Forecasting COVID-19 Epidemic Trends by Combining a Neural Network with Rt Estimation

On 31 December 2019, a cluster of pneumonia cases of unknown etiology was reported in Wuhan (China). The cases were declared to be Coronavirus Disease 2019 (COVID-19) by the World Health Organization (WHO). COVID-19 has been defined as SARS Coronavirus 2 (SARS-CoV-2). Some countries, e.g., Italy, France, and the United Kingdom (UK), have been subjected to frequent restrictions for preventing the spread of infection, contrary to other ones, e.g., the United States of America (USA) and Sweden. The restrictions afflicted the evolution of trends with several perturbations that destabilized its normal evolution. Globally, Rt has been used to estimate time-varying reproduction numbers during epidemics. Methods: This paper presents a solution based on Deep Learning (DL) for the analysis and forecasting of epidemic trends in new positive cases of SARS-CoV-2 (COVID-19). It combined a neural network (NN) and an Rt estimation by adjusting the data produced by the output layer of the NN on the related Rt estimation. Results: Tests were performed on datasets related to the following countries: Italy, the USA, France, the UK, and Sweden. Positive case registration was retrieved between 24 February 2020 and 11 January 2022. Tests performed on the Italian dataset showed that our solution reduced the Mean Absolute Percentage Error (MAPE) by 28.44%, 39.36%, 22.96%, 17.93%, 28.10%, and 24.50% compared to other ones with the same configuration but that were based on the LSTM, GRU, RNN, ARIMA (1,0,3), and ARIMA (7,2,4) models, or an NN without applying the Rt as a corrective index. It also reduced MAPE by 17.93%, the Mean Absolute Error (MAE) by 34.37%, and the Root Mean Square Error (RMSE) by 43.76% compared to the same model without the adjustment performed by the Rt. Furthermore, it allowed an average MAPE reduction of 5.37%, 63.10%, 17.84%, and 14.91% on the datasets related to the USA, France, the UK, and Sweden, respectively.     

Synthesis of Anellated Pyranose Derivatives on the Basis of Levoglucosenone

ABSTRACT

1,6-Anhydro-2-(dicyanomethylene)-2,3-dideoxy-4-S-ethyl-4-thio-β-D-erythro-hexopyranose (1) reacted with tosyl azide or sulfur and triethylamine to furnish the 5-aza-10, 11-dioxatricyclo[6.2.1.0^2,6]undeca-2(6),3-diene-3-carbonitrile 2 and the 10,11-dioxa-5-thiatricyclo[6.2.1.0^2,6]undeca-2(6),3-diene-3-carbonitrile 3, respectively. The reactions of 1 with arylisothiocyanates furnished the 11,12-dioxa-5-thiatricyclo[7.2.1.0^2,7]dodeca-2(7),3-diene-3-carbonitriles 4 and 5. 3 underwent cyclization with triethyl orthoformate and ammonia or hydrazine hydrate to afford the 5,7-diaza-14,15-dioxa-9-thiatetracyclo[10.2.1.0^2,10.0^3.8]pentadecatetra(tri)enes 7 and 8, respectively.     

Conformal Families of Measures for Fibred Systems

In this paper, we give sufficient conditions for the existence of (pseudo) weakly conformal and conformal families of measures for fibred systems. We describe a general construction principle for these families, modelled on the one developed by Denker and Urbanski for conformal measures. For those systems that are fibrewise local homeomorphisms, the constructed families are (pseudo) conformal. If a system is, moreover, weakly topologically exact along fibres, then each measure in the associated family is supported on the whole fibre where it is naturally defined.     

Dynamics of heart rate

Heart rate oscillates on several different time scales and has long-term variability in the form of 1/f noise. The physiological control of heart rate is briefly reviewed, and several typical patterns of heart rate variability, in health and sickness, are described. Considered briefly are some possible dynamical mechanisms for heart rate variability.     

The semigroup generated by certain operators on the congruence lattice of a clifford semigroup

Communicated by N. R. Reilly     

Holography in partially coherent light

A Michelson interferometer has been used to obtain good holographic carrierfringes of the order of 200 to 300 fringes/ mm over an area of 1 cm × 1.5 cm with a Hg-are source and extended aperture with and without filter. The fringes have been used to record holograms. The image reconstruction has been done with light from the Hg-arc without the use of any filter. Experimental results for a continuous-tone object have been presented. The advantages and disadvantages and some of the potential applications of this technique have been mentioned.     

EEG Fractal Analysis Reflects Brain Impairment after Stroke

Stroke is the commonest cause of disability. Novel treatments require an improved understanding of the underlying mechanisms of recovery. Fractal approaches have demonstrated that a single metric can describe the complexity of seemingly random fluctuations of physiological signals. We hypothesize that fractal algorithms applied to electroencephalographic (EEG) signals may track brain impairment after stroke. Sixteen stroke survivors were studied in the hyperacute (<48 h) and in the acute phase (∼1 week after stroke), and 35 stroke survivors during the early subacute phase (from 8 days to 32 days and after ∼2 months after stroke): We compared resting-state EEG fractal changes using fractal measures (i.e., Higuchi Index, Tortuosity) with 11 healthy controls. Both Higuchi index and Tortuosity values were significantly lower after a stroke throughout the acute and early subacute stage compared to healthy subjects, reflecting a brain activity which is significantly less complex. These indices may be promising metrics to track behavioral changes in the very early stage after stroke. Our findings might contribute to the neurorehabilitation quest in identifying reliable biomarkers for a better tailoring of rehabilitation pathways.     

Liquid-crystal phase equilibria of Lennard-Jones chains

Liquid-crystal phase equilibria of Lennard-Jones chain fluids and the solubility of a Lennard-Jones gas in the coexisting phases are calculated from Monte Carlo simulations. Direct phase equilibria calculations are performed using an expanded formulation of the Gibbs ensemble. Monomer densities, order parameters, and equilibrium pressures are reported for the coexisting isotropic and nematic phases of: (1) linear Lennard-Jones chains, (2) a partially-flexible Lennard-Jones chain, and (3) a binary mixture of linear Lennard-Jones chains. The effect of chain length is determined by calculating the isotropic-nematic coexistence of linear Lennard-Jones chain fluids made of 8, 10, and 12 segments (8-, 10-, 12-mer). The effect of molecular flexibility on the isotropic-nematic equilibrium is studied for a Lennard-Jones 10-mer chain fluid with one freely-jointed segment at the end of the chain. An isotropic-nematic phase split and fractionation are reported for a binary mixture of linear 7-mer and 12-mer chains. Simulation results are compared with theoretical results as obtained from a recently developed analytical equation of state based on perturbation theory. Excellent agreement between theory and simulations is observed. The solubility of a monomer Lennard-Jones gas in the coexisting isotropic and nematic phases is estimated using the Widom test-particle insertion method. A linear relationship between solubility difference and density difference at isotropic-nematic coexistence is observed. It is shown that gas solubility is independent of the nematic ordering of the fluid, at constant temperature and density conditions.     

A 1H NMR Study of the Kinetics of the Reaction of Diisocyanates with Ethlene Oxide-Dimethylsiloxane-Ethylene Oxide Block Copolymer

The reaction of pure 2–4 and 2–6 tolylene diisocyanate with an OH terminated ethylene oxide-dimethylsiloxane-ethylene oxide ABA block copolymer was carried out directly in a n.m.r. tube. The kinetic of the reaction was studied by ¹H nmr spectroscopy.