Total Variation Research Articles

On compressive self-calibration with structural constraints via alternating minimization

This paper considers the compressive bilinear self-calibration problem with explicit low-dimensional structural constraints. The celebrated proximal alternating linearized minimization (PALM) framework is adapted to simultaneously allow general sub-sampling schemes and structure-promoting regularizers. For the first time in literature, we refine the conditional convergence guarantees of PALM and show that the parameter commonly adopted to remove the scaling ambiguity as well as the structural penalties can ensure the unconditional convergence independent of strict assumptions on the statistical properties of the measurements, subspaces, number of snapshots, or initial iterates. In particular, we impose sparse and small total variation structures on the target signals and provide detailed numerical procedures for efficient computations. The extension to the complex-valued case is also made and extensive numerical experiments are carried out to corroborate the theoretical claims. Different choices of sub-sampling schemes and compression rates are simulated to support the effectiveness of the proposed algorithm under various settings. We also make comparisons with the state-of-art competing methods and the superiority of our proposed algorithm is empirically verified.

An Analysis of Psychological Capital and Influencing Factors Among Disaster Care Reservists

IntroductionIn recent years, with the frequent occurrence of public health emergencies, various infectious diseases and natural disasters (earthquakes, tsunamis, and fires have placed a burden on global public health and health care systems, especially on health care workers. This study aimed to investigate the current state of psychological capital among disaster care reservists and the factors influencing it. MethodsBetween January and February 2024, a total of 330 members of the disaster nursing reserve team from 4 tertiary general hospitals in Mianyang, China, were surveyed using an online platform named Wenjuanxing to obtain information on general demographics, psychological capital, and job burnout. ResultsThe total score of psychological capital was 91.10 ± 16.15. Psychological capital was negatively correlated with emotional depletion dimension and depersonalization dimension scores (P < .01) and positively correlated with personal achievement dimension scores (P < .01). The results of multiple regression analysis revealed that the psychological capital of members in disaster nursing reserve teams was influenced by various factors such as their marital status, having children, work experience in the department, level of public recognition and respect, number of disaster relief trainings, participation in disaster relief activities, types of disaster relief activities, and level of job burnout (P < .05). This accounted for 48.9% of the total variation. DiscussionThe psychological capital of disaster nursing reserve team members is affected by several aspects, which warrant great attention. Relevant management departments should adopt appropriate strategies to effectively mobilize their self-efficacy, improve their professional identity and sense of achievement, and enhance their psychological capital level.

A mean curvature flow arising in adversarial training

We connect adversarial training for binary classification to a geometric evolution equation for the decision boundary. Relying on a perspective that recasts adversarial training as a regularization problem, we introduce a modified training scheme that constitutes a minimizing movements scheme for a nonlocal perimeter functional. We prove that the scheme is monotone and consistent as the adversarial budget vanishes and the perimeter localizes, and as a consequence we rigorously show that the scheme approximates a weighted mean curvature flow. This highlights that the efficacy of adversarial training may be due to locally minimizing the length of the decision boundary. In our analysis, we introduce a variety of tools for working with the subdifferential of a supremal-type nonlocal total variation and its regularity properties.

Adaptive Weighted Bregman Huber Total Variation Method for Terahertz Computed Tomography

ABSTRACTTo improve the image quality of terahertz (THz) continuous wave (CW) computed tomography (CT) under sparse‐view projections, a sparse‐view adaptive‐weighted Bregman Huber total variation (AW‐BHTV) method is proposed and experimentally evaluated at 0.11 THz. The Huber function is served as the fidelity term and TV function is worked for the regularization term, optimized by the adaptive weights, incorporating with iterative algorithms containing the modified simultaneous algebraic reconstruction technique (MSART) and the iterative filtered back‐projection (FBP). Sparse‐view reconstruction experiments are carefully implemented via polystyrene (PS) foam samples: Sample 1 and Sample 2, respectively. Under 20 projection angles by MSART based AW‐BHTV, the values of rooted mean‐square‐error (RMSE), peak signal‐to‐noise ratio (PSNR), structure similarity (SSIM) and feature similarity (FSIM) are 0.0061, 22.1427, 0.8738 and 0.9902 for Sample 1 together with 0.0051, 22.9101, 0.8376 and 0.9885 for Sample 2 separately. All of the results above suggest that the proposed AW‐BHTV method can effectively protect image details and strengthen image quality in sparse‐view THz CW CT.

