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All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Regularized Differentiation for Bioburden Density Estimation in Planetary Protection

In this paper, we propose and investigate the performance of two novel shrinkage estimators for bioburden density estimation in planetary protection. The estimators are based on the regularized differentiation of a cumulative count of colony forming units collected throughout the data collecting session or the life cycle of the entire mission. The regularized differentiation recasts the problem of bioburden density estimation as a linear least squares problem. The least squares problem is then solved through regularization techniques, such as truncated singular value decomposition and penalized least squares. The regularization is necessary to avoid noise amplification during the differentiation of noisy data. The two regularization estimators are compared with four other commonly used estimators to simultaneously evaluate the means of multivariable independent Poisson distributions: the maximum likelihood, noninformative Bayes estimator with Jeffreys prior, Empirical Bayes using conjugate gamma-Poisson model with gamma parameters selected by method of moments, and the Clevenson-Zidek estimator. It is shown through computer-simulated data that the regularized differentiation based on ridge regression has the smallest mean-squared error among all estimators. The analysis of shrinkage mechanism implemented by regularized differentiation is performed, and it is shown that the regularized differentiation amounts to performing a weighted averaging of all the samples. The weights are determined by the regularization parameter automatically selected by the L-curve technique. Since the method of least squares makes no distributional assumptions about the data, it presents an attractive technique for bioburden density estimation when there are concerns about the misspecification of the distributional model. The paper concludes with the analysis of the bioburden data collected during InSight mission and directions for future work.

97 - MATHEMATICS AND COMPUTING↗
NASA NTRS2022

Alternative regularizations for Outer-Approximation algorithms for convex MINLP

In this work, we extend the regularization framework from Kronqvist et al. (Math Program 180(1):285–310, 2020) by incorporating several new regularization functions and develop a regularized single-tree search method for solving convex mixed-integer nonlinear programming (MINLP) problems. We propose a set of regularization functions based on distance metrics and Lagrangean approximations, used in the projection problem for finding new integer combinations to be used within the Outer-Approximation (OA) method. The new approach, called Regularized Outer-Approximation (ROA), has been implemented as part of the open-source Mixed-integer nonlinear decomposition toolbox for Pyomo—MindtPy. We compare the OA method with seven regularization function alternatives for ROA. Moreover, we extend the LP/NLP Branch and Bound method proposed by Quesada and Grossmann (Comput Chem Eng 16(10–11):937–947, 1992) to include regularization in an algorithm denoted RLP/NLP. We provide convergence guarantees for both ROA and RLP/NLP. Finally, we perform an extensive computational experiment considering all convex MINLP problems in the benchmark library MINLPLib. The computational results show clear advantages of using regularization combined with the OA method.

Convex Mixed-integer nonlinear programming↗
DOE OSTI2021

Bayesian Spatially Varying Multi-Regularization Image Deblurring

Many scientific experiments such as those found in astronomy, geology, microbiology, and X-ray radiography require the use of high-energy instruments to capture images. Since blur and noise are inevitably present in any imaging system, the images must be \deblurred" to extract the full information content. Mathematically, image deblurring is an ill-posed inverse problem that requires regularization. The regularization, in turn, has a large effect on the deblurred image: different regularization strengths, and types, lead to drastically different reconstructions. Moreover, many images contain a mixture of smooth and sharp features which suggests the use of multi-regularization, i.e., varying the type of regularization (e.g. Tikhonov or total variation) across the image. We address these issues by formulating the image deblurring problem within a hierarchical Bayesian framework in which we spatially adapt the strength of the regularization and also vary the regularization type across the image. In this way, the image itself, along with corresponding regularization strength at each pixel, are described jointly by a posterior distribution which we can sample by Markov chain Monte Carlo (MCMC) methods. We illustrate our techniques on simplified test problems and apply them to high-energy X-ray images taken at the Nevada National Security Site. Numerical tests show that our new method is robustly applicable and increases the quality of the image reconstruction when compared to other (Bayesian) methods.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

