Parameters Of Linear Model Research Articles

Cognitive framing modulates emotional processing through dorsolateral prefrontal cortex and ventrolateral prefrontal cortex networks: A functional magnetic resonance imaging study.

IntroductionIn this study, we show new evidence for the role of ventrolateral prefrontal cortex‐dorsolateral prefrontal cortex (VLPFC‐DLPFC) networks in the cognitive framing of emotional processing.MethodWe displayed neutral and aversive images described as having been sourced from artistic material to one cohort of subjects (i.e., the art‐frame group; n = 19), while identical images, this time identified as having been sourced from documentary material (i.e., the doc‐frame group; n = 20) were shown to a separate cohort.ResultsUsing functional magnetic resonance imaging (fMRI), we employed a linear parametric model showing that relative to the doc‐frame group the art‐frame group exhibited a modulation of amygdala activity in response to aversive images. The attenuated amygdala activity in the art‐frame group supported our hypothesis that reduced amygdala activity was driven by top‐down DLPFC inhibition of limbic responses. A psychophysiological interaction (PPI) analysis demonstrated that VLPFC activity correlated with amygdala activity in the art‐frame group, but not in the doc‐frame group for the contrast [Aversive > Neutral].ConclusionThe role of the VLPFC in cognitive control suggests the hypothesis that it alongside DLPFC insulates against embodied emotional responses by inhibiting automatic affective responses.

Stock Daily Price Regime Model Detection using Markov Switching Model

Changes in stock prices randomly occur due to market forces with reoccurrencepossibilities. This process, also known as the structural break model, is captured throughchanges in the linear model parameters among periods with the Markov Switching Model(MSwM) used for detection. Furthermore, using the smallest Akaike Information Criterion(AIC) value on all feasible MSwM alternatives formed for a daily stock price, the completeMSwM model with its Markov transition is determined. This method has been tested andapplied to daily stock price data in several sectors. The result showed that the number ofregime models coupled with its transition probability helped investors make investmentdecisions.

Neutrosophic linear programming using possibilistic mean

The paper discusses the concept of fuzzy set theory, interval-valued fuzzy set, intuitionistic fuzzy set, interval-valued intuitionistic fuzzy set, neutrosophic set and its operational laws. The paper presents the $$ \alpha ,\beta ,\gamma $$ -cut of single-valued triangular neutrosophic numbers and introduces the arithmetic operations of triangular neutrosophic numbers using $$ \alpha ,\beta ,\gamma $$ -cut. Then, possibilistic mean of truth membership function, indeterminacy membership function and falsity membership function is defined. The proposed approach converts each triangular neutrosophic number in linear programming problem to weighted value using possibilistic mean to determine the crisp linear programming problem. The proposed approach also considers the risk attitude of expert while deciding the parameters of linear programming model.

Evaluating parameters of econometric models with linear limitations and a rank deficient observation matrix

There considered the approach of the linear econometric dependences parameters estimating for the case of combining a set of special conditions arising in the simulation process. These conditions address the most important problems met in practice when implementing a series of classes of mathematical models, for the construction of which the matrix of explanatory variables can be used. In most cases the vectors that make up the matrix have a close correlation relationship; this leads to the need of performing calculations using a rank deficient matrix. There are also take place violations of the Gauss-Markov theorem condition. The list of above mentioned special conditions is augmented by the additional model parameters constraints. Cobb-Douglas's production function and the Solow model are known economic problems of this type. In this research the need to impose additional constraints on the model parameters is extended to a wider range of tasks. In general, the economic formulation of the problem with the specified features is presented.Known ways to solve these tasks are discussed. The authors’ approach proposed takes into account the whole spectrum of these features. This approach is based on the application of pseudorandom matrices and the use of singular matrix decomposition. The use of proposed mathematical tools makes it possible to improve the quality of estimating model parameters while using real economic processes data. The analytical definition is found for the parameter evaluating vector of a linear econometric model with all the above mentioned features. Analysis of the used definition provides determination of the conditions that the matrix must satisfy; this describes additional model parameters constraints. The term was also obtained to estimate the variance of a linear econometric model parameters vector.The results obtained can be used in machine learning systems in the implementation of problems of econometric dependencies or discriminant models.

