 30 pages, 17 figure

Natalizumab affects T-cell phenotype in multiple sclerosis: implications for JCV reactivation

The anti-CD49d monoclonal antibody natalizumab is currently an effective therapy against the relapsing-remitting form of multiple sclerosis (RRMS). Natalizumab therapeutic efficacy is limited by the reactivation of the John Cunningham polyomavirus (JCV) and development of progressive multifocal leukoencephalopathy (PML). To correlate natalizumab-induced phenotypic modifications of peripheral blood T-lymphocytes with JCV reactivation, JCV-specific antibodies (serum), JCV-DNA (blood and urine), CD49d expression and relative abundance of peripheral blood T-lymphocyte subsets were longitudinally assessed in 26 natalizumab-treated RRMS patients. Statistical analyses were performed using GraphPad Prism and R. Natalizumab treatment reduced CD49d expression on memory and effector subsets of peripheral blood T-lymphocytes. Moreover, accumulation of peripheral blood CD8+ memory and effector cells was observed after 12 and 24 months of treatment. CD4+ and CD8+ T-lymphocyte immune-activation was increased after 24 months of treatment. Higher percentages of CD8+ effectors were observed in subjects with detectable JCV-DNA. Natalizumab reduces CD49d expression on CD8+ T-lymphocyte memory and effector subsets, limiting their migration to the central nervous system and determining their accumulation in peripheral blood. Impairment of central nervous system immune surveillance and reactivation of latent JCV, can explain the increased risk of PML development in natalizumab-treated RRMS subjects

Persistence of anticancer activity in berry extracts after simulated gastrointestinal digestion and colonic fermentation

Fruit and vegetable consumption is associated at the population level with a protective effect against colorectal cancer. Phenolic compounds, especially abundant in berries, are of interest due to their putative anticancer activity. After consumption, however, phenolic compounds are subject to digestive conditions within the gastrointestinal tract that alter their structures and potentially their function. However, the majority of phenolic compounds are not efficiently absorbed in the small intestine and a substantial portion pass into the colon. We characterized berry extracts (raspberries, strawberries, blackcurrants) produced by in vitro-simulated upper intestinal tract digestion and subsequent fecal fermentation. These extracts and selected individual colonic metabolites were then evaluated for their putative anticancer activities using in vitro models of colorectal cancer, representing the key stages of initiation, promotion and invasion. Over a physiologically-relevant dose range (0–50 µg/ml gallic acid equivalents), the digested and fermented extracts demonstrated significant anti-genotoxic, anti-mutagenic and anti-invasive activity on colonocytes. This work indicates that phenolic compounds from berries undergo considerable structural modifications during their passage through the gastrointestinal tract but their breakdown products and metabolites retain biological activity and can modulate cellular processes associated with colon cancer