General Linear Processes Research Articles

Minimum entropy production in inhomogeneous thermoelectric materials

Due to their potential applications in energy production based on waste heat, direct solar radiation or other energy sources, semiconductor materials have for years attracted the attention of theoretical and experimental researchers. The focus has been on improving the performance of thermoelectric devices through several strategies and special interest has been placed on materials with spatially inhomogeneous transport properties. Inhomogeneity can be achieved in various ways, all of them leading, to a greater or lesser extent, to an improvement of the thermoelectric performance. In this paper, general linear heat and electric charge transport processes in inhomogeneous materials are addressed. The guiding idea followed here is that there exists a relationship between inhomogeneity (structuring), minimum entropy production and performance which may be fruitfully exploited for designing more efficient thermoelectric semiconductor devices. We first show that the stationary states of such materials are minimum global entropy production states. This constitutes an extension of the validity of Prigogine’s minimum entropy principle. The heat and charge transport equations obtained within the framework of classical irreversible thermodynamics are solved to find the stationary profiles of temperature and self-consistent electric potential in a one-dimensional model of a silicon–germanium alloy subjected to an external temperature difference. This allows us to assess the effect of the spatial inhomogeneity on the thermoelectric performance. We find that, regardless of the value of the applied temperature difference, the system may efficiently operate in a regime of minimum entropy production and high efficiency.

Combined control of multirate impulse processes in a cognitive map of COVID-19 morbidity

In this article, a cognitive map (CM) of COVID-19 morbidity in a given region was built. A general linear impulse process (IP) model in the CM was developed and measured, and unmeasured CM node coordinates were defined. The general IP model was decomposed into interrelated subsystems with measurable and unmeasurable node coordinates. For the subsystem with measurable node coordinates, multirate sampling of coordinates was conducted, resulting in the development of discrete dynamics models for quickly and slowly measured node coordinates. External controls were selected in IP models based on the possible variation of resources of node coordinates and CM weighting coefficients. IP control laws based on the variation of CM nodes and weight were designed. As a result, recurrent procedures for control generation in closed-loop control subsystems with multirate sampling were formulated. Experimental research on the control subsystems was carried out. It confirmed high efficiency for decreasing COVID-19 morbidity.

Finite sample theory for high-dimensional functional/scalar time series with applications

Statistical analysis of high-dimensional functional times series arises in various applications. Under this scenario, in addition to the intrinsic infinite-dimensionality of functional data, the number of functional variables can grow with the number of serially dependent observations. In this paper, we focus on the theoretical analysis of relevant estimated cross-(auto)covariance terms between two multivariate functional time series or a mixture of multivariate functional and scalar time series beyond the Gaussianity assumption. We introduce a new perspective on dependence by proposing functional cross-spectral stability measure to characterize the effect of dependence on these estimated cross terms, which are essential in the estimates for additive functional linear regressions. With the proposed functional cross-spectral stability measure, we develop useful concentration inequalities for estimated cross-(auto)covariance matrix functions to accommodate more general sub-Gaussian functional linear processes and, furthermore, establish finite sample theory for relevant estimated terms under a commonly adopted functional principal component analysis framework. Using our derived non-asymptotic results, we investigate the convergence properties of the regularized estimates for two additive functional linear regression applications under sparsity assumptions including functional linear lagged regression and partially functional linear regression in the context of high-dimensional functional/scalar time series.

Mediation and Moderation of Adiposity Indicators for the Association Between Grip Strength and Cardiovascular Disease Risk Scores.