Information Dynamics Analysis: A new approach based on Sparse Identification of Linear Parametric Models.

The framework of information dynamics allows to quantify different aspects of the statistical structure of multivariate processes reflecting the temporal dynamics of a complex network. The information transfer from one process to another can be quantified through Transfer Entropy, and under the assumption of joint Gaussian variables it is strictly related to the concept of Granger Causality (GC). According to the most recent developments in the field, the computation of GC entails representing the processes through a Vector Autoregressive (VAR) model and a state space (SS) model typically identified by means of the Ordinary Least Squares (OLS). In this work, we propose a new identification approach for the VAR and SS models, based on Least Absolute Shrinkage and Selection Operator (LASSO), that has the advantages of maintaining good accuracy even when few data samples are available and yielding as output a sparse matrix of estimated information transfer. The performances of LASSO identification were first tested and compared to those of OLS by a simulation study and then validated on real electroencephalographic (EEG) signals recorded during a motor imagery task. Both studies indicated that LASSO, under conditions of data paucity, provides better performances in terms of network structure. Given the general nature of the model, this work opens the way to the use of LASSO regression for the computation of several measures of information dynamics currently in use in computational neuroscience.

Information Transfer in Linear Multivariate Processes Assessed through Penalized Regression Techniques: Validation and Application to Physiological Networks.

The framework of information dynamics allows the dissection of the information processed in a network of multiple interacting dynamical systems into meaningful elements of computation that quantify the information generated in a target system, stored in it, transferred to it from one or more source systems, and modified in a synergistic or redundant way. The concepts of information transfer and modification have been recently formulated in the context of linear parametric modeling of vector stochastic processes, linking them to the notion of Granger causality and providing efficient tools for their computation based on the state–space (SS) representation of vector autoregressive (VAR) models. Despite their high computational reliability these tools still suffer from estimation problems which emerge, in the case of low ratio between data points available and the number of time series, when VAR identification is performed via the standard ordinary least squares (OLS). In this work we propose to replace the OLS with penalized regression performed through the Least Absolute Shrinkage and Selection Operator (LASSO), prior to computation of the measures of information transfer and information modification. First, simulating networks of several coupled Gaussian systems with complex interactions, we show that the LASSO regression allows, also in conditions of data paucity, to accurately reconstruct both the underlying network topology and the expected patterns of information transfer. Then we apply the proposed VAR-SS-LASSO approach to a challenging application context, i.e., the study of the physiological network of brain and peripheral interactions probed in humans under different conditions of rest and mental stress. Our results, which document the possibility to extract physiologically plausible patterns of interaction between the cardiovascular, respiratory and brain wave amplitudes, open the way to the use of our new analysis tools to explore the emerging field of Network Physiology in several practical applications.

Micro Level Speed Choice Behavior on a Rural Highway in an Heterogeneous Traffic Environment: Latent Class Modeling Approach

The modeling of driver speed choice behavior on a rural highway with heterogeneous traffic environment in a developing country is reported. The study explores the application of a latent class model as an alternative methodological approach, to relate factors such as road geometry, roadside environment, traffic mix and operational characteristics with speed choice at the micro level. In the conventional analysis based on lane-based homogeneous traffic environments, the impact of exogenous variables is kept constant across road segments; whereas those impacts might vary across different segments for different conditions. To check this possible variation, the study compares latent class linear regression with ordinary least square, as well as the random parameter linear regression model. The proposed models were estimated using data collected from two sections of a major national highway in Bangladesh. The entire roadway section was divided into several small segments and the critical segment length was estimated based on several sensitivity tests. The small segmental level exogenous variables were considered for the model building and estimation. The results obtained could be used to understand better the speed choice factors of drivers in the non-lane-based traffic environments of developing countries. Law enforcement agencies, traffic operation and maintenance officials, as well as roadway design and planning authorities, could gainfully use the findings of this study to inform more responsive speed management strategies.

