Linear Properties in a Continuous Time Linear Model

Linear completeness in a continuous time Gauss–Markov model

Identifying Restrictions for Finite Parameter Continuous Time Models with Discrete Time Data

This paper aims to study price dynamics in two different continuous time cobweb models with delays close to [Hommes, 1994]. In both cases, the stationary equilibrium may be not representative of the long-term dynamics of the model, since it is possible to observe endogenous and persistent fluctuations (supercritical Hopf bifurcations) even if a deterministic context without external shocks is considered. In the model in which markets are in equilibrium every time, we show that the existence of time delays in the expectations formation mechanism may cause chaotic dynamics similar to those obtained in [Hommes, 1994] in a discrete time context. From a mathematical point of view, we apply the Poincaré–Lindstedt perturbation method to study the local dynamic properties of the models. In addition, several numerical experiments are used to investigate global properties of the systems.

In this paper, the asymptotic normality and strong consistency for M estimators of the unknown regression coefficients in classical linear models are established under the assumptions that the errors are identically distributed φ-mixing random variables. The results obtained in this paper generalize the corresponding ones of Chen and Zhao [M-methods in linear model. Shanghai: Scientific and Technical Publishers; 1996] and Zhao [Strong consistency of M-estimates in linear model. Sci China Ser A. 2002;45:1420–1427] for independent errors. Finally, the simulation study is provided to verify the finite sample performance of the theoretical results and a real example is analysed for illustration.

On the relationship between the equilibrium constants of consecutive association reactions

This article focuses on production planning in the metallurgical sector. This study undertakes a detailed comparative study of mixed-integer linear programming models using different time representations: continuous and discrete. The analysis shows that the continuous model consistently outperforms its discrete counterpart in all evaluated scenarios. The key difference between the continuous and discrete models is the continuous model’s ability to deliver better makespan results, achieving an improvement of up to 15% compared to the discrete model. This advantage holds even in complex environments with a high number of tasks and machines, where the continuous model consistently outperforms the discrete model by over 6% in the scenario with the highest number of tasks and machines. This preference extends beyond makespan considerations. The continuous model also maintains an edge in terms of runtime efficiency, achieving better times with a 99% improvement over the discrete model in all scenarios except one. These findings provide concrete evidence for the use of continuous models, which promise more effective production planning in analogous manufacturing domains.

The application of the theory of variable structure control systems for the control of resonant DC-DC converters is illustrated. The full-bridge configuration of series-resonant converters (SRCs) is used. The converter is operated at resonant frequency to obtain both output-to-input voltage characteristics similar to those of the buck converter and high efficiency. To arrive at an exact mathematical model, the SRC is viewed as a piecewise linear system. However, under some approximations and a suitably selected set of state variables, the SRC is characterized by a linear continuous-time model which allows determination of the equivalent control via the sliding mode control (SMC) theory. To obtain a sliding regime, the appropriate sliding surface is selected by assigning poles. This control law constitutes a new approach to the control of resonant DC-DC converters. >

The optimally weighted least squares estimate and the linear minimum variance estimate are two of the most popular estimation methods for a linear model. In this paper, the authors make a comprehensive discussion about the relationship between the two estimates. Firstly, the authors consider the classical linear model in which the coefficient matrix of the linear model is deterministic, and the necessary and sufficient condition for equivalence of the two estimates is derived. Moreover, under certain conditions on variance matrix invertibility, the two estimates can be identical provided that they use the same a priori information of the parameter being estimated. Secondly, the authors consider the linear model with random coefficient matrix which is called the extended linear model; under certain conditions on variance matrix invertibility, it is proved that the former outperforms the latter when using the same a priori information of the parameter.

Here I propose a fundamentally new flexible model to reveal the association between a trait and a set of genetic variants in a genomic region/gene. This model was developed for the situation when original individual-level phenotype and genotype data are not available, but the researcher possesses the results of statistical analyses conducted on these data (namely, SNP-level summary Z score statistics and SNP-by-SNP correlations). The new model was analytically derived from the classical multiple linear regression model applied for the region-based association analysis of individual-level phenotype and genotype data by using the linear compression of data, where the SNP-by-SNP correlations are among the explanatory variables, and the summary Z score statistics are categorized as the response variables. I analytically show that the regional association analysis methods developed within the framework of the classical multiple linear regression model with additive effects of genetic variants can be reformulated in terms of the new model without the loss of information. The results obtained from the regional association analysis utilizing the classical model and those derived using the proposed model are identical when SNP-by-SNP correlations and SNP-level statistics are estimated from the same genetic data.

IntroductionThe length of hospital stay (LOHS) caused by COVID-19 has imposed a financial burden, and cost on the healthcare service system and a high psychological burden on patients and health workers. The purpose of this study is to adopt the Bayesian model averaging (BMA) based on linear regression models and to determine the predictors of the LOHS of COVID-19.MethodsIn this historical cohort study, from 5100 COVID-19 patients who had registered in the hospital database, 4996 patients were eligible to enter the study. The data included demographic, clinical, biomarkers, and LOHS. Factors affecting the LOHS were fitted in six models, including the stepwise method, AIC, BIC in classical linear regression models, two BMA using Occam's Window and Markov Chain Monte Carlo (MCMC) methods, and GBDT algorithm, a new method of machine learning.ResultsThe average length of hospitalization was 6.7 ± 5.7 days. In fitting classical linear models, both stepwise and AIC methods (R2 = 0.168 and adjusted R2 = 0.165) performed better than BIC (R2 = 0.160 and adjusted = 0.158). In fitting the BMA, Occam's Window model has performed better than MCMC with R2 = 0.174. The GBDT method with the value of R2 = 0.64, has performed worse than the BMA in the testing dataset but not in the training dataset. Based on the six fitted models, hospitalized in ICU, respiratory distress, age, diabetes, CRP, PO2, WBC, AST, BUN, and NLR were associated significantly with predicting LOHS of COVID-19.ConclusionThe BMA with Occam's Window method has a better fit and better performance in predicting affecting factors on the LOHS in the testing dataset than other models.

