Non-Linear Regression and the Selection of the Proper Functional Form

This research presents a model for prediction surface roughness in terms of process parameters in turning aluminum alloy 1200. The geometry to be machined has four rotational features: straight, taper, convex and concave, while a design of experiments was created through the Taguchi L25 orthogonal array experiments in minitab17 three factors with five Levels depth of cut (0.04, 0.06, 0.08, 0.10 and 0.12) mm, spindle speed (1200, 1400, 1600, 1800 and 2000) r.p.m and feed rate (60, 70, 80, 90 and 100) mm/min. A multiple non-linear regression model has been used which is a set of statistical extrapolation processes to estimate the relationships input variables and output which the surface roughness which prediction outside the range of the data. According to the non-linear regression model, the optimum surface roughness can be obtained at 1800 rpm of spindle speed, feed-rate of 80 mm/min and depth of cut 0.04 mm then the best surface roughness comes out to be 0.04 μm at tapper feature at depth of cut 0.01 mm and same spindle speed and feed rate pervious which gives the error of 3.23% at evolution equation.

Download Full-text

SINGLE-FACTOR LINEAR REGRESSION MODEL OF HODGKIN’S LYMPHOMA IN ADOLESCENTS

Problems in oncology ◽

10.37469/0507-3758-2017-63-2-320-325 ◽

2017 ◽

Vol 63 (2) ◽

pp. 320-325

Author(s):

Svetlana Kuleva ◽

Svetlana Ivanova ◽

Andrey Karitskiy ◽

Darya Zvyagintseva

Keyword(s):

Radiation Therapy ◽

Linear Regression ◽

Predictive Factors ◽

Hodgkin’S Lymphoma ◽

Risk Group ◽

Hodgkin's Lymphoma ◽

Regression Equations ◽

Single Factor ◽

Number Of Cycles ◽

Selection Of

With the use of regression and dispersion analyzes conducted in this study it was possible to identify predictive factors that significantly worsen the prognosis of Hodgkin’s lymphoma in adolescents however constructed regression equations did not pass the quality assessment of the models, which did not allow them to be used for the construction of point and interval predictions. In a cohort of patients enrolled in the study a risk-adapted treatment program based on the risk group for stratification was conducted. Negative aspects of the results of our study could be related to the already selected volume of the program for these patients. In turn our analysis proves the validity of the selection of therapeutic loads (a number of cycles of polychemotherapy, doses of radiation therapy) depending on the risk group, into which the adolescent is stratified.

Download Full-text

Is There a Relationship between the Elasticity of Brain Tumors, Changes in Diffusion Tensor Imaging, and Histological Findings? A Pilot Study Using Intraoperative Ultrasound Elastography

Brain Sciences ◽

10.3390/brainsci11020271 ◽

2021 ◽

Vol 11 (2) ◽

pp. 271

Author(s):

Santiago Cepeda ◽

Sergio García-García ◽

María Velasco-Casares ◽

Gabriel Fernández-Pérez ◽

Tomás Zamora ◽

...

Keyword(s):

Brain Tumor ◽

Diffusion Tensor Imaging ◽

Linear Regression ◽

Brain Tumors ◽

Diffusion Tensor ◽

Intraoperative Ultrasound ◽

Ultrasound Elastography ◽

Proliferation Index ◽

Strong Positive Correlation ◽

Non Linear

Intraoperative ultrasound elastography (IOUS-E) is a novel image modality applied in brain tumor assessment. However, the potential links between elastographic findings and other histological and neuroimaging features are unknown. This study aims to find associations between brain tumor elasticity, diffusion tensor imaging (DTI) metrics, and cell proliferation. A retrospective study was conducted to analyze consecutively admitted patients who underwent craniotomy for supratentorial brain tumors between March 2018 and February 2020. Patients evaluated by IOUS-E and preoperative DTI were included. A semi-quantitative analysis was performed to calculate the mean tissue elasticity (MTE). Diffusion coefficients and the tumor proliferation index by Ki-67 were registered. Relationships between the continuous variables were determined using the Spearman ρ test. A predictive model was developed based on non-linear regression using the MTE as the dependent variable. Forty patients were evaluated. The pathologic diagnoses were as follows: 21 high-grade gliomas (HGG); 9 low-grade gliomas (LGG); and 10 meningiomas. Cases with a proliferation index of less than 10% had significantly higher medians of MTE (110.34 vs. 79.99, p < 0.001) and fractional anisotropy (FA) (0.24 vs. 0.19, p = 0.020). We found a strong positive correlation between MTE and FA (rs (38) = 0.91, p < 0.001). A cubic spline non-linear regression model was obtained to predict tumoral MTE from FA (R2 = 0.78, p < 0.001). According to our results, tumor elasticity is associated with histopathological and DTI-derived metrics. These findings support the usefulness of IOUS-E as a complementary tool in brain tumor surgery.