Structure–retardation factor relationship of natural amino acids in two different mobile phases of RP-TLC

Separation of amino acids (AAs) and their simple and inexpensive determination/identification is an interesting topic in biological and protein science, different food industries, and drug factories. Also, the presentation of the chromatographic behavior of compounds in a predictive model can be effective to estimate the structural/chemical properties of analyte and mobile phases. In this work for the first time, retardation factor (RF) of 42 AAs in reversed-phase thin layer chromatography (RP-TLC) was modeled. Acetonitrile-sodium azide solution and 1,2 dioxane-sodium azide solution were two mobile phases which have been studied in this work. Results showed that the values of RF are correlated with the structural properties of AAs and these properties had some similarities and differences in two noted mobile phases. For the TLC data in two mobile phases, five parametric linear models were suggested (R2train = 0.93 and 0.97; R2test = 0.93 and 0.99). The models were also evaluated with different statistical approaches. It was shown that increasing the sum of geometrical distances between N and O in AAs causes decreasing their RF in RP-TLC using both mobile phases. Other structural effects of AAs on their separation in the desired RP-TLC system were also discussed.

Analyses of replicated spectrophotometric data by using soft computing methods

Soft computing based chemometric studies are needed to model and to optimize complex processes, such as the extraction stage. In this study, it was aimed to obtain optimal values of ethanol (EtOH) concentration, extraction time, extraction temperature, solvent/solid ratio for the ultrasound-assisted extraction (UAE) of grape seed polyphenols to maximize the total phenolic content (TPC) and total antioxidant activity (TAA) in multi-objective perspective by using soft computing methods. The experimental data set was composed with replicated response measures to see the behavior of the responses. The replicated response measured (RRM) data was recently modeled by using fuzzy linear regression in which the replicated responses were considered as triangular linear fuzzy numbers (TLFNs). Also, polynomial type fuzzy linear regression model parameters were dealt as TLFNs whereas the experiment conditions were crisp. The predicted fuzzy linear models were obtained by using least square (LS) approach. The predicted fuzzy models were optimized through the Non-dominated Sorting Genetic Algorithm-II (NSGA-II) and Pareto set was obtained. The obtained Pareto solution set was experimentally verified. A compromise solution was chosen among many non-dominated solutions of experimental conditions by using a distance function based on root mean square of fuzzy errors. According to the results, it is possible to say that the proposed soft computing based modeling and multi-objective optimization (MOO) approaches can be used as flexible analyses tools in chemometry.

A suitable state-space model for renewable source-based microgrids with hydrogen as backup for the design of energy management systems

This paper presents a methodological foundation to obtain a general state-space model for renewable source-based microgrids. The main novelty lies in developing a general control-oriented model that, taking into account all the parameters (technical and economic), enables the design of efficient energy management system (EMS) to make the best decisions both in the short-term (such as to adapt demand and production) and long-term (such as extending the lifespan of the most expensive and sensitive microgrid elements). The proposed approach guarantees a better approximation when compared to traditional models because most of them are linearized systems around a single operating point. The proposed model is more comprehensive since, apart from describing electrical performance for each device that makes up the microgrid, it also includes technical and economical parameters such as operating efficiency, degradation, losses and costs needed for microgrid optimization. The experimental results show the quality and excellent performance of the developed model. Additionally, a comparison between the reference models from the literature and the one proposed in this paper is undertaken. The results reflect a good performance in the evolution of the main parameters of the microgrid. Moreover, the use of the proposed methodology, based on the definition and calculation of the linear model parameters in each discretization period, guarantees a good fit of the model with respect to the non-linear behaviour of the microgrid.

A parametric recurrent neural network scheme for solving a class of fuzzy regression models with some real-world applications

In this paper, a hybrid scheme based on recurrent neural networks for approximate fuzzy coefficients (parameters) of fuzzy linear and polynomial regression models with fuzzy output and crisp inputs is presented. Here, a neural network is first constructed based on some concepts of convex optimization and stability theory. The suggested neural network model guarantees to find the approximate parameters of the fuzzy regression problem. The existence and convergence of the trajectories of the neural network are studied. The Lyapunov stability for the neural network is also shown. Some illustrative examples provide a further demonstration of the effectiveness of the method.