Background: This cross-sectional study evaluated mediation or moderation of adiposity indicators on the association between handgrip strength (HGS) and the 10-year cardiovascular disease risk scores (CVDR). Methods: In data of 15,206 Korean adults (6961 men and 8245 women) aged ≥30 years using the Korea National Health and Nutrition Examination Survey, HGS, body mass index (BMI), height, waist circumference, the components of Framingham CVDR, and covariates (sociodemographic factors, health behaviors, perceived stress, health, functional status, and nutritional status) were used. BMI, waist circumference, and waist-to-height ratio were used as adiposity indicators. Gender-specific general linear model and PROCESS Macro were applied. Results: HGS had an inverse association with the CVDR after adjusting for the covariates and BMI (or waist circumference), while adiposity indicators had positive associations with the CVDR after adjusting for the covariates and HGS. Mediation analysis shows indirect effects of adiposity indicators (0.010-0.019, P < 0.05) and direct effect of HGS on the CVDR (-0.08 to -0.09, P < 0.05) after adjusting for the covariates. Moderation analysis reveals positive interactions between HGS and adiposity indicators in the relationship with the CVDR after adjusting for the covariates (P < 0.05). The inverse association between the HGS and the CVDR tended to be stronger with decrease in adiposity levels. Conclusions: Adiposity indicators mediated and moderated the association between HGS and the CVDR in Koreans. The moderating effects indicate that the lower the levels of the adiposity indicators, the stronger the CVDR improvement effect of HGS.

ESTIMATION OF SPATIAL AUTOREGRESSIONS WITH STOCHASTIC WEIGHT MATRICES

We examine a higher-order spatial autoregressive model with stochastic, but exogenous, spatial weight matrices. Allowing a general spatial linear process form for the disturbances that permits many common types of error specifications as well as potential ‘long memory’, we provide sufficient conditions for consistency and asymptotic normality of instrumental variables, ordinary least squares, and pseudo maximum likelihood estimates. The implications of popular weight matrix normalizations and structures for our theoretical conditions are discussed. A set of Monte Carlo simulations examines the behaviour of the estimates in a variety of situations. Our results are especially pertinent in situations where spatial weights are functions of stochastic economic variables, and this type of setting is also studied in our simulations.

Breastfeeding and Childhood IQ: The Mediating Role of Gray Matter Volume

A substantial body of literature has established the positive effect of breastfeeding on child developmental outcomes. There is increasing consensus that breastfed children have higher IQs after accounting for key variables, including maternal education, IQ, and socioeconomic status. Cross-sectional investigations of the effects of breastfeeding on structural brain development suggest that breastfed infants have larger whole brain, cortical, and white matter volumes. To date, few studies have related these measures of brain structure to IQ in breastfed versus nonbreastfed children in a longitudinal sample. Data were derived from the Preschool Depression Study (PDS), a prospective longitudinal study in which children and caregivers were assessed annually for 8 waves over 11 years. A subset completed neuroimaging between the ages of 9.5 and 14.11 years. A total of 148individuals had breastfeeding data at baseline and complete data on all variables of interest, including IQ andstructural neuroimaging. General linear models and process mediation models were used. Breastfed children had significantly higher IQ scores and larger whole brain, total gray matter, total cortical gray matter, and subcortical gray matter volumes compared with the nonbreastfed group in models that covaried for key variables. Subcortical gray matter volume significantly mediated the association between breastfeeding and children's IQ scores. The study findings suggest that the effects of breastfeeding on child IQ are mediated through subcortical gray volume. This effect and putative mechanism is of public health significance and further supports the importance of breastfeeding in mental health promotion.

On the variance of a centered random value roundoff error

We derive two expressions for roundoff error variance, one for a rounded off random value with a zero mean and a given variance under uniform distribution and another for such a value under a normal. Also, an expression for truncation error variance for values under uniform distribution is obtained. An application of the expressions to analysis of processing essentially quantized data by a nonrecursive smoothing filter is shown. Also their applications to quantization error (quantization noise) analysis of general linear processing of quantized signals under uniform and normal distributions and to quantization error analysis of essentially quantized discrete transforms like DFT (discrete Fourier transform), DCT (discrete cosine transform), DWT (discrete Walsh transforms), wavelet transforms, and so on, to image, sound (audio), video and to general signal processing in many cases can be considered as useful. The effect of accuracy of using these expressions is the more, the more used quantization level and the less maximal signal amplitudes.

Asymptotic solutions of the Oosawa model for the length distribution of biofilaments.