An Empirical Study of Self-Supervised Learning with Wasserstein Distance

In this study, we consider the problem of self-supervised learning (SSL) utilizing the 1-Wasserstein distance on a tree structure (a.k.a., Tree-Wasserstein distance (TWD)), where TWD is defined as the L1 distance between two tree-embedded vectors. In SSL methods, the cosine similarity is often utilized as an objective function; however, it has not been well studied when utilizing the Wasserstein distance. Training the Wasserstein distance is numerically challenging. Thus, this study empirically investigates a strategy for optimizing the SSL with the Wasserstein distance and finds a stable training procedure. More specifically, we evaluate the combination of two types of TWD (total variation and ClusterTree) and several probability models, including the softmax function, the ArcFace probability model, and simplicial embedding. We propose a simple yet effective Jeffrey divergence-based regularization method to stabilize optimization. Through empirical experiments on STL10, CIFAR10, CIFAR100, and SVHN, we find that a simple combination of the softmax function and TWD can obtain significantly lower results than the standard SimCLR. Moreover, a simple combination of TWD and SimSiam fails to train the model. We find that the model performance depends on the combination of TWD and probability model, and that the Jeffrey divergence regularization helps in model training. Finally, we show that the appropriate combination of the TWD and probability model outperforms cosine similarity-based representation learning.

Assessing population structure and morpho-molecular characterization of sunflower (Helianthus annuus L.) for elite germplasm identification.

Sunflower (Helianthus annuus L.), known for its adaptability and high yield potential, is vital in global edible oil production. Estimating genetic diversity is a key pre-breeding activity in crop breeding. The current study comprised of 48 genotypes which were assessed for their biometrical traits at department of Oilseeds, Tamil Nadu Agricultural University, during the rainy season of 2022. The lines were subsequently characterised using 103 simple sequence repeat (SSR) markers for molecular diversity analysis. The results indicated that the net nucleotide distances indicated varying genetic divergence, with subpopulations II and V showing the highest (0.056) and I and IV the lowest (0.014). Subpopulation IV exhibited the highest heterozygosity (0.352), while subpopulation III had the lowest heterozygosity and a low Fst (0.173). Principal components analysis (PCA) and hierarchical cluster analysis were employed for assessing the morphological diversity, facilitating genotype grouping and parent selection for breeding programs. The first four components cumulatively accounted for 86.72% of the total variation. Cluster Analysis grouped 48 sunflower genotypes into three clusters based on genetic diversity. COSF 13B stands out for its high head diameter, oil content, seed yield, and oil yield based on mean performance of morphological data. Principal coordinate analysis (PCoA) mirrored the groupings from the Neighbor Joining method, with the first three components explaining 27.24% of the total variation. Molecular data analysis identified five distinct clusters among the germplasm. By integrating morphological and molecular marker data with genetic distance analysis, substantial diversity was revealed with the genotypes RHA 273 and GMU 325 consistently demonstrated high oil yield per plant. The genotypes GMU 477, GMU 450, COSF 13B, RHA 102, CMS 1103B, and RHA GPR 58 have been identified as suitable parents for enhancing oil content in sunflower breeding programs. These findings also aid in selecting SSR markers for genotype characterization and in choosing diverse parents for breeding programs.

Smoothness and Lévy concentration function inequalities for distributions of random diagonal sums

We present new explicit upper bounds for the smoothness of the distribution of the random diagonal sum S n = ∑ j = 1 n X j , π ( j ) S_n=\sum _{j=1}^nX_{j,\pi (j)} of a random n × n n\times n matrix X = ( X j , r ) X=(X_{j,r}) , where X j , r X_{j,r} are independent integer valued random variables, and π \pi denotes a uniformly distributed random permutation on { 1 , … , n } \{1,\dots ,n\} independent of X X . As a measure of smoothness, we consider the total variation distance between the distributions of S n S_n and 1 + S n 1+S_n . Our approach uses new auxiliary inequalities for a generalized normalized matrix hafnian and for inverse moments of non-negative random variables, which could be of independent interest. This approach is also used to prove upper bounds of the Lévy concentration function of S n S_n in the case of independent real valued random variables X j , r X_{j,r} .

