scholarly journals Dynamical Strategy to Control the Accuracy of the Nonlinear Bio-Mathematical Model of Malaria Infection

Mathematics ◽  
2021 ◽  
Vol 9 (9) ◽  
pp. 1031
Author(s):  
Samad Noeiaghdam ◽  
Sanda Micula
Keyword(s):  
Mathematical Model ◽  
Convergence Theorem ◽  
Malaria Infection ◽  
Absolute Error ◽  
Numerical Approximations ◽  
Cestac Method ◽  
Cadna Library ◽  
Numerical Instabilities ◽  
Better Than

This study focuses on solving the nonlinear bio-mathematical model of malaria infection. For this aim, the HATM is applied since it performs better than other methods. The convergence theorem is proven to show the capabilities of this method. Instead of applying the FPA, the CESTAC method and the CADNA library are used, which are based on the DSA. Applying this method, we will be able to control the accuracy of the results obtained from the HATM. Also the optimal results and the numerical instabilities of the HATM can be obtained. In the CESTAC method, instead of applying the traditional absolute error to show the accuracy, we use a novel condition and the CESTAC main theorem allows us to do that. Plotting several ℏ-curves the regions of convergence are demonstrated. The numerical approximations are obtained based on both arithmetics.

scholarly journals Advantages of the Discrete Stochastic Arithmetic to Validate the Results of the Taylor Expansion Method to Solve the Generalized Abel’s Integral Equation

Symmetry ◽  
2021 ◽  
Vol 13 (8) ◽  
pp. 1370
Author(s):  
Eisa Zarei ◽  
Samad Noeiaghdam
Keyword(s):  
Integral Equation ◽  
Taylor Expansion ◽  
Expansion Method ◽  
Absolute Error ◽  
Optimal Error ◽  
Cestac Method ◽  
Stochastic Arithmetic ◽  
Cadna Library ◽  
Numerical Instabilities ◽  
Termination Criterion

The aim of this paper is to apply the Taylor expansion method to solve the first and second kinds Volterra integral equations with Abel kernel. This study focuses on two main arithmetics: the FPA and the DSA. In order to apply the DSA, we use the CESTAC method and the CADNA library. Using this method, we can find the optimal step of the method, the optimal approximation, the optimal error, and some of numerical instabilities. They are the main novelties of the DSA in comparison with the FPA. The error analysis of the method is proved. Furthermore, the main theorem of the CESTAC method is presented. Using this theorem we can apply a new termination criterion instead of the traditional absolute error. Several examples are approximated based on the FPA and the DSA. The numerical results show the applications and advantages of the DSA than the FPA.

scholarly journals Predictive validity of effective shunt fraction in critically ill patients

2018 ◽  
Author(s):  
Emma M Chang ◽  
Andrew Bretherick ◽  
Gordon B Drummond ◽  
J Kenneth Baillie
Keyword(s):  
Mathematical Model ◽  
Gas Exchange ◽  
Predictive Validity ◽  
Absolute Error ◽  
Shunt Fraction ◽  
Surrogate Outcome ◽  
Non Invasive ◽  
Median Absolute Error ◽  
Better Than

AbstractAccurate measurement of pulmonary oxygenation is important for classification of disease severity and quantification of outcomes in clinical studies. We compared predictive validity of established tension-based methods with two new measures of shunt fraction: (1) a non-invasive effective shunt (ES); and (2) inferred values from an integrated mathematical model of gas exchange (DB). Median absolute error (MAE) values for the four measures considered were: alveolar-arterial difference, 7.30kPa; PaO2/FIO2 ratio, 2.41kPa; DB, 2.13kPa; ES: 1.88kPa. ES performed significantly better than other measures (p<10−10 in all comparisons). While the simplicity of P/F is suitable for routine use, the superior predictive validity of ES should make this measure the preferred choice where physiological accuracy is important, such as for use as surrogate outcome in clinical research.

scholarly journals Contactless Video-Based Heart Rate Monitoring of a Resting and an Anesthetized Pig

Animals ◽  
2021 ◽  
Vol 11 (2) ◽  
pp. 442
Author(s):  
Meiqing Wang ◽  
Ali Youssef ◽  
Mona Larsen ◽  
Jean-Loup Rault ◽  
Daniel Berckmans ◽  
...  
Keyword(s):  
Heart Rate ◽  
Estimation Error ◽  
Well Being ◽  
Absolute Error ◽  
Mean Value ◽  
Video Data ◽  
Window Functions ◽  
The Face ◽  
Short Time ◽  
Better Than