Nucleated polymerisation phenomena are general linear growth processes that underlie the formation of a range of biofilaments in nature, including actin and tubulin that are key components of the cellular cytoskeleton. The conventional theoretical framework for describing this process is the Oosawa model that takes into account homogeneous nucleation coupled to linear growth. In his original work, Oosawa provided an analytical solution to the total mass concentration of filaments; the time evolution of the full length distribution has, however, been challenging to access, in large part due to the nonlinear nature of the rate equations inherent in the description of such phenomena and to date analytical solutions for the filament distribution are known only in certain special cases. Here, by exploiting a technique based on the method of matched asymptotics, we present an analytical treatment of the Oosawa model that describes the shape of the length distribution of biofilaments reversibly growing through primary nucleation and filament elongation. Our work highlights the power of matched asymptotics for obtaining closed-form analytical solutions to nonlinear master equations in biophysics and allows us to identify the key time scales that characterize biological polymerization processes.

Effects of a nutritional liquid supplement designed for diabetes mellitus on postprandial glucose and pregnancy outcomes in patients with gestational diabetes mellitus

To explore the effects of nutritional liquid supplement designed for diabetes mellitus on postprandial glucose state and pregnancy outcomes in patients with gestational diabetes mellitus (GDM). A total of 69 cases of pregnant GDM women at Department of Obstetrics & Gynecology, First Affiliated Hospital, Chongqing Medical University from October 2011 to January 2012 were randomized into the intervention and control groups. But only 31 cases in intervention group finished the study versus 29 cases in control group. The inter-group differences were analyzed for general clinical profiles before intervention, 2-hour postprandial blood glucose levels and pregnancy outcomes, etc. The General Linear Model Repeated Measures process was used to analyze the variance of 2-hour postprandial blood glucose data. And the Mauchy's test of sphericity was employed to determine the correlation. (1) No significant difference in general clinical profiles before intervention between intervention and control groups (P > 0.05). (2) The mean values of 2-hour postprandial blood glucose were as follows: intervention group (mmol/L) : 6.2 ± 0.7(1w), 5.9 ± 0.5(2w), 5.7 ± 0.5(3w), 5.8 ± 0.6 (4w), 5.7 ± 0.5(5w), 5.7 ± 0.4(6w), 5.9 ± 0.3(7w), 6.0 ± 0.4(8w), 6.0 ± 0.5(9w); control group: 6.7 ± 0.3 (1w), 6.2 ± 0.4(2w), 6.2 ± 0.5(3w), 6.2 ± 0.4(4w), 6.1 ± 0.4(5w), 6.0 ± 0.3 (6w), 5.8 ± 0.4 (7w), 6.1 ± 0.4 (8w), 6.1 ± 0.4(9w). The results of Mauchy's test of sphericity indicated that the blood glucose level of the intervention group was significantly lower than that of the control group (P < 0.01). (3) The incidence of premature rupture of membranes and polyhydramnios, rate of neonatal pneumonia, weight of newborn and pregnancy women and level of glycosylated hemoglobin in intervention group were significantly lower than those in control group (P < 0.05). Compared with common diet, after using nutritional supplement, the postprandial blood glucose level is significantly reduced and the pregnancy outcomes also improved in GDM patients.

Nonparametric Sequential Signal Change Detection Under Dependent Noise

A nonparametric version of the sequential signal detection problem is studied. Our signal model includes a class of time-limited signals for which we collect data in the sequential fashion at discrete points in the presence of correlated noise. For such a setup we introduce a novel signal detection algorithm relying on the postfiltering smooth correction of the classical Whittaker-Shannon interpolation series. Given a finite frame of noisy samples of the signal, we design a detection algorithm being able to detect a departure from a reference signal as quickly as possible. Our detector is represented as a normalized partial-sum continuous time stochastic process, for which we obtain a functional central limit theorem under weak assumptions on the correlation structure of the noise. Particularly, our results allow for noise processes such as ARMA and general linear processes as well as α-mixing processes. The established limit theorems allow us to design monitoring algorithms with the desirable level of the probability of false alarm and able to detect a change with probability approaching one.