Incremental projection approach of regularization for inverse problems

This paper presents an alternative approach to the regularized least squares solution of ill-posed inverse problems. Instead of solving a minimization problem with an objective function composed of a data term and a regularization term, the regularization information is used to define a projection onto a convex subspace of regularized candidate solutions. The objective function is modified to include the projection of each iterate in the place of the regularization. Numerical experiments based on the problem of motion estimation for geophysical fluid images, show the improvement of the proposed method compared with regularization methods. For the presented test case, the incremental projection method uses 7 times less computation time than the regularization method, to reach the same error target. Moreover, at convergence, the incremental projection is two order of magnitude more accurate than the regularization method.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

On regularizing the ML-MCTDH equations of motion

In a recent paper [H.-D. Meyer and H. Wang, J. Chem. Phys. 148, 124105 (2018)], we have examined the regularization of the equations of motion (EOMs) of the multiconfiguration time-dependent Hartree (MCTDH) approach. We could show that the standard regularization scheme used by almost all researchers in the field is not optimal. The improved regularization allows for larger values of the regularization parameter ϵ, is less sensitive to the actual choice of ϵ, and performs the rotation of initially unoccupied single-particle functions into the “correct” direction in Hilbert space much faster than the old scheme. Here, the latter point increases both the accuracy and efficiency of time propagation for challenging problems. For simple problems, the new scheme requires some additional numerical work as compared with the old scheme, ranging from negligible to almost doubling the total numerical labor. For demanding problems, on the other hand, the additional numerical work of the new scheme is often overcompensated by less steps taken by the integrator. In the present paper, we generalize the new regularization scheme to the multi-layer (ML) extension of MCTDH. Although the principle idea of the new regularization scheme remains unaltered, it was not obvious how the new scheme should be implemented into ML-MCTDH. The ML-MCTDH EOMs are much more complicated than the MCTDH ones, and for optimal numerical performance it was necessary to derive a recursive algorithm for implementing the new regularization scheme.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2016

SU-F-R-41: Regularized PCA Can Model Treatment-Related Changes in Head and Neck Patients Using Daily CBCTs

Purpose: To use daily cone beam CTs (CBCTs) to develop regularized principal component analysis (PCA) models of anatomical changes in head and neck (H&N) patients, to guide replanning decisions in adaptive radiation therapy (ART). Methods: Known deformations were applied to planning CT (pCT) images of 10 H&N patients to model several different systematic anatomical changes. A Pinnacle plugin was used to interpolate systematic changes over 35 fractions, generating a set of 35 synthetic CTs for each patient. Deformation vector fields (DVFs) were acquired between the pCT and synthetic CTs and random fraction-to-fraction changes were superimposed on the DVFs. Standard non-regularized and regularized patient-specific PCA models were built using the DVFs. The ability of PCA to extract the known deformations was quantified. PCA models were also generated from clinical CBCTs, for which the deformations and DVFs were not known. It was hypothesized that resulting eigenvectors/eigenfunctions with largest eigenvalues represent the major anatomical deformations during the course of treatment. Results: As demonstrated with quantitative results in the supporting document regularized PCA is more successful than standard PCA at capturing systematic changes early in the treatment. Regularized PCA is able to detect smaller systematic changes against the background of random fraction-to-fraction changes. To be successful at guiding ART, regularized PCA should be coupled with models of when anatomical changes occur: early, late or throughout the treatment course. Conclusion: The leading eigenvector/eigenfunction from the both PCA approaches can tentatively be identified as a major systematic change during radiotherapy course when systematic changes are large enough with respect to random fraction-to-fraction changes. In all cases the regularized PCA approach appears to be more reliable at capturing systematic changes, enabling dosimetric consequences to be projected once trends are established early in the treatment course. This work is supported in part by a grant from Varian Medical Systems, Palo Alto, CA.