Heart rate (HR) is a vital bio-signal that is relatively easy to monitor with contact sensors and is related to a living organism’s state of health, stress and well-being. The objective of this study was to develop an algorithm to extract HR (in beats per minute) of an anesthetized and a resting pig from raw video data as a first step towards continuous monitoring of health and welfare of pigs. Data were obtained from two experiments, wherein the pigs were video recorded whilst wearing an electrocardiography (ECG) monitoring system as gold standard (GS). In order to develop the algorithm, this study used a bandpass filter to remove noise. Then, a short-time Fourier transform (STFT) method was tested by evaluating different window sizes and window functions to accurately identify the HR. The resulting algorithm was first tested on videos of an anesthetized pig that maintained a relatively constant HR. The GS HR measurements for the anesthetized pig had a mean value of 71.76 bpm and standard deviation (SD) of 3.57 bpm. The developed algorithm had 2.33 bpm in mean absolute error (MAE), 3.09 bpm in root mean square error (RMSE) and 67% in HR estimation error below 3.5 bpm (PE3.5). The sensitivity of the algorithm was then tested on the video of a non-anaesthetized resting pig, as an animal in this state has more fluctuations in HR than an anaesthetized pig, while motion artefacts are still minimized due to resting. The GS HR measurements for the resting pig had a mean value of 161.43 bpm and SD of 10.11 bpm. The video-extracted HR showed a performance of 4.69 bpm in MAE, 6.43 bpm in RMSE and 57% in PE3.5. The results showed that HR monitoring using only the green channel of the video signal was better than using three color channels, which reduces computing complexity. By comparing different regions of interest (ROI), the region around the abdomen was found physiologically better than the face and front leg parts. In summary, the developed algorithm based on video data has potential to be used for contactless HR measurement and may be applied on resting pigs for real-time monitoring of their health and welfare status, which is of significant interest for veterinarians and farmers.

scholarly journals Velody 2—Resilient High-Capacity MIDI Steganography for Organ and Harpsichord Music

2020 ◽  
Vol 11 (1) ◽  
pp. 39
Author(s):  
Eric Järpe ◽  
Mattias Weckstén
Keyword(s):  
Mean Absolute Error ◽  
Signal To Noise Ratio ◽  
High Capacity ◽  
Absolute Error ◽  
Music Technology ◽  
Alternative Methods ◽  
File Size ◽  
User Friendly ◽  
Different Levels ◽  
Better Than

A new method for musical steganography for the MIDI format is presented. The MIDI standard is a user-friendly music technology protocol that is frequently deployed by composers of different levels of ambition. There is to the author’s knowledge no fully implemented and rigorously specified, publicly available method for MIDI steganography. The goal of this study, however, is to investigate how a novel MIDI steganography algorithm can be implemented by manipulation of the velocity attribute subject to restrictions of capacity and security. Many of today’s MIDI steganography methods—less rigorously described in the literature—fail to be resilient to steganalysis. Traces (such as artefacts in the MIDI code which would not occur by the mere generation of MIDI music: MIDI file size inflation, radical changes in mean absolute error or peak signal-to-noise ratio of certain kinds of MIDI events or even audible effects in the stego MIDI file) that could catch the eye of a scrutinizing steganalyst are side-effects of many current methods described in the literature. This steganalysis resilience is an imperative property of the steganography method. However, by restricting the carrier MIDI files to classical organ and harpsichord pieces, the problem of velocities following the mood of the music can be avoided. The proposed method, called Velody 2, is found to be on par with or better than the cutting edge alternative methods regarding capacity and inflation while still possessing a better resilience against steganalysis. An audibility test was conducted to check that there are no signs of audible traces in the stego MIDI files.

scholarly journals Day-Ahead Forecasting of Hourly Photovoltaic Power Based on Robust Multilayer Perception

2018 ◽  
Vol 10 (12) ◽  
pp. 4863 ◽  
Author(s):  
Chao Huang ◽  
Longpeng Cao ◽  
Nanxin Peng ◽  
Sijia Li ◽  
Jing Zhang ◽  
...  
Keyword(s):  
Power Plants ◽  
Mean Squared Error ◽  
Absolute Error ◽  
Multilayer Perception ◽  
Squared Error ◽  
The Mean ◽  
Effectiveness And Efficiency ◽  
Mlp Network ◽  
Grid Operation ◽  
Better Than

Photovoltaic (PV) modules convert renewable and sustainable solar energy into electricity. However, the uncertainty of PV power production brings challenges for the grid operation. To facilitate the management and scheduling of PV power plants, forecasting is an essential technique. In this paper, a robust multilayer perception (MLP) neural network was developed for day-ahead forecasting of hourly PV power. A generic MLP is usually trained by minimizing the mean squared loss. The mean squared error is sensitive to a few particularly large errors that can lead to a poor estimator. To tackle the problem, the pseudo-Huber loss function, which combines the best properties of squared loss and absolute loss, was adopted in this paper. The effectiveness and efficiency of the proposed method was verified by benchmarking against a generic MLP network with real PV data. Numerical experiments illustrated that the proposed method performed better than the generic MLP network in terms of root mean squared error (RMSE) and mean absolute error (MAE).