Limit theory of quadratic forms of long-memory linear processes with heavy-tailed GARCH innovations

Let Xt=∑j=0∞cjεt−j be a moving average process with GARCH (1, 1) innovations {εt}. In this paper, the asymptotic behavior of the quadratic form Qn=∑j=1n∑s=1nb(t−s)XtXs is derived when the innovation {εt} is a long-memory and heavy-tailed process with tail index α, where {b(i)} is a sequence of constants. In particular, it is shown that when 1<α<4 and under certain regularity conditions, the limit distribution of Qn converges to a stable random variable with index α/2. However, when α≥4, Qn has an asymptotic normal distribution. These results not only shed light on the singular behavior of the quadratic forms when both long-memory and heavy-tailed properties are present, but also have applications in the inference for general linear processes driven by heavy-tailed GARCH innovations.

Representations of multidimensional linear process bridges

We derive bridges from general multidimensional linear non time-homogeneous processes using only the transition densities of the original process giving their integral representations (in terms of a standard Wiener process) and so-called anticipative representations. We derive a stochastic differential equation satisfied by the integral representation and we prove a usual conditioning property for general multidimensional linear process bridges. We specialize our results for the one-dimensional case; especially, we study one-dimensional OrnsteinUhlenbeck bridges.

The Hybrid Wild Bootstrap for Time Series

We introduce a new and simple bootstrap procedure for general linear processes, called the hybrid wild bootstrap. The hybrid wild bootstrap generates frequency domain replicates of the periodogram that imitate asymptotically correct the first- and second-order properties of the ordinary periodogram including its weak dependence structure at different frequencies. As a consequence, the hybrid wild bootstrapped periodogram succeeds in approximating consistently the distribution of statistics that can be expressed as functionals of the periodogram, including the important class of spectral means for which all so far existing frequency domain bootstrap methods generally fail. Moreover, by inverting the hybrid wild bootstrapped discrete Fourier transform, pseudo-observations in the time domain are obtained. The generated time domain pseudo-observations can be used to approximate correctly the random behavior of statistics, the distribution of which depends on the first-, second-, and, to some extent, on the fourth-order structure of the underlying linear process. Thus, the proposed hybrid wild bootstrap procedure applied to general time series overcomes several of the limitations of standard linear time domain bootstrap methods.

Non‐stationary regression with logistic transition

Summary This paper studies the non-stationary regression model with logistic transition in level or in slope. In the model, the level or slope is specified as a functional coefficient specified parametrically as the logistic function of an integrated state variable driven by a general linear process. For such a model, we derive the limit distributions of the non-linear least squares (NLS) estimators and their t-statistics. As for many other types of non-stationary non-linear regressions, the NLS estimators and the usual t-tests are generally inefficient and invalid in our model. We propose a new procedure, which yields efficient estimators and valid tests. Our simulation shows that they perform noticeably better than the standard NLS estimators and tests. Finally, our model and methodology are used to investigate the long-run relationship between per capita real income and consumption using US data.

Pattern recognition analyses of brain activation elicited by happy and neutral faces in unipolar and bipolar depression

ObjectivesRecently, pattern recognition approaches have been used to classify patterns of brain activity elicited by sensory or cognitive processes. In the clinical context, these approaches have been mainly applied to classify groups of individuals based on structural magnetic resonance imaging (MRI) data. Only a few studies have applied similar methods to functional MRI (fMRI) data.MethodsWe used a novel analytic framework to examine the extent to which unipolar and bipolar depressed individuals differed on discrimination between patterns of neural activity for happy and neutral faces. We used data from 18 currently depressed individuals with bipolar I disorder (BD) and 18 currently depressed individuals with recurrent unipolar depression (UD), matched on depression severity, age, and illness duration, and 18 age- and gender ratio-matched healthy comparison subjects (HC). fMRI data were analyzed using a general linear model and Gaussian process classifiers.ResultsThe accuracy for discriminating between patterns of neural activity for happy versus neutral faces overall was lower in both patient groups relative to HC. The predictive probabilities for intense and mild happy faces were higher in HC than in BD, and for mild happy faces were higher in HC than UD (all p < 0.001). Interestingly, the predictive probability for intense happy faces was significantly higher in UD than BD (p = 0.03).ConclusionsThese results indicate that patterns of whole-brain neural activity to intense happy faces were significantly less distinct from those for neutral faces in BD than in either HC or UD. These findings indicate that pattern recognition approaches can be used to identify abnormal brain activity patterns in patient populations and have promising clinical utility as techniques that can help to discriminate between patients with different psychiatric illnesses.