Breed Selection of Poplars Imposes Greater Selection Pressure on the Rhizosphere Bacterial Community

Breed selection alters the coevolution of plant–microbiome associations that have developed over long periods of natural evolution. We investigated the effects of breed selection on the rhizosphere microbiomes and metabolites of hybrid parents (I101 and 84K) and their offspring (Q1–Q5) using metagenomics and untargeted metabolomics. Rhizosphere archaeal, bacterial and fungal community β-diversity significantly differed among hybrid parents and offspring, but only the dominant bacterial phyla and bacterial community α-diversity revealed significant differences. Approximately 5.49%, 14.90% and 7.86% of the archaeal, bacterial and fungal species significantly differed among the poplar hybrid parents and offspring. Rhizosphere microbial functional genes and metabolites were both clustered into the following three groups: I101 and 84K; Q2 and Q4; and Q1, Q3 and Q5. Compared with the hybrid parents, 15 phytochemical compounds were enriched in the hybrid offspring and explained 7.15%, 18.24% and 6.68% of the total variation in the archaeal, bacterial and fungal community compositions, respectively. Rhizosphere metabolites significantly affected the bacterial community, rather than the archaeal and fungal communities. Our observations suggested that poplar breed selection imposed greater selection pressure on the rhizosphere bacterial community, which was mainly driven by metabolites.

Non-uniform Bounds and Edgeworth Expansions in Self-normalized Limit Theorems

We study Edgeworth expansions in limit theorems for self-normalized sums. Non-uniform bounds for expansions in the central limit theorem are established while imposing only minimal moment conditions. Within this result, we address the case of non-integer moments leading to a reduced remainder. Furthermore, we provide non-uniform bounds for expansions in local limit theorems. The enhanced tail accuracy of our non-uniform bounds allows for deriving an Edgeworth-type expansion in the entropic central limit theorem as well as a central limit theorem in total variation distance for self-normalized sums.

Variation in care in individuals hospitalised with abdominal aortic aneurysm in nine high-income countries: a cross-sectional cohort study

Abstract Background Abdominal aortic aneurysms (AAA) can be safely repaired using either endovascular aneurysm repair (EVAR) or open repair when intact, but after rupture morbidity and mortality are extremely high. Treatment patterns and outcomes for intact AAA are likely to differ between countries due to differences in AAA screening policies, health system capacity and payment approaches, and other factors, such as demographics and lifestyle, but are poorly studied. Methods We conducted a retrospective serial cross-sectional cohort study of adults aged ≥66 years hospitalised for with an intact AAA and repair procedure in the same admission between 2011 and 2019 in nine countries (US, Canada, England, Denmark, Netherlands, Switzerland, Taiwan, South Korea and Israel) using population-representative administrative data. We investigated age-sex standardised (to the 2019 US population) repair rates (open repair or EVAR) and health system performance measures, including hospital length of stay (LOS), 30-day readmission, and all-cause mortality (30 days and 1 year). Results The number of intact AAA hospital admissions between 2011 and 2019 ranged from 1,290 in Israel to 199,764 in the US. The rates of intact AAA repair per 1000 population varied between countries and over time, from 0.11 per 1000 (South Korea) to 0.69 per 1000 (US) in 2011 and from 0.14 per 1000 (Taiwan) to 0.57 per 1000 (the Netherlands) in 2019. Most countries saw a decline in the rate of AAA repair over the study period. The proportion repaired using open repair vs EVAR also varied widely across the countries. In the US, Israel and Taiwan open repair was used in 11% or fewer cases whereas in the remaining countries we observed open repair in 25.1 % (South Korea) to 56.7% (Denmark) of cases. (Figure 1) Mortality was generally higher following open repairs compared to EVAR in all countries. In 2019, following EVAR, 30-day mortality varied from 0.6% (8.1% at 1 year) in South Korea to 2.3% (11.7% at 1 year) in Israel and following open repair varied from 2.9 (4.4% at 1 year) in England to 7.6% (15.1% at 1 year) in the US. (Figure 2) Mean hospital LOS in 2019 ranged from 2.5 days (US) to 12.2 days (South Korea), following EVAR and from 9.1 days (Taiwan) to 21.5 days (South Korea) following open repair. The 30-day readmission rate in 2019 ranged from 8.1% (US) to 31.8% in Israel following EVAR and from 11.4% (US) to 22.2% (South Korea) following open repair. Conclusions We observed substantial between-country variation in surgical approaches, mortality, and health system performance measures for AAA. Further research is needed to understand and plan optimal, evidence-based AAA screening and treatment strategies.Rates of EVAR and open repairAdjusted 30-day all-cause mortality