60 APPLIED LIFE SCIENCES↗
NASA NTRS2002

A simple way to measure daily lifestyle regularity

A brief diary instrument to quantify daily lifestyle regularity (SRM-5) is developed and compared with a much longer version of the instrument (SRM-17) described and used previously. Three studies are described. In Study 1, SRM-17 scores (2 weeks) were collected from a total of 293 healthy control subjects (both genders) aged between 19 and 92 years. Five items (1) Get out of bed, (2) First contact with another person, (3) Start work, housework or volunteer activities, (4) Have dinner, and (5) Go to bed were then selected from the 17 items and SRM-5 scores calculated as if these five items were the only ones collected. Comparisons were made with SRM-17 scores from the same subject-weeks, looking at correlations between the two SRM measures, and the effects of age and gender on lifestyle regularity as measured by the two instruments. In Study 2 this process was repeated in a group of 27 subjects who were in remission from unipolar depression after treatment with psychotherapy and who completed SRM-17 for at least 20 successive weeks. SRM-5 and SRM-17 scores were then correlated within an individual using time as the random variable, allowing an indication of how successful SRM-5 was in tracking changes in lifestyle regularity (within an individual) over time. In Study 3 an SRM-5 diary instrument was administered to 101 healthy control subjects (both genders, aged 20-59 years) for two successive weeks to obtain normative measures and to test for correlations with age and morningness. Measures of lifestyle regularity from SRM-5 correlated quite well (about 0.8) with those from SRM-17 both between subjects, and within-subjects over time. As a detector of irregularity as defined by SRM-17, the SRM-5 instrument showed acceptable values of kappa (0.69), sensitivity (74%) and specificity (95%). There were, however, differences in mean level, with SRM-5 scores being about 0.9 units [about one standard deviation (SD)] above SRM-17 scores from the same subject-weeks. SRM-5 scores also deviated more from a Gaussian distribution than did SRM-17 ones. In a study with a sample size of 101, the new SRM-5 instrument yielded scores with a mean of 4.11 and an SD of 1.13. Correlations between lifestyle regularity and age, and between lifestyle regularity and morningness appeared similar whether 5-item or 17-item SRM measures were used. When a gender difference in lifestyle regularity appeared, it was detected by both SRM-5 and SRM-17 measures.

Non-NASA Center↗
NASA NTRS2021

GRACE Fast Mascons from Spherical Harmonics and a Regularization Design Trade Study

Mass concentration (mascon) solutions have become a prominent medium for investigating time-variable gravity recovered by GRACE and GRACE Follow-On. While GRACE Level-2 spherical harmonic products require various post-processing techniques to eliminate correlated noise, mascon formulations employ spatial regularization strategies during the estimation step to improve signal recovery. However, mascon estimation has traditionally required large computing resources and GRACE Level-1B processing capabilities. In this study, we show that a typical mascon estimation system can be reformulated to allow for the estimation of regularized mascons from Level-2 spherical harmonics. Provided that spherical harmonic solution covariances are available, the computed mascons will be mathematically equivalent to similar mascons estimated from Level-1B observations. This method is computationally efficient, better leverages GRACE spherical harmonics than past methods, and matches the performance of typical mascon solutions without locking scientists into pre-determined regularization designs. We develop a proof-of-concept solution using ITSG-Grace2018 and compare results with traditional mascons from JPL and NASA GSFC. We then assess the effects of spherical harmonic truncation and use of regularization correlations on basin signal recovery. We find that spherical expansions to degree and order 60 provide the minimum expansion necessary to study most basins, while larger expansions help further localize signals. We also find that diagonal regularizations (i.e., regularizations that do not contain inter-mascon correlations) are adversely affected by leakage, especially across boundaries such as coastlines where signals are not highly correlated, whereas including inter-mascon correlations and regional boundaries in the regularization greatly improves signal recovery.

M. J. Croteau↗
DOE OSTI2025

Improved Bayesian regularization of inverse problems in vibrations and acoustics using noise-only measurements

Here, this paper studies Tikhonov regularization (ridge regression) parameter selection for problems in vibrations and acoustics. The selection method is based on a popular Bayesian method, but it incorporates measurements of sensor noise. The regularization parameter is closely related to the ratio of system input energy to noise energy, so noise measurements inform the inference procedure and improve parameter identification. In cases where standard Bayesian regularization identifies zero as the optimal regularization parameter, noise measurements guarantee a unique nonzero optimum. Sufficient theoretical criteria are developed for this guarantee. The method is verified in even-determined and under-determined configurations in an acoustic source localization simulation and a vibration load identification experiment. It is shown to yield significant improvements over existing empirical Bayesian regularization. Improvements are larger in the even-determined case and smaller in the under-determined case, wherein the inverse solution is less sensitive to the regularization parameter.