Design and Experimental Analysis of Novel Refractometer Based on Photoelectric Sensor Technology

2011 ◽  
Vol 383-390 ◽  
pp. 5211-5215
Author(s):  
Yin Lin Li ◽  
Zhong Hua Huang ◽  
Kai Bo Hu
Keyword(s):  
Mathematical Model ◽  
Experimental Analysis ◽  
Differential Method ◽  
Theoretical Solution ◽  
Experimental Results ◽  
Sensor Technology ◽  
Photoelectric Sensor ◽  
Better Than

A novel refractometer based on photoelectric sensor technology and differential method is proposed. Sensing principle and mathematical model are introduced; structure and key parameters of sensing probe are designed through detail calculation. Theoretical solution shows resolution reaches order of 10-5. Preliminary experiments verify the feasibility of the design, experimental results show stability error better than ±1.02×10-4, error caused by temperature is 6.65×10-6/°C.

Evaluation of a method for noninvasive intracranial pressure assessment during infusion studies in patients with hydrocephalus

2000 ◽  
Vol 92 (5) ◽  
pp. 793-800 ◽  
Author(s):  
Bernhard Schmidt ◽  
Marek Czosnyka ◽  
Jens Jürgen Schwarze ◽  
Dirk Sander ◽  
Werner Gerstner ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Intracranial Pressure ◽  
Time Course ◽  
Cerebral Blood Flow Velocity ◽  
Absolute Error ◽  
Content Type ◽  
Arterial Blood ◽  
Potential Clinical Benefit ◽  
The Mean ◽  
Fine Print

Object. A mathematical model previously introduced by the authors allowed noninvasive intracranial pressure (nICP) assessment. In the present study the authors investigated this model as an aid in predicting the time course of raised ICP during infusion tests in patients with hydrocephalus and its suitability for estimating the resistance to outflow of cerebrospinal fluid (Rcsf).Methods. Twenty-one patients with hydrocephalus were studied. The nICP was calculated from the arterial blood pressure (ABP) waveform by using a linear signal transformation, which was dynamically modified by the relationship between ABP and cerebral blood flow velocity. This model was verified by comparison of nICP with “real” ICP measured during lumbar infusion tests. In all simulations, parallel increases in real ICP and nICP were evident. The simulated Rcsf was computed using nICP and then compared with Rcsf computed from real ICP. The mean absolute error between real and simulated Rcsf was 4.1 ± 2.2 mm Hg minute/ml. By the construction of simulations specific to different subtypes of hydrocephalus arising from various causes, the mean error decreased to 2.7 ± 1.7 mm Hg minute/ml, whereas the correlation between real and simulated Rcsf increased from R = 0.73 to R = 0.89 (p < 0.001).Conclusions. The validity of the mathematical model was confirmed in this study. The creation of type-specific simulations resulted in substantial improvements in the accuracy of ICP assessment. Improvement strategies could be important because of a potential clinical benefit from this method.

The Met Office operational global ocean forecast system FOAM-ORCA12

2021 ◽  
Author(s):  
Ana Barbosa Aguiar ◽  
Jennifer Waters ◽  
Martin Price ◽  
Gordon Inverarity ◽  
Christine Pequignet ◽  
...  
Keyword(s):  
Computational Cost ◽  
Absolute Error ◽  
Global Ocean ◽  
Background Error ◽  
Verification Methods ◽  
Climate Simulations ◽  
Forecast Models ◽  
The Mean ◽  
Lower Continuous ◽  
Better Than