SLERP-TVDRK (STVDRK) Methods for Ordinary Differential Equations on Spheres

We mimic the conventional explicit Total Variation Diminishing Runge–Kutta (TVDRK) schemes and propose a class of numerical integrators to solve differential equations on a unit sphere. Our approach utilizes the exponential map inherent to the sphere and employs spherical linear interpolation (SLERP). These modified schemes, named SLERP-TVDRK methods or STVDRK, offer improved accuracy compared to typical projective RK methods. Furthermore, they eliminate the need for any projection and provide a straightforward implementation. While we have successfully constructed STVDRK schemes only up to third-order accuracy, we explain the challenges in deriving STVDRK-r for r≥4\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$r\\ge 4$$\\end{document}. To showcase the effectiveness of our approach, we will demonstrate its application in solving the eikonal equation on the unit sphere and simulating p-harmonic flows using our proposed method.

Genetic Diversity and Population Structure Analysis of Soybean [Glycine max (L.) Merrill] Genotypes Using Agro-Morphological Traits and SNP Markers

Background/Objectives: Understanding the genetic diversity of soybean genotypes can provide valuable information that guides parental selection and the design of an effective hybridization strategy in a soybean breeding program. In order to identify genetically diverse, complementary, and prospective parental lines for breeding, this study set out to ascertain the genetic diversity, relationships, and population structure among 35 soybean genotypes based on agro-morphological traits and Single Nucleotide Polymorphic (SNP) marker data. Methods/Results: Cluster analysis, based on agro-morphological traits, grouped the studied genotypes into four clusters. The first two principal components accounted for 62.8% of the total phenotypic variation, where days to 50% flowering, days to 95% maturity, grain yield, shattering score, and lodging score had high and positive contributions to the total variation. Using the SNP marker information, mean values of 0.16, 0.19, 0.067, and 0.227 were obtained for minor allele frequency (MAF), polymorphic information content (PIC), observed heterozygosity (Ho), and expected heterozygosity (He), respectively. Using different clustering approaches (admixture population structure, principal component scatter plot, and hierarchical clustering), the studied genotypes were grouped into four major clusters. Conclusions:The agro-morphological and molecular analysis results indicated the existence of moderate genetic diversity among the studied genotypes. The traits identified to be significantly related to yield provide valuable information for the genetic improvement of soybeans for yield.

Code and Data Repository for On Discrete Subproblems in Integer Optimal Control with Total Variation Regularization in Two Dimensions

The goal of this repository to be able to trace and reproduce the results and plots in the referenced article. For the results in this article, we used the general purpose integer programming solver Gurobi version 10.0.0. In addition, you need to have the python packages pandas, numpy, scipy, and pybind11 installed to be able to build the code for computing the weights of the cutting planes from 5.1.1.

On Discrete Subproblems in Integer Optimal Control with Total Variation Regularization in Two Dimensions

We analyze integer linear programs that we obtain after discretizing two-dimensional subproblems arising from a trust-region algorithm for mixed integer optimal control problems with total variation regularization. We discuss NP-hardness of the discretized problems and the connection to graph-based problems. We show that the underlying polyhedron exhibits structural restrictions in its vertices with regard to which variables can attain fractional values at the same time. Based on this property, we derive cutting planes by employing a relation to shortest-path and minimum bisection problems. We propose a branching rule and a primal heuristic which improves previously found feasible points. We validate the proposed tools with a numerical benchmark in a standard integer programming solver. We observe a significant speedup for medium-sized problems. Our results give hints for scaling toward larger instances in the future. History: Accepted by Andrea Lodi, Area Editor for Design &amp; Analysis of Algorithms–Discrete. Funding: This work was supported by the Deutsche Forschungsgemeinschaft [Grant MA 10080/2-1]. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information ( https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2024.0680 ) as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2024.0680 ). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/ .