Determining the top electrode voltage in free-running oscillator radio frequency heating of soybeans under different electrode configurations

This study is focused on a computer simulation-based determination of top electrode voltages associated with the free running oscillator (FRO) radio frequency (RF) heating of soybeans. This is an extension of a previous study that used a single parameter linear regression model to a two-parameter model to better estimate the voltages by considering two different electrode configurations (with/without copper strips) and a wider range of moisture content. Soybeans at four moisture contents (i.e. 4.7%, 7.7%, 9.7% and 11.7% on wet basis, w.b.) and soybean flour (9.7% w.b.) were heated in a 6kW, 27.12MHz FRO RF heating system and the corresponding voltages under five electrode gaps were measured using a customized measuring device for model testing. The results demonstrated that the installed copper strips raised both anode and measured currents, and thus two different models were established for each electrode configuration (with/without copper strips). The relative error was less than 5% between voltages predicted by the improved model and the previous model under the same condition used in the previous study. Moreover, under the broader conditions, the voltage predicted by the improved model was much closer to the computer simulated values than observed with the previous model. Therefore, the developed method was more accurate for estimating the voltage for RF heating of soybeans, which can be applied in computer simulations.

1848-P: Insulin Sensitivity and Metabolic Profile of Subjects with Type 2 Diabetes and Nonalcoholic Steatohepatitis after Exposure to Cenicriviroc: A Subanalysis of the CENTAUR Study

Introduction: In mice, C-C motif chemokine receptor (CCR)5 deletion protects against insulin resistance, hepatic steatosis, and glucose intolerance. We aimed to characterize the metabolic effects of cenicriviroc (CVC), a potent CCR2/5 inhibitor, in type 2 diabetes mellitus (T2DM) patients with nonalcoholic steatohepatitis (NASH) fibrosis from the Phase 2b CENTAUR study. Methods: Subjects from CENTAUR with T2DM, biopsy-proven NASH, and fibrosis Stages F1-3 were included. CVC-exposed subjects for 1 year (Arm A) and placebo (PBO) [Arms B and C] were analyzed. Liver, metabolic, and inflammatory biomarkers were analyzed. Homeostatic model assessments (HOMA-IR and -b) were calculated. Change (from baseline to Year 1) was compared between groups using a general parametric linear model analysis of covariance (2-sided ANCOVA) based on the mITT population. Results: Of the 289 subjects in CENTAUR, 134 (46%) had T2DM and were included in this analysis. Baseline characteristics were similar for CVC (n=76) and PBO (n=58) groups (mean ±SD): age 57.5 ±7.75 years vs. 55.41 ±8.65 years, HbA1c 7.30 ±1.29 vs. 7.20 ±1.21 %, BMI 33.02 ±5.25 vs. 35.16 ±7.67 kg/m2, NAS 5.25 ±1.06 vs. 5.52 ±1.13, and fibrosis scores of F1 (31.6%), F2 (21%), and F3 (47.4%) vs. F1 (24.2%), F2 (22.4%), and F3 (53.4%), respectively. At 1 year, there was a significant decrease in HOMA-IR and interleukin (IL)-6 in the CVC group. The least squares mean changes (SE) in HOMA-IR (p=0.0159) and IL-6 (p=0.0094), respectively, were −2.75 (1.27) and −1.9 (0.35) for CVC and 1.94 (1.45) and −0.5 (0.39) for PBO. After 1-year exposure to CVC or PBO, no significant differences vs. baseline in HOMA-b, HDL cholesterol, LDL cholesterol, ALT, and AST were noted. Conclusion: CVC may improve HOMA-IR and pro-inflammatory cytokine IL-6, suggesting that CVC could potentially improve insulin resistance in NASH patients. These findings warrant further investigation. Disclosure A.D. Coviello: Consultant; Self; GI Dynamics Inc., Novo Nordisk Inc. Research Support; Self; Allergan plc., GENFIT, Orthus Health. Speaker’s Bureau; Self; Novo Nordisk Inc. G. Rodriguez: Employee; Self; Allergan plc. E.B. Martins: Employee; Self; Allergan plc. Stock/Shareholder; Self; Allergan plc. N. Alkhouri: Research Support; Self; Allergan plc. M.F. Abdelmalek: None. Funding Allergan plc

M137. HIGH CONFIDENCE FOR VISUOMOTOR ACTION RECRUITS THE VENTRAL STRIATUM – A METACOGNITIVE APPROACH FOR UNDERSTANDING NEGATIVE SYMPTOMS?

