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Linear and Non Linear Models

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lightbulbAbout this topic
Linear and Non-Linear Models refer to mathematical representations used in statistics and data analysis. Linear models assume a direct proportionality between variables, while non-linear models account for more complex relationships, allowing for curvature and interaction effects. These models are essential for understanding and predicting behaviors in various scientific and social phenomena.
lightbulbAbout this topic
Linear and Non-Linear Models refer to mathematical representations used in statistics and data analysis. Linear models assume a direct proportionality between variables, while non-linear models account for more complex relationships, allowing for curvature and interaction effects. These models are essential for understanding and predicting behaviors in various scientific and social phenomena.

Key research themes

1. How do nonlinear mixed-effects models enhance growth curve analysis in biological systems compared to fixed-effects or linear models?

This research area focuses on applying nonlinear mixed-effects modeling frameworks to capture individual variability and complex growth dynamics in biological systems, particularly in animal growth studies. Mixed-effects approaches extend classical nonlinear fixed-effect models by incorporating random effects to account for between-subject heterogeneity, enabling more accurate and biologically interpretable parameter estimation. This matters because biological growth processes are inherently nonlinear and subject-specific, and traditional linear or fixed models may fail to capture this complexity and variability.

Key finding: By applying nonlinear mixed-effects models with random effects on asymptotic weight and maturity rate parameters, the Morgan-Mercer-Flodin function was identified as providing the best fit for growth curves of male and female... Read more
Key finding: This work elucidates the equivalencies and differences between nonlinear mixed-effects models and nonlinear latent curve models for longitudinal data, highlighting situations where partially nonlinear mixed-effects models... Read more

2. What are the computational and statistical advances enabling the use of ordinary differential equations (ODEs) and skew-elliptical error distributions for nonlinear regression modeling beyond classical linear frameworks?

This theme investigates methodological innovations in regression modeling where the response dynamics are captured via differential equations or modeling error distributions that exhibit asymmetry and heavy tails. These approaches extend standard linear regression by directly incorporating derivative information or error structures aligned with real data features, thereby enabling robust modeling of nonlinear trends and skewed residuals observed in complex datasets such as survival data or financial time series. They matter because they address limitations of conventional transformations or linear assumptions, improving interpretability and fidelity of fitted models.

Key finding: Proposes an efficient analytical method to fit real-world data using first-order linear ODEs by numerically estimating derivatives and solving for ODE parameters through minimizing sum of squared errors. The model... Read more
Key finding: Introduces a nonlinear regression model incorporating skew-elliptical error distributions with exponentiated components to effectively model data exhibiting high asymmetry and kurtosis. The proposed maximum likelihood... Read more

3. How do advanced linear and nonlinear models perform in complex system modeling and statistical inference, and what are the comparative benefits in different application domains?

This theme evaluates and compares the applicability, performance, and interpretability of linear models, nonlinear extensions, and sophisticated estimation techniques including ridge regression in seemingly unrelated regression (SUR) frameworks, model selection criteria for nonlinear time series, and performance modeling in computing systems. It is crucial in guiding model choice and methodology across disciplines where data complexity, multicollinearity, or system dynamics challenge traditional linear assumptions.

Key finding: Presents a two-parameter ridge regression solution that extends classical ridge regression to SUR models to tackle multicollinearity. Simulation and real data application demonstrate that this estimator outperforms both... Read more
Key finding: The text establishes foundational linear model theory important for numerous statistical applications including regression, ANOVA, and linear mixed models. It reconciles various conceptual approaches (algebraic, geometric,... Read more
Key finding: Through empirical testing using both linear and nonlinear models on stock return data, the study finds evidence rejecting weak-form efficient market hypothesis (EMH) via nonlinear analyses, while linear methods support it.... Read more