42 ENGINEERING↗
DOE OSTI2017

Addressing first derivative discontinuities in orbital-optimized opposite-spin scaled second-order perturbation theory with regularization

Orbital-optimized opposite-spin scaled second-order perturbation theory (O 2 ) generates a single-reference wave function composed of approximate Brueckner orbitals with fourth-order computational scaling. While O 2 provides significantly improved treatment of radicals by reducing spin contamination, it has been shown to suffer from first derivative discontinuities for bond stretching near the unrestriction point. That qualitative failure is resolved in this work by the implementation of regularized O 2 , which includes a regularization parameter in the denominator of its second-order term. The value of the regularization parameter is semi-empirically chosen to qualitatively describe bond stretching energetics of hydrogen, ethane and ethene, while also considering the effect of the regularization parameter on thermochemical errors for the well-known Gaussian-2 (G2) test set. The generality of the empirical scaling and semi-empirical regularization parameter is studied by application to the 3dMLBE20, DBH24, RSE43 and W4-11 test sets. We demonstrate that accuracy of O 2 is roughly maintained and sometimes even improved by regularization, with root mean squares of regularised O 2 between factors of 1.6 and 0.8 from corresponding root mean squares of O 2 .

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2018

Investigation of the influence of frictional viscosity regularization on quasi-static gas-solid flow predictions in a conical spouted bed with non-porous draft tube

The stress in the quasi-static particle flow is often modeled through the Mohr-Coulomb failure criterion. In the extension to complex three-dimensional flows, a granular viscosity is introduced through a tensorial rheology and the deviatoric frictional stress tensor is assumed aligned with the strain rate tensor. This granular viscosity is singular as the shear rate approaches zero, regardless of the local rheology. We discuss the influence of regularizing such a frictional viscosity on the particle circulation rate and other measured characteristics in a laboratory scale draft tube spouted bed. Here, the friction between particles is modeled either with a constant Coulomb rheology or using a local particle pressure and strain-rate based friction known as μ ( I )-rheology. The predictions appear very dependent on the regularization parameter introduced by the method. The mean properties of the flow (e.g. circulation and pressure drop) monotonically converge towards the measurements when the regularization parameter tends to zero. In other respects, the two regularization models regarded in this study induced similar hydrodynamics within the spouted bed of interest. But the analysis of the conditional averages of the inertial number and the fraction of the solids in the quasi-static regime shows that the extent and staticity of the quasi-static region is sensitive to changes to the regularization parameter or regularization function.

36 MATERIALS SCIENCE↗
DOE OSTI2018

On regularizing the MCTDH equations of motion

The Multiconfiguration Time-Dependent Hartree (MCTDH) approach leads to equations of motion (EOM) which become singular when there are unoccupied so-called single-particle functions (SPFs). Starting from a Hartree product, all SPFs, except the first one, are unoccupied initially. To solve the MCTDH-EOMs numerically, one therefore has to remove the singularity by a regularization procedure. Usually the inverse of a density matrix is regularized. Here we argue and show that regularizing the coefficient tensor, which in turn regularizes the density matrix as well, leads to an improved performance of the EOMs. The initially unoccupied SPFs are rotated faster into their “correct direction” in Hilbert space and the final results are less sensitive to the choice of the value of the regularization parameter. For a particular example (a spin-boson system studied with a transformed Hamiltonian), we could even show that only with the new regularization scheme could one obtain correct results. Lastly, in Appendix A, a new integration scheme for the MCTDH-EOMs developed by Lubich and co-workers is discussed. It is argued that this scheme does not solve the problem of the unoccupied natural orbitals because this scheme ignores the latter and does not propagate them at all.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Optimizing the regularization in size-consistent second-order Brillouin-Wigner perturbation theory