Genetic variability, heritability, and genetic advance estimates in selected groundnut genotypes (&lt;i&gt;Arachis hypogaea&lt;/i&gt; L.) for agro-morphological and yield traits.

Groundnuts (Arachis hypogaea L.), is a crucial food and oil crop in the tropics, require genetic variability assessment for efficient breeding programs using appropriate parameters like genetic coefficient of variation, heritability estimates, association among yield related traits and genetic advance. This study aims to identify genotypes with desirable traits to improve yield and adaptability, contributing to better crop improvement strategies. The study used a randomized complete block design with three replications, consisting of fourteen selected genotypes. Quantitative traits were used to estimate genetic variability parameters, heritability, and genetic advance. The analysis of variance revealed significant differences (p &lt; 0.005) for all studied traits, indicating greater variability in genotypes. Characters exhibited different levels of variability, heritability, and genetic advance among the genotypes. The estimate of the broad-sense heritability ranged from 13.33% to 33.33% for canopy spread and days to maturity respectively. Low to high phenotypic coefficient of variation (PCV) and genotypic coefficient of variation (GCV) were recorded. The study found that traits such as number of branches, pods per plant, fresh and dry plant weight, kernel yield, pod yield, and shelling percentage showed high genotypic coefficient of variation, moderate broad sense heritability, and high genetic advance. These traits can be beneficial for groundnut improvement through effective phenotypic selection, resulting in high expected genetic gain. The study found that pod yield is significantly correlated with kernel yield, grain length, grain width, 100-seed weight, fresh and dry 100-pod weight, and number of pods per plant. Kernel yield is positively correlated with the number of branches per plant, pod per plant, fresh and dry 100-pod weight, 100-seed weight, grain length, and grain width. In addition, the first four principal components accounted for 90.37% of total variation in all morphological traits.

Preliminary Exploration of Variations in Measures of Pharyngeal Area During Nonswallowing Tasks.

Age- and disease-related changes in oropharyngeal anatomy and physiology may be identified through quantitative videofluoroscopic measures of pharyngeal area and dynamics. Pixel-based measures of nonconstricted pharyngeal area (PhAR) are typically taken during oral bolus hold tasks or on postswallow rest frames. A recent study in 87 healthy adults reported mean postswallow PhAR of 62%(C2-4)2, (range: 25%-135%), and significantly larger PhAR in males. The fact that measures were taken after initial bolus swallows without controlling for the presence of subsequent clearing swallows was identified as a potential source of variation. A subset of study participants had completed a protocol including additional static nonswallowing tasks, enabling us to explore variability across those tasks, taking sex differences into account. Videofluoroscopy still shots were analyzed for 20 healthy adults (10 males, 10 females, Mage = 26 years) in head-neutral position, chin-down and chin-up positions, a sustained /a/ vowel vocalization, and oral bolus hold tasks (1-cc, 5-cc). Trained raters used ImageJ software to measure PhAR in %(C2-4)2 units. Measures were compared to previously reported mean postswallow PhAR for the same participants: (a) explorations of sex differences; (b) pairwise linear mixed-model analyses of variance (ANOVAs) of PhAR for each nonswallowing task versus postswallow measures, controlling for sex; and (c) a combined mixed-model ANOVA to confirm comparability of the subset of tasks showing no significant differences from postswallow measures in Step 2. Overall, PhAR measures were significantly larger in male participants; however, most pairwise task comparisons did not differ by sex. No significant differences from postswallow measures were seen for 5-cc bolus hold, chin-down and chin-up postures, and the second (but not the first) of two repeated head neutral still shots. PhAR during a 5-cc bolus hold was most similar to postswallow measures: mean ± standard deviation of 51 ± 13%(C2-4)2 in females and 64 ± 16%(C2-4)2 in males. PhAR is larger in men than in women. Oral bolus hold tasks with a 5-cc liquid bolus yield similar measures to those obtained from postswallow rest frames.