Download Full-text

Relationship between Age and Value of Information for a Noisy Ornstein–Uhlenbeck Process

Entropy ◽

10.3390/e23080940 ◽

2021 ◽

Vol 23 (8) ◽

pp. 940

Author(s):

Zijing Wang ◽

Mihai-Alin Badiu ◽

Justin P. Coon

Keyword(s):

Value Of Information ◽

Markov Models ◽

Upper Bounds ◽

Distribution Functions ◽

Lower And Upper Bounds ◽

Uhlenbeck Process ◽

Source Data ◽

Non Linear ◽

Queue Model ◽

Selection Of

The age of information (AoI) has been widely used to quantify the information freshness in real-time status update systems. As the AoI is independent of the inherent property of the source data and the context, we introduce a mutual information-based value of information (VoI) framework for hidden Markov models. In this paper, we investigate the VoI and its relationship to the AoI for a noisy Ornstein–Uhlenbeck (OU) process. We explore the effects of correlation and noise on their relationship, and find logarithmic, exponential and linear dependencies between the two in three different regimes. This gives the formal justification for the selection of non-linear AoI functions previously reported in other works. Moreover, we study the statistical properties of the VoI in the example of a queue model, deriving its distribution functions and moments. The lower and upper bounds of the average VoI are also analysed, which can be used for the design and optimisation of freshness-aware networks. Numerical results are presented and further show that, compared with the traditional linear age and some basic non-linear age functions, the proposed VoI framework is more general and suitable for various contexts.

Download Full-text

Machine Learning Based Device Simulation Using Multi-variable Non-linear Regression to Assess the Impact of Device Parameter Variability on Threshold Voltage of Double Gate-All-Around (DGAA) MOSFET

2020 IEEE 2nd International Conference on Circuits and Systems (ICCS) ◽

10.1109/iccs51219.2020.9336608 ◽

2020 ◽

Author(s):

Sandeep Moparthi ◽

Chandan Yadav ◽

Gopi Krishna Saramekala ◽

Pramod Kumar Tiwari

Keyword(s):

Machine Learning ◽

Linear Regression ◽

Threshold Voltage ◽

Device Simulation ◽

Double Gate ◽

Device Parameter ◽

Non Linear ◽

The Impact

Download Full-text

Non-Parametric Generalized Additive Models as a Tool for Evaluating Policy Interventions

Mathematics ◽

10.3390/math9040299 ◽

2021 ◽

Vol 9 (4) ◽

pp. 299

Author(s):

Jaime Pinilla ◽

Miguel Negrín

Keyword(s):

Linear Regression ◽

Regression Models ◽

Linear Trend ◽

Generalized Additive Models ◽

Additive Models ◽

Linear Regression Models ◽

Non Linear ◽

Nonlinear Trends ◽

The Impact ◽

Non Parametric

The interrupted time series analysis is a quasi-experimental design used to evaluate the effectiveness of an intervention. Segmented linear regression models have been the most used models to carry out this analysis. However, they assume a linear trend that may not be appropriate in many situations. In this paper, we show how generalized additive models (GAMs), a non-parametric regression-based method, can be useful to accommodate nonlinear trends. An analysis with simulated data is carried out to assess the performance of both models. Data were simulated from linear and non-linear (quadratic and cubic) functions. The results of this analysis show how GAMs improve on segmented linear regression models when the trend is non-linear, but they also show a good performance when the trend is linear. A real-life application where the impact of the 2012 Spanish cost-sharing reforms on pharmaceutical prescription is also analyzed. Seasonality and an indicator variable for the stockpiling effect are included as explanatory variables. The segmented linear regression model shows good fit of the data. However, the GAM concludes that the hypothesis of linear trend is rejected. The estimated level shift is similar for both models but the cumulative absolute effect on the number of prescriptions is lower in GAM.

Download Full-text