Despite its simplicity and relatively low computational cost, second-order Møller-Plesset perturbation theory (MP2) is well-known to overbind noncovalent interactions between polarizable monomers and some organometallic bonds. In such situations, the pairwise-additive correlation energy expression in MP2 is inadequate. Although energy-gap dependent amplitude regularization can substantially improve the accuracy of conventional MP2 in these regimes, the same regularization parameter worsens the accuracy for small molecule thermochemistry and density-dependent properties. Recently, we proposed a repartitioning of Brillouin-Wigner perturbation theory that is size-consistent to second order (BW-s2), and a free parameter ($α$) was set to recover the exact dissociation limit of H 2 in a minimal basis set. Alternatively $α$ can be viewed as a regularization parameter, where each value of $α$ represents a valid variant of BW-s2, which we denote as BW-s2($α$). In this work, we semi-empirically optimize $α$ for noncovalent interactions, thermochemistry, alkane conformational energies, electronic response properties, and transition metal datasets, leading to improvements in accuracy relative to the ab initio parameterization of BW-s2 and MP2. We demonstrate that the optimal $α$ parameter ($α$ = 4) is more transferable across chemical problems than energy-gap-dependent regularization parameters. This is attributable to the fact that the BW-s2($α$) regularization strength depends on all of the information encoded in the t amplitudes rather than just orbital energy differences. While the computational scaling of BW-s2($α$) is iterative $\mathcal{O}$($N^5$), this effective and transferable approach to amplitude regularization is a promising route to incorporate higher-order correlation effects at second-order cost.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Deblurring galaxy images with Tikhonov regularization on magnitude domain

Abstract We propose a regularization-based deblurring method that works efficiently for galaxy images. The spatial resolution of a ground-based telescope is generally limited by seeing conditions and is much worse than space-based telescopes. This circumstance has generated considerable research interest in the restoration of spatial resolution. Since image deblurring is a typical inverse problem and often ill-posed, solutions tend to be unstable. To obtain a stable solution, much research has adopted regularization-based methods for image deblurring, but the regularization term is not necessarily appropriate for galaxy images. Although galaxies have an exponential or Sérsic profile, the conventional regularization assumes the image profiles to behave linearly in space. The significant deviation between the assumption and real situations leads to blurring of the images and smoothing out the detailed structures. Clearly, regularization on logarithmic domain, i.e., magnitude domain, should provide a more appropriate assumption, which we explore in this study. We formulate a problem of deblurring galaxy images by an objective function with a Tikhonov regularization term on a magnitude domain. We introduce an iterative algorithm minimizing the objective function with a primal–dual splitting method. We investigate the feasibility of the proposed method using simulation and observation images. In the simulation, we blur galaxy images with a realistic point spread function and add both Gaussian and Poisson noise. For the evaluation with the observed images, we use galaxy images taken by the Subaru HSC-SSP. Both of these evaluations show that our method successfully recovers the spatial resolution of the deblurred images and significantly outperforms the conventional methods. The code is publicly available from the GitHub 〈https://github.com/kzmurata-astro/PSFdeconv_amag〉.

Murata, Kazumi↗
DOE OSTI2022

DIAS: A Data-Informed Active Subspace Regularization Framework for Inverse Problems

This paper presents a regularization framework that aims to improve the fidelity of Tikhonov inverse solutions. At the heart of the framework is the data-informed regularization idea that only data-uninformed parameters need to be regularized, while the data-informed parameters, on which data and forward model are integrated, should remain untouched. We propose to employ the active subspace method to determine the data-informativeness of a parameter. The resulting framework is thus called a data-informed (DI) active subspace (DIAS) regularization. Four proposed DIAS variants are rigorously analyzed, shown to be robust with the regularization parameter and capable of avoiding polluting solution features informed by the data. They are thus well suited for problems with small or reasonably small noise corruptions in the data. Furthermore, the DIAS approaches can effectively reuse any Tikhonov regularization codes/libraries. Though they are readily applicable for nonlinear inverse problems, we focus on linear problems in this paper in order to gain insights into the framework. Various numerical results for linear inverse problems are presented to verify theoretical findings and to demonstrate advantages of the DIAS framework over the Tikhonov, truncated SVD, and the TSVD-based DI approaches.