All papers in Linear and Non Linear Models

Numerical modelling of turbulence plays a crucial role in providing accurate microscale wind fields which are necessary to predict transport and dispersion of pollutants in the vicinity of buildings reliably. Although more elaborate... more
Numerical modelling of turbulence plays a crucial role in providing accurate wind fields, which are necessary to predict transport and dispersion of pollutants in the vicinity of buildings reliably. Although the standard k-e has some... more
Data centers are large-scale, energy-hungry infrastructure serving the increasing computational demands as the world is becoming more connected in smart cities. The emergence of advanced technologies such as cloud-based services, internet... more
For semi-submersible units, the magnitude of air gap or local wave impact in the survival condition is a key design driver. Linear analyses are widely used in the industry to predict survival air gap for semi-subs. Large relative motions,... more
Cities are complex, networked and continuously changing social ecosystems, shaped and transformed through the interaction of different interests and ambitions. They are linked to places, where various aspects of past events are projected... more
Universities are isomorphic not because of the effectiveness of their processes but because of the legitimacy assigned by institutional logic. However, sustainable development discourses invoke a novel mission for producing knowledge and... more
Cities are complex, networked and continuously changing social ecosystems, shaped and transformed through the interaction of different interests and ambitions. They are linked to places, where various aspects of past events are projected... more
This paper deals with the turbulence closure problem associated with the Reynolds-averaged Navier-Stokes equations for compressible flows. Due to the known limitations faced by the turbulent closure model based on the Boussinesq... more
Data centers are large-scale, energy-hungry infrastructure serving the increasing computational demands as the world is becoming more connected in smart cities. The emergence of advanced technologies such as cloud-based services, internet... more
Universities are isomorphic not because of the effectiveness of their processes but because of the legitimacy assigned by institutional logic. However, sustainable development discourses invoke a novel mission for producing knowledge and... more
Efficient stock market plays important role in stimulating economic development through providing channel for mobilising domestic savings and facilitating the allocation of financial resources from dormant to more productive activities.... more
This paper uses a case based study-"product sales estimation" on real-time data to understand the applicability of linear and non-linear models. We use a systematic approach to address the given problem statement of sales estimation for a... more
This document discusses the evaluation of a consolidated linear performance model of Texas State University's HPC LEAP Cluster, and the development of a non-linear model to represent the performance of the NVIDIA V100 Graphics... more
Understanding conservation needs relies on robust estimates of key population parameters, such as survival, abundance and somatic growth. We investigated the somatic growth and abundance dynamics of 2 aggregations of immature green... more
An increasing number of engineering applications require accurate predictions of the flow around buildings to guarantee performance and safety. This paper investigates the effects of variations in the turbulent inflow, as predicted in... more
The present work is a numerical simulation of flow over buildings. The numerical simulation was carried out using an open source Computational Fluid Dynamics (CFD) tool called OpenFOAM®. The Reynolds Averaged Navier Stokes Equations... more
This paper presents a study of the hydraulic behaviour of a gully under surcharge conditions using both numerical and experimental models. These results can be useful for the validation of the linking elements in Dual Drainage (DD)... more
This document discusses the evaluation of a consolidated linear performance model of Texas State University's HPC LEAP Cluster, and the development of a non-linear model to represent the performance of the NVIDIA V100 Graphics Processing... more
Important mathematical models for data science and how we do estimate with these models?
Cities are complex, networked and continuously changing social ecosystems, shaped and transformed through the interaction of different interests and ambitions. They are linked to places, where various aspects of past events are projected... more
In the present paper, the analysis of concentration and flow fields around a model building was performed using two different approaches in turbulence modeling. In the first approach, the non-linear model of Ehrhard and Moussiopoulos was... more
During the last decade, there has been an increased interest on cloud computing and especially on the adoption of public cloud services. The process of developing cloud-based public services or migrating existing ones to the Cloud is... more
Understanding conservation needs relies on robust estimates of key population parameters, such as survival, abundance and somatic growth. We investigated the somatic growth and abundance dynamics of 2 aggregations of immature green... more
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