&lt;div&gt; &lt;p&gt;The importance of oceans for atmospheric forecasts as well as climate simulations is being increasingly recognised with the advent of coupled ocean / atmosphere forecast models. Having comparable resolutions in both domains maximises the benefits for a given computational cost. The Met Office has recently upgraded its operational global ocean-only model from an eddy permitting 1/4 degree tripolar grid (ORCA025) to the eddy resolving 1/12 degree ORCA12 configuration while retaining 1/4 degree data assimilation.&amp;#160;&lt;/p&gt; &lt;/div&gt;&lt;div&gt; &lt;p&gt;We will present a description of the ocean-only ORCA12 system, FOAM-ORCA12, alongside some initial results.&amp;#8239;Qualitatively, FOAM-ORCA12 seems to represent better (than FOAM-ORCA025) the details of mesoscale features in SST and surface currents. Overall, traditional statistical results suggest that the new FOAM-ORCA12 system performs similarly or slightly worse than the pre-existing FOAM-ORCA025. However, it is known that comparisons of models running at different resolutions suffer from a double penalty effect, whereby higher-resolution models are penalised more than lower-resolution models for features that are offset in time and space. Neighbourhood verification methods seek to make a fairer comparison using a common spatial scale for both models and it can be seen that, as neighbourhood sizes increase, ORCA12&amp;#8239;consistently has lower continuous ranked probability scores (CRPS) than&amp;#8239;ORCA025. CRPS measures the accuracy of the pseudo-ensemble created by the neighbourhood method and generalises the mean absolute error measure for deterministic forecasts.&amp;#160;&lt;/p&gt; &lt;/div&gt;&lt;div&gt; &lt;p&gt;The&amp;#160;focus over the next year will be on diagnosing the performance of both the model and assimilation. A planned development that is expected to enhance the system&amp;#160;is the update of the background-error covariances used for data&amp;#160;assimilation.&amp;#160;&lt;/p&gt; &lt;/div&gt;

scholarly journals Charuco Board-Based Omnidirectional Camera Calibration Method

Electronics ◽  
2018 ◽  
Vol 7 (12) ◽  
pp. 421 ◽  
Author(s):  
Gwon An ◽  
Siyeong Lee ◽  
Min-Woo Seo ◽  
Kugjin Yun ◽  
Won-Sik Cheong ◽  
...  
Keyword(s):  
Camera Calibration ◽  
Mean Absolute Error ◽  
Three Dimensional ◽  
Absolute Error ◽  
Calibration Method ◽  
Feature Points ◽  
Omnidirectional Camera ◽  
Reprojection Error ◽  
Conventional Methods ◽  
Better Than

In this paper, we propose a Charuco board-based omnidirectional camera calibration method to solve the problem of conventional methods requiring overly complicated calibration procedures. Specifically, the proposed method can easily and precisely provide two-dimensional and three-dimensional coordinates of patterned feature points by arranging the omnidirectional camera in the Charuco board-based cube structure. Then, using the coordinate information of the feature points, an intrinsic calibration of each camera constituting the omnidirectional camera can be performed by estimating the perspective projection matrix. Furthermore, without an additional calibration structure, an extrinsic calibration of each camera can be performed, even though only part of the calibration structure is included in the captured image. Compared to conventional methods, the proposed method exhibits increased reliability, because it does not require additional adjustments to the mirror angle or the positions of several pattern boards. Moreover, the proposed method calibrates independently, regardless of the number of cameras comprising the omnidirectional camera or the camera rig structure. In the experimental results, for the intrinsic parameters, the proposed method yielded an average reprojection error of 0.37 pixels, which was better than that of conventional methods. For the extrinsic parameters, the proposed method had a mean absolute error of 0.90° for rotation displacement and a mean absolute error of 1.32 mm for translation displacement.

scholarly journals An Improved Whale Algorithm for Setting Standard Scheduled Block Time Based on the Airline Fairness

2020 ◽  
Vol 2020 ◽  
pp. 1-14
Author(s):  
Qian Wang ◽  
Yong Tian ◽  
Lili Lin ◽  
Ratnaji Vanga ◽  
Lina Ma
Keyword(s):  
Mathematical Model ◽  
Mathematical Models ◽  
Optimization Algorithm ◽  
Whale Optimization Algorithm ◽  
Civil Aviation ◽  
Convergence Factor ◽  
Suggested Approach ◽  
Whale Optimization ◽  
Block Time ◽  
Better Than

Standard scheduled flight block time (SBT) setting is of great concern for Civil Aviation Administration of China (CAAC) and airlines in China. However, the standard scheduled flight block times are set in the form of on-site meetings in practice and current literature has not provided any efficient mathematical models to calculate the flight block times fairly among the airlines. The objective of this paper is to develop and solve a mathematical model for standard SBT setting with consideration of both fairness and reliability. We use whale optimization algorithm (WOA) and an improved version of the whale optimization algorithm (IWOA) to solve the SBT setting problem. A novel nonlinear update equation of convergence factor for random iterations is used in place of the original linear one in the proposed IWOA algorithm. Experimental results show that the suggested approach is effective, and IWOA performs better than WOA in the concerned problem, whose solutions are better compared to the flight block times released by CAAC. In particular, it is interesting to find that MSE, RMSE, MAE, MAPE and Theil of the reliability in 60%–70% range are always the smallest and the average fairness of airlines is better than that of 60%–75% range. The model and solving approach presented in this article have great potential to be applied by CAAC to determine the standard SBTs strategically.

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