Nguyen, Hai↗
DOE OSTI2022

Regularized inversion of aerosol hygroscopic growth factor probability density function: application to humidity-controlled fast integrated mobility spectrometer measurements

Abstract. Aerosol hygroscopic growth plays an important role in atmospheric particle chemistry and the effects of aerosol on radiation and hence climate. The hygroscopic growth is often characterized by a growth factor probability density function (GF-PDF), where the growth factor is defined as the ratio of the particle size at a specified relative humidity to its dry size. Parametric, least-squares methods are the most widely used algorithms for inverting the GF-PDF from measurements of the humidified tandem differential mobility analyzer (HTDMA) and have been recently applied to the GF-PDF inversion from measurements of the humidity-controlled fast integrated mobility spectrometer (HFIMS). However, these least-squares methods suffer from noise amplification due to the lack of regularization in solving the ill-posed problem, resulting in significant fluctuations in the retrieved GF-PDF and even occasional failures of convergence. In this study, we introduce nonparametric, regularized methods to invert the aerosol GF-PDF and apply them to HFIMS measurements. Based on the HFIMS kernel function, the forward convolution is transformed into a matrix-based form, which facilitates the application of the nonparametric inversion methods with regularizations, including Tikhonov regularization and Twomey's iterative regularization. Inversions of the GF-PDF using the nonparameteric methods with regularization are demonstrated using HFIMS measurements simulated from representative GF-PDFs of ambient aerosols. The characteristics of reconstructed GF-PDFs resulting from different inversion methods, including previously developed least-squares methods, are quantitatively compared. The result shows that Twomey's method generally outperforms other inversion methods. The capabilities of Twomey's method in reconstructing the pre-defined GF-PDFs and recovering the mode parameters are validated.

54 ENVIRONMENTAL SCIENCES↗
NASA NTRS1992

Inverse problems: Fuzzy representation of uncertainty generates a regularization

In many applied problems (geophysics, medicine, and astronomy) we cannot directly measure the values x(t) of the desired physical quantity x in different moments of time, so we measure some related quantity y(t), and then we try to reconstruct the desired values x(t). This problem is often ill-posed in the sense that two essentially different functions x(t) are consistent with the same measurement results. So, in order to get a reasonable reconstruction, we must have some additional prior information about the desired function x(t). Methods that use this information to choose x(t) from the set of all possible solutions are called regularization methods. In some cases, we know the statistical characteristics both of x(t) and of the measurement errors, so we can apply statistical filtering methods (well-developed since the invention of a Wiener filter). In some situations, we know the properties of the desired process, e.g., we know that the derivative of x(t) is limited by some number delta, etc. In this case, we can apply standard regularization techniques (e.g., Tikhonov's regularization). In many cases, however, we have only uncertain knowledge about the values of x(t), about the rate with which the values of x(t) can change, and about the measurement errors. In these cases, usually one of the existing regularization methods is applied. There exist several heuristics that choose such a method. The problem with these heuristics is that they often lead to choosing different methods, and these methods lead to different functions x(t). Therefore, the results x(t) of applying these heuristic methods are often unreliable. We show that if we use fuzzy logic to describe this uncertainty, then we automatically arrive at a unique regularization method, whose parameters are uniquely determined by the experts knowledge. Although we start with the fuzzy description, but the resulting regularization turns out to be quite crisp.

Kreinovich, V.↗
NASA NTRS2003

The relationship between lifestyle regularity and subjective sleep quality

In previous work we have developed a diary instrument-the Social Rhythm Metric (SRM), which allows the assessment of lifestyle regularity-and a questionnaire instrument--the Pittsburgh Sleep Quality Index (PSQI), which allows the assessment of subjective sleep quality. The aim of the present study was to explore the relationship between lifestyle regularity and subjective sleep quality. Lifestyle regularity was assessed by both standard (SRM-17) and shortened (SRM-5) metrics; subjective sleep quality was assessed by the PSQI. We hypothesized that high lifestyle regularity would be conducive to better sleep. Both instruments were given to a sample of 100 healthy subjects who were studied as part of a variety of different experiments spanning a 9-yr time frame. Ages ranged from 19 to 49 yr (mean age: 31.2 yr, s.d.: 7.8 yr); there were 48 women and 52 men. SRM scores were derived from a two-week diary. The hypothesis was confirmed. There was a significant (rho = -0.4, p < 0.001) correlation between SRM (both metrics) and PSQI, indicating that subjects with higher levels of lifestyle regularity reported fewer sleep problems. This relationship was also supported by a categorical analysis, where the proportion of "poor sleepers" was doubled in the "irregular types" group as compared with the "non-irregular types" group. Thus, there appears to be an association between lifestyle regularity and good sleep, though the direction of causality remains to be tested.

NASA Program Biomedical Research and Countermeasur↗