BackgroundMetacognition refers to the ability to discriminate between one’s own correct and incorrect decisions, thus representing a key function for goal-oriented behavior. The neurobiological underpinnings of metacognition have mainly been studied in perceptual decision-making and memory-related processes; therefore, mechanisms and neural correlates underlying metacognitive processes during visuomotor actions are still poorly characterized and the specific role of confidence remains to be elucidated. This is of particular interest as deficits in goal-directed behavior and insight both are a hallmark of the negative symptoms of schizophrenia.MethodsWe examined 31 healthy controls who were asked to draw straight reaching trajectories towards a visual target, while measuring their brain activity with functional Magnetic Resonance Imaging (fMRI). Deviations were introduced in 70% of the trajectories seen on the screen. Participants then reported awareness of deviations (first-order), followed by (second-order) confidence in their response. The amount of deviation was titrated to reach a 71% average detection rate using an adaptive staircase procedure. Metacognition was measured using the M-Ratio, which estimates the ratio of first-order information available for confidence computation (Maniscalco & Lau, 2012). Whole brain activity was analyzed via a parametric general linear model (GLM).ResultsParticipants showed good metacognitive abilities at evaluating the correctness of their first-order responses (M-Ratio: 0.98±0.25). Movements were decomposed into two phases based on peaks in the variance of the trajectory deviation and actual joystick position. We found that confidence ratings after deviated trials were explained by a combination of the trajectory deviation in the initial phase (p=0.006; linear mixed model) and the amount of motor correction in the final phase of the movement (p<0.001). At the neural level, as expected, conscious detection of deviation engages strongly the visual cortex, whereas higher visuomotor corrections engage primarily the primary motor cortex. Importantly, we show that high confidence specifically recruits the ventral striatum bilaterally (p<0.05 corrected for multiple comparisons), suggesting a role for confidence in motivating action.DiscussionTaken together, these results show for the first time in healthy controls that confidence for visuomotor action strongly engages motivational regions in line with a key role of metacognition in goal directed behavior and accurate insight into self-performed actions. These results in healthy controls are currently being tested in a cohort of schizophrenia patients and our hypothesis is that patients with higher level of apathy will display lower metacognitive confidence and lower ventral striatum activity

Self-tuning robust adjustment within multivariate regression time series models with vector-autoregressive random errors

The iteratively reweighted least-squares approach to self-tuning robust adjustment of parameters in linear regression models with autoregressive (AR) and t-distributed random errors, previously established in Kargoll et al. (in J Geod 92(3):271–297, 2018. https://doi.org/10.1007/s00190-017-1062-6), is extended to multivariate approaches. Multivariate models are used to describe the behavior of multiple observables measured contemporaneously. The proposed approaches allow for the modeling of both auto- and cross-correlations through a vector-autoregressive (VAR) process, where the components of the white-noise input vector are modeled at every time instance either as stochastically independent t-distributed (herein called “stochastic model A”) or as multivariate t-distributed random variables (herein called “stochastic model B”). Both stochastic models are complementary in the sense that the former allows for group-specific degrees of freedom (df) of the t-distributions (thus, sensor-component-specific tail or outlier characteristics) but not for correlations within each white-noise vector, whereas the latter allows for such correlations but not for different dfs. Within the observation equations, nonlinear (differentiable) regression models are generally allowed for. Two different generalized expectation maximization (GEM) algorithms are derived to estimate the regression model parameters jointly with the VAR coefficients, the variance components (in case of stochastic model A) or the cofactor matrix (for stochastic model B), and the df(s). To enable the validation of the fitted VAR model and the selection of the best model order, the multivariate portmanteau test and Akaike’s information criterion are applied. The performance of the algorithms and of the white noise test is evaluated by means of Monte Carlo simulations. Furthermore, the suitability of one of the proposed models and the corresponding GEM algorithm is investigated within a case study involving the multivariate modeling and adjustment of time-series data at four GPS stations in the EUREF Permanent Network (EPN).