Center-Related Variation in Hospitalization Cost for Patients Undergoing Percutaneous Left Atrial Appendage Occlusion

BackgroundThe commercial use of percutaneous left atrial appendage occlusion with the Watchman device is increasing in the United States. The purpose of this study was to evaluate center-related variation in total hospital costs for Watchman device implantation and identify factors associated with high hospital costs at a national level. MethodsAll adults undergoing elective left atrial appendage occlusion with Watchman were identified in the 2016-2018 National Inpatient Database. Mixed models were used to evaluate the impact of center on total hospital costs, adjusting for patient and center characteristics and length of stay. ResultsA total of 30,175 patients underwent Watchman device implantation at a median cost of $24,500 and demonstrated significant variability across admissions (interdecile range, $13,900-37,000). Nearly 13% of the variability in patient-level costs was related to the center performing the procedure rather than patient factors. Higher-volume centers had lower total costs and demonstrated lesser total cost variation. Centers with low procedural volume, occurrence of procedural complications, congestive heart failure, and length of stay were independent predictors of a high-cost hospitalization. Though complications were associated with increased expenditure, they did not explain the observed cost variation related to the center. ConclusionsA significant proportion of variation in total hospital cost was attributable to the center performing the procedure. Addressing variability of Watchman-related costs is necessary to achieve high-quality value-based care.

Dyadic Partition-Based Training Schemes for TV/TGV Denoising.

Due to their ability to handle discontinuous images while having a well-understood behavior, regularizations with total variation (TV) and total generalized variation (TGV) are some of the best-known methods in image denoising. However, like other variational models including a fidelity term, they crucially depend on the choice of their tuning parameters. A remedy is to choose these automatically through multilevel approaches, for example by optimizing performance on noisy/clean image pairs. In this work, we consider such methods with space-dependent parameters which are piecewise constant on dyadic grids, with the grid itself being part of the minimization. We prove existence of minimizers for fixed discontinuous parameters under mild assumptions on the data, which lead to existence of finite optimal partitions. We further establish that these assumptions are equivalent to the commonly used box constraints on the parameters. On the numerical side, we consider a simple subdivision scheme for optimal partitions built on top of any other bilevel optimization method for scalar parameters, and demonstrate its improved performance on some representative test images when compared with constant optimized parameters.

A modified non-convex Cauchy total variation regularization model for image restoration

A modified non-convex Cauchy total variation regularization model for image restoration

X-ray coronary angiography background subtraction by adaptive weighted total variation regularized online RPCA

Objective.X-ray coronary angiograms (XCA) are widely used in diagnosing and treating cardiovascular diseases. Various structures with independent motion patterns in the background of XCA images and limitations in the dose of injected contrast agent have resulted in low-contrast XCA images. Background subtraction methods have been developed to enhance the visibility and contrast of coronary vessels in XCA sequences, consequently reducing the requirement for excessive contrast agent injections.Approach.The current study proposes an adaptive weighted total variation regularized online RPCA (WTV-ORPCA) method, which is a low-rank and sparse subspaces decomposition approach to subtract the background of XCA sequences. In the proposed method, the images undergo initial preprocessing using morphological operators to eliminate large-scale background structures and achieve image homogenization. Subsequently, the decomposition algorithm decomposes the preprocessed images into background and foreground subspaces. This step applies an adaptive weighted TV constraint to the foreground subspace to ensure the spatial coherency of the finally extracted coronary vessel images.Main results.To evaluate the effectiveness of the proposed background subtraction method, some qualitative and quantitative experiments are conducted on two clinical and synthetic low-contrast XCA datasets containing videos from 21 patients. The obtained results are compared with six state-of-the-art methods employing three different assessment criteria. By applying the proposed method to the clinical dataset, the mean values of the global contrast-to-noise ratio, local contrast-to-noise ratio, structural similarity index, and reconstruction error (RE) are obtained as5.976,3.173,0.987, and0.026, respectively. These criteria over the low-contrast synthetic dataset were4.851,2.942,0.958, and0.034, respectively.Significance.The findings demonstrate the superiority of the proposed method in improving the contrast and visibility of coronary vessels, preserving the integrity of the vessel structure, and minimizing REs without imposing excessive computational complexity.