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In this note we present a new special function that behaves like the error function and we provide an approximated accurate closed form for its CDF in terms of both Chèbyshev polynomials of the first kind and the error function. Also we provide its series representation using Padé approximant. We show a convincing numerical evidence about an accuracy of 10-6 for the approximants in the sense of the quadratic mean norm. A similar approach may be applied to other probability distributions, for example, Maxwell–Boltzmann distribution and normal distribution, such that we show its application using both of those distributions.

In this paper we show the way to apply some and analytical and numerical techniques in order to solve the forced Van der Pol oscillator. We illustrate the obtained results with examples. A comparison with Runge–Kutta numerical method is made in order to see the accuracy of the approximated analytical solution.

The nonlinear differential equation governing the periodic motion of the one-dimensional, undamped, and unforced cubic-quintic Duffing oscillator is solved exactly by obtaining the period and the solution. The period is given in terms of the complete elliptic integral of the first kind and the solution involves Jacobian elliptic functions. We solve the cubic-quintic Duffing equation under arbitrary initial conditions. Physical applications are provided. The solution to the mixed parity Duffing oscillator is also formally derived. We illustrate the obtained results with concrete examples. We give high accurate trigonometric approximations to the Jacobian function cn.

The Jacobi elliptic function method is applied to solve the generalized Benjamin-Bona-Mahony equation (BBM). Periodic and soliton solutions are formally derived in a general form. Some particular cases are considered. A power series method is also applied in some particular cases. Some solutions are expressed in terms of the Weierstrass elliptic function.

In this work, we give approximate expressions for Jacobian and elliptic Weierstrass functions and their inverses by means of the elementary trigonometric functions, sine and cosine. Results are reasonably accurate. We show the way the obtained results may be applied to solve nonlinear ODEs and other problems arising in nonlinear physics. The importance of the results in this work consists on giving easy and accurate way to evaluate the main elliptic functions cn, sn, and dn, as well as the Weierstrass elliptic function and their inverses. A general principle for solving some nonlinear problems through elementary functions is stated. No similar approach has been found in the existing literature.

In this note we present a new special function that behaves like the error function and we provide an approximated accurate closed form for its CDF in terms of both Chebyshev polynomials of the first kind and the error function. Also, we provide its series representation using Padé approximant. We show convincing numerical evidence of an accuracy of \\(10^-6\\) for the approximants in the sense of the quadratic mean norm. A similar approach may be applied to other probability distributions, for example, the Maxwell--Boltzmann distribution and the normal distribution, and we show its application using both of those distributions.

Visual inspection of histopathology slides is one of the main methods used by pathologists to assess the stage, type and subtype of lung tumors. Adenocarcinoma (LUAD) and squamous cell carcinoma (LUSC) are the most prevalent subtypes of lung cancer, and their distinction requires visual inspection by an experienced pathologist. In this study, we trained a deep convolutional neural network (inception v3) on whole-slide images obtained from The Cancer Genome Atlas to accurately and automatically classify them into LUAD, LUSC or normal lung tissue. The performance of our method is comparable to that of pathologists, with an average area under the curve (AUC) of 0.97. Our model was validated on independent datasets of frozen tissues, formalin-fixed paraffin-embedded tissues and biopsies. Furthermore, we trained the network to predict the ten most commonly mutated genes in LUAD. We found that six of them—STK11, EGFR, FAT1, SETBP1, KRAS and TP53—can be predicted from pathology images, with AUCs from 0.733 to 0.856 as measured on a held-out population. These findings suggest that deep-learning models can assist pathologists in the detection of cancer subtype or gene mutations. Our approach can be applied to any cancer type, and the code is available at https://github.com/ncoudray/DeepPATH . A convolutional neural network model using feature extraction and machine-learning techniques provides a tool for classification of lung cancer histopathology images and predicting mutational status of driver oncogenes

Intensive basal-bolus insulin therapy has been shown to improve glycaemic control and reduce the risk of long-term complications that are associated with type 1 diabetes mellitus. Insulin degludec is a new, ultra-longacting basal insulin. We therefore compared the efficacy and safety of insulin degludec and insulin glargine, both administered once daily with mealtime insulin aspart, in basal-bolus therapy for type 1 diabetes. In an open-label, treat-to-target, non-inferiority trial, undertaken at 79 sites (hospitals and centres) in six countries, adults (aged ≥18 years) with type 1 diabetes (glycated haemoglobin [HbA1c] ≤10% [86 mmol/mol]), who had been treated with basal-bolus insulin for at least 1 year, were randomly assigned in a 3:1 ratio, with a computer-generated blocked allocation sequence, to insulin degludec or insulin glargine without stratification by use of a central interactive response system. The primary outcome was non-inferiority of degludec to glargine, assessed as a reduction in HbA1c after 52 weeks, with the intention-to-treat analysis. This trial is registered with ClinicalTrials.gov, number NCT00982228. Of 629 participants, 472 were randomly assigned to insulin degludec and 157 to insulin glargine; all were analysed in their respective treatment groups. At 1 year, HbA1c had fallen by 0·40% points (SE 0·03) and 0·39% points (0·07), respectively, with insulin degludec and insulin glargine (estimated treatment difference −0·01% points [95% CI −0·14 to 0·11]; p<0·0001 for non-inferiority testing) and 188 (40%) and 67 (43%) participants achieved a target HbA1c of less than 7% (<53 mmol/mol). Rates of overall confirmed hypoglycaemia (plasma glucose <3·1 mmol/L or severe) were similar in the insulin degludec and insulin glargine groups (42·54 vs 40·18 episodes per patient-year of exposure; estimated rate ratio [degludec to glargine] 1·07 [0·89 to 1·28]; p=0·48). The rate of nocturnal confirmed hypoglycaemia was 25% lower with degludec than with glargine (4·41 vs 5·86 episodes per patient-year of exposure; 0·75 [0·59 to 0·96]; p=0·021). Overall serious adverse event rates (14 vs 16 events per 100 patient-years of exposure) were similar for the insulin degludec and insulin glargine groups. Insulin degludec might be a useful basal insulin for patients with type 1 diabetes because it provides effective glycaemic control while lowering the risk of nocturnal hypoglycaemia, which is a major limitation of insulin therapy. Novo Nordisk.

Explosion monitoring is performed by infrasound and seismoacoustic sensor networks that are distributed globally, regionally, and locally. However, these networks are unevenly and sparsely distributed, especially at the local scale, as maintaining and deploying networks is costly. With increasing interest in smaller-yield explosions, the need for more dense networks has increased. To address this issue, we propose using smartphone sensors for explosion detection as they are cost-effective and easy to deploy. Although there are studies using smartphone sensors for explosion detection, the field is still in its infancy and new technologies need to be developed. We applied a machine learning model for explosion detection using smartphone microphones. The data used were from the Smartphone High-explosive Audio Recordings Dataset (SHAReD), a collection of 326 waveforms from 70 high-explosive (HE) events recorded on smartphones, and the ESC-50 dataset, a benchmarking dataset commonly used for environmental sound classification. Two machine learning models were trained and combined into an ensemble model for explosion detection. The resulting ensemble model classified audio signals as either “explosion”, “ambient”, or “other” with true positive rates (recall) greater than 96% for all three categories.