General relativity and quantum mechanics: towards a generalization of the Lambert W function A Generalization of the Lambert W Function

We present a canonical form for a natural and necessary generalization of the Lambert W function, natural in that it requires minimal mathematical definitions for this generalization, and necessary in that it provides a means of expressing solutions to a number of physical problems of fundamental nature. This generalization expresses the exact solutions for general-relativistic self-gravitating N-body systems in one spatial and one time dimension, and a previously unknown mathematical link between the (1+1) gravity problem and the Schrödinger wave equation.     

Mesomorphic behavior of polydiethylphosphazenes as described by13C,14N,and2H NMR

The existence of mesomorphism in polydiethylphosphazene was recently established by MAS NMR and X-ray diffraction characterization. In the present work the mechanism of motion of the ethyl side groups in the high-temperature polymorph tabove 45 C) is identified and compared to the arrangement of side groups in the low-temperature polymorph. For this purpose a few NMR active nuclei (¹³C,¹⁴N, and²H) were exploited to define the side-chain motions occurring at transition. Experiments performed at varying temperatures close to the onset of solid transition suggest the presence of jumps between two conformations in the pretransition state. Rotor-synchronized triple-resonance NMR of the high-temperature phase determined the average distances between the carbons and the nitrogens in the polymorphs. The theoretical prediction of the dipolar interaction between the nuclei supports the hypothesis that ethyl groups can undergo a complete rotation about the P CH₂ bond by jumping across a conformational barrier. The mechanism of motion of the ethyl groups must be cooperative and the collapse of the rigid shell around the main chain is described at the transition.     

Incremental wrapper-based gene selection from microarray data for cancer classification

Gene expression microarray is a rapidly maturing technology that provides the opportunity to assay the expression levels of thousands or tens of thousands of genes in a single experiment. We present a new heuristic to select relevant gene subsets in order to further use them for the classification task. Our method is based on the statistical significance of adding a gene from a ranked-list to the final subset. The efficiency and effectiveness of our technique is demonstrated through extensive comparisons with other representative heuristics. Our approach shows an excellent performance, not only at identifying relevant genes, but also with respect to the computational cost.     

Mathematical modelling of the alcoholic fermentation of glucose by Zymomonas mobilis mobilis

The kinetics of alcoholic fermentation of a strain of Zymomonas mobilis, isolated from sugarcane juice, has been studied with the objective of determining the constansts of a non-structured mathematical model that represents the fermentation process. Assays in batch and in continuous culture have been carried out with different initial concentrations of glucose. The final concentrations of glucose, ethanol and biomass were determined. The following kinetic parameters were obtained: μ_max, 0·5 h^?1; K_s, 4·64 g dm^?3; P_max, 106 g dm^?3; Y_x/s, 0·0265 g g^?1; m, 1·4 g g^?1 h^?1; α, 17·38 g g^?1; β, 0·69 g g^?1 h^?1.     

The impact of risk and protective factors on online teaching experience in high school Italian teachers during the COVID-19 pandemic

The lockdown due to COVID-19 in Italy resulted in the sudden closure of schools, with a shift from traditional teaching to the online one. Through an online questionnaire, this survey explores teachers' experience of online teaching, the level of risk factors (e.g., stress) and protective factors (e.g., locus of control) and their impact on satisfaction levels during the social distancing. One hundred seven high school teachers from Lombardy, an Italian region very affected by the COVID-19 outbreak, participated. Results show that depression and stress are the main predictors of satisfaction levels for online teaching. In addition, coping, locus of control and self-efficacy emerge as important protective factors. Finally, although there is great satisfaction with the online teaching experience, critical elements emerged. This study is relevant because it describes the critical elements of the online teaching experience, and identifies some protective factors and the main risk factors in teachers operating in an area strongly marked by social restrictions imposed by the pandemic. High school teachers emerge as a sub-group of the general population with specific psychological reactions. Considering the results, it is possible to suggest providing high-quality educational support and crisis-psychological oriented services to teachers, and help to maintain the psychological well-being.     

Evolutionary Generalized Radial Basis Function neural networks for improving prediction accuracy in gene classification using feature selection

Radial Basis Function Neural Networks (RBFNNs) have been successfully employed in several function approximation and pattern recognition problems. The use of different RBFs in RBFNN has been reported in the literature and here the study centres on the use of the Generalized Radial Basis Function Neural Networks (GRBFNNs). An interesting property of the GRBF is that it can continuously and smoothly reproduce different RBFs by changing a real parameter τ. In addition, the mixed use of different RBF shapes in only one RBFNN is allowed. Generalized Radial Basis Function (GRBF) is based on Generalized Gaussian Distribution (GGD), which adds a shape parameter, τ, to standard Gaussian Distribution. Moreover, this paper describes a hybrid approach, Hybrid Algorithm (HA), which combines evolutionary and gradient-based learning methods to estimate the architecture, weights and node topology of GRBFNN classifiers. The feasibility and benefits of the approach are demonstrated by means of six gene microarray classification problems taken from bioinformatic and biomedical domains. Three filters were applied: Fast Correlation-Based Filter (FCBF), Best Incremental Ranked Subset (BIRS), and Best Agglomerative Ranked Subset (BARS); this was done in order to identify salient expression genes from among the thousands of genes in microarray data that can directly contribute to determining the class membership of each pattern. After different gene subsets were obtained, the proposed methodology was performed using the selected gene subsets as new input variables. The results confirm that the GRBFNN classifier leads to a promising improvement in accuracy.     

Complementary Effects of Carbamylated and Citrullinated LL37 in Autoimmunity and Inflammation in Systemic Lupus Erythematosus

LL37 acts as T-cell/B-cell autoantigen in Systemic lupus erythematosus (SLE) and psoriatic disease. Moreover, when bound to “self” nucleic acids, LL37 acts as “danger signal,” leading to type I interferon (IFN-I)/pro-inflammatory factors production. T-cell epitopes derived from citrullinated-LL37 act as better antigens than unmodified LL37 epitopes in SLE, at least in selected HLA-backgrounds, included the SLE-associated HLA-DRB1*1501/HLA-DRB5*0101 backgrounds. Remarkably, while “fully-citrullinated” LL37 acts as better T-cell-stimulator, it loses DNA-binding ability and the associated “adjuvant-like” properties. Since LL37 undergoes a further irreversible post-translational modification, carbamylation and antibodies to carbamylated self-proteins other than LL37 are present in SLE, here we addressed the involvement of carbamylated-LL37 in autoimmunity and inflammation in SLE. We detected carbamylated-LL37 in SLE-affected tissues. Most importantly, carbamylated-LL37-specific antibodies and CD4 T-cells circulate in SLE and both correlate with disease activity. In contrast to “fully citrullinated-LL37,” “fully carbamylated-LL37” maintains both innate and adaptive immune-cells’ stimulatory abilities: in complex with DNA, carbamylated-LL37 stimulates plasmacytoid dendritic cell IFN-α production and B-cell maturation into plasma cells. Thus, we report a further example of how different post-translational modifications of a self-antigen exert complementary effects that sustain autoimmunity and inflammation, respectively. These data also show that T/B-cell responses to carbamylated-LL37 represent novel SLE disease biomarkers.