On the accuracy of interpolation based on single-layer artificial neural networks

In the present paper, we consider one-hidden layer ANNs with a feedforward architecture, also referred to as shallow or two-layer networks, so that the structure is determined by the number and types of neurons. The determination of the parameters that define the function, called training, is done via the resolution of the approximation problem, so by imposing the interpolation through a set of specific nodes. We present the case where the parameters are trained using a procedure that is referred to as Extreme Learning Machine (ELM) that leads to a linear interpolation problem. In such hypotheses, the existence of an ANN interpolating function is guaranteed. The focus is then on the accuracy of the interpolation outside of the given sampling interpolation nodes when they are the equispaced, the Chebychev, and the randomly selected ones. The study is motivated by the well-known bell-shaped Runge example, which makes it clear that the construction of a global interpolating polynomial is accurate only if trained on suitably chosen nodes, ad example the Chebychev ones. In order to evaluate the behavior when growing the number of interpolation nodes, we raise the number of neurons in our network and compare it with the interpolating polynomial. We test using Runge's function and other well-known examples with different regularities. As expected, the accuracy of the approximation with a global polynomial increases only if the Chebychev nodes are considered. Instead, the error for the ANN interpolating function always decays and in most cases we observe that the convergence follows what is observed in the polynomial case on Chebychev nodes, despite the set of nodes used for training

Epigenetics: an Opportunity to Shape Innate and Adaptive Immune Responses

Epigenetics connects genetic and environmental factors: it includes DNA methylation, histone post-translational modifications and the regulation of chromatin accessibility by non-coding RNAs, all of which control constitutive or inducible gene transcription. This plays a key role in harnessing the transcriptional programs of both innate and adaptive immune cells due to its plasticity and environmental-driven nature, piloting myeloid and lymphoid cell fate decision with no change in their genomic sequence. In particular, epigenetic marks at the site of lineage specific transcription factors and maintenance of cell type-specific epigenetic modifications, referred to as "epigenetic memory", dictate cell differentiation, cytokine production and functional capacity following repeated antigenic exposure in memory T cells. Moreover, metabolic and epigenetic reprogramming occurring during a primary innate immune response leads to enhanced responses to secondary challenges, a phenomenon known as "trained immunity". Here we discuss how stable and dynamic epigenetic states control immune cell identity and plasticity in physiological and pathological conditions. Dissecting the regulatory circuits of cell fate determination and maintenance is of paramount importance for understanding the delicate balance between immune cell activation and tolerance, in healthy conditions and in autoimmune diseases. This article is protected by copyright. All rights reserved