ON AUGMENTED HEGY TESTS FOR SEASONAL UNIT ROOTS

In this paper we extend the large-sample results provided for the augmented Dickey–Fuller test by Said and Dickey (1984, Biometrika 71, 599–607) and Chang and Park (2002, Econometric Reviews 21, 431–447) to the case of the augmented seasonal unit root tests of Hylleberg, Engle, Granger, and Yoo (1990, Journal of Econometrics 44, 215–238), inter alia. Our analysis is performed under the same conditions on the innovations as in Chang and Park (2002), thereby allowing for general linear processes driven by (possibly conditionally heteroskedastic) martingale difference innovations. We show that the limiting null distributions of the t-statistics for unit roots at the zero and Nyquist frequencies and joint F-type statistics are pivotal, whereas those of the t-statistics at the harmonic seasonal frequencies depend on nuisance parameters that derive from the lag parameters characterizing the linear process. Moreover, the rates on the lag truncation required for these results to hold are shown to coincide with the corresponding rates given in Chang and Park (2002); in particular, an o(T1/2) rate is shown to be sufficient.

Theory and application of general linear image processing

Image modeling in terms of physical/mathematical formation and the human visual system plays an important role in developing new image processing techniques. Parameters such as scale, orientation, texture, morphology, and color must be taken into consideration in order to solve complicated image processing problems efficiently. Although the classical linear image processing (CLIP) approach has played a central role in image processing, it is not necessarily the best and even the right choice. General linear image processing (GLIP) approaches based on different image modeling techniques have been studied to overcome some of the problems associated with CLIP. Indeed, using general linear algebra, it is possible to develop entirely new general linear operators and transforms. It is even possible to define entirely new general linear operations (addition, scalar multiplication, convolution, etc.) in order to describe how images are combined, amplified, transformed, analyzed, compared, and measured.

On Fixed Design Regression for General Linear Processes

This article is concerned with recovering a regression function g(x) on the basis of noisy observations taken at design points x i . The corresponding observations are corrupted by additive dependent noise induced by a general linear process. The regression function is estimated by a smoother, which is shown to have an asymptotic multivariate normal distribution at multiple points. The problem of finding confidence bands for g(x) is discussed. An illustrative example is also exhibited. The results for finite samples are evaluated by computer simulations.

Preliminary test estimation for spectra

For a general non-Gaussian stationary linear process, quasi-maximum likelihood estimation of a subset of the parameters of the spectral density is considered when the complementary subset is suspected to be superfluous. A preliminary test quasi-maximum likelihood estimator (q-MLE) of parameters is introduced and, in the light of its mean square error, is compared with the restricted and unrestricted q-MLE.

Optimal Orthogonal Precoding for Power Leakage Suppression in DFT-Based Systems

A solution to the power leakage minimization problem in discrete Fourier transform (DFT) based communication systems is presented. In a conventional DFT based system, modulated subcarriers exhibit high sidelobe levels, which leads to significant out-of-band power leakage. Existing techniques found in the literature either do not achieve sufficient sidelobe suppression or suffer from significant spectral efficiency loss. Precoding can be seen as a general linear processing method for power leakage reduction, however, how to design the optimal linear precoder is still an open problem. In this paper, the power leakage suppression is first treated as a matrix Frobenius norm minimization problem, and then the optimal orthogonal precoding matrix design for the power leakage suppression is proposed based on singular value decomposition (SVD). By further exploiting the extra degrees of freedom in the precoding matrix, two kinds of optimized precoding matrices, one with multi-carrier property and the other with single-carrier property, are developed to take the advantages of orthogonal frequency division multiplexing (OFDM) and single carrier frequency division multiple access (SC-FDMA), respectively. Simulation results show that both the multi-carrier and the single-carrier precoding schemes achieve significant power leakage suppression, and have similar peak-to-average power ratio (PAPR) and bit-error-rate (BER) to those of OFDM and SC-FDMA systems, respectively.