Predictive algorithms for some elementary functions in radix 2

AbstractWe investigate the integrability of Euler–Lagrange equations associated with 2D second-order Lagrangians of the form $$\begin{aligned} \int f(u_{xx},u_{xy},u_{yy})\ \mathrm{d}x\mathrm{d}y. \end{aligned}$$ ∫ f ( u xx , u xy , u yy ) d x d y . By deriving integrability conditions for the Lagrangian density f, examples of integrable Lagrangians expressible via elementary functions, Jacobi theta functions and dilogarithms are constructed. A link of second-order integrable Lagrangians to WDVV equations is established. Generalisations to 3D second-order integrable Lagrangians are also discussed.

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A Comparison of Feature Selection and Forecasting Machine Learning Algorithms for Predicting Glycaemia in Type 1 Diabetes Mellitus

Applied Sciences ◽

10.3390/app11041742 ◽

2021 ◽

Vol 11 (4) ◽

pp. 1742

Author(s):

Ignacio Rodríguez-Rodríguez ◽

José-Víctor Rodríguez ◽

Wai Lok Woo ◽

Bo Wei ◽

Domingo-Javier Pardo-Quiles

Keyword(s):

Diabetes Mellitus ◽

Machine Learning ◽

Type 1 Diabetes ◽

Feature Selection ◽

Blood Glucose ◽

Type 1 Diabetes Mellitus ◽

Support Vector ◽

Chronic Hyperglycemia ◽

Predictive Algorithms

Type 1 diabetes mellitus (DM1) is a metabolic disease derived from falls in pancreatic insulin production resulting in chronic hyperglycemia. DM1 subjects usually have to undertake a number of assessments of blood glucose levels every day, employing capillary glucometers for the monitoring of blood glucose dynamics. In recent years, advances in technology have allowed for the creation of revolutionary biosensors and continuous glucose monitoring (CGM) techniques. This has enabled the monitoring of a subject’s blood glucose level in real time. On the other hand, few attempts have been made to apply machine learning techniques to predicting glycaemia levels, but dealing with a database containing such a high level of variables is problematic. In this sense, to the best of the authors’ knowledge, the issues of proper feature selection (FS)—the stage before applying predictive algorithms—have not been subject to in-depth discussion and comparison in past research when it comes to forecasting glycaemia. Therefore, in order to assess how a proper FS stage could improve the accuracy of the glycaemia forecasted, this work has developed six FS techniques alongside four predictive algorithms, applying them to a full dataset of biomedical features related to glycaemia. These were harvested through a wide-ranging passive monitoring process involving 25 patients with DM1 in practical real-life scenarios. From the obtained results, we affirm that Random Forest (RF) as both predictive algorithm and FS strategy offers the best average performance (Root Median Square Error, RMSE = 18.54 mg/dL) throughout the 12 considered predictive horizons (up to 60 min in steps of 5 min), showing Support Vector Machines (SVM) to have the best accuracy as a forecasting algorithm when considering, in turn, the average of the six FS techniques applied (RMSE = 20.58 mg/dL).

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Quantum periods and TBA-like equations for a class of Calabi-Yau geometries

Journal of High Energy Physics ◽

10.1007/jhep01(2021)002 ◽

2021 ◽

Vol 2021 (1) ◽

Author(s):

Bao-ning Du ◽

Min-xin Huang

Keyword(s):

Large Class ◽

Bethe Ansatz ◽

Difference Equations ◽

The Other ◽

Elementary Functions ◽

Quantum Dilogarithm ◽

Thermodynamic Bethe Ansatz ◽

Dilogarithm Function ◽

Quantum Operators

Abstract We continue the study of a novel relation between quantum periods and TBA(Thermodynamic Bethe Ansatz)-like difference equations, generalize previous works to a large class of Calabi-Yau geometries described by three-term quantum operators. We give two methods to derive the TBA-like equations. One method uses only elementary functions while the other method uses Faddeev’s quantum dilogarithm function. The two approaches provide different realizations of TBA-like equations which are nevertheless related to the same quantum period.

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Predictive Policing and Crime Control in The United States of America and Europe: Trends in a Decade of Research and the Future of Predictive Policing

Social Sciences ◽

10.3390/socsci10060234 ◽

2021 ◽

Vol 10 (6) ◽

pp. 234

Author(s):

Ishmael Mugari ◽

Emeka E. Obioha

Keyword(s):

Crime Control ◽

Predictive Accuracy ◽

Criminal Activity ◽

The United States ◽

Modern Technology ◽

Predictive Policing ◽

Software Applications ◽

Predictive Algorithms ◽

Developed Nations ◽

Predictive Software

There has been a significant focus on predictive policing systems, as law enforcement agents embrace modern technology to forecast criminal activity. Most developed nations have implemented predictive policing, albeit with mixed reactions over its effectiveness. Whilst at its inception, predictive policing involved simple heuristics and algorithms, it has increased in sophistication in the ever-changing technological environment. This paper, which is based on a literature survey, examines predictive policing over the last decade (2010 to 2020). The paper examines how various nations have implemented predictive policing and also documents the impediments to predictive policing. The paper reveals that despite the adoption of predictive software applications such as PredPol, Risk Terrain Modelling, HunchLab, PreMap, PRECOBS, Crime Anticipation System, and Azevea, there are several impediments that have militated against the effectiveness of predictive policing, and these include low predictive accuracy, limited scope of crimes that can be predicted, high cost of predictive policing software, flawed data input, and the biased nature of some predictive software applications. Despite these challenges, the paper reveals that there is consensus by the majority of the researchers on the importance of predictive algorithms on the policing landscape.

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Series and Products for Elementary Functions

Series and Products in the Development of Mathematics ◽

10.1017/9781108709453.016 ◽

2021 ◽

pp. 365-395

Keyword(s):

Elementary Functions

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Application of the Efros Theorem to the Function Represented by the Inverse Laplace Transform of s−μ exp(−sν)

Symmetry ◽

10.3390/sym13020354 ◽

2021 ◽

Vol 13 (2) ◽

pp. 354

Author(s):

Alexander Apelblat ◽

Francesco Mainardi

Keyword(s):

Laplace Transform ◽

Operational Calculus ◽

Inverse Laplace Transform ◽

Elementary Functions ◽

Hyperbolic Functions ◽

Error Functions ◽

Convolution Integrals ◽

Special Case ◽

Integral Identities ◽

Finite Integrals

Using a special case of the Efros theorem which was derived by Wlodarski, and operational calculus, it was possible to derive many infinite integrals, finite integrals and integral identities for the function represented by the inverse Laplace transform. The integral identities are mainly in terms of convolution integrals with the Mittag–Leffler and Volterra functions. The integrands of determined integrals include elementary functions (power, exponential, logarithmic, trigonometric and hyperbolic functions) and the error functions, the Mittag–Leffler functions and the Volterra functions. Some properties of the inverse Laplace transform of s−μexp(−sν) with μ≥0 and 0<ν<1 are presented.

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