The purpose of this study was to create synthetic vocal fold models with nonlinear stress-strain properties and to investigate the effect of linear versus nonlinear material properties on fundamental frequency (F0) during anterior-posterior stretching. Three materially linear and 3 materially nonlinear models were created and stretched up to 10 mm in 1-mm increments. Phonation onset pressure (Pon) and F0 at Pon were recorded for each length. Measurements were repeated as the models were relaxed in 1-mm increments back to their resting lengths, and tensile tests were conducted to determine the stress-strain responses of linear versus nonlinear models. Nonlinear models demonstrated a more substantial frequency response than did linear models and a more predictable pattern of F0 increase with respect to increasing length (although range was inconsistent across models). Pon generally increased with increasing vocal fold length for nonlinear models, whereas for linear models, Pon decreased with increasing length. Nonlinear synthetic models appear to more accurately represent the human vocal folds than do linear models, especially with respect to F0 response.

The profitability of insurance companies has been the focus of several studies within the rise of economies across the countries worldwide. This study aimed to identify determinants of profitability of insurance companies in Ethiopian. The study used nine insurance companies selected by purposive sampling technique among the total 17 insurance companies in Ethiopia from period of 2011 to 2020 based on their establishment. Descriptive, causal research design and quantitative research approach were adopted in carrying out this study. Classical linear regression model under estimation of ordinary least square was employed to identify the determinants of profitability of insurance companies in Ethiopia at 5% level of significance. The classical linear regression model revealed that variable age of the company, tangibility of an asset, size of the company, managerial efficiency, leverage ratio, premium growth and GDP have a positive coefficient relationship with return on asset while loss ratio and inflation have a negative coefficient relationship with return on asset. On the other hand, age of the company size, managerial efficiency, leverage ratio, liquidity ration inflation and premium growth have statistically significant at 5% confidence interval level, whereas the other variables such tangibility of asset and GDP have no statistical significance at 5% confidence interval level. The insurance companies’ previous profit, age of the company, company size, managerial efficiency, leverage ratio, liquidity ratio, loss ratio, premium growth and inflation rate variables are significant key drivers of profitability of Ethiopian insurance companies. Giving due attention to the sector in line with key factors affecting the profitability will improve the overall performance of the insurance companies in Ethiopia.

Robust Adaptive Control

The global diabetes epidemic is largely attributed to obesity-triggered metabolic syndrome. However, the impact of insulin resistance (IR) prior to obesity on the high prevalence of diabetes and the molecular mediators remain largely unknown. This study aims to compare the metabolic profiling of apparently healthy lean/overweight participants with IR and insulin sensitivity (IS), and identify the metabolic pathways underlying IR. In this cross-sectional study, clinical and metabolic data for 200 seemingly healthy young female participants (100 IR and 100 IS) was collected from Qatar Biobank. Orthogonal partial least square analysis was performed to assess the extent of separation between individuals from the 2 groups based on measured metabolites. Classical linear models were used to identify the metabolic signature of IR, followed by elastic-net-regularized generalized linear model (GLMNET) and receiver operating characteristic (ROC) analysis to determine top metabolites associated with IR. Compared to lean/overweight participants with IS, those with IR showed increased androgenic steroids, including androsterone glucuronide, in addition to various microbiota byproducts, such as the phenylalanine derivative carboxyethylphenylalanine. On the other hand, participants with IS had elevated levels of long-chain fatty acids. A ROC analysis suggested better discriminatory performance using 20 metabolites selected by GLMNET in comparison to the classical clinical traits (area under curve: 0.93 vs 0.73, respectively). Our data confirm the multifactorial mechanism of IR with a diverse spectrum of emerging potential biomarkers, including steroids, long-chain fatty acids, and microbiota metabolites. Further studies are warranted to validate these markers for diagnostic and therapeutic applications.

It is well known that the least squares estimator is the best linear unbiased estimator of the parameter vector in a classical linear model. But, it is `too long' as a vector and unreliable, confidence intervals are broad for some components especially in the case of multicollinearity. Shrinkage (contraction) type estimators are efficient remedial tools in order to solve problems caused by multicollinearity. In this study, we consider a class of componentwise shrunken estimators with typical members: Mayer and Willke's contraction estimator, Marquardt's principal component estimator, Hoerl and Kennard's ridge estimator, Liu's linear unified estimator and a discrete shrunken estimator. All estimators considered are shorter than the least squares estimator with respect to the Euclidean norm, biased, but insensitive to multicollinearity and admissible within the set of linear estimators with respect to unweighted squared error risk. Some behaviors of these estimators are illustrated geometrically by tracing their trajectories as functions of shrinkage factors in a two- dimensional parameter space.