Robust identification for fault detection in the presence of non-Gaussian noises: application to hydraulic servo drives

Intensive research in the field of mathematical modeling of hydraulic servo systems has shown that their mathematical models have many important details which cannot be included in the model. Due to impossibility of direct measurement or calculation of dimensions of certain components, leakage coefficients or friction coefficients, it was supposed that parameters of the hydraulic servo system are random. On the other side, it has been well known that the hydraulic servo system can be approximated by a linear model with time-varying parameters. An estimation of states and time-varying parameters of linear state-space models is of practical importance for fault diagnosis and fault-tolerant control. Previous works on this topic consider estimation in Gaussian noise environment, but not in the presence of outliers. The known fact is that the measurements have inconsistent observations with the largest part of the observation population (outliers). They can significantly make worse the properties of linearly recursive algorithms which are designed to work in the presence of Gaussian noises. This paper proposes the strategy of parameter–state robust estimation of linear state-space models in the presence of all possible faults and non-Gaussian noises. Because of its good features in robust filtering, Masreliez–Martin filter represents a cornerstone for realization of the robust algorithm. The good features of the proposed robust algorithm to identification of the hydraulic servo system are illustrated by intensive simulations.

Two-stage additive network DEA: Duality, frontier projection and divisional efficiency

In the previous literature, it is demonstrated that the dual equivalence of multiplier and envelopment models that exists in standard data envelopment analysis (DEA) is not necessarily true for network DEA to derive frontier projection and divisional efficiency. Multiplier network model is often used for computing the divisional efficiency while envelopment network model is often used for identifying the frontier projection for inefficient decision making units (DMUs). In this paper, we show that the duality of standard DEA can be extended to two-stage additive network DEA. We propose an improved golden section method to solve parametric linear multiplier network model. Based on the primal-dual correspondence of parametric linear programming, we subsequently develop envelopment network model in parametric linear form to determine frontier projection and to find divisional efficiency as well.

On Treed Gaussian Processes and piecewise-linear NARX modelling

In the scope of nonlinear system identification, traditional parametric models are widely adopted as simplifying approaches to modelling the complexity of nonlinearity. However, many high-order parametric models are disadvantaged due to their inherent demand for model detection and their tendency to overfit in the absence of additional validation processes. Nonparametric models, such as the Gaussian Process (GP), though being naturally exempt from model detection, can involve expensive procedures of model optimisation. This article presents a Linear Kernel Chipman-based Treed Gaussian Processes (LK-CTGP), which is essentially an assembly of simple linear parametric models using a decision tree framework, to model nonlinear systems. The piecewise-linear structure of the LK-CTGP offers a natural geometric solution to modelling nonlinear systems, where no model detection is required. The essence of simplicity from the traditional parametric model is also completely retained within each of the submodels. The effectiveness of the LK-CTGP is illustrated here via a number of case studies from simple synthetic data to experimental data, on which Nonlinear Autoregressive eXogenous (NARX) systems will built from the data for in-depth study.

An adaptation of pseudo-score confidence interval method for linear mixed models

We adapt a confidence interval method based on a generalized Chi-Square test for fixed effect parameters of linear mixed models. Under different correlation structure of a response variable of a linear mixed model, the performances of the adaptation method pseudo-score and some of the existing confidence interval methods are investigated by carrying out a Monte Carlo simulation study. The simulation study suggests that pseudo-score method provides better results for small to moderate sample size cases with dependent observations in terms of coverage probability rates and average expected lengths. A depression study is analyzed for demonstrating the adaptation method.

Research on Iterative Calibration Method of Linear Model Parameters of Gravity Sensor

In recent years, the calibration method of Strapdown gravimeter has become the bottleneck of relative gravity measurement accuracy. Based on this situation, this thesis studies the parameter iterative calibration method of SGA-WZ03 strapdown gravimeter to break the bottleneck of relative gravity measurement and further improve the measurement accuracy of relative gravimeter in flight experiment through the improvement of calibration method Degree. The parameter iterative estimation algorithm is based on the pulse output model of a single accelerometer to establish the linear pulse output model of the accelerometer components. Using the idea of parameter separation, the two-step iterative estimation of the model parameters and the tilt vector can complete the calibration of the linear model and the secondary model of the accelerometer. Compared with the traditional 24 bit calibration method, the parameter estimation iterative estimation calibration method has better stability than the traditional method.